POLICY MAKING FOR ECONOMIC DEVELOPMENT: A SYSTEM SIMULATION MODEL OF THE AGRICULTURAL ECONOMY OF SOUTHERN NIGERIA Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY MICHAEL HOWARD ABKIN 1972 {fllgvh‘nnr I‘. J ‘ r ‘ - ' ‘t ‘ - v I WRITE-WE». $654531“? IIIIIII III IIIIIIIIII 312 293 006335 ‘F""“* _‘__,- LIBRAR Y Michigan State ‘. -- University r This is to certify that the thesis entitled POLICY MAKING FOR ECONOMIC DEVELOPMENT: A SYSTEM SIMULATION MODEL OF THE AGRICULTURAL ECONOMY OF SOUTHERN NIGERIA presented by Michael Howard Abkin has been accepted towards fulfillment of the requirements for Ph . D ._ degree in Wins—Science I3 0!; ,Nn; a, A"/-I ”71.5... 73/ Date «(I/s L1 ’0‘, H 7‘2, I 0-7639 amomc BY 1 HURE 5 SUNS I finest BINDERY MI I LIBRARY am DERSI manna! “III .______,_._.—-- ABSTRACT POLICY MAKING FOR ECONOMIC DEVELOPMENT: A SYSTEM SIMULATION MODEL OF THE AGRICULTURAL ECONOMY OF SOUTHERN NIGERIA BY Michael Howard Abkin The problems of planning for economic development in. the new states of Africa and Asia as well as in the more established countries of Latin America arise from the inter- play of the political, social and economic subsystems of a developing country. These problems are compounded by the uncertainty necessarily inherent in any process of planning for the future. In this thesis, a system simulation model of a developing agricultural economy is presented as one approach to the planning problem. (This is actually a sub- model of a larger Nigeria model developed under USAID contracts AID/csd1557 and AID/csd2975.) A preliminary model of the agricultural economy of southern Nigeria is described. The model simulates, over time, land use and modernization decisions and the production of five major commodities--cocoa, oil palm, rubber, food and tobacco-~of the region. The time path of simulated behavior may be influenced by user-specified policies. Policy options currently allowable in the model include commodity marketing board surpluses, export taxes, income taxes, commodity pro- duction (modernization) campaigns and the modernization of Michael Howard Abkin agricultural processing. Perennial commodities play an important role in the agricultural economy of southern Nigeria. Thus, to capture the dynamics of perennial production, a demographic model of perennial populations is used. This model is a lumped ap- I proximation to a distributed parameter process. Specifically, production cohorts are defined and modeled as distributed delays to account for stochastic maturation times. The simulation model is composed of five basic com- ponents. The first includes the perennial model discussed above and computes land allocation and modernization decisions among relevant alternatives within each of four ecological I zones. Land use transition rates are functions of perceived relative profitabilities of alternatives and of the amount of available information, both from exogenous sources (extension agents) and from other farmers in a diffusion process. Tran- sitions are constrained by available land and capital. The second major component of the model simulates the production, processing and marketing of agricultural com— modities. Commodity yields are endogenously determined as functions of time (essentially a learning curve of farmer experience), degree of modernization and producer prices. Subsistence and cash food production are computed separately, where subsistence food demands (and hence production) depend on the subsistence level or, conversely, the degree to which reliance is placed on the food market. This level is a function of food prices, food market stability, revenue from Michael Howard Abkin non-food cash crops and the size of the agricultural popu- lation. The remaining three components of the model: 1) gener- ate world, market, processor and producer prices; 2) provide policy entry points, and 3) compute accounting and performance criteria and balance the agricultural sector budget. The remainder of the dissertation discusses and illus- trates the use of the model to deal with uncertainty in the formulation of agricultural development policies. Data un- certainty can be handled by sensitivity tests to determine how important uncertain data are and by a more qualitative, less quantitative analysis of simulated results, in particular, by attending to the relative consequences of alternative policy options rather than to the absolute projections simulated. A potentially powerful tool in this regard is the use of Monte Carlo techniques where uncertain parameters are given pro- bability distributions and many runs of the model generate output statistics. Another kind of uncertainty--process uncertainty-- may also be reduced by use of the model. Many complex re- lationships and interactions-~including feedbacks, non- linearities, discontinuities and time delays--may be incorpo- rated in a computerized simulation model to make projections which would be impractical or even impossible to make by analytical or other methods, such as paper-and-pencil or intuition. In addition, the process of analyzing and Michael Howard Abkin explaining simulated behavior observed in sensitivity runs and policy runs does much to deepen one's understanding of, and insights into, the system. The thesis concludes with a discussion of what form an implementation of the model in the development planning process might take and of improvements, modifications and extensions of the model which would be necessary as an on- going part of such an implementation. POLICY MAKING FOR ECONOMIC DEVELOPMENT: A SYSTEM SIMULATION MODEL OF THE AGRICULTURAL ECONOMY OF SOUTHERN NIGERIA BY Michael Howard Abkin A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Electrical Engineering and Systems Science 1972 To my parents, who laid the foundation. ii ACKNOWLEDGEMENTS Breaking with tradition, my first acknowledgement is to my wife, Graciela. For her, the role of student's wife was compounded by the added duties of editorial consultant and typist for this thesis. It can be fairly said that this dissertatiOn is as much hers as mine. My Work leading to this thesis was as part of a simulation Egam_under contract to the United States Agency for International Development (contracts AID/csd1557 and AID/csd2975). Although I had major responsibility for the development of the southern model, and while I hold the responsibility for it--particularly its shortcomings--it could not have come about without the guidance, suggestions and advice of the whole team. In particular, I give special thanks to Professor Glenn Johnson for his overall guidance as administrator of the project, to Dr. Thomas Manetsch whose on-line direction of operations gave cohesiveness and moti- vation to the project team, and to Gloria Page, our computer programmer, for her efforts in trying to interpret what I wanted to do. Finally, I thank my guidance committee for their acceptance of my program and for their patience in wading through this volume. I am particularly indebted to iii iv Dr. Manetsch who, as my major advisor, gave me direction and inspired my interest in the socio-economic application of systems science as a career and as a vocation. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES P A R T I - THE PROBLEM Introduction CHAPTER 1 - The Context: Development, System Simulation and Nigeria Development and Planning The Evolution of the Systems Simulation Approach to Economic Problems The Nigeria Model CHAPTER 2 - The Dynamic Demography of Perennials: A Model of a Distributed Parameter Process General Population Balance Model Lumped Approximations Demography of Perennials Summary ‘P A R T II - MODEL DESCRIPTION Introduction and Summary CHAPTER 3 - Land Allocation and Modernization Decisions--Annuals/Perennials (LAMDAP) Ecological Zones Land Uses Perennials Annuals Other Land Uses Alternatives Economic Decisions Profitabilities Information Units Availability of Land Transition Responses Noneconomic Responses Summary CHAPTER 4 - Agricultural Marketing, Production and Processing--Annuals/Perennials (AMPPAP) Subsistence Level Yields Food Production H‘ra 35 35 38 38 47 49 49 51 51 57 59 71 76 77 77 82 87 vi Perennial Production Marketing Processing Capacity Modernization Investment Processing Outputs Input Demands and Accounting Summary CHAPTER 5 - Price Generation (PG) Export, Market and Processor Prices Domestic Palm Oil Market Producer Prices, Price Averages and Wage Rates Summary CHAPTER 6 - Policy Entries Parameter Sensitivity and Policy Making Policies Production Campaigns Marketing Boards Taxes CHAPTER 7 - Criteria and Macro-Budget Accounting (CRTMBA) Performance Criteria Budget Accounting Summary P A R T III - VALIDATION AND TESTING Introduction CHAPTER 8 - Data Usage and Model Tuning Data System Parameters Technological Coefficients Initial Conditions ‘Tuning General Validation CHAPTER 9 - Sensitivity Analysis: Results and General Applications Applications Model Development Policy Making Data Collection Analysis of Results Methodology Production Coefficients Land Allocation Coefficients Price Parameters Summary Simulation Time Cycles 104 118 119 119 124 130 134 135 135 136 136 140 141 ' 142 142 148 160 161 161 163 164 164 170 174 176 180 182 182 182 184 187 188 188 191 199 206 211 211 vii P A R T IV - TOWARDS A SOLUTION Introduction CHAPTER 10 - Policy Formulation Policy Experimentation Run Definitions and Organization Policies Related to the Cattle Industry Northern Regional Policies Southern Regional Policies Policies Viewed on the National Level Varying Production Campaign Budget Levels Conclusions Policy Sensitivity Summary CHAPTER 11 - Summary and Conclusions Summary Conclusions Understanding the System Policy Formulation Research Activities Improvements and Extensions of the Model Improvements Extensions Implementation BIBLIOGRAPHY Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table 11.1. 11.2. III.1. III.2. III.3. III.4. III.5. III.6. III.7. III.8. III.9. III.10. 111.11. 111.12. III.13. IV.1. IV.2. IV.3. LIST OF TABLES Alternative land uses Production campaigns Profitability response parameters for traditional perennials (dimensionless) Profitability response parameters for annuals and bush Diffusion parameters Production parameters Perennial yields (lbs./acre-year) Input requirements for perennials Mean length of perennial production stages (years) Selected initial conditions (1953) Time series tracking Results of sensitivity tests of produc- tion coefficients of the southern model Results of sensitivity tests of land allocation coefficients of the scuthern model sensitivity tests of price of the southern model Results of parameters sensitivity tests on time DT and DTX Results of increments Policy simulation runs Results of policy sensitivity tests under three policy situations Greatest deviations of three output variables from 29 parameter variations under three policy situations (percent of base values) viii 139 166 167 168 169 171 172 173 175 179 195 202 209 214 224 281 285 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure I103 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 II.12 III.1 LIST OF FIGURES National model of interacting submodels Northern region ecological zones Southern region ecological zones interactions of the agricultural model Major sectors and northern Nigerian interactions of the agricultural model Major sectors and southern Nigerian Model of the nonagricultural economy and the national accounts A model of a generalized amphipod instar Building blocks of the southern model A Venn diagram of the ecological zones of southern Nigeria Perennial production cohorts The gamma distribution of maturation rates, R m Land-use decision mechanism The profitability response function Abandonment response Land constraint Subsistence level determination Price generation component The palm oil market: three cases Modernization budget profile Approximate solutions of agricultural exports (AFORXS) and value added (ATVAS) for different simulation cycles ix 16 17 19 26 32 36 41 41 52 63 7O 74 81 120 129 138 216 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 111.2 111.3 IV.1 IV.2 IV.3 IV.4 IV.5 IV.6 IV.7 IV.8 IV.9 IV.10 Approximate solutions of per capita disposable income (PCDINA) and market price of food (PRFD) for different simulation cycles Simulation run times when varying one or both simulation Cycles Cattle population of males (PM) and females (PF), 1970-1995, with and without a fly eradication program Cattle income from animal sales (YA) and milk (YM), 1970-1995, with and without a fly eradication program Fly-free grazing land, 1970-1995, with and without a fly eradication program Range condition index (the ratio of range land grass yields at a point in time to those yields at the initial time, 1970), 1970-1995, with and without a fly eradication program Total value added in agriculture in the North, 1970-1995, under various policy conditions Foreign exchange from northern agri- cultural exports (including imports of cotton and beef), 1970-1995, under various policy conditions Total marketing board net revenues from northern commodities, 1970-1995, under various policy conditions Disposable income per agricultural worker in the North, 1970-1995, under various policy conditions Market price of food in the North, 1970-1995, under various policy conditions Caloric consumption (of staples) per capita of the northern nonagricultural population, 1970-1995, under various policy conditions 217 218 233 234 235 236 241 242 243 244 245 246 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure IV.11 IV.12 IV.13 IV.14 IV.15 IV.16 IV.17 IV.18 IV.19 IV.20 IV.21 IV.22 IV.23 xi Total value added in agriculture in the South, 1970-1995, under various policy conditions Foreign exchange from southern agricul- tural exports, 1970-1995, under various policy conditions Total marketing board net revenues from southern commodities, 1970-1995, under various policy conditions Foreign exchange from palm oil exports, 1970-1995, under various policy conditions Real disposable income per agricultural worker in the South, 1970-1995, under various policy conditions Market price of food in the South, 1970- 1995, under various policy conditions Caloric consumption (of staples) per capita of the southern nonagricultural population, 1970-1995, under various policy conditions Total value added in northern agriculture, 1970-1995, under various policy conditions Total value added in southern agriculture, 1970-1995, under various policy conditions Foreign exchange from northern agricul- tural exports (including imports of cotton and beef), 1970-1995, under various policy conditions Foreign exchange from southern agri- cultural exports, 1970-1995, under various policy conditions Total marketing board net revenues from northern and southern commodities, 1970- 1995, under various policy conditions Gross domestic product (assuming marketing board and export taxes are not put to productive use), 1970-1995, under various policy conditions 251 252 253 254 255 256 257 262 263 264 265 266 267 Figure Figure Figure Figure Figure Figure Figure Figure Figure IV.24 IV.25 IV.26 IV.27 IV.28 IV.29 IV.30 IV.31 IV.32 xii Total exports (agricultural and non- agricultural), 1970-1995, under various policy conditions Total imports, 1970-1995, under various policy conditions Market price of food in the North, 1970- 1995, under various policy conditions Caloric consumption (of staples) of the southern nonagricultural population, 1970-1995, under various policy conditions Agricultural exports in the North (including beef and cotton imports) (EN) and South (ES), in 1995, under varying production campaign budgets Total marketing board net revenues from northern and southern commodities in 1995 under varying production campaign budgets Modern annuals cotton, groundnut and food land in 1995 under varying production campaign budgets Modern perennials land in new planted cocoa (NC), replanted cocoa (RC), replanted palm where no other perennial competition (RP), replanted palm where rubber competition (RPR) and replanted rubber (RR) in 1995 under varying production campaign budgets System simulation and the policy- making process 268 269 270 271 273 274 275 276 308 P A R T I THE PROBLEM Introduction The problems of planning for economic development in the new states of Africa and Asia as well as in the more es- tablished nations of Latin America arise from the interplay of political, social and economic subsystems. In this introductory part, Chapter 1 briefly reviews theSe problems and discusses the "systems approach" to dealing with them, including a review of previous model-building ef- forts. The global model of the Nigerian agricultural economyl/, with its regional and sectoral submodels, is then described briefly. Chapter 2 discusses how the southern agricultural submodel, the subject of this dissertation, employs a lumped approximation to a distributed parameter process--specifically, the distribution of a population over time and over m pro- perties--to model the demography of perennial commodities, i.e., populations of trees. Part II describes in detail the components of the southern model. Chapters 3 through 7 cover respectively the l/ The work was supported by the United States Agency for International Development, contracts AID/csd1557 and AID/csd2975. l land allocation and modernization decisions component, the agricultural production, processing and marketing component, the price generation component, policy entry points and the criteria and macro-budget accounting component. Part III looks at testing and validation procedures and results. Chapter 8 discusses data needs and the process of tuning the model to track time series of recorded behavior. The results and implications of sensitivity tests on model parameters are presented in Chapter 9 along with an investi- gation of the sensitivity of the model's numerically generated solution to changes in the time increment used. Policy applications of the model, conclusions and areas for further work are diSCUSSEd in Part IV. Chapter 10 presents the results and analyses of runs experimenting with various agricultural development policy options. Experiments include an investigation of the sensitivity of policy results to changes in certain parameter values. Finally, Chapter 11 presents summary and conclusions and outlines areas for further work in refining, improving and extending the model; it con- cludes with a discussion of the form an implementation of the model might take. CHAPTER 1 The Context: Development, System Simulation and Nigeria Development and Planning Development planning is basically a political process. To be sure, the goals of development are generally socio- economic in nature; however, defining those goals and charting the paths to their attainment (i.e., planning) are necessarily political problems. That is, there are problems of reconciling conflicting interests and aspirations of various segments of the society and of evaluating the trade-offs among "goods" and "bads" as projected by psychological, sociological and economic analyses. Colm and Geiger define development plan- ning as ... deliberate, rational, continuous efforts by governments to accelerate the process of development and to channel it into desired directions by means of the comprehensive and detailed choice of objectives and the deter- mination and allocation of the resources necessary for their achievement. [6,. p. 272] But what is "development"? Or what is it to be "developed"? Chandrasekhar and Hultman point out that there is no universal acceptance of a definition or even of the criteria of development. They cite a number of definitions tint.have been offered. The common thread that seems to run 3 through them says something about relative levels of consump- tion and material well-being and the degree of application of science and technology to increase those levels [5, pp. viii-ix]. Colm and Geiger, in the passagequoted above, leave it to the domestic political process to choose the goals of development and to determine the means to reach them. The definition of development planning quoted above implies, in those few words, a range of complex problems which have bedeviled planners. The basic problem, that which makes planning essential to the development process, is the alloca- tion of scarce resources in an environment of complex inter- actions among physical, social, economic and political compo- nents. These interactions generate multiple and often con- flicting development objectives. Examples might be employ- ment, price stability, income, nutrition, balance of payments, education, etc. Planners and decision makers who are res- ponsible for the allocation of scarce developmental resources need information on the many possible trade-offs among objec- tives under alternative policy conditions. That is, a display cm'the set of attainable output combinations is needed. Another complication in development planning is due to imperfect knowledge about the present state and uncertainty as to the future consequences of policy options [48]. Data resources in most developing countries are notoriously lacking in both quantity and quality. Short- and long-run effects of alternative strategies are uncertain. In particular, the degree to which policies aimed at one set of economic phenomena '. may have unintended side effects, "good" or "bad", on other aspects of the society is often even more in doubt than the direct consequences. In short, development planners are trying to design controls for a system which is complex and non-linear, is unobservable and may not even be controllable. (in the control theory sense [49, pp. 75-85]) . The Evolution of the Systems Simulation Approach to Economic Problems These difficulties imply the virtual nonexistence of analytical solutions. Researchers have thus turned to simula- tion as a possible means of generating numerical solutions and hence providing policy makers with information about the likely consequences of alternative resource allocations. Given specific assumptions about system structure (causal factors and relationships among them and values of system parameters) and exogenous variables, a simulation model gener- ates time paths of relevant endogenous variables, including the vector of criterion variables needed by decision makers txJevaluate alternative development strategies. A number of such strategies can thus be tested and their outcomes compared and evaluated. In addition, decision makers can creatively interact with a simulation model, using previous simulation results to assist in the design of new and improved strategies as well as to continuously validate and improve the model itself [20]. Early simulation modeling efforts began after World ‘War II and expanded concomitantly with the development of analog and digital computing machines and techniques. The excellent bibliography in [ 9] lists thousands of papers, books and monographs which have appeared since about 1950 reporting simulation models of behavioral and social aspects of human systems. A few examples of economic and, specifically, economic development models will set the scene for a brief introduction to the Nigeria simulation model in general and the southern regional submodel in particular. While most early economic simulation model-building activity was concentrated on electronic analogs, Phillips constructed a mechanical model of production, consumption and price adjustment using colored water in a hydraulic system [42]. The accuracy of an electronic model was foregone for the illustrative advantages of a model whose dynamic behavior could be visually observed. Phillips also briefly describes other, more complicated macro-economic hydraulic models, some including components for government taxation. and expenditures. More typical of the early models is Smith and Erdly's electronic analog of a macro-economic system of investment, consumption and income generation [47]. Their model incor- porates a time lag between investment and the delivery of capital goods. A perfect time delay is approximated by a cascaded series of three "time-constant delays", each with the same time constant. Smith and Erdly maintain that this approximation is actually closer to reality than a perfect delay since it generates a distribution of delay times about a mean; i.e., not all capital goods have the same production 7 lag. This delay model is analogous to the digital computer. model of a third-order distributed lag described later in Chapters 2 and 3 (in connection with Equations 3.1) [16, 31, 331. Smith and Erdly found that their linear model was unstable. They attributed this to information lost in the delay and to the positive feedback loop of income to con- sumption to income. They concluded that nonlinearities and other factors omitted from their model work to keep the real system within bounds. Moving from models, such as the above, of single components of economic processes (e.g., investment and income generation, market price mechanisms, production decisions) to models of whole systems was a big step. Howard used the building-block approach in developing an analog computer simulation model of a colonial socio-economic system [23]. Two components were built and joined to simulate a three-class society--colonials, organized (urbanized) natives and primi- tives. The two components--national growth and national Ibehavior--are very aggregative models of macro-economic growth and political behavior, the latter defined as the choice of the organized natives between the two political alternatives of status quo and change. Production and consumption functions are included as well as a limiting natural resource. Researchers, however, concerned about the problems of economic development in the then fast-emerging, newly inde- pendent nations, were becoming frustrated with the limitations of electronic analog computers. Disaggregated and complex analog simulation models necessary to address effectively real policy questions proved unwieldy, impractical and unfeasible [21]. Forrester's development [16] of the "industrial dynamics" approach provided the methodology and techniques (and even a programming language--DYNAMO [43]) needed to convert to the more versatile digital computer. Holland did so with his generalized model of a develop- ing economy [21] and went on, with the Simulmatics Corporation, to build policy-oriented models of the VeneZuelan economy [22]. These were a series of increasingly disaggregated models to be used by policy makers in projecting consequences of policy options. The final one was generalized and quite disaggregated; it could simulate an economy (not necessarily Venezuela's) of I up to 25 sectors. Manetsch's model of the U.S. plywood industry [33] also follows the industrial dynamics approach to digital simulation. His model simulates the interactions of thousands of firms in the industry by aggregating them into seven rela- tively homogenous sectors: two producing sectors, three whole- saling sectors and two retailing sectors. As Smith and Erdly did in an electronic analog model, Manetsch uses a distributed delay process to aggregate the production lags of a large number of individual firms. A complex price mechanism is also included which incorporates a number of proportional and rate feedbacks from other system variables. Drawing on the techniques and experiences of these and other modeling efforts, an agricultural simulation team was formed at Michigan State University to investigate the feasi- bility of applying the systems approach to real development- planning and policy-making situations. Taking advantage of the wealth of resources and expertise on Nigerian agricultural development available at MSU (primarily the work of the Consortium for the Study of Nigerian Rural Development, CSNRD [24]), the team developed a policy-oriented simulation model of the Nigerian agricultural economy [35]. The southern regional model of an agricultural economy typified by competi- tion between perennial (tree) and annual crops for scarce productive resources——the subject of this dissertation--was part of that effort. The Nigeria Model The Nigeria simulation model is oriented specifically towards agricultural development because of the special role agriculture plays in the developing nations. Typically, agriculture accounts for 40-60% of national income and employs 50-80% of the labor force in these countries [25]. Johnston and Mellor cite a number of ways in which agriculture con- tributes to the development process. First, high population growth rates and positive income elasticities of demand mean agriculture is called upon to meet an increasing demand for food. Secondly, agricultural exports make important contri- butions to national income and foreign exchange earnings. Agriculture also provides, through rural-urban migration, 10 much of the nonagricultural labor force. Finally, agriculture can stimulate industrial growth by providing capital necessary for nonagricultural investment and by increasing agriculture's demand for consumer goods. The simulation model of the Nigerian agricultural economy is composed of three major submodels: the northern regional agricultural submodel, the southern regional agri- cultural submodel and the nonagricultural/national accounts submodel. In addition, there are components which model the -national food market and the population. Figure 1.1 indicates the major interactions of these submodels as well as the prin- cipal inputs and outputs of the system. Nigeria, with a population of over 55 million as of 1963 [12] and an area of over 356,000 square miles [13], is conceptually divided into two distinct regions: the North consisting of the six northern states of the federation (Figure ' I.2) and the South consisting of the six southern states (Figure 1.3). The basis for this "political" definition rests on ecological, cultural and (thus) economic considerations. Ecologically, the six southern states range from rain forest to intermediate savanna, while the North goes from savanna to near desert. In the South, annual crops typically compete with perennials (cocoa, rubber and oil palm) for scarce resources. The competition in the North is among 1/ annuals (primarily cotton, groundnuts— and food). Cattle 1/ —. The British word for peanuts, groundnuts, will be used in this thesis as that is the word used in Nigeria. 11 .maoooansm unaccououcw mo autos Hmcofiuuz H.H enough .3333 .28... . 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Since the primary focus of the national model is on agriculture, the broad, aggregated nonagricultural submodel enables the key interactions between agriculture and nonagriculture--e.g., agriculture's demands for consumer goods and capital inputs, nonagriculture's demands for raw materials and food, rural-urban migration--to be investigated [ 4]. This submodel also constructs the national accounts. The population component (Figure 1.1) simulates the Nigerian demography. Births and deaths are computed for a population of 27 three-year age cohorts. In addition, the. total labor force is determined and split between agricultural and nonagricultural occupations in each region and each eco- logical zone. Rural and urban food demands are computed as is rural-urban migration. The market and interregional trade component (Figure I.l) models the national food market. It takes cash food supplies from the agricultural submodels and food demands from the population component, computes the price of trans- portation (based on investments in transport capacity) and interregional shipments of food, and thus determines the Inltl 2.8"). '1 19 nonoh -< V U 8.303- 2. " .mucsooom HMGOHum: on» can hfiocooo amusuasowumoco: 0:0 mo H0002 w.H ou50wh U- ugh 0.0000— 000020. 3 0000.! «...-LIE .330 to}... 0000000.- 33-80 000— .95 «09:00 oflmwflflm 3 ruL 0050 2§0I0< 300:. .I.-50050— 35095 00850-00000 I] ”dwi- uucaurn 83h 30002 100 .5 300040 :0 50...; - L 8030‘ ink Ion-800.0- 3c .8. =0 . .0333}!!! 0n3~33~d< 3..an v2... .232 t .I( 3h. EOE-:00} 2 o n . .... ...-85.2.0. " 00000.01.- . P In. an vanguaocw "Pun”... mum muouoou ... .138 an venomoummo . imwo moanmaum> .N ..rnfiufi 333033 53 FF mxcwa unencummu .1 .der3 baa-.932: mOGflH COxOHQ . H «nouoz 5 25.6 18... 5 .I.-Ion «00:00.0— 38.58 5 oifl f llllll our“, ..fiu. . anti-on T n unwary-town.- 0'000— 1000.0l 028: 5 .030 .30: ......... IJ.-- l ‘0 6039090000 H . « IMF—$132004. 0....0—200t .0002 ‘00 -< o . o 035...:- 0300.135 I< (I (I p h t 0‘ '1 20 market price of food in both regions. In addition, the per capita consumption of food by the agricultural and nonagri- cultural populations in each region is calculated. In summary, the national model is a very complex computer simulation model of the Nigerian agricultural economy. It is capable of investigating the consequences of various policy options, including interactions with the nonagricul- tural economy. The total model contains some 2,000 to 3,000 equations and requires about 60 to 70 seconds of central processor time on MSU's CDC 6500 computer for a run of 42 years of simulated time. The southern regional agricultural submodel to be discussed here incorporates behavioral charac- teristics peculiar to an agricultural economy exhibiting competition between perennial and annual commodities for scarce resources. Included, thus, is a model of the dis- tributed parameter process of the demography of perennials, which is developed in the next chapter. CHAPTER 2 The Dynamic Demography of Perennials: A Model of a Distributed Parameter Process A perennial crop consists of a population of trees of various ages, i.e., trees planted at different times. Since certain characteristics of these trees depend on their age, e.g., yields and labor requirements, the age distribu- tion of trees is very important in determining the output of the crop and thereby the foreign exchange, tax revenue, income and other benefits accruing to the public and private sectors. Thus, it is useful to model the tree crops along the lines of a demographic model. That is, the perennial population ages through time, with births (new plantings) and deaths generating a dynamic and crucial age distribution. Equation 3.1 in Chapter 3 employs Euler's method to generate a numerical solution to the lumped approximation of a distributed parameter phenomenon-~the growth of a po- pulation of trees. In this chapter, a general population balance model is presented, examples of lumped approximations are given, and the lumped approximation represented by Equation 3.1 is developed wherein distributedlags are in- corporated to deterministically generate probability dis- tributions which capture the effects of genetic and 21 22 environmental differences among individuals in the population. General Population Balance Modell/ Population dynamics in general may be distributed in several dimensions in addition to time, depending on the needs and interests of the observer. Examples would be po- pulation distributions by spatial location, by age, by size, by productivity, by mass, by education, by income, by color (the visible spectrum of light), by emission of pollutants, etc.--in short, any property of individuals of the popula- tion which can be regarded as a continuum. This model can be applied to such disparate populations as people, cocoa trees, caterpillars (and butterflies), bacterial cells, - cattle, shrimp, roses and even automobiles. Let w(t, n1, n2, ..., um) be the distribtuion (i.e., density) of individuals over time t3/ and properties “i’ i = 1, ..., m. Thus, wAV is the number of individuals at time t in the m-dimensional region of volume V in the pro-3 perty space, where V = AnlAn2---Anm; that is, the number of individuals with property values in the interval (H, H+AH) = (n1, n1+Aw1)X(n2, n2+An2)X°--X(wm, nm+Anm). The p0pulation balance requires that the rate of accumulation of individuals in an arbitrary, small volume V 1/ - This section is drawn from the developments of [10, pp. 66-67] and [19,p. 38]. 2! The time dimension is shown apart from the others since it is virtually always of interest while the others are not, i.e., we might have m = 0. 23 of the property space be equal to the rate of net generation-- i.e., births minus deaths--within V. Thus, d ajc-fvupdv = [Vua-mdv (2.1) where B = B‘tpfllp 000’ TI’ births/(unit time-unit property changg) D = D(t, n1, ..., deaths/(unit time-unit property changg) dV = dflldfl2°°'dfl m IV = Inlfnz...lnm' Equation 2.1 can be written (assuming the necessary dif-- ferentiability and continuity conditions [ 3, pp. 120-1221) as I {3w + ? 2--(v w) + D - B}dV = 0 (2 2) V i=1 ani i ° where vi = dni/dt, i.e., the rate of change of property i as an individual ages through time. Since V is arbitrary, we must have 3 3 5% + -£1 5?; (viw) + D - B = o, (2.3) 1 Equation 2.3 is the general population balance equation. The birth and death terms, B and D, will generally be derived from characteristics of the particular popula- tion. For instance, in [10, p. 38], microbial cell popula- tions are discussed, where "births" and "deaths" consist of cell divisions and natural deaths. Also, Himmelblau and 24 and Bischoff [19, pp. 192-193] give an illustration of par- ticle agglomeration where "births" and ”deaths" occur as a result of particle collisions. Lumped Approximations In what follows, we assume m = 1, that is, only one property p is of interest. The lumping is completely generalizable to the cases m > 1. l/ . . . Suppose —- p ex1sts in an interval pmipgpM, where pm and pM may be infinite. We can divide the population into n p-cohorts Pi' i = l, ..., n, by defining correspond- ences P2 f+ palpl. p2) Pn ++ palpn_1. pn] where p0 = pm and pn = pM. The points p1, p2, ..., Pn-l may be arbitrary but would probably be chosen in some way meaningful for the particular population. Then, defining Pi ~ . ' Yi(t) = I w(t,p)dp , 1 = 1, ..., n, (2.4) p1-1 where yi(t) = the number of individuals in cohort i, and integrating Equation 2.3 with respect to p, we have dyi(t) p. = (vw) - (vw) + 1 (B-o)dp (2.5) at pi-l Pi £i_l l/ Generalized from.[27, Po 7]- 25 where v = dp/dt and (mp)pi is the rate at which individuals leave cohort Pi and enter cohort Pi+l' and where the integral term is the net generation per unit time of individuals in Pi' Coulman, Reice and Tummala [ 7] developed a model for populations of amphipods. (The model is generalizable to other animals whose life spans can be lumped as below.) The property p is maturity m, which can be represented by pro- portion of life span lived. The total life span is divided into seven identifiable stages, called instars. Thus, mm = 0, mM = l and n = 7. The basic model is composed of six equations (Figure. 1/ I.7).~ The first is a difference equation— representation of Equation 2.5. Yi(n+l) = Yi(n) + Si_l(n) - Pi(n) - Mi(n) (2.6) Pi(n) = pi(n)Yi(n) (2.7) ‘ ' ni(T)-l . Mi(n) = Si_1[n-ni(1)]o 520 [l-pi(n-j)] (2.8) Di(n) = di(n)Mi(n) (2.9) Si(n) = Mi(n) - Di(n) (2.10) Bi(n) = bi(n)Si(n) (2.11) i/ Kharkar [27, p.6] indicates that Equations 2.6 - 2.8 reduce to the differential equation in(t) t _aE___.= -pi(t)yi(t)+si_1(t)-{1- [ pi(s)ds}Si_1(t-ni(r)). t-ni(r) 26 «n————————————| —-——————— Y - pOpulation B - birth D - natural death M - mature P - predation S - supply Figure 1.7 A model of a generalized amphipod instar. 27 where = population = predation maturation out = deaths = maturation in I'll U) U 3 "U K II = births maturation time as a function of temperature T n(T) p, d, b = proportions i = indexes the instars n = indexes time (days). Note (Figure 1.7) that deaths occur after maturation, births occur after deaths and there are no births into an instar (i.e., B = 0 in Equation 2.5) unless i = l. The number of individuals maturing from the ith instar at time n (Equation 2.8) is the number which entered the instar ni(1) days pre- viously and which has survived predation. In a simulation model of the cocoa industry of the Dominican Republic [36], Mathis considers populations of cocoa trees, where the property of interest is productivity. As in the model described above, the property is related to stages in the life span, so the distribution is lumped into 13 production cohortsl/ of length di years, i = l, ..., l3. 1/ The demographic model used by Mathis may be written- l/ This is for traditional cocoa. Modern cocoa has 12 cohorts and is modeled similarly. 28 as three of the above equations. (No births or deaths are assumed.) Ai(t+DT) = Ai(t) + Mi_1(t) - Mi(t) - Ri(t) (2.12) Mi(t) = Ai(t)/d1 (2.13) Ri(t) = 0 p l = 1, 00., lo (2.14) Pi(t) , i = 11, 12, 13 where A = population (acres of trees) M = maturation R = removal for replanting P = removal policy d = maturation time i = indexes the cohorts DT,= time increment (years). Note the assumption that the distribution within a cohort is . uniform for all t; thus, if d1 = 10, for example, one-tenth of the individuals (acres) of cohort i pass to cohort i+l each year (Equation 2.13). Removal of traditional cocoa is limited to the oldest three cohorts and is a matter of policy (constrained by available acres). In the next section, we will look at the demographic model used in the southern regional agricultural submodel, where no assumption is made about the age distribution within a cohort and where the maturation lag (analogous to ”i of Equation 2.8) is a random variable. 29 Demography of Perennials The most important property of perennials, parti- cularly for a production model, is productivity. It is essential for determining the output of the crop and there- by the benefits accruing to the public and private sectors. Modeling the productivity dimension directly, however, is not feasible, for a given productivity value (yield) may characterize different segments of the population, i.e., young trees whose yields are rising and old ones whose yields are declining. In the notation of Equation 2.5, v>0 for part of w and v<0 for the rest of 0. Thus, it is convenient to substitute, as Mathis does, the age dimension as a sur- rogate for productivity. The lumping can be done, however, in terms of production cohorts (or stages). In this manner, the demographic model of the tree crops contains the five production cohorts described in Chapter 3, Figure 11.3. The population balance model is virtually the same as Mathis' (Equation 2.12), where Ri in this case represents removal in order to transfer land to other commodities or for abandonment. The removal rate R1 is determined by the decision mechanism discussed in Chapter 3. The major de- parture from Equation 2.12 is in the determination of the unturation rate dMi/dt. The model here is vaguely similar to that of Coulman, gt_§1. (Equation 2.8), in that it incor- porates a maturation lag. However, in the present model, the maturation lags are random variables which account for genetic and environmental differences among individuals in 30 the population. Kharkar suggests (following Wangersky and Cunning- ham [52]) an exponential distribution for the maturation times [27, pp. 8-9]. Here we use the more general kth-order gamma distribution (Figure II.4, Chapter 3). The effects of these probabilistic lag times can be simulated deter- th-order distributed delays, ioe'l a ministically with k series of k first-order (eXponential) delays [31,32]. This is accomplished by Equation 3.1, where trees entering a production cohort are lagged DEL years on the average and where the output distribution looks like Figure 11.4, depending on the value of k. Summary We have seen how Equation 3.1 in Chapter 3 uses Euler integration to generate numerical solutions to a lumped approximation (Equation 2.5) of the distributed para- meter process (Equation 2.3) of population dynamics.) In Part II, we shall see how this model serves as one component in the larger model of the agricultural economy of southern Nigeria, which in turn is a submodel of the Nigeria model outlined in Chapter 1. P A R T II MODEL DESCRIPTION Introduction and Summary The computer simulation model of the agricultural economy of southern Nigeria is composed of five basic compo- nents or building blocks (Figure 11.1). The first, the land allocation and modernization decisions component (LAMDAP), allocates land among various commodities in each of four ecological zones of competing cropping activities. Land use decisions are based on perceived relative profitabilities and the availability of information, either from farmer to farmer in a diffusion process or from extension agents (or other communications media) as part of modernization promo- tion efforts. Expansion of total cultivated land may occur as a result of these economic decisions 229.35 a consequence of a natural increase in the number of agricultural decision makers. The second principal component of the southern model (AMPPAP) takes the allocation of land from LAMDAP and, given commodity prices and yields, computes agricultural produc- tion, processing and marketing for the five commodities con- sidered—-cocoa, oil palm, rubber, food and tobacco. The subsistence food production depends on the level of 31 32 .Hapoa 0005500 000 00 3.00.3 933.30 000000 0.00 003000 00.000008 0000002.... .0 000000 03000 000390tu< .n .033...» 00000000 000030! .N 0000 «00000-000 >1 003300.. 00303000 .— 8923000< Fungal .OIU§ 02¢ (um—H.500 0000000< 030058.00 0'35 ‘85. :3 02005500 00 0030000., I0300000< 0.000501 .000.- 0503.00! 050000000 030090000 0301 0000 000 03095000 00000000090 00 02.04 .34660'0‘00' gnaw-Ii 92¢ 02—88050 000.00 SCHUQCOU «B Opp-u. O’B- 00000. 00000 100 000000 00001000 00000000 02030000000 000000 0000—0000 000.00 000000000 00300 .0000! 4:06.60; 000.00 300’ §0—JOA- 33 agricultural subsistence, or, conversely, on the degree to which farmers depend on the market for their staple food needs. This subsistence level is computed endogenously for. each ecological zone as a function of food market stability, the food price level, the level of agricultural sector food consumption and cash income from non-food commodities. The processing component determines the investment in processing capacity necessary to process the raw material inputs: palm fruit bunches are processed into palm oil and palm kernels, rubber latex is processed into sheets and raw tobacco is cured. A third unit of the model (PG) generates world, market, processor and producer prices. The domestic market prices of food and palm oil are determined endogenously as functions of excess domestic demand. Export commodity prices depend on export and marketing board tax policies and exo— genous world prices. Producer prices are exponentially averaged; these averages are used for the projections made to determine profitabilities in component LAMDAP and as bases to which current prices are compared in AMPPAP to determine short run harvest supply responses. The remaining two components are the primary entry and exit points of the system. As policy entry points, com- modity production campaigns are specified and conducted, marketing board and export tax policies are set, and income taxes may be levied. Finally, in the criteria and macro- budget accounting component (CRTMBA), the agricultural sector 34 budget is balanced, performance variables are generated and agricultural sector accounts are computed for the nonagri- cultural/national accounts component of the total Nigeria model. Each of these five building blocks of the southern agricultural submodel will be described in some detail in Chapters 3 through 7, respectively. CHAPTER 3 Land Allocation and Modernization Decisions-- Annuals/Perennials (LAMDAP) Component LAMDAP of the simulation model allocates land to the production of the various commodities grown in each of the four ecological zones (or crop sectors) described below (Figure II.2): the Cocoa-Food Sector, the Palm-Food Sector, the Rubber-Palm-Food Sector and the Food-Cash Annual Sector. In making these allocations, LAMDAP simulates farm- er's choices among the alternative uses for their land based on economic and cultural factors. Modernization of current land uses is an alternative as is transferring land into the production of alternative commodities. Ecological Zones Land use decisions in the South are based on the four ecological zones (or crop sectors) of competing cropping activities defined in the model. The sectors are determined roughly by climatic and soil conditions [15]. Figure II.2 is a Venn diagram of these zones. Sector 1 is the area where cocoa competes with food crops for land and capital. This sector covers all of the Western State (except Egbado, Oyo and Okitipupa Divisions) and Afenmai Division of the Midwest. 35 36 Although palm is a possible competitor to cocoa, the simpli- fying assumption is made that it is not really an economically viable alternative in this crop sector. In the major cocoa growing areas of the Western State, the profitability of cocoa relative to palm is such that cocoa production by far dominates palm production. Aside from the mere collection of wild palm fruits, farmers do not consider investment in the cultivation or modernization of palm a significant alter- native. Thus, in Figure II.2, the Cocoa Sector circle does not overlap the Palm Sector circle. The wild palm harvested in the Cocoa Sector is included in the model as a product of the bush areas. The model can be revised if further evidence calls this assumption into serious question. Cash Annual- Food Sector 4 Rubbe r- Penn-- Food Sector 3 Cocoa- ‘ Food Sector 1 IPdhn-. Food Sector 2 Figure II.2 A Venn diagram of the ecological zones of southern Nigeria. 37 In Sector 2, oil palm is the primary competitor with food for inputs. This includes all of the three Eastern states with the exception of the following divisions: Brass, Degema, Nsukka, Udi, Abakaliki, Ogoja, Obudu and Ikom. Okitipupa Division of the West and the Midwest State minus Afenmai and Western Ijaw Division comprise Sector 3, where oil palm, rubber and food all compete for resources. The remainder-~including Lagos State, those parts of the West not in Sector 1, those parts of the East not in Sector 2, and Western Ijaw Division of the Midwest—-comprises Sector 4, the areas where only annual crops can be economically farmed. In portions of this sector, cash annuals--e.g., cotton or tobacco--may compete with food. These ecological zones are not entirely internally homogeneous. For example, not all the food land in the Cocoa Sector is suitable for cocoa, and vice versa. Thus, although the crop sectors are defined for ecologically competitive crops, compromises were made to delineate the ecological zones as contiguous areas (except the Food Sector). The , primary reasons for this are twofold. First, any given farmer may hold some land suitable only for cocoa, some only for food and some where either is feasible. Since the infra- structure (roads, communication links, etc.) and the behavior- al characteristics of farmers--e.g., risk aversion and confi- dence in government experts--which control the land use and modernization decisions are likely to be somewhat determined by contiguous areas of social contact, a case can be made for ’U '11 l_'-‘ 38 compromising strictly “ecological" zones. Secondly, we will be interested in performing an agricultural sector budget accounting for each ecological zone. This budget includes not only agricultural income and investment but also con- sumption expenditures of the population. To the extent that consumption depends on common behavioral considerations, contiguous crop sectors again appear suitable. Land Uses In general, the land uses in the ecological zones include traditional and modern perennials, annuals, and bush. Specifically, Sector 1 has traditional and modern cocoa, foodl/, and bush, while Sector 2 has traditional and modern palm, food and bush. Sector 3, with two perennials competing, includes traditional and modern rubber, traditional and modern palm, food and bush. In Sector 4, the alternative to food and bush is tobacco, although the general mechanism could incorporate consideration of a cash annual other than tobacco, e.g., cotton or kenaf. Perennials Perennial commodities are modeled dynamically as populations distributed over time and productivity l/ "Food" is defined as a weighted composite of the major staples produced and consumed in the South: yam, maize, cassava and cocoyam. The weights used are as follows: yam--.315; maize--.278; cassava--.310; and cocoyam--.097. These weights were derived from acres in production as reported in [14]. They are used with the four staples to determine the food yield, labor inputs, biological inputs, chemical inputs and the calorie yield of food. 39 (Chapter 2). The demographic model of the tree crops is divided into five production cohorts of varying lengths (Figure 11.3). The respective cohort lengths reflect the five production stages of a perennial crop which the model identifies: a gestation stage, a stage of rising yields, a stage of maximum yields, a declining yield stage, and a stage of old trees where yields remain at some nominal level. The aging of trees through the first four cohorts is modeled by distributed lags (discussed below and Equation 3.1a). When trees finally enter the old age cohort, their aging rate is no longer modeled, and trees remain there indefinitely producing nominal yields to reflect their being phased out of production. The model may easily be modified to incor- porate a death rate for trees in this last stage. However, rather than actual "death", this is more of an economic decision of the farmers to permanently abandon old trees (thus allowing eventual reversion to bush), i.e., an economic death rather than a physical death. Such abandonment is thus determined in the model as a land use decision in the same manner as are planting rates (births) and transitions out of the population to other commodities, modern or tra- ditional. The distributed lag model [31] allows us to simulate, in effect, a probability density [32] for the time it takes trees to mature from each production stage to the next, i.e., not all trees entering a particular production stage at the same time will leave it at the same time. For example, 40 suppose the stage of rising yields is a six—year cohort (as it is for traditional palm). Some trees entering this stage after gestation may actually mature to maximum yields in less than six years, while others may require considerably more time. On the average, however, traditional palm trees take about six years, once they begin to bear, to reach maximum yields. A parameter k determines the shape of the probability_ density of maturation rates (Figure II.4). If k'= 1, an exponential distribution is assumed, and, as k + w, the dis- tribution (a gamma distribution) approaches a normal dis- tribution. The lag is called a kth -order delay, and it is equivalent to k first-order (exponential) delays in series, where the output of one stage is the input to the next. What- ever the value of k, the mean lag time for the cohort (the mean of the distribution) is given by the parameter DEL. Each production cohort is modeled as third-order distributed lag. The value k = 3 is used in the model as a compromise between what might be a realistic distribution of maturation times (perhaps k = 6) and the desire to limit computer storage requirements. If experimental evidence suggests a larger value of k and if model tests indicate this is a sensitive parameter, the model may be modified accordingly. The aging rates and levels of the cohorts are updated each time period by Equations 3.11/, where transitions -‘ ll FORDYN simulation uses the Euler method for numerical integration [31]. Equations appearing in this disserta- tion will be presented in this format. out- 41 treneition : rue \ planting rate Geetetion Stage \ Rieing Yielde \ \ Figure 11. 3 Perenniel production cohorte. I l It: 1 DEL Figure 11.4 The game dietribution of meturetion rates, “:1: Maximum Declining @ Yields Yielde m I I l I I 1 3 k: 3 DEL t m». 0.1.. 00. 42 c3t1t of the population come from each of the intermediate rates proportionately. = DT * _ con ijn‘t) COHDRi3 n(t- -DT) + W [COHDR(i_1)jn(t DT) - COHDRiJ n(t- DT)] , i = 1, 2, 3' (3.1a) CC)2EIIDRi3 n(1:) = COHi n(t)*{l - 'I'REXI'I'jn (t) *DT*3/[DELjn* 3 [conij nun} (3.110) i=1 DEL. TLPERj n(1:) =——5j3*i 21 COHDRjJ n(t) (3.lc) virieauzre: COHDRi = the three intermediate rates (i = l, 2, 3) of a third-order cohort delay after ac- counting for transitions out of the popu- lation--acres/year DEL = the mean lag time of a production cohort-- years DT = the time period of a simulation cycle-- years TREXIT = the rate at which land leaves a cohort by transferring out of the population to other uses (determined endogenously by the decision component discussed below)-- acres/year TLPER = the amount of land in a cohort—-acres j = indexes the cohorts—-j = l, ..., 4 n = indexes the perennial population streams-- 11:1, 000' 80 when i = 1, COHDR is the rate land enters the cohort. If Ojn 5 == 1, (the first cohort--gestation stage--of a perennial Population stream), COHDR is the planting rate determined Oln 43 13}; the land use decisions. Otherwise, COHDROjn is the output zyarte of the previous cohort, where the output rate of cohort (j—l) is COHDR3(j_1)n. The level equation, Equation 3.1c, indeed gives the exact storage of the cohort delays for all tgj. We can see t;11;i.s by examining the differential equation describing the ith stage of the kth—order distributed delay process (1 = l, 2,3, ...,k): dxi(t) 1 dt = ri-1It) ' 1'1“” D1 =D2 = ... =Dk=DELjn/k' and ri(t) - COHDRijn(t) in Equation 3.lb. licensee, ri(t) is the total outflow from the delay stage and Jer-—11(t) the total inflow. Clearly, the right side is the rate of change of storage in the ith delay stage. Hence: dri(t) in(t) 1 dt = dt V011eertn Qi = the storage in the ith stage. 0n integrating we get: Q 0 - = r — It can be shown that 01(0) = Diri(0) and thus that: \ L-/ This representation and the following development of it were suggested by Dr. T. J. Manetsch. 44 Q1 (t) = Diri(t) for all t. The total storage, Q(t) , in a k-stage delay process is, therefore: k Q ( t: ) = iglnirim where: Q(t) = TLPERjn(t) in Equation 3.1c. Modern vs. Traditional. There are eight perennial population streams in the model: 1) traditional cocoa, 2) modern cocoa, 3) traditional palm (Palm Sector), 4) modern palm (Palm Sector), 5) traditional rubber, 6) modern rubber, '7) traditional palm (Rubber-Palm Sector), and 8) modern palm (Rubber-Palm Sector) . All streams are modeled by Equations 3-1 as shown in Figure II.3, but the maturation lags of the Production stages differ from one perennial population to a1'l<>t:her. Such biological differences (e.g., cohort lengths, Yields) are the primary reason for modeling modern and tra- ditional perennials separately. However, the differences lDe‘tween the modern and traditional population streams of a perennial commodity are not only biological--i.e., modern high-yielding and/or disease resistant hybrids versus tra- ditional low-yielding, diseased varieties--but also cultural. The term "modern” also encompasses improved managerial prac- tices such as spraying, weeding, fertilizing, spacing and Pruning. Improved harvesting techniques, particularly rubber 45 tapping, are also subsumed under "modern". Substreams. Each perennial population stream is further divided (Equation 3.2) into two subpopulations or substreams. In the case of the traditional perennials (i.e., traditional biological varieties), the two substreams-- improved and traditional--are distinguished by the cultiva- tion practices used, i.e., modern inputs and methods versus traditional. The modern cultivation practiced in the improved traditional substreams is the same as that prac- ticed in the modern streams, but the latter include new higher— yielding, disease resistant hybrid varieties. The two sub- streams of the modern perennial population streams-~replanted and newly planted--represent new varieties planted on former traditional perennial land and on former bush or food land (or, in the case of Sector 3, on land formerly in the tra- ditional stream of the other perennial, i.e., rubber or palm). respectively. The two substreams of each perennial population stream are treated as proportions. Specifically, the model keeps trackof the proportion of land in the first substream via Equation 3.2. = 0 * * 0 - 0 - * PSPERjn(t) [RINRJn(t) DT PSPER(J_1)n(t DT) + PSPERJn(t DT) .. _ * {TLPERjn(t DT) (ROUTRjn(t) + TREXITjn(t) PTOUT)*DT} - TRMODjn(t)*DTl/TLPERjn(t) (3.2) 46 where: PSPER = proportion of land which is in the first substream RINR = the rate land enters the cohort--acres/ year . ROUTR = the rate land leaves the cohort to the next older cohort-—acres/year TREXIT = the rate land leaves the cohort to alter- native commodities-—acres/year PTOUT a parameter determining how much of the land leaving a perennial stream comes ‘ from the first substream (PTOUT = 1 means proportionately from each substream)-- dimensionless TRMOD = the rate land moves from the first to the second substream within the same cohort (i.e., improvement of traditional peren- nials)--acres/year j = indexes the cohorts-~j = l,..., 5 n = indexes the perennial streams-~n = l, ..., 8. For j - l (the first cohort), RINR is the planting rate and PSPER0n is the proportion planted into the first substream. Otherwise, RINR is the ROUTR of the previous cohort (equals COHDR3(j_1)n discussed in connection with Equations 3.1). The primary reasons for defining two distinct sub- streams is that yields and input demands may differ between them. This is certainly the case for the traditional and improved substreams of the traditional perennials. Such differences between newly planted and replanted modern peren- nial commodities are less obvious, however, and a case could be made for simplifying the model by merging these two sub- streams. But there is a third, important advantage to be 47 gained by maintaining the distinction. Improvement, replant- ing and new planting are all modern alternatives that may be stimulated by overt, exogenous production campaign policies. As such, it is essential that the economic returns and Costs of each of them separately be available in order to evaluate the alternative promotion policies. Thus, the model keeps track of replanted and newly planted modern perennials separately, as it does with traditional perennial varieties cultivated under improved and traditional methods. Annuals Food land (Equation 3.3) is land on which either subsistence or cash food is actually in production. There are also two subcategories (or "substreams", although there is no aging process as with the perennials) of food land: modern and traditional. The same rationale discussed above for the perennial substreams holds for the food substreams, the modernization of food production also being a potential production campaign policy. Tobacco in Sector 4--or any other cash annual--is treated in the same manner as food, but there are no sub- streams. (It is assumed there is no cash annual other than food traditional to the area. Therefore, any production of tobacco, cotton or whatever will have to have been exogenous- ly promoted; thus we can assume it will be only modern. Bush is all unused arable land, including land in fallow. Swamps, other wastelands, forest reserves and the 48 like—-commonly called "bush” but not available for small- holder agricultural production--are not treated in the model. Food land is computed by Equation 3.3. Cash annual (tobacco) land and bush land are computed by similar equa- tions. TLFDk(t) = TLFDk(t-DT) + [RINFk(t-DT) - ROUTFk(t-DT)]*DT (3.3) where: TLFD = total food land—~acres RINF = rate land from other commodities is planted in food--acres/year ROUTF = rate food land is transferred to the production of other commodities-- acres/year k = indexes the crop sectors--k = l, ..., 4. The proportion of food land in traditional production (the first substream) is determined by an equation similar to Equation 3.2. Although, as mentioned earlier in the discussion of the ecological zones, the simplifying assumption is made that palm does not compete with cocoa in Sector 1, there is a significant level of wild palm production there. The model handles this by including wild palm in the Cocoa Sector as a proportion of the bush. It is further assumed that the wild palm is uniformly distributed therein, and any land leaving or entering the bush category does not change the proportion of bush that is wild palm. This treatment 49 applies only to the Cocoa Sector; wild palm in the Palm and Rubber-Palm Sectors-—where it is the major or one of the major productive enterprises--is included in the traditional palm perennial population streams. Other Land Uses No further possible land uses are considered in the model. Alternative perennials (such as citrus, coffee and kola), non-staple foods (such as pineapple, banana, plantain, beans and green vegetables), and more than one cash annual I alternative are ignored. Such simplifications--necessitated by our resource constraints (principally data and computer time and storage)——are justified by the relative economic insignificance, current and potential, of the omitted alter- natives to the agricultural economy of southern Nigeria. Further research will be necessary to either confirm this judgment or to expand the model to treat the potential pro- duction of more commodities. Alternatives In principle, every current land use is a conceiv- able alternative to every other present use in the same ecological zone. In practice, however, certain behavioral assumptions can be made which will reduce the myriad alter- natives to be considered and to simplify the model. Table 11.1 displays the present and alternative land uses currently considered in the model. The last column shows the minimum planning horizon relevant to each use 50 .0005 0:00 0>00000000< .H.HH 00909 .0000 0 000000 00 00000 Aeev 030000000 000 :00: 000: 0000000 000 00>00000000< 00 .0000 M 000000 00 00000 Aev 00000000 000 :00: 00>00000000< 0 .0 000000 00 00000 00: 00 00>000000000 000000000 0000 0 000000000 002000 0000 .000 0000 0 0000 .0 000000000 00w 0:0 0000» on 00 00000000 300 00000: .00 000000000 000 000 we 00000 on 00 00000000 :00 00000: .0 000000000 0s~ 0:0 no 00000 on 00000000 :0: 00000000009 .00 000000000 000 0:0 «0 00000 on 00000000 :0: 00000000009 .0 I: :00: .n 0000 0 A0000aouv 000000 £000 .000 A30000u 00:0 00:00v 000000000 00a 0:0 :00: 00 00000000000 .0 00000 an 00 00000000 300 00000: .00 000000000 0s~ 0:» 00 000000000 000 050 00000000 :0: 00000000009 .00 00000 on no 00000000 :00 00000: .0 000000000 000 000.00 0000 0 0000 no 000000000000: .0 00000000 300 00000000009 .0 0000 .0 0000 0 00:0 00 00030000040 .0 0000 0 0000 .0 I: 000000000 009000 0000 .nee 000000000 00:00 0:0 «0 00000000 300 00000: .00 000000000 00:00 000 no «0000000 :0: 00000000009 .00 9000000000 00000: .0 0000000000 00000000009 .0 0000» on 00 0u00 000000500 0050 00 00080000000 .0 0000 .0 0000000000 00000: .~ 00000 On 00 0000 000000600 00:: 00 000000000A< .0 000000000 00:00 050 we 0000:0000 00:00 0:0 00 0000» on 00000000 300 00000: .00 00000000 :0: 00000000009 .00 0000» on 0000000000 00000: .0 0000000000 00000000009 .0 00000 cm 00 0000 000000000 0:000:00000 .0 0000 .0 0000000000 00000000009 .0 000000: uc000000 VOHO-Vw 080 00>d QUE 09 d‘ 0000030 00>000000u0< 00: 0000000 51 (discussed below). The second column in Table 11.1 lists the conceivable alternatives that we have "assumed away". While some of these assumptions are quite reasonable (for example, it may be safe to assume that modern cocoa won't be cleared and replanted with traditional varieties; or that traditional cocoa won't be cleared and the land planted directly in food), others may bear closer scrutiny and may possibly have to be reconsidered, especially if they un- realistically constrain the land allocations. Economic Decisions Land use decisions depend on the relative profita- bility of each alternative, on modernization promotion ef- forts, on diffusion effects, on the availability of land and capital, and on the behavioral characteristics of the farmers making decisions. Figure 11.5 indicates how these consider- ations, discussed in detail below, determine land use patterns. Profitabilities Farmers' decisions among the alternative uses for their land are based upon their perceptions of the rela- tive profitabilities (Equation 3.4) of the available alter- natives. DPVSUM.(t)-DPVSUM.(t) PDRij(t) = WUMJJHIJ , i = 1, ..., nj (3.4) where: PDR = the relative profitability differential-- dimensionless expected yields 52 input requirements and costs discount 9 rates Ymputatiory Profitability establishment KEY ®® ©©©®= costs profitabilities of alternatives relative to current uses behavioral @ availability fResponse\ ‘® response of land KFunctionj parameters profitability response diffusion . information promotion and information . . and efficiency efficiency ® Transitions capital constraint “1‘8?“ land transition rates . . _ Decision- multiplication Administrative exogenous Delays price component (PG) criteria/budget component (CR TMBA) modernization campaign policy 1t production component transition (AMPPAP) rates land allocation component (LAMDAP) Figure 11.5 Land-use decision mechanism. 53 DPVSUM = the discounted sum of returns over the planning horizon (see Equation 3.5)-— £/acre— i = indexes the alternatives to a present use-- 1:1, 000' n. J n. = the number of alternatives open to a 3 present use (see Table 11.1) j = indexes the present uses of a crop sector. Land use profitabilities are defined as the present value of the stream of net income which farmers expect to receive over some relevant planning horizon. (See the last column in Table 11.1.) The model computes (Equation 3.5) the sum of the discounted present value of returns to a land use from the present up to the planning horizon. This discounted sum is the "profitability" of that land use. n DPVSUM(t) = 2 f (3.5) i=1 (1 + DR) where: DPVSUM = as defined above n = the meaningful planning horizon (see Table II.l)--years TR = total revenue (Equation 3.6a)--£/acre- year TC = total cost (Equation 3.6b)--£/acre- year DR' = the relevant discount rate—-proportion/ year i/ One Nigerian pound (£) equals US $2.30. VI H '0. 01. 00 ‘l ...e 54 i = indexes the n years of the planning horizon-~i = 1, ..., n. In general, comparing the discounted present value of the total future returns accruing to an alternative (for instance, new planting of a modern perennial) with that of a present use (food) would be meaningless in view of the fact that each is based on a different planning horizon. In this case, the planning horizon for new planting is 30 years, while that of continuing with food production (an annual crop) is only one year (Table 11.1). To avoid this diffi- culty, profitabilities are computed using the longest plan? ning horizon of the alternatives being compared as common to all. The discount rates used to compute the present value of future returns are behavioral parameters in the model. The discount rates for each alternative are dif- ferent, the relative differences reflecting varying atti— tudes towards the adoption of the alternative land uses, particularly modern alternatives. The assumption is that the more risky and unfamiliar the alternative, the higher the discount rate. For example, discount rates for re- planting are higher than for improvement of traditional perennials, while discount rates for planting annuals are lower than those for planting perennials. Continuing in the present use has the lowest discount rate. Since we are concerned with farmer decision makers, the streams of future revenues and costs (Equations 3.6) 55 used in the profitability calculations should reflect the farmers' expectations. Thus, the producer prices used here are five-year exponential averages of recent prices. These price averages are projected into the future with trend factors (Equation 3.7) which are also exponential averages of recent producer price fluctuations. The form and compu- tation of producer price averages and trends are discussed more fully later in the description of the price generating component of the southern model (Chapter 5). Similarly, the stream of yields farmers expect are the yields they currently experience rather than the potential production reported by experiment stations. Actual yields approach their poten- tials with time as farmers gain experience. This concept will be discussed more fully later in the AMPPAP component description (Chapter 4). Additions to expected revenues are any cash and/or price subsidies which may be offered as part of a modernization program. The cost side includes-~as technological coeffi- cients--biological, chemical, labor, and capital (tools and equipment) input requirements over the planning period. Associated input prices are in the model as exogenous constants. The agricultural wage rate increases linearly with time (Equation 5.10a). Total revenue and total cost are computed simply as: TRi(t) = PTi(t)*Yi(t) + FNCEi(t) (3.6a) TCi(t) = PL(t) *XLi*PLHIRE (t) + PBC*XBC1 + PXE where: PT FNCE PL XL PLHIRE PBC XBC PXE PXP 56 i + PXPi (t) (3.6b) the expected producer price (Equation 3.7)-- £/1b. ' the yield (Equation 4.4)--1bs./acre-year cash subsidy grant (policy--see Chapter 6) --£/acre-year agricultural wage rate (Equation 5.10a)-- £/man-year labor input requirement--man-years/acre- year proportion of labor hired (Equation 4.29a) the composite price for chemical and biological inputs (possibly subsidized)-- £/lb. the composite chemical and biological input requirement--lbs./acre-year equipment costs (replacement investment = depreciation)--£/acre-year processing costs when producers do their own processing (=PAGCST, Equation 4.32e)-- £/acre-year indexes the n years of the planning horizon--1 = 1’ .00, no Note the perhaps unrealistic assumption of zero opportunity cost for family and own labor. While Equations 3.6 thus probably underestimate costs, there is no basis to assume that farmers value family labor at the going wage rate or at any particular function of the wage rate. Costs would prob- ably be overestimated if family labor were valued at the wage rate. a - y‘- Prr. ‘1. NE h; :‘ I‘f 57 The producer price projected over the planning horizon has a trend factor applied to it at every fifth year of the profitability series. PTi(t) = PY(t)*(PYR(t))[i/5] (3.7) where: PY = the five-year exponential average of recent producer prices (=PPAV of Equation S.8a)-- g/lb. = the trend factor--the averaged ratio of PYR - the current producer price to the previous time period's producer price (=PPAVR of Equation 5.8c)--dimensionless the largest integer in the quotient in brackets. [i/5] Information Units In estimating the profitability differentials of the various alternatives, the farm decision makers require certain informational inputs. These include information on future producer prices, expected yields, government or pri- vate subsidy and loan programs, and expected costs. The model provides this needed information through "information units". We introduce the general concept of an information unit so that consideration can be given to various possible alternative means of disseminating information and promoting production campaigns. Of course, extension agents will be the main form of promotional information units. (In fact, diffusion and promotion information are both modeled in L7" r+ E? 1! la 58 units of extension agent equivalents.) But, in addition, radio broadcasts, film showings, and newspaper coverage can be used by both government and private agencies. At present, the use of newspapers and other printed matter may not always be the most effective medium; however, as literacy rates increase in the population, this means of communication may become more important in Nigeria and other developing coun~ tries. While promotional information units (extension agent equivalents) are endogenously generated as a policy (Chapter 6), the model also computes (Equation 3.8) diffusion infor- mation units to represent the demonstration effect of farmers learning from one another about alternative land uses. The demonstration effect of an alternative to a present land use depends on the amount of land in each use: if there is no land in either, no diffusion information units are generated, while the diffusion rate is greatest when there is as much land in the alternative use as in the present use. Thus, the rate at which diffusion information units are generated re- flects the s-shaped curve of diffusion theory [45]. TLAVDi . (t) *TLALTi (t) *CIUDi . DINFij(t) TLAVDij(tY+“TfALTi t (3'8) where: DINF = diffusion information units--units (extension agent equivalents) TLAVD = land in a present use suitable for an alter- native by diffusion (Equation 3.9e)--acres TLALT land in the alternative use--acres 59 CIUD = a coefficient reflecting the information effect of demonstration land units-~units/ acre 1 = indexes the alternatives j = indexes the present uses. Availability of Land Several factors contribute to determining the pro- portion of land in a present use which would be suitable for a particular alternative use, i.e., land available for a particular decision. The major factor derives from the imperfect homogeneity of the crop sectors (discussed earlier). The consequences of this are that in considering the alter- natives to a present land use (Table 11.1), not all the land in the present use will necessarily be available for transi- tion to a given alternative (Equations 3.9d and 3.9a). Let's consider the Cocoa-Food Sector as an example. Not all food land is suitable for cocoa, nor is all traditional cocoa land even suitable for replanting. Soil and rainfall con- ditions in certain traditional Amelonado cocoa areas, for instance, may not be good for modern Upper Amazon cocoa. Another factor, a policy one, may dictate that the proportion of land available for a particular alternative use will be different for land transferring as a result of promotion campaigns than from diffusion effects. Moderniza- tion program policies could be rather restrictive as to soil conditions, local road conditions, farmer experience, etc., in allowing farmers to enter the program, whereas such li bu. v? Vite 60 limitations won't exist for the diffusion effect. Finally, there is a special restriction on how much bush land can be put to other uses. This restriction stems from the fact that "bush”, as defined in the model, includes fallow land, both short-cycle and long-cycle. An amount of bush land (Equation 3.9a)--representing short-cycle fallow which farmers expressly reserve to maintain subsistence food production yields in future years-—is considered not available for other uses (Equation 3.9b). FALNEC(t) = SUBFDL(t)*[FFT*PSFD(t) + FFM*(1 - PSFD(t))] (3.9a) TLPTb(t) = maX{[(TLPb(t) - FALNEC(t)) - DADva(t)], 0.)} (3.9b) TLPTj(t) = TLPj(t) - DADLVj(t), j 7‘ b (3.9e) TLAVP.. t = TLPT. t *CLA .. t 3.9d 13() J<> vn13< ) ( ) TLA .. t = TLPT. t * LAVRD.. t 3.9e vnlj() J()C 13¢) < ) where: TLPT = total land in a present use available for transition decisions--acres TLP = total land in a present use (e.g., Equations 3.lc and 3.3)--acres DADLV = land in the decision and administrative delay (see discussion below, preceding Equation 3.13)--acres TLAVP = land in a present use available for a par- ticular alternative by promotion--acres TLAVD = as defined in Equation 3.8 61 CLAVR = proportion of land in a present use avail- able for a particular alternative by pro- motion (see Equations 3.10) CLAVRD = proportion of land in a present use avail- able for a particular alternative by dif- fusion (see Equations 3.10) FALNEC = fallow land necessary to maintain subsist- ence food yields-~acres SUBFDL = subsistence food land (Equation 4.7)--acres FFT(FFM)= proportion of traditional (modern) subsist- ence food land which must be cycled into fallow to maintain yields PSFD = proportion of food land that-is traditional (Equation 3.2) i = indexes the alternatives j = indexes the present uses (j = b = bush). Perennial and food land uses have a further restric- tion--a behavioral one-~affecting the proportion of land available for alternative uses. (Bush proportions are con- stant.) For food land, the assumption is made that only cash food land will be considered for possible transition to other uses (Equation 3.10a). In the case of perennials, it is assumed that land in some stages of production will not be transferred to other uses (Equation 3.10b). For example, farmers won't remove traditional cocoa trees in the stage of maximum yields. Obviously, such behavior should not be as— sumed but rather be a result of economic decisions. However, simulating this decision for each cohort of each perennial population stream would vastly complicate and enlarge the model. Therefore, the decisions are modeled for each peren- nial stream in its entirety, and land leaves each cohort in 62 the same proportion as that cohort's proportion of the total population of those production stages which are available for transition. Again, modernization program constraints may indicate certain cohorts to be available by promotion, while behavioral characteristics of the farmers will decide the diffusion responses. Equations 3.10 compute the availability proportions for promotion. Those for diffusion (CLAVRD) are the same, with "P" prefixes and suffixes replaced with ”D”. CLAVRif(t) = CLAVFi*[l - SUBFDL(t)/TLFD(t)] (3.10a) 5 TLPE . t *PCT . _ *kgl Rk3( ) “RR: 3 10b TLPE .(t) k=l RRJ where: TLPER = defined in Equation 3.1 TLFD = defined in Equation 3.3 CLAVT, CLAVF = proportion of traditional perennial and food land available for promotion, respec- tively, due to soil, climatic, etc. condi- tions PCTR = parameters indicating perennial cohorts available for transition to alternative uses by promotion (= 0 or 1) i = indexes the alternative uses f = indexes the food present use j = indexes the traditional perennial present uses--j = l, ..., 4 k = indexes the perennial cohorts . 63 Transition Responses Changes in land use patterns reflect a farmer's res- ponses to the perceived profitabilities of the cropping alternatives available to him. The assumption is made that the most profitable alternative is likely to be the first choice of most of the decision makers, and so on, in order of decreasing profitability. The profitability response function (Equation 3.ll)£/ determines how many acres of land an information unit (either extension agent promotion or demonstration effect) can "convert" per year from one use to another. This calculation depends on the profitability of the alter— native, the efficiency of the information unit (discussed be- low), the land available for transition and the behavioral characteristics of the farm decision makers (see Figure 11.6). C3 ' THRLD PDR Figure 11.6 The profitability response function. 5/ Equations 3.11 - 3.13 compute the response to exogenous promotion. Similar equations handle the diffusion res- ponse. 64 PR1j(t) = max{C3ij*(l - expl-SHAPEij*(PDRij(t) - THRLDij)]), 0.} (3.11) where: PR = the profitability response to promotion efforts—~proportion C3 = the maximum proportion attainable (Equation 3.12) exp = the exponential function max = takes the maximum of the term within the braces ' SHAPE = the rate of promotion response with respect to profitability--dimensionless ' THRLD = the promotion response threshold-- dimensionless PDR = the relative profitability differential (Equation 3. 4)--dimensionless i = indexes the alternatives j = indexes the present uses. The efficiency of an extension agent (the same holds for a demonstration unit) is the maximum number of acres he is able to convert in a year as the profitability of the alternative grows. Figure 11.6 shows that the response function, Equation 3.11, actually computes the proportion of that efficiency (profitability response) which can be attained for a given profitability. The maximum propor- tion is, of course, 1.0; however, if there is a land constraint relative to the number of information units and their efficiency, the maximum attainable will be some- thing less than the potential efficiency (Equation 3.12). 65 TLAVPij(t) C3.. = min[ 13 , 1.] (3.12) EINFij(t)*CEFF*DT where: TLAVP = as defined in Equation 3.9d EINF = promotion (extension agents) information units (policy--see Chapter 6)--units CEFF = potential efficiency of promotion-- acres/information unit-year i = indexes the alternatives j = indexes the present uses. The threshold and response rate parameters shown in Figure 11.6 reflect the farmers' attitudes and behavior- al characteristics which affect the rate of their response to the relative profitabilities of the various alterna- tives facing them. The factors represented by both of these parameters include, for instance, the degree to which the trees are fixed assets, risk aversion, the amount of inconvenience the farmers may see in an alter- native use (including the extent and quality of roads and the transport system), farmers' attitudes towards govern- ment programs and promises in general, and the land tenure system. The threshold parameter of an alternative marks the point (relative profitability of the alternative to a current use) below which there will be no transition to that alternative. Since farmers will have different attitudes towards extension agents (or other promotional efforts) than they will towards one another, the values of 66 these parameters may be different for promotion responses than for diffusion responses. The transition rates (Equation 3.13) are cons- trained by available capital and lagged to account for decision-making delays and (in the case of externally pro- moted alternatives) delays involved in program administra- tion and distribution of necessary inputs and subsidies. Land currently stored in these delays (i.e., already allocated) is assumed unavailable for further allocation (see Equation 3.9c above). The capital available in an ecological zone for investment in alternatives includes capital generated endogenously as income (after allowing for consumption) and potential credit, which in turn depends on the capitalized value of cultivated land. The availability of capital and credit will be discussed more fully later in the discussion of the Criteria and Macro- Budget Accounting component (Chapter 7). Any capital constraint in a crop sector is applied uniformly to all alternative land uses in that sector. = * .. * .. * .1 TRLDPij(t) CEFF EINFlj(t) PR13(t) CNSIN(t) (3 3) where: TRLDP = unlagged promoted land transition rate-~acres/year PR = as defined in Equation 3.11 CNSIN = investment constraint (capital avail- ability--Equation 7.12b)--proportion 67 i indexes the alternatives j indexes the present uses. The demand for capital--which is compared (component CRTMBA, Chapter 7) with available resources to determine if capital is a constraint—~is merely the sum of the establish- ment costs (Equation 3.14a) incurred by the decisions to move land to alternative productive uses. The establishment cost of an alternative is defined as the net cost which would be incurred in the first year of the establishment of an alter- native on a particular piece of land (Equation 3.14c). This cost will include items such as tools, biological and chemical materials and hired labor necessary for land-clearing and planting. This definition of establishment cost is used—- rather than total net costs over the planning period until positive net revenues occur or, alternatively, until produc- tion begins--so the capital required in the year the transi- tion is made can be used to compare with what is available that same year. Since this is the major cost which would need to be met with either credit or the currently available cash flow, it would be the primary financial constraint to production enterprise changes. Costs incurred over the remainder of what might otherwise be called the establishment period are included as Operating expenses computed in compo- nent AMPPAP. ECAPRT(t) = g ECSHRij(t)*(DTRLPij(t) + DTRLDij(t)) (3.14a) 68 CSHRij(t) = max(ESTABij(t), 0) (3.14b) ESTABij(t) = [TRlij(t) - TClij(t)]/(1 + DRij) (3.14c) where: ECAPRT = total capital required for land use transitions in a crop sector--£/year CSHR = capital required for alternatives-- £/acre-year DTRLP, DTRLD = lagged values of TRLDP and TRLDD (see Equation 3.12), respectively--acres/ year ESTAB = establishment cost--£/acre-year l = the values of TR and TC (Equations 3.5 and 3.6) in the first year of the planning horizon--£/acre-year DR = discount rate i = indexes the alternatives j = indexes the present uses. In addition to capital resources, demands for modern inputs generated by farmer responses to the moderni- zation programs are computed (Equations 3.15). These include biological inputs, such as new hybrid seedlings and other planting materials, and chemicals, such as fer- tilizers and sprays. ECAPMPmit) = CSHRij(t)*DTRLPij(t) (3.153) EBIOMPm(t) = LLM UM I'd-M p.54 * EBTij DTRLPij(t) (3.15b) 69 ECHEMPm(t) = Z Z ECHT. j.*DTRLP ij(t) (3.15c) j i ‘where: ECAPMP = capital demands--£/year EBIOMP = modern biological input demands-- V units/year ECHEMP = chemical input demands-—1bs./year' EBT = biological input requirements for establishment--units/acre ECHT = chemical input requirements for establishment--lbs./acre m = indexes the modernization programs-- m =1, ..., 5 i = indexes the modern alternatives relevant to program m j = indexes the present uses relevant to program m. A final economic decision to be made is whether escame perennial land is to be abandoned indefinitely (as caraposed to a short term "abandonment" discussed in the r1eext chapter as a supply price response), thus reverting 't<> bush. Such an abandonment decision would be made if 9221 the current returns (PRFT in Equation 4.28m) are neegative 229.the long-run profitability (DPVSUM in IEGIuation 3.5, above) is below some threshold value. ‘Fiugure 11.? shows how the model (Equation 3.16) handles tJLis decision. Thus, even if current returns are negative, n£> abandonment will occur unless the long-term profitabi- lity also drops below some threshold value (which may be 70 ---------- - r-PMXAB 0 ==DPVSUM \B THREE Figure 11.7 Abandonment response. p><>ssitive, negative, or zero, depending on behavioral charac- tzeezristics of farmers particular to a given perennial commodi- ‘tjf and possibly depending on potential income which might be deaJrived from nonagricultural occupations), in which case, ak>aandonment will occur at an increasing rate, up to a maximum, as the profitability continues to fall. ABANRj(t) = TLPTj(t)*max{PMXABj*(1 - epr-SHPABj*(THRAB. J - DPVSUMj(t))], 0.} (3.16) ‘WhEBIEH ABANR = abandonment rate--acres/year TLPT = defined in Equation 3.9c DPVSUM = defined in Equation 3.5 PMXAB = maximum proportion that will be abandoned-- proportion/year SHPAB = a parameter regulating the abandonment rate--dimensionless 71 THRAB abandonment threshold--£/acre H. II indexes the present uses. giganeconomic Responses In addition to the economic land use decisions (cieascribed so far, the number of acres cultivated will in— crease as the number of decision makers increases with the population. The economic decisions discussed above repre- sseaxnt the activities of established farmer decision makers, i -e., whether to increase or decrease the amount of land cztzjltivated or whether and how to shift land currently in E>J:<3duction to alternative uses. Those young men coming of alggee and starting new farms of their own, on the other hand, vv<>11't make that economic decision (as long as there is at 'leeaist a positive profitability--Equations 3.19). Cons- txraiined by the available bush land (Equations 3.20), new latrid comes into production (Equation 3.17a) at a rate proportional (Equation 3.18) to the rate of increase in the number of decision makers (Equation 3.17c) . If there is an economic or land constraint, then those new farmers not acquiring 'land of their own will wait until conditions are more favorable, adding to the pressure of new decision makers :for? land (Equation 3.21). This "pressure" would be a significant factor to consider if rural-urban migration is to be determined endogenously in the model. Equations 3.17 to 3.21 are given for the first perennial commodity of a crop sector. Similar equations fin». 72 (zcxmpute this response for the second perennial in the Rubber- I?zllm Sector, for tobacco in Sector 4 and for food. IZJLTTPk(t) = AlPk(t)*[RAGDMXk(t) + RPSP RAGDMXk(t) 1;};(SDMAk(t) ‘wwuaare: * k RAGDSPk(t)] *EIPAk(t)*BAPXFk(t) (3.17a) *DLABOR RLTPP AlP RAGDMX RAGDMA RAGDMAk(t-DT) + RAGDCM = RAGDSP RPSP maxIRAGDMAk(t), 0.] . (3.17b) DT. * _ PEXDEL [RAGDCM2(t DT) k12 - RAGDMAk(t-DT)] (3.17c) rate land transfers to the first perennial of a crop sector due to agricultural population growth-- acres/year average landholding of the first perennial (Equation 3.18)--acres/ decision maker the positive rate of change of agri- cultural decision makers--decision makers/year the lagged rate of change of agri- cultural decision makers in a crop sector--decision makers/year unlagged rate of change of agricul- tural decision makers in the South (from the population component)-- decision makers/year population "pressure" for land (i.e., those constrained out by economic conditions and the availability of land (Equation 3.21)--decision makers the rate constrained new decision makers acquire land as the constraints are eased (a model parameter)--propor- tion/year 73 EIPA lagged economic constraint coefficient for the first perennial of a crop sector, 0 : EIPA i 1 (Equation 3.19b)--dimension- less BAPXF bush land availability constraint coef- ficient, 0 < BAPXF : 1 (Equation 3.20b) --dimensionIess DLABORk12 - proportion of southern agricultural labor in each crop sector (a parameter of the population component) PEXDEL the smoothing lag for the population growth effect on land use--years k = indexes the perennial crop sectors-- k = 1’ 2' 30 Note that this process is constrained so that a decline in the number of agricultural decision makers will not cause a decline in the number of acres cultivated. Equation 3.18 computes the average landholdings in the first perennial, AlP. TLTk(t) + TLMk(t) Alpk(t) = W215 (3‘18) Where: TLT, TLM = total acres in the first perennial of a crop sector, traditional and modern, respectively--acres agricultural decision makers in the South in each crop sector (from the population component)--decision makers AGDCMkz k = indexes the perennial crop sectors-- k = l, 2, 3. The economic constraint coefficient (EIPA) computed in.Equations 3.19 requires the profitability of the first perennial to be at least the threshold value for full 74 response (EIPA = l) and at least zero for any response. PDR b(t) EIPk(t) = maxlm1n(THRLpr , 1), 0.] (3.19a) DT *(EIPk(t-DT) - EIPAk(t-DT)) (3.19b) where: EIP = unsmoothed economic constraint coefficient --dimensionless PDR = the relative profitability differential (Equation 3.4 )--dimensionless - THRLD = the profitability response threshold indicates perennial alternatives = indicates the bush present use k = indexes the perennial crop sectors-- k = l, 2, 3. The bush land availability constraint coefficient goes to zero as non-fallow bush land decreases with time (Figure II.8). The constraint is relative to time zero; therefore, BAPXF = l initially. BAPXF CBPXF snudl 335:57EAPX Figure 11.8 Land constraint. 75 BAPXk(t) = TLBFk(t) - TRTOBk(t)*DT (3.20a) ‘ BAPXO BAPXFk(t) = epr-CBPXF*(§x§i;%ET - 1)] , (3.20b) where: BAPXF = bush land availability constraint factor-- dimensionless exp = exponential function CBPXF = a parameter BAPX = bush land available--acres BAPXO = initial value of BAPX (at t = 0) TLBF = non-fallow bush land (= TLPTb of Equation 3.9b)--acres TRTOB = total rate land transfers out of bush to all alternatives as a result of economic decisions--acres/year k = indexes the crop sectors--k = l, ..., 4. The population "pressure" for land due to economic and land constraints is computed by Equation 3.21. = t * RAGDSPk(t+DT) (1 RPSPk*EIPAk(t) BAPXFk(t)) RAGDSPk(t) + (1 - EIPAk(t)*BAPXFk(t))*RAGDMXk(t)*DT (3.21) hflhere: RAGDSP = as defined in Equation 3.17a EIPA = as defined in Equation 3.19b RAGDMX = as defined in Equation 3.17b ‘RPSP = as defined in Equation 3.17a k = indexes the perennial cr0p sectors—- k = 1, 2, 3. 76 Summary Component LAMDAP simulates the demography of pe- rennial commodities (cocoa, palm and rubber) and allocates land to alternative productive activities among perennials and annuals. Included in these alternatives are the modernization options promoted exogenously and diffused within the agricultural sector. These land use decisions are based on the discounted profitabilities of alterna- tives relative to current uses. The discounting depends on farmers' expectations regarding prices and yields, while the decision responses are determined by such be- havioral characteristics as risk aversion and confidence in outside information sources. An essentially noneconomic expansion of cultivated land also takes place as the number of farm decision makers increases. CHAPTER 4 Agricultural Marketing, Production and Processing-- Annuals/Perennials (AMPPAP) Component AMPPAP generates the production, process- ing, and marketing activities of the six agricultural com- modities (cocoa, palm oil, palm kernels, rubber, food, and tobacco), determines the food subsistence level of the population in each ecological zone (crop sector) and the yields of the various commodities. Subsistence Level Of the staple food produced in each crop sector, one portion is consumed directly by the agricultural popu- lation of that sector while the rest goes through the cash food market. The portion retained for subsistence con- sumption is determined by the total demand for calories by the agricultural population and the proportion of that demand met by food consumed directly from the farm. The :remainder of the total food demand is purchased in the <2ash food market. The assumption is that the subsistence Jgevel proportion is not necessarily one (total subsistence) l>tut may be less depending on conditions in the food market a:11d.the cash income generated from the cash crops. Since the cash crops and (thus) the degree of dependence on the 77 78 cash economy differ across the crop sectors, the subsistence level is sector-specific. Farmers will change their desired subsistence level depending on the degree of stabilityl/ in the cash food market, on the food price level and on the income from cash (primarily export) crops. Instability in the food market will tend to increase a farmer's reliance on his own efforts for his food needs, i.e., the subsistence level will go up. This effect on the subsistence level is generated by the magnitudes of the relative food price changes (up or down) summed for the three preceding years (Equations 4.1). This assumes farmers have a three-year memory regarding the effect of market food prices on market stability. While the impact of Equations 4.1 loses much of its force and meaning because the model does not simulate seasonal price fluctuations, it does capture general trends. In any case, the concept of food market stability is a meaningful and useful one. pnpnzm - PRFD2(i-DT) 2 FPRA(i) = W— , i = t-3, t“3+DT, ..., t 2 t (4.1a) FPSF(t) = izZ-BFPRAH) (4.110) where: FPRA(i) = the square of the relative change of the ' food price in the South at time i-- dimensionless PRFD2 = market price of food in the South (=PPRCM5 of Equation 5.2b)--£/lb. lz/ "Stability" in the food market means, here, that food prices are constant. 79 FPSF = the food price stability factor-— dimensionless i = indexes three years of time periods incremented by DT. Squaring the relative price change has the effect of in- cluding price decreases as well as price increases as a factor of instability in the market. It also gives rela- tively more weight to large deviations than to small ones. Perfect stability in the food market, however, is not enough to lower the subsistence level. The second factor determining changes in the level of subsistence is represented as the ratio of the value, at market prices, of the food consumed by the agricultural population to the net revenue from cash crops (other than cash food). This formulation (Equations 4.2) incorporates as a factor the food price level in addition to the price changes of Equations 4.1. However, the price level must also be related to the cash revenue farmers have available to purchase food in the market and to how much food would have to be pur- chased to meet the demand for calories. Decreases, for example, in the food expenditure/cash revenue ratio--due tn: falling food prices, rising producer prices for cash <:Jrops or falling costs in cash crop production-dwill tend t:c> decrease the subsistence level, i.e., increase producer Jreeliance on the food market for their caloric needs. Equations 4.3 combine these two factors--food market s‘tability and the food expenditure/cash revenue ratio--to 80 determine the subsistence level in each crOp sector (Figure 11.9). DEMRSk(t) FXCRk(t) = EXPFDk(t)/CSHRNk(t) (4.2b) FXCRAk(t) = FXCRAk(t-DT) + [figg—E]*[Fxcak(t-DT) - FXCRAk(t-DT)] (4.2c) where: CSHRN = total net cash revenue to the agricultural sector in an ecological zone from non-food crops (= REVCN of Equation 4.28j aggregated by crop sector)-- f/year EXPFD = value of food consumed by the agricultural sector in an ecological zone-- f/year DEMRS = the caloric requirements of the agricultural sector in an ecological zone (from the population component)--Calories/year CALY = the caloric content of food--Calories/1b. PYCNS = the proportion of food which is actually consumed (after spoilage and waste) FXCR = the food expenditure cash revenue ratio-- dimensionless FXCRA = the lagged food expenditure cash revenue ratio of an ecological zone FXDEL = the length of the smoothing lag-- years k = indexes the erennial crop sectors-— _ 19 k - l, 2, — . SLRSPk(t) = SLSHPk*FPSF(t)EFPSF (4.3a) 41” . . . ’ ‘*' ‘The agricultural population 1n the annuals sector (Sector 4) is assumed to maintain total subsistence. This as- sumption can be relaxed if desired. 81 susunsv 1.0 SLhflfil SLRSP .---J V SLTHR FXCRI Figure 11.9 Subsistence level determination. SUBLEVk(t) = max{ [(1 -SLMINk)*exp(-SLRSPk(t-DT) where: *(FXCRAk(t—DT) - SLTHRk))], SLMINk} (4.3b) EFPSF SLRSP SLSHP SLMIN SLTHR SUBLEV a parameter which controls the effect of the food price stability factor on the subsistence level response rate subsistence level response rate adjusted by market instability subsistence level response rate in a perfectly stable food market the minimum level of subsistence farmers will maintain--proportion of food demand the value of FXCRA which is the subsist- ence level response threshold the subsistence level: the proportion of the food requirements of the agricultural population of an ecological zone which is not obtained from the market economy 82 k = indexes the perennial crop sectors-- k = l, 2, 3. Yields There are three determinants of commodity yields. First, provision is made in the model for yields to increase spontaneously (i.e., independently of outside influences) as farmers gain production experience. We might call this a learning curve yield response. Secondly, the yields of the 1/ substreams— are combined, weighted by the amount of land in each substream, to obtain an average yield for each cohortl/ (in the case of perennials) of each stream. Finally, com- modity yields are adjusted to account for a short run harvest supply response to the current producer prices. Each of these factors will now be discussed in more detail. Learning curves for the perennial and food yields serve two functions in the model. Since we are interested in keeping the definitions of "modernization" and "moderniz- ing programs" as rigid as possible in order to evaluate these programs, the learning curve allows us to simulate past be— havior which included spontaneous adoption, to a limited degree, of certain modern methods and inputs. For simulation runs including modernization programs, the learning curve also allows us to simulate behavior whereby farmers, in adopt- ing modern methods and inputs, do not immediately achieve the maximum potential yield of the crop. Initially, modern land l/ These terms are defined above in the discussion of the land allocation and modernization component, Chapter 3. 83 will not be yielding its potential, but this yield will in- crease over time towards that potential as farmers gain experience with the new methods and materials. Since this learning behavior represents a diffusion phenomenon (i.e., farmers learning from one another), the learning curve effect (modeled by Equation 4.4) won't take place unless a minimum number of acres in a particular use has been surpassed. Equation 4.4 gives the learning curve increase for, as an example,the first substreams of the perennial popula- tion streams. Similar equations simulate the learning curves for yields of the second perennial substreams, YPERZij, and for yields of the first and second substreams of food, YFl and YF2. YPERlij(t) = YPERlij(t-DT) + (DT/YMDEL1)*(YPER1Mi. J - YPERlij(t—DT)) (4.4) where: YPERl = the yield of the first substream of peren- nials—-lbs./acre—year YPERlM = the maximum potential yield of perennials in the first substream--lbs./acre-year YMDELl = a lag regulating the rate at which the current yield approaches the potential yield--years i = indexes the yielding cohorts--i = l, ..., 6 j = indexes the perennial streams-—j = 1' 000' 8. 84 After the learning curve adjustment, the yield of each crop is averaged across land use substreams, i.e., tra- ditional and modern food, newly planted and replanted modern perennials, and traditional and improved traditional peren- nialsl/. In calculating this average (Equation 4.5), the yield of each substream is weighted by the proportion of the crop land in that substream. Again, similar equations apply to the food yields, YFA and YFAP. YPERA.. t = PSPER.. *Y . + — * 13( ) 13(t) PERliJ(t) [1 PSPERij(t)] YPER21j(t) (4.5) where: YPERA = the perennial yields averaged across the substreams--lbs./acre-year PSPER = the proportion of land in a perennial stream which is in the first substream (Equation 3.2): i = indexes the yielding cohorts--i = l, ..., 6 j = indexes the perennial streams-- j = l, ..., 8. The proportion of the total capacity (acreage) of a commodity actually harvested is a function of that proportion under "normal" producer price conditions (a behavioral pa- rameter) and the ratio of the current price to the normal Price. The normal price is taken to be an exponential aver- age of past producer prices. The model (Equation 4.6a) l "/ These terms are defined above in the discussion of the land allocation and modernization component, Chapter 3. 85 incorporates behavioral parameters which can generate nega- tively sloped, positively sloped, or perfectly inelastic supply curves. Finally, while the harvest response is a short-term response, the input response is medium-term. In perennial crop production, farmers may put forth less harvest effort (as we have seen above) in response to unfavorable prices. However, they may also cut back on some cultivational prac- tices, particularly in the case of modern production. The practices which may be affected include weeding, spraying, fertilizer application, and similar modern techniques. The cut-back, albeit temporary, in the application of these practices will result in reduced yields later-~one to three years, say. This deferred yield effect is a factor contri- buting to the determination of the yield actually attained (Equation 4.6b) in any given year. Perennial yields are shown in Equations 4.6; food yields adjusted for a supply response, YFAP, are similarly computed. ' PPPCk(t) ZSUPRSPk -__- * * YPERij(t) YPERAij(t) PPLHVj PPKVfiiTE) ESRIA. *(SRIAk(t)) 3 (4.6a) PPPCk (t) SUPRSI Where: YPER = the yield of perennials adjusted for a price response—-lbs./acre-year 86 PPPC = the current agricultural producer-processor price (Equation 5.9)--— S/lb. PPAVH ='a ten-year exponential average of recent agricultural producer-processor prices (Equation 5 . 8b) -- s/lb. SUPRSP = perennial supply response elasticity PPLHV = the proportion of perennial land harvested SRIA = the lagged input application response (computed as a first-order lag)--dimension- less ESRIA = exponent regulating the effect of the input response on yields SRI = the unlagged input application response SUPRSI = input response elasticity i = indexes the yielding cohorts--i = l, ..., 6 j = indexes the perennial streams—~j = 1' 0.0, 8 k = indexes the perennial commodities--k = l, 2, 3. Notice how the price response works. If the current agricultural producer-processor price, PPPC (Equation 5.9), is greater than exponentially averaged recent prices, for example, the supply response exponent, SUPRSP, will work as follows: if it is zero, the supply is perfectly inelastic; if SUPRSP is positive, an upward sloping supply curve is assumed; if SUPRSP is negative, a negatively sloped supply curve is assumed. The supply response is based on a ten-year .moving average of recent pricesso that farmers respond to deviations from what might be called a normal price level, ‘Where farmers have a ten-year memory of what is "normal". 87 Food Production In computing food production, AMPPAP first calculates (Equation 4.7a) the food land necessary to meet the subsist— ence demand of the agricultural population. A constraint is placed on the total food land in production so that it at least covers what is necessary to produce subsistence food (Equation 4.7b). Any remaining food land goes for cash food production (Equation 4.7c). DEMRSk (t) "SUBLEVk (t) = _ * SUBFDLk(t) SUBFDLk(t DT) + (DT/SDEL) CALY YFAk t PYCNS - SUBFDLk(t-DT)) (4.7a) TLFDk(t) = max(TLFDUk(t), SUEFDLk(t)) (4.7b) CSHFDLk(t) = TLFDk(t) - SUBFDLk(t) (4.7c) where: SUBFDL = subsistence food land-~acres DEMRS = demand for Calories from the agricultural sector of the population (population compo— nent)--Calories/year SUBLEV = the subsistence level, i.e., the propor- tion of DEMRS that farmers produce them- selves (Equation 4.3b) CALY = the Calorie content of food-~Calories/lb. YFA = the food yield averaged between modern and traditional (Equation 4.5)—-lbs./acre-year PYCNS = the consumable proportion of food produced, after accounting for loss and spoilage TLFD = total food land--acres TLFDU = unconstrained food land (= TLFD of Equation 3.3)-~acres 88 CSHFDL = cash food land-~acres SDEL = the subsistence food land smoothing lag-- years k = indexes the crop sectors--k = l, ..., 4. Notice that Equation 4.7a calculates the subsistence food land requirement and at the same time smoothes changes in that requirement by lagging it a period SDEL. The output of food, then, is a function of food yields, food land and food intercropped with perennials in the gestation stage of production. The amounts of food produced for consumption by the agricultural and nonagricul- tural populations are also computed for use in the national accounts component of the total Nigeria model. 8 TLPER1.(t) PDCNCF (t) = YFAP (t)*(CSHFDLk(t) + Z YDMIX* 3 k k j=l 3 (4.8a) PDCNSFk(t) = SUBFDLk(t)*YFAk(t) . (4.8b) 4 4 TFPAG(t) = Z PDCNSF (t) + [ Z PDCNCF (t) - DEMBIO (t)]* - k _ k 4 k-l k-l (TDCFS(t) - DEMCFS(t)) - TbCFS(t) (4'8c) TFPNAG(t) - [ Z PDCNCF (t) - DEMBIO (t)]*DEMCFS(t) (4 8d) ‘ k=1 k 4 TEEF§TET” ’ 'where: TLPERlj = total perennial land in cohort l of stream j (Equation 3.lc)--acres PDCNCF = the production of cash food-—lbs./year CSEFDL = cash food land (Equation 4.7c)--acres 89 YFAP = the averaged and price-response-adjusted food yield (Equations 4.5 and 4.6)--lbs./ acre-year YDMIX = a factor adjusting food yield for food intercropped on land in the first cohort (gestation) of the perennial streams-- dimensionless PDCNSF = production of subsistence food--lbs./year SUBFDL = subsistence food land (Equation 4.7a)-- acres YFA = averaged food yields (not price adjusted-- Equation 4.5)--lbs./acre-year TFPAG = total food produced for agricultural consumption--lbs./year TFPNAG = total food produced for nonagricultural consumption—~lbs./year DEMBIO4 = demand for food biological materials for replanting the following year (Equation 4.26f)--lbs./year DEMCFS = demand for cash food Calories from the nonagricultural population (population component)--Calories/year TDCFS = total demand (agricultural and nonagricul- tural) for cash food Calories--Calories/ year k = indexes the crop sectors-~k = l, ..., 4. There are two basic assumptions to be noted in these equa- tions. First, it is assumed that food will be intercropped 1/ on land in the first third of the perennial gestation period— and that this food will be cash food. Secondly, Equation 4.8b assumes that subsistence food production does not respond E ‘i/ Strictly speaking, Equation 4.8a uses one-third of the land in the gestation stage as an approximation to the amount of land in the first third of the gestation period. 90 to changes in price (except through the subsistence level adjustment in Equations 4.1 - 4.3). Perennial Production The production of each perennial population stream-- traditional cocoa, modern cocoa; traditional palm and modern palm in the Palm Sector; traditional rubber, modern rubber, and traditional palm and modern palm in the Rubber-Palm Sector--is computed (Equation 4.9a) as the sum of the output (yield times acres) of each producing cohort of that stream. As discussed in Chapter 3, wild palm in the Cocoa Sector is considered a product of bush land (Equation 4.9b). The out- puts of streams of like commodities (e.g., traditional and modern cocoa) are then added to get production by commodity, i.e., cocoa, palm and rubber (OPTi, i = l, 2, 3). 8 IPDCNP. t = TLPER.. t *YPE . t (4.9a) J( ) 1Z3 13( ) Rk13( ) PPPC2(t) SUPRSB = * * * * PDCNWP(t) PBWP TLBSH1(t) YBWP PPAVH2 t PBLHV (4.9b) where: PDCNP = the production of perennials--lbs./year TLPER = land in perennials, by cohort (Equation 3.1c)--acres YPER = yield of perennials, by cohort (Equation 4.6a)--lbs./acre-year PDCNWP = wild palm output from Cocoa Sector bush land--lbs./year the proportion of Cocoa Sector bush land in wild palm production PBWP 91 TLBSH = total bush land in the Cocoa Sector (Equa- tion 3.3)--acres YBWP = the wild palm yield of bush land—-lbs./ acre-year PPPC2 = the current agricultural producer-processor price of oil palm products (Equation 5.9)-- £/lb. PPAVH2 = the exponentially weighted average of recent palm prices (Equation 5.8b)--£/1b. SUPRSB = a parameter determining the price respon- siveness of wild palm products (elasticity) PBLHV = proportion of wild palm normally harvested k = indexes the producing cohorts--i = 3, ..., 8 corresponds to k = l, ..., 6 i = indexes the cohorts--i = 3, 4, 5 corresponds to the second cohort; i = 6, 7, 8 corre- sponds to the third through fifth cohorts (see below) j = indexes the perennial streams--j = l, ..., 8. The second cohort (rising yields) is divided in three parts to more accurately compute production outputs during this ‘period of rapidly increasing yields. Marketing, Accounting equations model the marketing and pro- cessing of the agricultural output. The marketing of each commodity is represented by proportions of marketable output (Equations 4.11) going to processing, domestic consumption, or export. The model currently assumes these proportions to be fixed parameters which characterize the place of each commodity in the domestic economy, i.e., how much of it is processed domestically (before consumption or export), how 92 much is consumed domestically, and how much is exported. The marketable output is the portion of the total production of a commodity (Equation 4.10b) which is neither consumed on the farm nor lost (due to spoilage or waste) between field and market. OUTSUBi(t) = SUBPi(t)*OPTi(t) (4.10a) OUTMKTi(t) = PLOSSi*[OPTi(t) - OUTSUBi(t)] (4.10b) 4 SUBP4(t) = { Z PDCNSFk(t) + DEMBIO4(t)}/OPT4(t) (4.10c) k=l where: OUTSUB = the portion of output consumed on the farm --lbs./year SUBP = the proportion of total output that is consumed on the farm OPT = the total output of a commodity--lbs./year OUTMKT = the marketable output of a commodity-~lbs./ year PLOSS = the proportion of a crop not lost between field and market DEMBIO4 = demand for food biological materials for planting the following year (Equation 4.26f)--lbs./year i = indexes the commodities-—i = 1, ..., 5. The only commodity which may be consumed directly on the farm is, by assumption, food.‘ None of the export crops are so consumed. Palm oil is consumed domestically, but only after Processing. The marketable output of each commodity is directed tO consumption, processing or export, and the supply of cash ......' “a"; ”‘_-i .go' —_..‘ 93 food calories is computed to be used in determining the food prices in the North and South and the interregional trade in food, the major link between the regional submodels. OMCNSi(t) = POMCi*OUTMKTi(t) (4.11a) OMPRCi(t) = POMPi*OUTMKTi(t) (4.11b) OMXPTi(t) = POMXi*OUTMKTi(t) (4.11c) SUPCFS(t) = CALY*OMCNS4(t)*PYCNS (4.11d) where: OMCNS = marketed output consumed directly-~lbs./ year POMC = proportion of marketed output that is consumed OMPRC = marketed output processed--lbs./year POMP = proportion of marketed output that is processed before consumption or export OMXPT = marketed output exported directly--lbs./ year POMX = proportion of marketed output that is 'exported SUPCFS = supply of cash food in the South-~Calories/ year CALY, PYCNS grocessing defined in Equation 4.7a indexes the commodities—-i = l, ..., 5. Of the commodities produced in southern Nigeria, palm fruit, rubber latex, and raw tobacco are processed (in the y 94 model) into palm oil, palm kernels, rubber sheets, and cured tobacco. The production of cocoa and food is assumed to include any processing performed on those commodities, e.g., the drying of the cocoa beans or the making of gari from cassava . Capacity The capacity of the processing industry for each com- modity (i.e., the physical limit on the amount that can be processed at a given time) is a function (Equation 4.12b) of the raw material input. The assumption is made that the nature of agricultural processing methods is such that there is enough flexibility for total capacity to exceed raw ma- terial input even when that input may be rising. Total ca- pacity will decrease if excess capacity, exponentially aver- aged over the last few years (Equation 4.13), exceeds some critical value (say sixty percent). Rather than overt dis- ‘mantling or disinvestment, replacement investment ceases until a desired (lower) level of capacity is attained (Equa— tions 4.14). Thus, if excess capacity does not exceed its critical value, Equations 4.12 hold. = * .. * .. Ci(t) PCTi PRTi(t DT) + PCMi PRMi(t DT) (4.12a) PCAPi(t) = maxlCi(t)*PRMSi(t), PCAPi(t-DT)] (4.12b) where: C = a proportion greater than 1 PCT a proportion greater than 1 for traditional processing PCM PRT PRM PCAP PRMS 95 a proportion greater than 1 for modern processing proportion of total processing capacity that is traditional proportion of total processing capacity that is modern total processing capacity--lbs.(of input)/ year smoothed raw material input (a first-order lag on OMPRC of Equation 4.llb)--lbs./year indexes the commodities processed--i = l, 2, 3. Thus, increasing production will see increasing processing capacity to handle it. Decreasing production will only lower capacity, however, if excess capacity, exponentially averaged, exceeds.some critical value. XESCAPi(t) = PCAPi(t) - RMi(t) (4.13a) _ _ DT _ _ _ PXSCAi(t) — PXSCAi(t DT) + fi§E§§IXESCAPi(t DT) PXSCAi(t DT)] (4.13b) where: XESCAP = excess capacity--lbs./year RM = unsmoothed raw material input (=OMPRC of Equation 4.llb)—-lbs./year PXSCA = exponentially averaged excess capacity--‘ lbs./year DELXS = the averaging lag time--¥ears i = indexes the commodities processed--i = l, 2, 3. If excess capacity exceeds a critical proportion of total capacity, capacity is reduced by stopping replacement investment. 96 DCAPi(t) = Ci(t)*PRMSi(t) (4.14a) PREPITi(t) = - _ - * * ________ PCAPi(t) max({PCAPi(t DT) [PRTi(t DT) PDTi PKCRTi I PREPIMi(t) .. * * J t + PRMi(t DT) PDMi PKCRMi ] DT}, DCAPi(t)) (4.14b) PREPIMi(t) = _ * * __________ * CAPMDi(t) PRMi(t DT) PDMi PKCRMi DT (4.14C) where: DCAP = desired capacity-~lbs./year PREPIT = replacement investment in traditional ca- pacity (Equation 4.18a)--£/year PREPIM = replacement investment in modern capacity-- £/year PKCRT = capital-capacity ratio (traditional)—- £-years/lb. PKCRM = capital—capacity ratio (modern)-—£-years/lb. CAPMD = decrease in modern capacity--lbs./year PDT, PDM = parameters (which may be given values of 0, l or reciprocals of PRT and PRM, res- pectively) controlling the contributions to the decrease in total capacity from traditional and modern processing-- dimensionless i = indexes the commodities processed--i = l, 2, 3. Modernization While the model focuses principally on policies re- lated to agricultural production, there may be significant benefits to be gained by the agricultural sector (pri— marily since agricultural producers essentially do their own processing, either as individuals or in cooperatives) 97 by increasing processing efficiency and/or improving the quality of processed commodities. Modern processing capacity can be generated (Equation 4.15) by exogenous (policy) modern- ization investment. PINVMXi(t) = ° .. * __.__________ .. PCAPMi(t) m1n[{PCAPMi(t DT) + DT PKCRMi. CAPMDi(t)}, PPCAPXi*PCAPi(t)] (4.15) where: PCAPM = modern processing capacity--lbs./year PINVMX = exogenous net investment in modern capacity (a policy)--£/year PPCAPX = desired modern proportion of capacity (a policy) i = indexes the commodities processed--i = 1' 2' 30 Once a desired level (proportion) of modern capacity (also a policy) has been attained, the exogenous investment (:eases, and any further investment subsequently required to maintain that proportion, as total capacity changes over time, is endogenous to the agricultural sector (Equations 4.18). Modern capacity is thereafter maintained at a con— stant proportion of total capacity. PCAPMi(t) = PPCAPXi*PCAPi(t). (4.15) This model of investment in modern agricultural proc- essing is admittedly rudimentary and even unrealistic. The in- vestment should be endogenous (possibly with exogenous credit made available) and based on profitability considerations. 98 This could be done if eventually deemed necessary for valid applications of the model; however, given both the model's concentration on agricultural production and the computer constraints imposed on the current (total Nigeria) model, the present processing investment mechanism appears sufficient. In any case, once modern capacity has been determined, the remainder of total capacity will be provided by tradition- al facilities: PCAPTi(t) = PCAPi(t) - PCAPMi(t) (4.17) where: PCAPT = traditional processing capacity--lbs./ year. Investment Replacement investment in traditional and modern agricultural processing is assumed to equal depreciation of the capital stock (Equation 4.18a), while net investment is the investment required to change capacity. Capital stock is defined as the time integral of net investment. Investment in traditional processing is computed endogen- ously in the model (Equation 4.18b) as the replacement and net investment which must take place to generate the traditional capacity. Modern investment (PINVM) is sim- ilarly determined once the exogenous policy investment ceases. Since the investment computed in Equation 4.18b is intended to be endogenous (agricultural sector) investment, PINVM consists only of replacement investment as long as any 99 exogenous net investment is being made (PINVMX >0). Equa- tions 4.18 show the computation of traditional investment and capital stock. The modern equations are exactly analogous, with the "T” suffixes replaced by "M". PREPITi(t) = PDRTi*PCAPITi(t-DT) (4.18a) = .__1.* _ .. * PINVTi(t) PREPITi(t) + om (PCAPTi(t) PCAPTi(t DT)) PKCRTi > (4.18b) PCAPITi(t) = max{[PCAPITi(t-DT) + DT*(PINVTi(t) where: PREPIT = replacement investment in traditional capacity--£/year PDRT = depreciation rate for traditional proc- essing facilities-—proportion/year PCAPIT = capital invested (stock) in traditional processing--£ PINVT = gross investment in traditional process- ing--£/year PKCRT = capital-capacity ratio (traditional)—- £~years/lb. PCAPT = traditional processing capacity (Equation 4.17)--lbs./year i = indexes the commodities processed-- i = 1, 2, 3. Processing Outputs The amount of raw material input processed is conStrained by capacity and processing losses and waste. 100 RMAi(t) = min(RMi(t), PCAPi(t)) (4.19a) NRMAi(t) = PCLi(t)*RMAi(t) (4.19b) where: RMA = constrained raw material input--lbs./ year NRMA = input processed (not wasted or lost)-- lbs./year PCL = proportion not lost or wasted (Equation 4.21a). ‘ One or two outputs may then be derived from an input, depending on the particular commodity. For example, palm fruit is processed into palm oil and kernels, while rubber latex becomes only sheets. POUTli(t) = NRMAi(t)*PROPli(t) (4.20a) POUTZi(t) = NRMAi(t)*PROPZi(t) (4.20b) where: POUTl = the first processed output--lbs./year PROPl = the proportion of input going to the first output (Equation 4.21b) POUT2 = the second processed output--lbs./ year PROP2 = the proportion of input going to the second output (Equation 4.21c). The loss and input/output proportions are weighted be tween traditional and modern capacities. PCL. = * * 1.(t) PCLMi PRMi(t) + PCLTi PRTi(t) (4.213) 101 PROPli(t) = PROPlMi*PRMi(t) + PROPlTi*PRTi(t) (4.21b) PROP21(t) = PROP2M1*PRMi(t) + PROP2T1*PRTi(t) (4.21c) where: PCLM, PCLT proportions of input weight not lost in modern and traditional processing, respec- tively PROPlM, PROPlT proportions of input going to the first output in modern and traditional process- ing, respectively PROPZM, PROPZT = proportions of input going to the second PRM, PRT output in modern and traditional process- ing, respectively proportions of total capacity that are modern and traditional, respectively. Domestic consumption and export of processed outputs are computed by Equations 4.22. POPXj(t)*{ POUTli(t) . jfz OPXPTj(t) = POUT21(t) ' j=2 (4.22a) POUTli(t) . jfz = * o OPCNSj(t) POPCj(t) POUT21(t) . j=2 (4 22b) adierre: OPXPT = processed output exported-~lbs./year POPX = proportion of processed output that is exported OPCNS = processed output consumed domestically-- lbs./year POPC = proportion of processed output that is consumed domestically 102 i = indexes the raw material input commodities (palm fruit bunches, rubber latex, tobacco) -—i = l, 2, 3 j = indexes the processed output commodities (palm oil, palm kernels, rubber sheets, cured tobacco)--j = l, 2, 3, 4. In the case of palm oil, these proportions (POPX and POPC) are determined endogenously. Fixed proportions are assumed for rubber and tobacco. In addition, if the domestic market price of palm oil equals the import price plus the import tax, then palm oil will be importedl/. ‘_._.__-_4__...._.' . 3' 2 . DEMPO(t) = { Z POCNS *(TPOPAG (t) + TPOPNAm(t))}* m=l m m EDPO DMPPO(t) [w] (4.233) _ . DEMPO(t) POPC1(t) - m1n[§fi§§5TEy, 1] (4.23b) POPX1(t) = l. - POPC1(t) (4.23c) max[(DEMPO(t)-SUPPO(t)), 0.] if DMPPO(t)= POIMP(t) = WPIPO(t)*(l+TXIMPO) 0 , otherwise (4.23d) “daeere: POCNS = per capita consumption of palm oil--lbs./ person-year TPOPAG, TPOPNA = total agricultural and nonagricultural population, respectively (from the popu- lation component)-—persons ‘ See Chapter 5 for a detailed discussion of the palm oil Inarket model. 103 DEMPO = the domestic demand for palm oil--lbs./ year SUPPO = the total supply of palm oil (=POUT11 of Equation 4.20a)--lbs./year DMPPO = domestic market price of palm oil (Equa- tions S.4)--£/lb. PPOMI = initial market price of palm oil--£/lb. EDPO = elasticity of demand for palm oil-- dimensionless POIMP = palm oil imports-~lbs./year WPIPO = palm oil import price (Equation 5.4b)-- £/lb. TXIMPO = palm oil import tax--proportion of price m = indexes the regions (North and South)-- m = l, 2. The model deals only with smallholder production. Therefore, it is necessary to include a mechanism to generate the output of rubber and palm plantations and estates. Thus, an exogenous growth of the output of rubber estates (Equa- tions 4.24) is modeled. Oil palm production is similarly augmented by an oil palm estates factor (OPESF) . RUBESF(t) = RUBESF(t-DT) + Dr§*[.5 - RUBESF(t-DT)] (4.24a) XPI'4 (t) = OPXPT3(t)*[1 + RUBESF(t)] (4.24b) Wheezae: RUBESF = rubber estates factor--dimensionless XPT4 = rubber exports--lbs./year. NOte the assumption that the contribution of estates increases gradually to one-third of total exports. WFL‘T‘“_“‘_H—fi—E:' 41"." A V 104 Input Demands and Accounting Finally, component AMPPAP computes the input demands and performs the macroeconomic commodity accounting for agri- cultural production, processing and marketing. Production input demands are calculated by Equations 4.25 and 4.26. First, demands for labor by commodity and by crop sector are generated. Equation 4.25a is for the perennials produced in the Rubber-Palm Sector; the other perennial sectors are analogous. Labor is assumed not to be a constraint; any shortage will be made up by seasonal migration from the Northl/. ji+l 5 = * * DEMLSP3i(t) ij {[nZl[pLA1jn PSPERjn(t) + PLAzjn i _ (1 - PSPERjn(t))]*TLPERjn(t)] + PDCNPj(t)* PAGEMP.(t) PLY. + 1 , i = 2, 3 (4.25a) j OPTi(t) .DEMLSPk4(t) = [FDLAB1*PSFDk(t) + FDLABZ*(1 — PSFDk(t))]* TLFDk(t) + FDLABY*[PDCNSFk(t) + PDCNCFk(t)] (4.25b) 5 DEMLSk(t) = Z DEMLSPk.(t) (4.25c) i=1 1 4 , DEMLP.(t) = Z DEMLSP .(t) (4.25a) 1 _ k1 k—l 12’ . . . . " The current Situation 1n Niger1a, and indeed in many developing countries, may dictate the eventual inclusion of a labor constraint in the model. This will be dis- cussed in Chapter 11. (‘1 “7“" M‘ +—5' TLABD(t) where: 105 4 S = kZ Z DEMLSPki(t) (4.25e) =1 i=1 DEMLSP = demand for labor by sector and commodity-- man-years/year ji = indexes the traditional perennial stream corresponding to commodity i in Sector 3 (i=2=palm corresponds to j. = 7; i=3= rubber corresponds to ji = 5) PLAl , PLA2 = labor input requirements in each cohort of the first and second perennial sub- streams, respectively--man-year/acre-year PSPER = proportion of land in the first substream of a perennial population stream, by cohort (Equation 3.2) TLPER = land in each cohort of a perennial popula- tion stream (Equation 3.1c)--acres PLY = labor required for perennial harvesting-- man-years/lb. PAGEMP = agricultural employment in processing (Equation 4.32f)--man-years/year PDCNP = output of a perennial stream (Equation 4.9a)--lbs./year OPT = total output of a commodity--lbs./year FDLABl, FDLAB2 labor input requirements for traditional and modern food, respectively--man-years/ acre-year FDLABY = labor required for harvesting food--man- years/lb. PSFD = proportion of food land which is tradi- tional (Equation 3.2) TLFD = total food land (Equation 3.3)—-acres PDCNSF, PDCNCF = production of subsistence and cash food, respectively (Equations 4.8)--lbs./year 106 DEMLS = labor demand by crop sector-~man-years/year DEMLP = labor demand by commodity--man-years/year TLABD = total agricultural labor demanded in the South--man-years/year i = indexes the commodities--i = l, ..., 5 k = indexes the crOp sectors--k = l, ..., 4 j = indexes the perennial streams--j = l, ..., 8 n = indexes the perennial cohorts--n = l, ..., 5. Chemical, capital and biological inputs are computed by Equations 4.26. The equations are given for cocoa and food (i = l, 4); inputs for the other perennials are treated simi- larly. 2 5 = * DEMCH1(t) .Z Z [PCAljn*PSPERjn(t) + PCAZjn j-l n-l (1 - PSPERjn(t))]*TLPERjn(t) (4.26a) 4 DEMCH4(t) = X [FDCH1*PSFDk(t) + FDCH2*(1 - PSFDk(t))]* k=l TLFDk(t) (4.26b) . 2 5 CHAPDEP1(t) = Z EQPER.*( Z TLPER. (t)) (4.26c) ._ J _ 3n j-l n—l 4 _ CAPDEP4(t) = Z [EQFT*PSFDk(t) + EQFM*(1 - psrnk(t))]* k=l TLFDk(t) (4.26d) 03113101“) = EBIOT1*RINPT11(t) + EBIOM1*RINPM11(t) (4.26e) 4 Cflibmsxo4(t) = FDBIO* Z [TLFDk(t) + (RINFk(t) - ROUTFk(t))*DT] k=1 (4.26f) where: alb<>ve. 107 DEMCH = the demand for chemicals to produce a commodity--lbs./year PCAl , PCA2 = the per acre chemical requirement of the first and second perennial substreams, respectively--lbs./acre-year FDCHl, FDCHZ = the per acre chemical requirement of tra- ditional and modern food, respectively-- lbs./acre-year CAPDEP = capital invested (depreciation = equipment replacement) in a commodity--£/year EQPER, EQFT, EQFM - = equipment (capital) costs for perennial and traditional and modern food production, respectively--£/acre-year DEMBIO = the demand for biological inputs--units (seedlings or lbs.)/year EBIOT, EBIOM, FDBIO = biological input rate for traditional and modern perennials and food, respectively-— units/acre-year RINPTl, RINPMl = planting rate of traditional and modern perennials, respectively (output of the decision mechanism, component LAMDAP, Chapter 3)--acres/year RINF, ROUTF = rate land enters and leaves food production, respectively (output of the decision mechanism)--acres/year k = indexes the crop sectors-~k = l, ..., 4. Processing capital is calculated in Equations 4.18 Chemicals and labor for processing and labor for marketing are computed in Equations 4.27. No marketing labor is assumed (necessary for the portion of production output which is wasted or lost in processing. ‘-'~‘-pJ p—rr 108 EMPPMkUZ) = RMAk(t) *PRMk(t) *PLIRMk (4.273) EMPPTR (t) .3 Wk (1:) *PRTk (t) *PLIRTk (4 . 27b) ‘UKZXJLCHPk(t) = PCHTk*OPCTk(t) + PCHMk*OPCMk(t) (4.270) PCAPk(t) = - * .. ‘ (4.27d) DEMLMi (t) = OLABMi(t) *OUTMKTi(t) *PWLOSSiUZ) (4.278) vvluueexe: EMPPM , EMPPT = modern and traditional processing labor, respectively--man-years/year PLIRM, PLIRT = labor input requirements for modern and traditional processing, respectively-- man-years/lb. VALCHP = the value of chemical inputs to processing --£/year PCHT , PCHM = proportions of traditional and modern processing operating costs, respectively, that are chemical inputs OPC'I' , OPCM . = traditional and modern processing operating costs, respectively (Equation 4.31e)-- £/year PWLOSS = processing weight loss factor-~dimensionless DEMLM = demand for labor in the marketing sector-- man-years/year OLABM = the labor required to market a pound of produce-~man-years/lb. OMPRC = marketable output processed (Equation 4.11b) --lbs./year OUTMKT = marketed production output (Equation 4.10b) --lbs./year 109 PCAP = processing capacity (Equations 4.12b or 4.14b)--lbs./year POMP = defined in Equation 4.llb PCL = defined in Equation 4.19b k = indexes commodities processed (k = l, 2, 3 corresponds to i = 2, 3, 5) i indexes commodities produced—-i = l, ..., 5. The accounting and criteria variables for agricultural production and marketing are computed in Equations 4.28 for each commodity. The capitalized value equation (Equation 41 ..i28q) is given for food; the values of the other commodities are similarly computed. WAGi(t) = PL(t) *DEMLPi(t) *PLHPi (t) (4.28a) WMKTi(t) = PLM(t) *DEMLMiUI) , (4.231)) _ PLMW) (2(213EIi(t) = PCIi*DEMCHi(t) + PBIi*DEMBIOi(t) + CAPDEPi(t) (4.28d) REVSUBiH-J = PPRCi(t)*OUTSUBi(t) (4.28e) REVCSH. (t) = PPRC. (t)*OUTMKT. (t)* ”“01“” (4.28f) 1 1 1 PLOSSi J VALADPi(t) = PPRCi(t)*OPTi(t) - [CCBEIi(t) - CAPDEPi(t)] (4.289) VALADMi (t) = PPRCMi (t) *OUTMKTi (t) wpsomi (t) *PWLOSSi (t) - REVCSHi(t)*(1 - POMPi) - PINCi(t) (4.28h) 110 REVCNiH'.) = REVCSHiH'.) - CCBEIi(t) - WAGi(t) + PAGREVi(t) (4.28j) TAXMS (t) = max [TAXMRi* (PPRCMi (t) *OUTMKTi (t) *PSOLDi (t) * PWLOSSi(t) - WMKTi(t)), 0.] (4.28k) TAXPSi(t) = maxITAXPR.*(REVCN. (t) - PAGREV.(t)). 0.] 1 1 1 (4.28.1) ‘PRF'Ii(t) = PPRCi(t)*OPTi(t) - CCBEIi(t) - TAXPSi(t) - WAGi(t) + PAGREVi(t) ~ PTAxi(t) (4.28m) PRE‘TMi (t) = PPRCMi (t) "'OUTMKTi (t) "'PSOLD:.L (t) *PWLOSSi (t) - WMKTi(t) - TAXMSi(t) - REVCSHi(t)* (1 - POMPi) - PINCi(t) (4.28n) PRFTLBi(t) = [PRFTi(t) + WAGi(t)]/DEMLPi(t) (4.280) PRF'I‘LDi(t) = PRFTi(t)/TLDi(t) (4.28p) CAPVAL4(t) = §%*max[(PRFT4(t) + TAXPS4(t) + PTAX4(t)). 0.] (4.28q) Where; WAG = cash wages paid--£/year PL = wage rate in the agricultural sector (Equation 5.10a)--£/man-year PLHP = proportion of labor which is hired (Equa- tion 4.29b) WMKT = wages paid in the marketing sector-—£/year PLM = wage rate in the marketing sector (Equation 5.10b)--£/man-year COSTML PPRCM CCBEI PCI PBI REVSUB PPRC 'PSOLD PLOSS PWLOSS REVCSH VALADP VALADM REVCN PAGREV TAXPS TAXPR TAXMS TAXMR PTAX PRFT PRFTM 111 marketing labor costs (to be used in the price generating component, Equation 5.5b) --proportion of market price market price (Equations 5.2)--£/lb. cost of chemical, capital and biological inputs--£/year the price of chemical inputs--£/lb. the price of biological inputs--£/unit (seedling or lb.) revenue in kind--£/year producer price (Equation 5.7)--£/lb. proportion of output sold (Equation 4.30) proportion of output not lost between field and market proportion of output not lost in processing (Equation 4.27b) cash revenue--£/year value added in the production sector--£/year value added in the marketing sector--£/year net cash revenue--£/year processing revenue to the agricultural sector (Equation 4.32d)--£/year tax revenue from the production sector-- £/year tax rate in the production sector tax revenue from the marketing sector—-£/year tax rate in the marketing sector tax revenue from processing (Equation 4.32a) --£/year profit in the production sector--£/year profit in the marketing sector--£/year 112 POMP = defined in Equation 4.llbi PINC = gross income to agricultural processing (Equation 4.3la)--£/year PRFTLB = returns to labor--£/man-year PRFTLD = returns to land--£/acre-year CAPVAL = capitalized value of commodity land-~£ RI = interest rate-~proportion/year i = indexes the commodities--i = l, ...,5. A note is in order here about two factors affecting wages paid and cash revenues in Equations 4.28a‘ and 4.28f-- 't:11ea proportion of labor which is hired (PLHP) and the pro- 1;~:>J:tion of marketed output which is sold (PSOLD). First, I! —7“—“._-"“ ‘ _“__’ WI? ‘tzlzea proportion of agricultural labor hired for the production c>iE each commodity reflects two concepts (Equation 4.29b). One i.es the extent to which non-family (hired) labor is employed 1:<> .maintain and harvest a commodity. This will differ from <=<>nnmodity to commodity depending on the farmers' attitudes 1Z<>vvards each--attitudes such as trust in non-family workers with a given commodity and the social desirability of a Particular type of work (e.g., rubber tapping). Assuming that labor is not a constraint, as this model does, any POsitive excess demand for agricultural labor is met by _ labor from outside the region, i.e., seasonal migration fIl‘om the North. Such hired labor is arbitrarily assigned t!) each commodity in proportion to the commodity's total labor usage . Secondly, the quantity of output sold on the market dapends on the ratio of demand to supply. If there is excess 113 demand, everything is sold. For the major cash crops-—cocoa, palm, rubber and tobacco--demand is assumed to equal supply. arrizat is, Nigeria can sell all it wants on the export market, aizméi the Nigerian Tobacco Company buys all the tobacco proé duced. It is only for food, the demand for which is endogen- ous 1y generated in the population component of the total model, that supply may exceed demand and vice versa (Equation P i 4.- 23(3). The proportions of labor hired by commodity and by crop sector are, then,functions of non-family indigenous 151:1)“ s‘.‘ .. fit _— labor and seasonal migration. DEMLSk(t) - LABASk(t) 5 = _ * PLHIRERM) max musk“) , o. + iglPNFLi DEMLSP .(t) k1 (4.29a) ——TT' DEMLSk t 4 DEMLSk(t) - LABASk(t) P = ’1 * ILIII?i(t) PNFLi + kElmax[ DEMLSRTt) . 0.] DEMLSPki(t) .( ) DEMLP1 t (4.29b) 5 RSMIGL(t) = max{[TLABD(t) - Z maskun. 0.} (4.29c) k=l ‘thEEre: defined in Equation 4.25c DEMLS defined in Equation 4.25a DEMLSP defined in Equation 4.25d DEMLP defined in Equation 4.25e TLABD labor supply (from the population component) --man-years/year LABAS . .\<*-’ KL. W. n, .4 ill ......Iav... .Hfil’abfiw PNFL PLHIRE PLHP RSMIGL i k 114 proportion of a commodity's labor require- ments hired from the indigenous (to a crop sector) population--a model parameter proportion of labor hired (including migration into the crop sector), by crop sector proportion of labor hired (including migration), by commodity seasonal labor migration into the South—- man-years/year indexes the commodities—-i = l, ..., 5 indexes the crop sectors--k = l, ..., 4. The proportion of food output sold is the demand- supply ratio constrained so as not to exceed one. The pro-— portion of the other commodities sold is assumed. fixed and equal to one . I?£3Inocessing in Nigeria is performed by the producers themselves, either as individuals or in cooperative ventures. Therefore, 'tdle portion of processing revenues returning to the agricul- tlural sector (PAGREV) is computed so it can be included as agricultural income available for investment in production, fem consumption or for taxation (Equations 4.28j, 4.282, 4.28m). Also, the processing costs per unit of input (PAGCST) 117 is; computed for the agricultural producers' contribution to processing. This figure is used on the cost side of the land use profitability equation (= PXP of Equation 3.6b) . Simi- .1aazflyu agricultural labor employed in processing activities (PAGEMP) is calculated in Equation 4.32f and added to labor IJ£5€Bd in production (Equation 4.25a). PTAXi(t) = TAXTi(t) + TAXMi(t) (4.32a) PVALADi(t) = VALADTi(t) + VALADMi(t) (4.3210) PRFTPi(t) = GROSPTi(t) + Gnospmiu) - PTAxi(t) (4.32c) PAGREVi(t) = GROSPT'l(t)*PAGTi + GROSPMi(t)*PAGMi (4.32d) PAGCSTi(t) = [(opcmivc) + PREPIMi(t) + EMPPMi(t)*WRMi)* PAGMi + (opcwi(t) + PREPITi(t) + EMPPTi(t)* WRTi)*PAGTi]/RMi(t) (4.32e) PAGEMPiH‘.) = EMPPMi(t) *PAGMi + EMPPTi(t) *PAGTi (4.32f) wheexre: PTAX = total taxes paid from agricultural processing--£/year PVALAD = total value added in agricultural process- ing--£/year PRFTP = profits from agricultural processing-- £/year PAGREV = returns to the agricultural sector from agricultural processing--£/year PAGT, PAGM = proportion of traditional and modern 118 processing, respectively, performed by the agricultural sector--a model parameter PAGCST = processing cost rate incurred by agricul- tural producers-~2/lb. PAGEMP = agricultural employment in processing-- man-years/year i = indexes the commodities processed--i = 1, 2, 3. EStxmmary In summary, AMPPAP simulates the production, process- ing and marketing of agricultural commodities for southern Nigeria. In doing so, it determines commodity yields and 1:11e agricultural population's subsistence level. In addition, IthPPAP generates input demands and macroeconomic performance <31:iteria for use by other components of the southern model and the national model. "“7”“7_J 1 CHAPTER 5 Price Generation (PG) Component PG services the rest of the southern model .5 _ ‘,_.L . by generating world prices for the export commodities and market, processor and producer prices of all six commodities considered-~cocoa, oil palm products (oil and kernels), rubber, -H __A- ___, “um. _' food, and tobacco. The domestic palm oil market is also ”E modeled by PG. In addition, five- and ten-year exponential averages of the producer prices and price trends are computed for use by component LAMDAP in the profitability calculations for the land allocation decisions and by component AMPPAP in the determination of the price response of yields. EXEort, Market and Processor Prices 'Figure II.10 indicates schematically how prices are generated. It is assumed participants further down in the PrOducer-to-consumer chain are price takers in general. Thus, COS ts (including taxes) are passed on down the line. At the top . world prices for the export commodities are exogenously generated by Equation 5.1. 119 120 World Prices L :: CR TMBA + - Z : Export f Taxes Export ;‘ AMPPAP Market fi' CRTMBA Prices Marketing Costs 2 ' _ Food Market 4» - # Market Profits AMPPAP Processor 4.: -—— 13““. CRTMBA Processing Costs 2: - Processing Taxes Producer :3 AMPPAP Prices AMPPAP Price 1‘ m Averages and Trends lay to coqonenta using the various prices: MAP - Agricultural aarketing. production and procaasiw-annuals/perannisls cam — Criteria and users-budget actuating won - Land allocation and aodernisation dacisions—annualslparanniala Figure 11.10 Price generation component. 121 . r .5. .. VALWP11 + 13*(VALWP13i VALWPli) , 0l7 (5.1) vvraere: WP = world (FOB) price--£/lb. VALWPki = recorded world price of commodity i at time k, k = 1953, 1954, ..., 1965 WP1970 = recorded world price in 1970 WPR = rate of change of world price after 1970 --proportion/year t = simulated time (t = 0 is l953)--years i = indexes the export commodities (cocoa, palm oil, palm kernels, rubber)—-i = l, ..., 4. Equations 5.2 compute the prices received by the Inaazrketing boards (or other export marketers in the case of r1113ber) for export commodities and by the domestic marketers 025 food. The domestic price of palm oil is discussed below (Equations 5.4) . The tobacco price to the Nigerian Tobacco Company is an exogenous constant. PPRCMi(t) WPi(t)*(l - EXTAXi) , i = l. .... 4 (5.2a) PPRCM5(t) = PPRCM5(t-DT) + DT*CF1*PPRCM5(t-DT)* [TDCFS(t-DT) - SUPCFS(t-DT) - SFNS(t-DT)] TDCFS(t-BT) (5.2b) PPRCM6 (t) PMCA (5-26) where : PPRCM EXTAX PMCA TDCFS SUPCFS SFNS CF1 122 market price--£/lb. export tax-~proportion of world price constant cash annual (tobacco) market price--£/lb. ‘ total demand for cash food in the South from the agricultural and nonagricultural populations--Calories/year supply of cash food in the South (Equation 4.11d)--Calories/year shipments of food, North to South (from the market component, linking the northern and southern submodels)--Calories/year parameter regulating the food price response to excess demand (see the dis- cussion below)--proportion/year indexes the commodities marketed-—i = l, 6. sea, Equation 5.2b, which generates the market price of ft><>d.as a function of excess demand, is derived directly from tines definition of the demand price elasticity e: A969 e= AP P Where Aq = qt - qt-DT and Ap = pt - pt-DT and the ratios are tJillcen relative to the initial price and quantity, pt-DT and qt~DT' Thus, 1 pt-DT AP = p - p = -(q ' q )— t t-DT e t t-DT qt_DT and: ._ 1 qt ' qt-DT Pt “ pt-DT + EPt-DT ' qt-DT Equation 5.2b assumes that the target change in quantity, 123 Ag, will be the excess demand in the previous period and that tale equilibrium price will not necessarily be reached in one loseriOd, i.e., if DT*CFl < 1/8. The domestic palm oil price rneechanism (Equation 5.6a) is similarly derived. The next price computed (Equation 5.3) is the price t:c> the processor for those commodities whose processing is explicitly modeled-114 namely, palm oil, palm kernels, rubber .4 — and tobacco. For cocoa and food, the prices computed here ‘vrj.ll be the producer prices, PPRC. These prices are the nnaarket.prices less marketing costs, taxes and profit surplus. “ A's-:i'!‘ ” --“"'—: ~ IPCJr'the commodities marketed through marketing boards, the profit surplus represents the marketing board tax policy. 2111 the case of palm oil, this price may be modified somewhat 13§( Equations 5.5 if there is positive excess domestic demand. PPRCPi(t) = PPRCMi(t)*(1 - SRPMBi - COSTMi - COSTMLi(t) - TAXMRi)*PLOSSi (5.3) Where: PPRCP = processor price--£/lb. SRPMB = marketing board (or other marketer) profits --proportion of market price COSTM = marketing costs--proportion of market price COSTML = marketing labor costs (Equation 4.28c)-- proportion of market price TAXMR = marketing tax rate-~proportion of market price 1/ ’ See the description of component AMPPAP, Chapter 4. 1.5/11 . . I 124 PLOSS = marketing loss factor-~proportion indexes the commodities marketed-~i = 1 I 0 a a p 6 a H- II Domestic Palm Oil Market The domestic consumption of palm oil competes con- siderably with exports. Indeed, as the domestic demand grows with the population and unless current production trends are reversed by programs to modernize oil palm production, by 1980 Nigeria may have ceased to export palm oil and may even have become an importer. Thus, the determination of the market and processor prices of palm oil is considerably more compli- cated than Equations 5.2 and 5.3. The palm oil supply-demand- price relationships are discussed below in connection with Figure 11.11. The market price of palm oil computed in Equation 5 . 2a, PPRCMZ, is the price received by the export marketer, the palm oil marketing board. The domestic market price (Equations 5.4) depends on the processor price set by the marketing board, on the domestic excess demand and on the import price of palm oil. DMPPO(t) = min{WPIPO(t)*(l + TXIMPO), maxlDMPPOU(t) , DMPPOL(t)]} (5.4a) where, WPliPouz) = WP2(t) + WPOTC (5.41:) 125 INMPPOU(t) = PPRCP2(t)/[(1 - SRPMB5 - COSTMS - COSTML5(t) - TAXMR2)*PLOSSZ] (5.40) _ _ DT _ .EMMPPOL(t) — DMPPOL(t DT) + pfififififi*[DMPP0U(t DT) - DMPPOL (t-DT)] (5 . 4d) and where: P a 5. DMPPO = actual domestic market price of palm oil ; —-£/lb. ‘ I WPIPO = import price of palm oil--£/lb. ( TXIMPO = import tax-~proportion of price Lg DMPPOU = unlagged domestic market price of palm oil --£/1b. DMPPOL = lagged domestic market price of palm oil --£/lb. WP2 = export (FOB) price of palm oil (Equation 5.1)--£/lb. WPOTC = palm oil world transport cost-és/lb. PPRCP2 = processor price of palm oil (Equation 5.5a) SRPMBS, COSTMS, COSTMLS, TAXMRZ, PLOSS2 = defined in Equation 5.3 (5 = food; 2 = palm oil) POMDEL = exponential lag time--years. Several points are to be noted in Equations 5.4. Filtsst, it is assumed that the domestic marketing costs and Pr<>1fit margin for palm oil are the same as for food. This is Ilot unreasonable since palm oil and food pass through muc=11 the same market system. Secondly, the import (CIF) Fri-Ce of palm oil is the FOB price plus the cost of transport 126 to Nigeria. The domestic market price is bounded above by the import price and below by the processor price (Equations 5.5) plus marketing margins. If the processor price is falling, the domestic market price will lag behind it, creating extra profits for the marketers. However, if the processor price is rising, the market price will be constrained to cover costs and a minimum profit margin. As long as there is negative excess domestic demand for palm oil (i.e., there are exports), the processor price paid by both export and domestic marketers will be as set by the marketing board in Equation 5.3. If domestic demand exceeds supply, however, a lagged price rise will occur (Equations 5.6) until the market price equals the import price (Equation 5.4b), at which time the processor price will be set by the domestic marketers. This behavior is modeled by Equations 5.5. (Pd(t) if POIMP(t-DT)>0 PPRCP2(t) = (DPPO(t) if POIMP(t-DT)=0 and DEMPO(t-DT):SUPPO(t-DT) (Px(t) if DEMPO(t-DT) (consumption. If the demand for investment exceeds the available supply, a demand for credit from outside the agri- ‘3‘13utural sector is generated (Equations 7.11). This demand for credit is constrained by the availability of credit, which is a straight proportion of the equity value of cul- tivated land. Equity value is defined as the capitalized va lue of the land minus the outstanding debt. SAGDIIk(t) = (1 - APC)*SAGDIk(t) (7.10a) 155 SAGDICk(t) = IAPC*SAGDIk(t) + max[0., -(ECAPRTk(t) - SAGDIIk(t))] (7.10b) 4 TAGDIP2(t) = Z SAGDICk(t) (7.10c) k=1 . where: SAGDII = agricultural income available for invest- ment--£/year - SAGDIC = agricultural income available for consump- tion--£/year APC = agricultural average propensity to consume --proportion of income ECAPRT = agricultural demand for net investment (Equation 3.14a)--£/year TAGDIP2 = total agricultural consumption in the South--£/year k = indexes the crop sectors--k = 1, ..., 4. (:Izrxravk(t) = maxto, PEQCR*(SCVk(t) - SDBTk(t-DT))] (7.11a) (Irzrxrk(t) = minfCRDTAVk(t), max[(ECAPRTk(t) - SAGDIIk(t)), 0.] + max[(CNSMINk(t) - SAGDIUk(t)). 0.]} (7.11b) 4 TDc'rsm = Z CRDTk(t) (7.11c) k=1 lelfiere: CRDTAV = credit available--£/year PEQCR = proportion of equity which can be used as a credit base CRDT = agricultural sector credits—-£/year 156 total demand for credit in the South-- TDCTS = E/year SAGDIU = agricultural disposable income (Equation 7.9a)—-£/year CNSMIN = subsistence non-food consumption (Equa- tion 7.9b)--£/year k = indexes the crop sectors-~k = 1, ..., 4. If the investment capital available from agricultural (disposable income and the credit available from sources out— sside the agricultural sector together do not meet the demand for investment (ECAPRT), a constraint is placed on the land anJocation decisions (as discussed earlier in component :IJAMDAP, Equation 3.13). The constraint is the ratio (Equa- ‘tzion 7.12a) of the available investment capital to the invest- ment demand if this ratio is less than unity£/. The ratio .143 applied directly to the land transition response (Equation l3..l3). The constraint mechanism is purposely simple; however, 111? further evidence should indicate that this formulation does Iicrt sufficiently represent the actual capital constraint faced txy' the farm decision makers and its (the constraint's) conse- DT. This is necessary to keep the computer running time of the model within reason and is justified since prices, yields and, hence, relative pro- fitabilities don't change rapidly. Model sensitivity to DT and DTX is discussed in Chapter 9. 157 the whole question of the distribution of income in the agri- cultural sector is modeled into the land allocation decisions and production responses. (See the discussion in Chapter 11.) CRDTAVk (t) + SAGDIIk (t) = ' 1e _. l. CNSINUk(t+DT) min ECAPRTth) , (7.12a) _ DT n _ CNSINk(t+DT) —- CNSINk(t) + Bi?" [CNoINUk(t) CNSINk(t)] (7.12b) where: CNSINU = consumption constraint on agricultural investment--dimensionless CNSIN = averaged constraint-—dimensionless DTX = the decision cycle--years k = indexes the crop sectors--k = l, ..., 4. The disposable income generated by agricultural Processing, part of which is included with agricultural income, is computed (Equations 7.13) in a manner similar to tlie: agricultural disposable income discussed above. The Processing debt service, interest payments, operating costs, taxes} and [investments are subtracted from gross income to generate disposable income for consumption. It is assumed that a proportion of the processing investment (discussed it! (component AMPPAP, Chapter 4) is financed by credits granted from outside the agricultural processing sector. These credits make up the processing debt. The portion of disposable income from processing, which is added to agricul- tnll‘al income (Equation 7.6c) is proportional to the amount of Processing done by agricultural producers. 158 PCDSi(t) = maxIPCDSRi*PCDBTi(t-DT), 0.] (7.13a) PCINTi(t) = PRI*PCDBTi(t-DT) (7.13b) PCDBTi(t) = PCDBTi(t-DT) + DT*[PICTi*PINVTi(t) + PICMi*PINVMi(t) - PCDSi(t)] (7.13c) CHAPDIi(t) = PINCi(t) - PTAXi(t) - (1 - PICTi)*PINVTi(t) - (1 - PICMi)*PINVMi(t) - PCDSi(t) - PCINTi(t) - opcri(t) - OPCMi(t) (7.13a) CAPDIAi(t) = PAGi(t)*CAPDIi(t) (7.13s) CAPDINi(t) = (l - PAGi(t))*CAPDIi(t) (7.13f) “Huerta: PCDS = the debt service for the agricultural processing sector--£/year PCDSR = repayment rate for agricultural processing loans--proportion of debt repaid/year PCINT = interest payments--£/year PRI = interest rate on agricultural processing loans-—proportion/year PCDBT = agricultural processing debt--£ PICT, PICM = proportion of traditional and modern processing investment, respectively, fi- nanced by credits from outside the process- ing sector 159 PINVT, PINVM = traditional and modern investment in agri- cultural processing, respectively (Equa- tion 4.18b)--£/year CAPDI = disposable income from agricultural process- ing--£/year PINC = gross income to agricultural processing (Equation 4.31a)--£/year PTAX = processing taxes (Equation 4.32a)-—£/year OPCT, OPCM = traditional and modern processing operating costs, respectively (Equation 4.31e)-- £/year PAG = proportion of agricultural processing dOne by the agricultural producers themselves CAPDIA = disposable income from agricultural process- ing going to the agricultural sector accounts--£/year CAPDIN = disposable income from agricultural process- ing going to the nonagricultural sector accounts--£/year ‘ i = indexes the commodities processed--i = l, 2, 3. Finally, disposable income in the marketing sector (Ekaliation 7.14) is marketing profits plus wages paid in the marketing sector plus the marketing board overhead. The last item assumes that overhead goes primarily for the salaries of marketing board personnel. 5 TAGDIM2(t) = TMOVHDz(t) + .Z (PRFTMi(t) + WMKTi(t)) (7.14) 1=1 wt“31fie: TAGDIM2 = disposable income in the agricultural ' marketing sector in the South-—£/year TMOVHD2 = southern marketing board overhead costs (Equation 7.3e)--£/year 160 PRFTM = marketing profits (Equation 4.28n)-- £/year WMKT = wages paid in the marketing sector (Equa- tion 4.28b)--£/year i = indexes the commodities marketed--i = 1, see, Se 5&ummagy Component CRTMBA, then, computes performance criteria both as exit points of the southern model and to be fed back ‘tc> the national accounts/nonagricultural sector model. It also determines agricultural consumption and investment by balancing the agricultural sector budget. P A R T III VALIDATION AND TESTING Introduction For a decision maker to base policy decisions on the experimental results of a model--§2y model, verbal or mathemat- ical, paper and pencil or computer--he must have some degree of confidence in the validity of that model, i.e., how well it simulates the relevant behavior of the real system or phenom- enon it is supposed to represent. There are primarily three ways in which the model under discussion may be validated. The first is by a sort of knowledgeable intuition. During the building of the model, much reliance for both data and structural and causal relationships was placed on people with a great deal of experience in Nigeria and other developing countries. In addition, secondary sources were used. The ex- periences of the Consortium for the Study of Nigerian Rural Development proved invaluable as a background and basis for the simulation work. By studying the simulated behavior of the mod- el, these same people and others like them may, through their expertise, have an intuitive feel for how well the model repre- sents the real economy. This would be an on-going process, continuing even once the model has been implemented and is in routine use. 161 162 More concretely, behavior predicted by the model under various policy conditions can be compared with what actually occurs as real time passes under the same conditions. Alterna- tively, the model can be compared with historical data from the real world which has not been used in the model—building. process. Once the model has been implemented, it would be tuned and updated as an on-going process by making such comparisons. A common criticism leveled at the validity and useful- ness of the system simulation approach in the economic develop- ment context concerns the vast data needs of the model where the available data are notoriously unreliable or even non- existant. Chapters 8 and 9 briefly discuss the model's data requirements and problems and examine a couple of approaches to dealing with some of those problems; namely, tuning the model to track recorded time series and analyzing the model's sensitivity to variations in parameter values. CHAPTER 8 Data Usage and Model Tuning Socio—economic research often runs into data problems even in the so-called developed countries. Needed data may not exist. Techniques for directly gathering data of a par- ticular kind may be unknown, forcing the researcher to indi- rectly infer necessary data from other sources. The reliabi— lity of existing data may be suspect because of questionable sampling procedures. In the less developed countries, these and other problems are often compounded by poor or erratic communications and data processing facilities, a shortage of well-trained data collecting manpower, an even greater short- age of funds (government or private) to support and maintain data collecting and processing activities, and, frequently, a distrust on the part of respondents of outsiders (i.e., in- terviewers) in general and of government in particular. Nevertheless, researchers, planners and policy makers cannot wait for perfectly reliable data (which may never come,‘ anyway) to recommend, plan and make decisions on policies and. programs for development. Techniques must be found and used not only to improve the quality of data but also to make best use of the data available at the time. The system simulation approach used in the Nigeria 163 164 model offers three ways of at least meeting, if not solving, the data problem; Sensitivity tests (discussed in the next two chapters) can demonstrate the implications of parameter variability both for the validity of the model and for policy formulation. They can also indicate the directions data col- lecting efforts could most profitably take. Secondly, given coarse probability distributions for a set of key parameters, running the model in a Monte Carlo mode can directly generate output statistics reflecting data uncertainties [35, Chapter 4]. Finally, the model may be tuned to track a number of reliable recorded time series by adjusting uncertain para- meter values. This procedure will be discussed later in this chapter. Data Data for the southern annuals/perennials model fall into three broad categories: system parameters, technological coefficients, and initial conditions. The data requirements of each category number in the hundreds, and each class of data has its own particular needs and sources. In this section, we will briefly discuss the three categories and their data sources . 1/ System Parameters— System parameters are primarily parameters reflecting the behavioral characteristics of the system being modeled. ‘ ‘L/ See Tables III.1-III.4 for tabulated values of selected system parameters used in the southern model. 165 Thus, in a sense, they, along with the structural equations, actually define the system. A few examples of the many system parameters of the southern model are: l. the land use profitability response parameters (THRLD, SHAPE in Equation 3.11); 2. the profitability discount rates (DR in Equation 3.5); 3. the many delays and averaging and Smoothing lags of the model (e.g., PEXDEL in Equation 3.17:» SDEL in Equation 4.7a and PRCDEL in Equations 5.8); ' 4. the subsistence level parameters (SLMIN, SLTHR, EFPSF in Equations 4.3); 5. the short-term supply response elasticities (SUPRSP in Equation 4.6a); 6. the marketing distribution parameters (POMC, POMP, POMX in Equations 4.11); 7. the average propensity to consume (APC in Equations 7.10). Little data exist on most of the behavioral system parameters. The kinds of field research which would be. necessary to estimate many of them have never been conducted. Values used in the early stages of building and testing the model were educated and intuitive guesstimates. The education and intuition were acquired from various secondary sources (e.g., [14, 17, 24, 28, 30, 41, 44]) and from such primary sources as interviews with Nigerian officials and farmers and a number of man-years of personal experience in Nigeria and other developing countries. Let's look at the land use tran- sition response thresholds for traditional perennial land as an illustration (THRT in Table 111.1). The values shown (.1, .3 and .5) mean that the alternatives of improvement, replanting and new planting a different perennial (Table II.2) Table III.1. .166 Profitability response parameters for traditional perennials (dimensionless). Alternative Uses Variables Present (Eqn. No.) Uses (° . (definition) improvement replanting new planting other perennial THRT Cocoa .l .3 -- (3.11) (response Palm threshold) (Palm Sector) .1 .3 -- Rubber .1 .3 .5 Palm (Rubber Sector) .1 .3 .5 SHPT Cocoa 1.1 l. -- (3.11) (governs Palm response (Palm Sector) 1.1 l. -- rate) Rubber 1.1 l. .9 Palm (Rubber Sector) 1.1 l. .9 DRT (3a5) (discount .03 .04 .06 .07 rate) Source: Initial guesstimates and model tuning. Table III.2. .167 Profitability response parameters for annuals and bush. Present Variables {Uses (Eqn. No.) Alternative Uses ' Traditional Modern Food Tobacco 3 perennials Bush DRB (3.5) .06 .07 .05 .05 SHPB (3.11) .6 .3 .01 l. THRB (3.11) .3 .5 .2 .2 Modern Modern Tobacco food perennials Food DRF (3.5) .04 .07 .05 SHPF (3.11) 1.1 .8 l. , THRF (3.11) .2 .4 .2 Food Tobacco DRCAF (3.5) .04 SHPCA (3.11) l. THRCA (3.11) .2 2/ Variables are defined by prefixes: DR 8 discount rates 8H5; = governs response rates THR_ - response thresholds Source: Initial guesstimates and model tuning. 168 Table 111.3. Diffusion parameters. Present Variables Uses (Eqn. No.) Alternative Uses Crop a/ Traditional Modern Food Tobacco Sector- perennial perennial Bush CIUDB l .001 .002 .0005 -- (3.0) 2 .001 .002 .0005 -- 3 .002/.001 .002/.002 .0005 -- 4 -- -- a001 0001 Crop Modern Modern Tobacco Sector food perennial Food CIUDF l .001 .01 -- (3.8) 2 .001 .01 -- 3 .001 .01/.01 -— 4 .001 -- .01 Present Improvement Replanting Other Use modern perennial Traditional CIUDT Cocoa .10 .005 -- Perennials (3.8) Palm (Sector 2) .05 .003 -- Rubber .05 .01 .002 Palm (Sector 3) .05 .003 .001 Crop Food Sector Tobacco CIUDC (3.8) 4 .001 5/ Crop Sectors: l - Cocoa-Food Sector; 2 - Palm-Food Sector; 3 - Rubber- Palm-Pood Sector; 4 - Food-Cash Annual Sector Source: 1nitial guesstimates and model tuning. Table III.4. 169 Production parameters. Variable (Eqn. No.) (definition) Commodity Cocoa Palm Rubber Food Tobacco PLOSS (4.10b) (marketing loss factor) POHC (4.11a) (proportion consumed) POMP (4.11b) (proportion processed) POMX (4.11c) (proportion exported) SUPRSP (SUPRSP) (4.6a) (perennials (food) harvest supply elasticity) PROFIT (4.21b) (proportion of raw material processed as the first processed output) PNFL (4.29) (proportion of non-family labor used in production) PPNPLT (4.31c) (proportion of non-family labor used in traditional processing) .9 .05 .60 .2 .95 .25 .05 Sources: [15] and initial guesstimates and model tuning. 170 must be at least 10%, 30% and 50% more profitable, respec- tively, than the traditional perennial crop currently on that land before farmers will transfer the land to the alternative use. The relative values hypothesize different farmer atti- tudes (e.g., risk aversion; see the discussion of component LAMDAP in Chapter 3) towards the three alternatives. Parameters such as this one play an important role in the validation of the model in spite of the uncertainty as to their "actual" values. Some of them provide a number of degrees of freedom with which to tune the model to track historical time series and to adjust the model's behavior to conform, where appropriate, with the expectations of economic and social theory and of the intuitions and knowledge of people with experience in Nigeria. Others, as shown by sensitivity tests, are not crucial to the model's performance, i.e., changing the values of these parameters has little effect. 1/ Technological Coefficients- Technological coefficients are perhaps the easiest to come by. Our principal sources for values of these parameters were several publications [15, 42, 17, 41, 54], Nigerian agri- cultural seminar reports [37, 38, 39, 40] and project pro- posals of Nigerian federal and state ministries [55, 56]. The existence of data for these parameters does not mean there is either perfect confidence or general agreement on them. Further i/ See Tables III.5-III.7 for tabulated values of selected technological coefficients used in the southern model. Table III .5. 171 Perennial yields (lbs./acre-year). Production Cohort Variable Perennial (Eqn. NO') Iziggtream) Maximum Declining Old Rising Yields Yields Yields Age 1 2 3 YPERl 1. traditional (4.4) cocoa (trad.) 100 250 300 350 250 100 2. mod. cocoa (replanted) 300 550 750 850 750 650 3. trad. palm (Palm Sector) (trad.) 1000 2300 3600 4500 2300 1900 4. mod. palm (Palm Sector) (replanted) 1500 3400 5500 6700 3400 2900 5. trad. rubber (trad.) 100 250 350 400 350 350 6. mod. rubber (replanted) 450 700 900 1000 950 900 7. trad. palm (Rubber Sec.) (trad.) 1000 2300 3600 4500 2300 1900 8. mod. palm (Rubber Sec.) 1500 3400 5500 6700 3400 2900 YPERZ 1. trad. cocoa (4.4) (improved) 150 350 450 510 350 175 2. mod. cocoa (new planted) 350 600 850 950 850 750 3. trad. palm (Palm Sector) (improved) 1250 2800 4500 S600 2800 2400 4. mod. palm (Palm Sector) (new planted) 1500 3400 5500 6700 3400 2900 5. trad. rubber (improved) 200 350 450 500 450 450 6 . mod . rubber (new planted) 450 700 900 1000 950 900 7. trad. palm (Rubber Sec.) (improved) 1250 2800 4500 5600 2800 2400 8. mod. palm (Rubber Sec.) (new planted) 1500 3400 5500 6700 3400 2900 Sources: A composite of data from [15, 55, 56, 42, 37, 38, 39, 40), some of it adjusted by model tuning. Table III.6. 172 Input requirements for perennials. Variable Perenn§7l Production Cohorts (figgts?o.) Stream- Gestation Rising Maximum Declining Old Yields Yields Yields Age pLA19/ 1 25 10 12 12 6 (4.258) 2 80 33 40 40 42 (man-days/ 3 8 6 4 4 2 acre-year) 4 40 12 10 10 12 S 12 8 6 6 4 6 3O 16 12 12 14 7 8 6 4 4 2 8 40 12 10 10 12 PLAZE/ 1 40 20 13 18 20 (4.258) 2 60 33 42 ' 42 44 (man-days/ 3 20 10 8 8 10 acre-year) 4 40 12 10 10 12 5 20 12 8 8 10 6 30 16 12 12 14 7 20 10 8 8 10 8 40 12 10 10 12 PCAlE/ 1 0 0 0 0 0 (4.26a) 2 165 10.4 16.3 16.3 16.3 (lbs./acre-year) 3 0 0 0 0 0 4 140 132 132 132 132 5 0 0 0‘ 0 0 6 190 190 190 190 190 7 O 0 0 0 0 8 140 132 132 132 132 pcazE/ 1 .0730 10.4 15.3 16.3 16.3 (4.26a) 2 .0730 210 296 296 296 (lbs./acre-year) 3 0 0 0 0 0 4 140 132 132 132 132 5 0 0 0 0 0 6 217 0 0 0 0 7 0 0 0 0 0 8 140 132 132 132 132 Commodity Value PLYQ/ Cocoa .0117 man-days/lb. (4.25a) Palm .0015 man-days/lb. Rubber .0275 man-days/lb. 3] Definitions of the perennial population streams above. b/ Does not include harvesting labor. g] Harvesting labor only. site of data from [15, 54, 55, Sources: A compo of it adjusted by model tuning. are given in Table 111.5 c/ composite of recommended sprays, fertilizers, etc. 56, 37, 38, 39, 40], some 173 Table III.7. Mean length of perennial production stages (years). Production CohortsE/ Variable Perennggl b/ (Eqn. No.) Stream— 1 2 3 4 — DEL l 6 7 14 13 -- (3.1) 2 3 7 20 10 ~- 3 6 6 20 8 -- 4 3 5 20 12 -- 5 8 4 25 3 -- 6 6 6 20 8 -- 7 6 6 20 8 -- 8 3 5 20 12 -- a/ See Tables III.5 and 111.6 for definitions of the perennial population streams and the production cohorts. b/ Trees remain in the old age stage indefinitely--see '- the description of component LAMDAP, Chapter 3. Sources: [15, 55, 56]. rese leve gice the 111 th )1 (7 174 research and field work will be necessary to increase the level of confidence in the values given many of the technolo- gical coefficients. Some examples of technological coefficients used in the southern model are: 1. commodity yields (YPERl, YPER2, YFl, and YF2 in Equation 4.4); 2. labor input rates (PLAl, PLA2, PLY, FDLABl, FDLAB2, and FDLABY in Equations 4.25); 3. chemical input rates (PCAl, PCA2, FDCHl, and FDCHZ in Equations 4.26); 4. input prices (PCI, PL, PLM, and PBI in Equations 4.28); 5. proceSsing capital/capacity ratios (PKCRT, PKCRM in Equations 4.14, 4.15 and 4.18); 6. mean times spent in the perennial production stages (DEL in Equation 3.1a). Almost all of the technological coefficients remain constant throughout a simulation run. A notable exception is commodity yields. Learning curves and supply responses for yields are discussed in detail above in component AMPPAP, Equations 4.4— 4.6. 1/ Initial Conditions- Initial conditions (1953) of variables whose values change during the course of a run must be reset at the start of each run. Some of these include: ~l. land usage (TLPER in Equation 3.1c and TLBSH in Equation 3.3); l/ See Table 111.8 for tabulated values of selected initial conditions used in the southern model Table 111.8. 175 Selected initial conditions (1953). . a/ Variable Perennggl Production Cohorts— Total (Eqn. No.) Stream— 1 2 3 4 5 (definition) TLPER l 125 175 425 250 150 1125 (3.1c) 2 0 0 0 0 0 0 (perennial land) 3 280 280 1120 280 840 2800 (thousand acres) 4 0 0 0 0 0 0 5 115 60 170 25 10 380 6 0 0 0 0 0 0 7 90 90 360 90 270 900 8 0 0 0 0 0 0 Crop Sector§/: l 2 3 4 TLBSH (3.3) (bush land) (thousand acres) 5300 2000 2000 5000 SUBLEV (4.3b) (subsistence level) b/ (proportion) .8 .9 .9 1.— g/ Definitions of perennial population streams, production cohorts and crop sectors are in Tables 111.3, 111.5 and III.6. b/ Sector 4 is assumed to always have total subsistence. Sources: [15, 50] and initial guesstimates and model tuning. 176 2. perennial substream proportions (PSPER in Equation 3.2); 3. cpmmodity prices and price averages (component PG, Chapter 5 : 4. traditional and modern processing proportions (PRT and PRM in Equations 4.12-4.21); 5. subsistence levels (SUBLEV in Equation 4.3b). A few of these variables present no data problems. For instance, assuming all agricultural processing at time zero (1953) is traditional, we have PRT = l and PRM = 0. Others, particularly initial land usages, are more elusive. Initial acreages were estimated from FAO and ministry figures and land surveys [15, 50]. The model is quite sensitive to the initial land usages, as we shall discuss later (Chapter 9), so more complete and accurate land surveys would be a pro- fitable venture from the point of view of increasing this model's accuracy (if that were desired). In concluding this section, it must be stressed that the model can be useful to the policy maker in spite of imprecise parameter estimates. Runs can be made in a Monte Carlo mode where parameter values are drawn from a probability distribution; a range of statistics for each performance criterion can then be generated, which may be more realistic than a "precise" point prediction. More importantly, however, predicting the relative consequences of alternative policy options are usually of more decision-making value than accu- rate predictions of absolute output levels. 177 Tuning Before the model is ready to be implemented it must be "tuned" to track one or more time series of past behavior. The tuning may require adjusting the values of certain system parameters, the addition of new mechanisms, or the modifica- tion of structural relationships. In attempting to track a particular time series, dozens of parameters may be likely candidates for adjustment. It takes an understanding of the real system and a deep familiarity with the simulation model to focus on the one or two parameters which would be meaning- ful to adjust, or to know where a structural relation must be added to the model to make its behavior conform more closely to experienced behavior. Four time series (1953-1965) were used to initially tune the southern model: exports of cocoa, palm oil and rubber, and food prices. The measure of goodness-of-fit used (one of many possible [8]) is: 4 TSS = .Z 551 1=1 where: A 2 13 Y. - Y.. 55. = Z ( 13 11) , 1 = l, 2, 3, 4 1 _. j=l Yi — _ 13 , 1 = 1, 2, 3, 4 Y1 — 13 Z Yi. 1=1 3 and where: SS = the sum of squared normalized deviations for series i 178 TSS = the total sum of squared deviations Yij = the real data value at year j of series 1 Yij = the simulated data value at year j of series 1 Y1 = the mean of the real series 1. The squared deviations are normalized so the four sums have equal weight when added together. The closer to zero, the better the fit. If the model generated nothing but zeros A (i.e., Yij = 0 for all i and j), we would have: 12512 SS. = 13 + , i = l, 2, 3, 4 1 Y.2 1 where: 812 = the sample variance of series i. Thus, TSS would be somewhat greater than 52. During the 13 years of time series tracking, the model uses the actual FOB prices received by Nigeria and producer prices set by the marketing boards in those years (1953-1965). These values are used in place of values computed in Equations 5.1 and 5.3. Table 111.9 displays the four time series resulting after the initial coarse tuning. Data values generating this fit were used in the policy runs discussed in Chapter 10. Adjustments made in the tuning process included data ‘values and structural relationships. For example, the model *was not simulating the rapid increase in either cocoa or rubber exports. In the case of cocoa, it was necessary to incorporate the diffusion of improved practices (defined in 179 ooaoo.a u was aomomm. Hammooo. ooomoo. oomoom. mm osooaso. oomamao. .~o~.ooa .omo.~ma .moo.om~ .ooo.omm .moo.omo .oo~.aam mood oomoaao. oommaao. .moo.oma .mmo.aos .Noo.mm~ .ooe.oom .Hos.omo .oo~.Hoo some ommmaso. oomooao. .mmo.mma .Hmo.aoe .om~.mm~ .oo~.~o~ .omo.mao .ooo.~om mood asmoaao. oomomno. .oam.o~a .oom.mma .oo~.~o~ .oao.mo~ .oao.mom .omo.omo mood «moooHo. oommmao. .saa.o~a .oom.m~a .oo~.mam .ooo.oom .no~.oom .ooo.aao Home ommooao. ooommso. .oma.m~n .moa.oms .ooo.osm .oma.oao .ooo.mmm .oao.~mm oooa oooooao. oomooao. .ooa.oaa .omm.oaa .ooo.o~m .ooo.oom .mao.mmm .mao.oam omoa ooomoao. oooaaooo. o.oom.oo o.som.~o .~oo.oom .omo.som .Hoo.oom .Hmm.oos omoa ooososo. oooomao. ~.oom.oo o.~om.oo .omm.aom .oo~.Nam .aom.oo~ .Noo.mom ammo oooooao. ooaaoao. a.m~o.oa o.omo.mo .omo.~om .omo.oao .mmo.ma~ .oam.~o~ omoa amoooao. oooomao. o.oom.oa o.amo.oo .aam.oam .ooo.ooo .omo.oo~ .moo.ooa mood mmaooao. oomooao. o.~m~.so o.oao.oo .oom.oom .ooo.ooo .ooo.om~ .mmm.o- soon oomooao. oooooHo. m.os~.om o.-o.oo .oom.omo .mso.ams .oom.oo~ .moo.om~ mood amemqosHm mean amamqosz mean omaauosz «Baa amaaqosz .aean mam» x.aa\oo l.sm\.maa .mnoauo A.um\.maa .msoauo I.s»\.mas .maoauo mona coca memoaxm «mamas mamoaxm qu 24am mamoaxm aoooo .ocflxomuu weapon mEoB ( .m.HHH magma 180 Table 11.2), a process which actually did take place in the 1950's and 1960's in Nigeria. This was accomplished in the model by setting, as an initial condition, 5% of the tra- ditional cocoa in the improved substream (PSPER1k(0) = .95 for all k, in Equation 3.2) and adjusting the diffusion para- meter (CIUD in Equation 3.8 and CIUDT in Table 111.3) so 11 that by the end of the tracking period (1965), about 95% of the traditional cocoa in the model was being managed under improved practices. Similarly, simulated smallholder rubber production was not generating the exports actually experienced. FAO estimates of acreages and outputs of rubber estates [15] indicated that this would make up most of the discrepancy. Thus, the rubber estates factor discussed earlier (Equations 4.24) was added to the model. Further agreement with actual rubber exports was obtained by increasing the initial (1953) estimated rubber acreage (TLPER5k(0) for all cohorts R) from a total of 350,000 acres to 380,000 acres. General Validation Tuning the model to track four time series is not nearly enough. The southern model, merged with the other major components of the total Nigeria model, was further refined in a process of intuitive, theoretical, and empirical consistency analyses. Indeed, this process is continuing. Some aspects of simulated behavior considered are: l. the national accounts have to balance; 2. the agricultural and nonagricultural per capita con- sumption of food have to be in the "right" neighborhood according to intuitive judgments and empirical evidence about nutritional levels in the Nigerian population; 181 3. the market price of food has to be in a "reasonable" range, neither too large nor too small, and growing at a "reasonable" rate; 4. GDP and value-added growth rates in the agricultural and nonagricultural sectors have to approximate ex- pectations based on economic theory and empirical and simulated conditions in Nigeria; 5. land use decisions have to respond "properly" to changing profitabilities of alternatives. This process of general validation is very judgmental and often intuitive in nature. In spite of this--or even because of it--the process must be an on-going part of the model's application if the model is to remain both useful and credible. CHAPTER 9 Sensitivity Analysis: Results and General Applications Sensitivity tests identify those parameters to which the model is most sensitive. That is, such tests can com- pare the relative response of the model to changes in the values of different parameters. Such information is useful not only for model tuning and validation but also for poli- cy making and as a guide to data collection priorities. A brief discussion of these applications follows, and then an analysis is presented of the results of a series of sensi- tivity runs of the southern model. Applications Model Development Sensitivity tests play an essential role in model building and validationl/. For one thing, they identify those parameters which can most effectively be used in tuning the model to track recorded behavior of the economy l/ Actually, these two processes--model building and vali- dation--are intimately linked. The validation proce- dure may (most likely will) point up weaknesses in the model and suggest areas that need further development. The model-building activity then addresses these pro- blems, preparing the model for another round of valida- tion, and so forth. 182 183 (discussed in Chapter 8). The diffusion response parameters (Table 111.3) are prime examples of this, as we shall see below (Table 111.11). In addition to time series tracking, sensitive parameters such as these may be adjusted, as part of the validation process, to bring the model's behavior in line with the expectations of accepted theory and knowledge- able intuition. For example, the supply elasticity of food (SUPRSF in Table 111.10) was adjusted-~within a range accept- able to that same theory and intuition-~to "validate" the demand—supply behavior--i.e., consumption levels and price 1evels--of the food market. An analysis of sensitivity test results may also be used in validation to check the logic and internal consis- tency of the model. Troublespots can be located in the course of tracing through the model to find explanations for simulated behavior exhibited as a result of a change in the value of some parameterl/. For example, initial tests on an early version of the southern model indicated an extreme sensitivity of the model to variations in oil palm production coefficients. The model was (realistically) projecting the future disappearance of Nigerian palm oil exports as domestic demand increased with the population and eventually surpassed production. The price mechanism then translated an increasing excess demand into higher and higher prices. It was a serious shortcoming of the model i/ It.:b this process which is most exemplified by the detailed analyses presented later in this chapter. 184 that there were no factors limiting the price rise. Further development of the palm oil market mechanism in the model placed bounds on the palm oil price by giving domestic demand a non-zero elasticity (Equation 4.23a) , by modeling a domestic palm oil market (Equations 5.4-5.6) and by allowing the importation of palm oil (Equation 4.23d) once the domestic price has reached the import price, thus placing an upper bound on the former. Another illustration of the use of sensitivity test results as a check on internal consistency is described in. [35, Chapter 8]. Briefly, a not unreasonable change (upward) in the parameter controlling the rural-urban migration rate caused the model to blow up. It was then discovered that the consequently larger nonagricultural population was demanding and consuming food in excess of the nonagricultural income available to pay for it. An income constraint was duly added to the model. ?olicy Making The model has the built-in capability of directly nd explicitly evaluating three policy areas--commodity roduction campaigns, marketing board pricing and various axing policies. These are discussed in Chapter 6 and 2monstrated in Chapter 10. Sensitivity tests can supple- nt these features in two ways. First, a policy or program goal may be assumed to re been achieved and the model thus run to examine the 185 consequences. For example, rather than running a produc- timicmmmign to modernize food production and simulating the promotion and diffusion of the requisite technologies wiU1tMaattendant consequences, it might be assumed from the outset that average food yields have attained a higher value. The model would then be run with this higher value to see the likely effects on income, exports, food con- sumption, etc. Other examples might include investigations into the consequences of: 1) population control policies by appropriately modifying birth and death rates in the po- pulation component; 2) modernizing the processing of agricultural commodities (e.g., rubber and oil palm) by making the necessary changes in relevant processing coefficients; 3) policies to stimulate regional specializa- tion in agriculture (i.e., the South con- centrating on perennial export crops and relying on the North for food) by appro- priately lowering southern subsistence levels, thus increasing reliance on the food market; and l/ 4) increasing the availability of credit— to agricultural entrepreneurs. Sensitivity analyses may be used not only to experi- ment with pre-specified policy options as discussed above but This would be a potential experiment. However, it would not be feasible with the present model, for currently, the model inadequately reflects the very real capital constraint faced by Nigerian farmers desiring to invest in expanded capacity or new techno- llcugiras. 186 also to help pinpoint and design new and potentially effec- tive alternatives. A knowledge of the relative sensitivity of relevant parameters and coefficients will indicate the most promising areas for policy attention, that is, those areas which would be the most responsive at the least cost. For example, a quick look at Tables 111.10 and 111.12 below will show that for a policy to increase exports, efforts to decrease spoilage and waste in marketing (Runs 9-12) may prove more fruitful than attempts to decrease marketing costs (e.g., labor and transportation) (Runs 50-54) . To the extent that sensitivity tests are conducted to reflect the degree of confidence in the values given key parameters in the model, such tests can be valuable in the design of policies in the face of uncertainty. It is important to develop policies whose simulated consequences It are relatively insensitive to parameter variation. would be disastrous to allocate scarce resources to the implementation of a policy which, due to the uncertainty of model parameters, produced effects vastly different from, and perhaps even negative to, those intended. Thus, sensi- tivity tests can identify policies which are relatively stable for some appropriate range of parameter values. An important and essential extension of sensitivity testing procedures for the design of stable policies is the Monte Carlo analyses mentioned in Chapter 8. Rather than deterministically testing one parameter at a time, 187 probability distributions for a number of key parameters may be specified to reflect a range of likely values, and a large number of simulation runs may be made, each drawing samples from all the specified distributions. The statis- tics generated for the output criteria can then be used to evaluate the relative sensitivity of a policy to Variations '9», not in one parameter (nor even many parameters one at a time) but in a number of parameters simultaneously. Rela- tively small variances for the output criteria would indi- 1/ cate a stable policy— . The words "relative" and "relatively" have been ‘ s 7122?... “‘—"‘- -. used extensively here to emphasize the importance of evaluat- ing and comparing a number of policy alternatives rather than one in isolation. Indeed, the term "sensitivity" is meaningless in an absolute sense. It must refer to compa- 'isons of policies or to comparisons of the results of arying a series of parameter values (as in Tables III.10- II.12) . ta Collection Finally, sensitivity tests can identify the most >fitable uses of data collection resources. For example, model is relatively sensitive to the diffusion response ameters (Table III.11) , while variations in the harvest I; Chapter 11 discusses some problems which raise questions as to the feasibility of using Monte Carlo techniques in this framework . 188 elasticities for perennial crops have negligible effect (Table III.10) . From the point of view of the model's data needs, eXpenditures to estimate the latter would be virtually wasted. It would be worthwhile, on the other hand, to devote resources to sharpening estimations of the former. Again it must be stressed that running the model in the Monte Carlo mode could greatly reduce the urgency of acquiring improved data. Analysis of Results Methodology The series of 69 sensitivity runs conducted with the southern submodel may be grouped into four sets. The first three investigate the effects of varying selected production coefficients, land allocation coefficients and price para- meters, respectively. The fourth set of runs examines the sensitivity of the numerical solution of the model to changes in the time period increments used in the simulation. Each run simulates the agricultural economy of southern Nigeria over a 32-year period, 1953-1985. These test runs were conducted with the southern submodel alone, that is, without the rest of the Nigeria model. Thus, the results presented below and in Tables III.10-III.12 may differ somewhat from those which would be obtained in the presence of: 1) links with northern agriculture through the food market and 2) interactions with the nonagricultural economy. For example, with the North supplementing the 189 southern food supply, food prices in the South would be generally lower (by about 25% for the base run) than was the case here. Furthermore, the presence of interregional trade would probably make the market price of food less sensitive to parameter variations than is indicated by these runs. A strict test of parameter sensitivity would require all parameters to be varied in the same way, e.g., plus 20%. The results could then be compared on the basis of a given deviation. This procedure would contribute nothing, how— ever, either to understanding the nature of or coping with the uncertainty arising from varying degrees of confidence in parameter values. In statistical terms, is it meaningful :0 compare the relative consequences of 20% variations in each of two parameters, one of which has a standard deviation erhaps 1/10 to 1/5 of that 20% and the other of which has standard deviation 10 to 20 times 20%? The general rule followed, therefore, in defining 1e sensitivity runs described here, was to vary each para- ter by an amount which I felt covered most of its uncer- inty distribution,say two standard deviations. It must cautioned, however, that the term "two standard devia- >ns" may convey a degree of precision which did not exist. 'king informed judgments or other estimates of relevant tributions, the variations used were extreme guesstimates my part. They do reflect, however, the relative lengths ”'17 ,- T}. ” .——‘._ .-_.. ‘ "Ia ‘ ‘ *‘IJA‘; 190 of subjective confidence intervals. Where possible, similar parameters were varied similar amounts. For example, the perennial yields were each increased 20% (Table III.10) and the diffusion parameters were each increased 400%, i.e., to five times the base value (Table 111.11). The output criteria tabulated in Tables III.10- III.12 include agricultural exports (AFORXS), value added (ATVAS) and net revenues (ATRCN) accumulated over the simu- lation run, and marketing board net revenues (ATRMBS), also accumulated over the 32-year simulation. In addition, effects of parameter variations are shown for agricultural per capita disposable income (PCDINA), nonagricultural per capita food consumption (PCFNAG) and the market price of food (PRFD). A final criteria displayed is the aggregate measure of goodness-of-fit, TSS, defined and discussed in Chapter Bl/. A final comment must be made preliminary to the analyses which follow immediately. The reader may find the level of detail in that discussion somewhat tedious. (Indeed, not all that might be said will be said, for some effort is made to limit the discussion to the major explanations of the more appreciable output deviations.) However, the com- ments and explanations presented are quite illustrative of l/ As a reminder: the closer T58 is to zero, the better the fit, i.e., the better the time series tracking. 191 how sensitivity analyses may be used not only for model validation but also to add to one's understanding of the real system being simulated. I found it so in my own case. Production Coefficients Twenty-seven production coefficients were tested: the yields of four perennials; food yields in each of the 5 four crop sectors; marketing losses for each of the four 5 commodities (a cash annual--tobacco--was not assumed for % these runs); processing losses for palm and rubber; the ? proportions of acres harvested under normal conditions for L four perennials and wild palm in the Cocoa Sector; short- term supply (harvest) elasticities for three perennials, wild palm in the Cocoa Sector and food; the caloric content of food; and the per capita consumption of palm oil in the North and South. Parameter deviations and results are shown in Table III.10. One observation that can be made concerning all 61 runs presented in Tables III.10-III.12 is that the effects of parameter changes on nonagricultural food consumption and the market price of food are consistently (with one exception) in opposite directions and roughly proportional. Phat is, the change in food consumption is generally 30 to 10 percent of the change in market price and of opposite sign. This is due to the fact that the former is a function 3f the latter in the population component of the model. kxxi consumption is also a function of nonagricultural 192 income, but this is determined exogenously in the absence of links between the agricultural and nonagricultural sectors, as discussed above. If these interactions were present, we wouldn't expect the consistency of the relative responses of food consumption and price to be maintained. For example, in Run 12, the increase in agricultural income would lead to increases in nonagricultural income (due to multiplier effects discussed in Chapter 1), and thus the 2.67 percent decrease in food consumption would be consi- derably lessened and perhaps even reversed, showing, in the latter case, an increase in both_food price and consumption. Another consistent result of these sensitivity runs Ls the nil response of marketing board net revenues to :hanges in parameters concerning rubber production, e.g., tuns 3, ll, l4, l7 and 22. This is because rubber marketing .5 not handled by a marketing board. The tests increasing perennial yields 20 percentl/ Runs 1-4) show effects on AFORXS, ATVAS, ATRCN and ATRMBS (n the same direction (i.e., increases) except for cocoa ields. Increasing traditional cocoa yields depresses these utput variables. It was discussed in Chapter 8 that the odel simulates a diffusion of improved practices in tra- itional cocoa production in order to reflect what actually '— / ‘YPERlM(i), in Table III.10, is a proportion of the yields of all the producing cohorts of perennial stream i. _“ ‘.“ yr“, 45" A ‘t'm--‘h._’ A _ 193 took place in the late 1950's and early 1960's. Increasing traditional cocoa yields in Run 1 decreased the relative profitability differential of improved over traditional cocoa production. This slowed up the diffusion of improved cultural practices and, so, resulted in less output as re- flected in the decrease in the criteria variables.) '71 Palm yields (Runs 2 and 4) appear to be substantially '.‘.."..~n .I.; more sensitive than the other perennial yields. In fact, most of the parameters related to oil palm production are relatively quite sensitive (Runs 13, 16, 18, 19, 21, 26, and ‘ - .ou..--w1.-.7" I x" _ ‘E. 27). This sensitivity is due to the competition between the domestic and export palm oil markets. While the extreme sensitivity reported earlier in this chapter has been cor- rected, the present level of sensitivity of palm parameters is not unreasonable. A final comment that can be made about palm yield sensitivity is that although the time series tracking fit may be improved by better than 20 percent (Run 4), there is currently no empirical evidence to support an assumption that palm yields are higher in the Rubber-Palm Sector than in the Palm Sector. There may be grounds, on the other mand, for assuming a lower per capita palm oil demand in :he North in order to attain a better fit (Run 27). There ;s still some uncertainty in Nigeria, however, as to what :ould accurately be assumed to be the domestic palm oil lemand in either region [39] . 194 While palm parameters appear to be the most sensi- tive of the perennial production coefficients, the rubber parameters are almost invariably the least sensitive (Runs 3, ll, 14, and 17). Only the short-run supply elasticity (Run 22) shows mixed results. The lack of a rubber marketing board, as already discussed, explains the nil effect on ATRMBS. An additional explanation is the relatively smaller part rubber plays in overall southern cash crop production. For example, rubber exports in the base run at the end of the 32-year simulation period account for less than 14% of total agricultural exports, while cocoa accounts for about 68%. The production coefficients for food are most sen- sitive, naturally, for the food market price and nonagri- cultural consumption, PRFD and PCFNAG (Runs 5-8, 12, 24, and 25). Value added, ATVAS, is also somewhat affected, due primarily to food making up about 75% of value added. Varying food yields causes the sharpest output deviations in the Cocoa and Food Sectors (Runs 5 and 8) because these crop sectors have most of the food land in the South. It is potentially significant that the Calorie content of food (Run 25) is rather sensitive. This may have important implications for Nigerian policy makers should the food composite used for southern production in the model--defined as a weighted average of yam, cocoayam, maize and cassava--shift in reality to higher proportions of I‘m-2.4L..- 7“ 1-. 195 no.~ mm.~ o.-n wH.oI nmm.l vn.n| mo.vu novo.a mmv. can. o~.~ vo.a homo. mv~.t Na.NI oo~.u ao.~l vn.ml omm.l com. was. cow. Name. and. oNH. mv.n mo.m vo.~| mod. Ana. on.~ dam. no.a mH.A o~.n oh.~| nc.NI vn~.t oo.nl Nh.al 0N0. Ham. om.~ om~.I ammo. whoo. mna. 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J r‘u‘101giii‘li.|{‘lly' o.uut .Hmn nva.l hm.u ~N.v com. oo.o o.ddl NH.on uoN.I oo.~| nH.v onno. No.~ omno.t ~w.an wh.o ooN.I mooo. oo.nn v~.~ no.0 no.vl Non.u Hoa.l Noo.I «ma. nm.au oo.n| o-.u en.n o~.o mo.ml ohmo.l oo~.I mov.l one. mm.~l aao.u o~.~ mm.a mh.nl mono.u hmH.I om.~u o~o.s ov.n hm.mu on~.u ammo. Hou.l o~o.u 556.! and. mN.Ht av.m| .vN .hwo mo. .on .omh Ho. o.m~+ an.oe o.mN+ o.m~+ .oo~+ .oo~+ o.ocv o.o~| n.v~n ..ua acoouoa\.nn~. case: can as :Ouuaasacou duo Edam ..u»: coauoa\.unac zu30m on» :w samuQESucou duo Edam ..n~\.uaauo noon no use» Icou cascano coca new saunauaaao uno>uaz AuOuoom 000 :00. Eden paw) new auuowunaao uno>uaz uonnau new suaoauaaso um0>ua= seam uOu auaoauuaso uno>uux 00000 new auwowuuoao umo>um= lacuoom coo IOU. pmumw> anon mouum Edna can: no acquuoaoum AuOuuom non unsmc coumo> tum: mason Edna acacia neoouu mo nodquQOum ZmZUOm mszOm >4‘U hmmmbm mmmmam Anommmaam Ancmmmmbm Aaommmmam >xqmm Aho>zqmm h~ um nN on MN Nfi AN o~ ma ca cam omen EOum muauuomoo ucoouom mo~.H .na\u novno. .uhnc0u -uoa\.~oo oom.mmm .uxucou nuoa\u ov.ma u :Owaawn moon. u newaaun vmv.n u cobssan on.~a u coassab moo.~ o=Ho> cam Oman on~a> cam once mm? H Ohma F Uk< a mxxOh< \Q IUMHUU «MU UUCQEONHUA w5~o> cam amok cam chum EOuu mococu accouoa noduanuoo houOEJuom paumwe nouoEcumm cam ..o.ucou. .o~.HHH wand? 198 .mCflxomnu mowumm wEHu mo pawlmou Immocpoom mo wannabe u mmB poem mo moanm umxumfi u Chum coaumfismcoo coon muammo mom Housuasoaummcos u omn um: cumon mcauwxumfi mo Hmumwusfl meu u mmzmem mmscm>on rmmo um: HmHDUHUOflHmm mo Hmummuce mafia u zuma< cocoa wsHm> HonsuHsOflHmM mo Hmummucw wEHu u m<>9€ manomxm Housuasufinmm mo kumouca was» u mxmomd .mnm moanmanm> .Ammmac can coeumasfiam Hmmmlmm w No new or» um ohm mosam> \m A.U.uaoov 0H.HHH OHQMB 199 high caloric grains (such as maize or rice) or of higher caloric roots and tubers (i.e., to less yam and more cas- sava). This would also have implications for further model development activities (discussed in Chapter 11) since the current model makes no provisions for a dynamic shift in the food composite and, hence, parameters -such as the food yields, the caloric content of food and the labor and other input requirements for production. Land Allocation Coefficients Runs 28-49 test the sensitivity of a number of land allocation coefficients and initial conditions. Included in these 22 runs are the initial (1953) acreages in four perennial streams and in bush for each crop sector, diffu- sion response parameters of bush for traditional perennial and food alternatives, profitability response parameters of bush, and proportions of bush land available for parti- cular alternatives. The results are tabulated in Table III.11. It is perhaps conspicuous that all the coefficients tested are for land currently in bush faced with productive alternatives of traditional perennials and food. No para- meters pertaining to decisions among alternatives to peren- nial or food present uses (e.g., CIUDT, CIUDF, THRT, THRF, etc. in Tables III.1—III.3, Chapter 8) are tested. This is oecause the alternatives to traditional perennials and to food all involve some sort of modernization--replanting 3! fl—-—‘-"' l-' ' b‘arxhd' .5.— 11‘ .-.}.“A E8_§v 200 perennials, for example (Table 11.1, Chapter 3)—-requiring the model to execute a series of production campaigns in order to test the relevant parameters. While the runs for the series of tests reported in this chapter included no such policies, a few of the decision parameters omitted here are tested in Chapter 10 with some of the policy runs examined -4? there. Initial land use conditions appear to be somewhat sensitive. Again, palm and cocoa acreages are substantially ‘M' A-I—A “M1.“ more sensitive than rubber (Runs 28-31). While initial “. to perennial acreages have relatively little effect on per capita income (PCDINA) and food criteria (PCFNAG and PRFD), the initial amount of unused but cultivable bush land in the four ecological zones has substantial impact on those out- put variables (Runs 32-35). Initial bush land in the Palm Sector (Run 33) is particularly sensitive because that area has the largest and densest population, and the relative scarcity of land available for the expansion of food crops in that crop sector will be reflected in the more dramatic deviation in food prices. Of the land allocation coefficients, the diffusion parameters are the most sensitive (Runs 36-41). As might be expected, increasing the spread of perennials into bush diminishes the potential expansion of food land, causing higher prices and lower consumption. The reverse happens when food diffusion is favored. The extreme sensitivity of 201 cocoa (Run 36) relative to the other perennials may be ex- plained in two ways. First, as mentioned earlier, cocoa makes up the major part of exports and nearly all of market- ing board revenues, particularly toward the end of the simulated time period as palm oil exports decline and disap- , pear. Secondly, and more significantly, the Cocoa Sector has initially more than 2 1/2 times as much bush land avail- able for expansion as the other perennial sectors (see base run values of Runs 32-34) , a resource which is apparently tapped. Similar explanations hold for food diffusion being more sensitive in the three perennial sectors than in the Food Sector (Runs 40 and 41): there is more bush land in total in the perennial sectors than in the Food Sector alone, and since the Cocoa Sector has most of it, we might expect CIUDB(3) to cause most of the output deviations. As for the profitability response parameters, changing the discount rate and the response thresholds has almost no effect, while the parameter controlling the res- >onse rates are fairly sensitive (Runs 42-46) . A look at 'igure 11.6 in Chapter 3 will explain why. Since bush has ero profitability (except in the Cocoa Sector with wild alm, as explained in Chapter 3), the alternatives are far It on the PDR axis, so the response is nearly at its :ymptotic maximum. Even a ten-fold increase in the thres- »ld, i.e. , shifting the curve to the right, has only a gligible effect. Decreasing the response rate, on the —..__—_.-—— 4M ‘2; ‘- 202 nvn.a ov.N ~h~.| v.vau n~.N h.H~I ha.~ om.n oo.o an.v nov. vnm. an.” Non. ~o.~| no.N| Hm.Hn ~n~.n ooa.u Hav.u NaH.u vo.~ No.~ om.m N0.H OnH.I man. can. cam. och.a HH.~I vo.m| on.~ NmNo.| oo.v oo.m YIIIIII' 11.! 1‘ wt'ldl'l'} il' moo. ohm. oo.~ v~n.o vnv. 0mm. Nv.a oo.~ m~o. mo.~ oN.n aov. Han. nn.a o~.~ ma.~u o~o.c No.0! H~.~ who. ~5.n mo.v .coom .oooN .ooo~ .oonm .ooov .oooa .oooa .ovnv .ONI .owu .onn .oun o.oa+ o.ou+ o.o~+ o.oa+ .oouoa can. sacruVAMmaac hauuom coon or» ad tuna rush Hauuucu Aconc- venosozuc Annmac uou noon henna: 0:» cu on.“ cash ~a«u«c~ A-ouuc can. nsonuc.nma~c wouuom Edam ind cu ocau roan uiwuucn .nouo- can. usozucxnnaa. nouooa .0000 0:» c« can" scan adwuucu .nnoa. .uou noon nonnamc used Each auscuudonuu «nauacu «0 noduuoaouu .mnoa. fiend nonnsu accoduwvcuu «cuuaca «0 noduuonoum .nmoa. luau noon Edna. vans saga ~a=o«u«vquu «nausea uo noduuonoum Annoao used aouoo floccuufivauu Haquwca no co«uuo&ou& ...:mnaa .nosmnAh «NonnnAB auclunaa Abolinhdh AnoxzunAh «notzmmqa .chuuaaa an vn an «n an on om ow cam anon Souk ouauucmoo acouuom mOH.H .nd\u novno. .uhoCOn au0a\.ano oom.mnm .HXICOQ Iu0m\u ov.m~ u c0«-«n coon. :Owaawn vnv.n u :Owanwn oh.- u codaawn moa.~ unau> :5: Oman 03 Hfl> g“ OOUQ mm? _ Ohflm _ UP¢ — mx10h4 . OUOE c a a a H uflnuJOn 0:0 uo macawu uuooo c0 yucca a o A I'll vn—QH H3 0).)! v on~a> cam once can mean scum con-:u accouum noduacquoo nouosdunm caucus nouasau-m 203 .oma No.m «#6.: .onm oo.~l .voa n.nhc o.~ou va.o oo.o nifl‘ .1r<-...I|. {... . 4. «.I...- o.~m No.NI Nh.nc HN.@I Hm.nt o.vvu o.mnn mv.m NmNo.| oa.nu mmn. om.~u m.nnn v.0HI hm.¢ oo.o no.6 o.hnn N.h~t ch.~ ~v.~ mm.n| chN. aa.o N.oH oo.o mooo. mooo. mooo. Aco. doc. Noo. Hoo. Moo. mwoo. mNoo. mNoo. woo. woo. Ho. moo. moo. .ooo+ .cov+ .oov+ .oov+ .oov+ .oov+ .oov+ .oov+ .oov+ aquaccouoa floccuuavauu 0» cash no cocoa-on no unannounu av uauunauuuoun .ouua\uuacn .Oucuo rash :0 Anne» .00. and: snowed. coca no uuouuo cod-suuuo .ouoa\uua:: .Ou:«. gush no “nauoom coon. coca uo uoouuo cohesuuua .ouuo\uuw:: .Oucwc raga co .uouuom sobnsac Essa auscuuacouu no uoouuo codesuuao .ouoo\nuwcn .Oucuc noon :0 nonasu deceauwcouu no uncuuo saw-suuwo .ouoa\uuass .Oucfic noon :0 Aneuoom Edam. Edam Hacoduwvnuu no uoouuo scansuuuo .ouua\nuucs .Oucwc noon no 00000 mononuwcuuu no uoouuo cod-amuse auonxlh .aacaoano .mcmooao Ancmoauo Anacmoano AGVQODHU Anemoauo .vcmoanu Aacmoanu «v no av on on hm on can on an scum unauuoaoo ucoouom moa.~ .na\u novwo. .uhu:0u -uoa\.~uo oom.mnm .uxa:0u -uoa\u ov.ma u coassan moan. u :Owaaan vmv.n u caudawn ah.ma u coaaawn moa.~ osuo> :5: once moa— ch¢m_ U‘Zhum a CZHQUA— mmtxht — ZU¢P<~ m<>9dfi mxm0m< I‘MHOUMHU OUCQEHOuhflm o=~n> cam ouam osac> an: away can omen scum ooconu accouom noduwcwuoo nouoaauam OOUOOF heave-nan can \o a .3 J:D.Ja .44.-~ candh 204 ~5~.I no.«| no.0: «moo. m5.~u ~0.m Hoo.| 5mm. v~.n H~.5 .man How. vv.~ can.n 050.: ~0.N: 5muo. n.5nu m5no. Nvm.l vmv. av.d n~.o .ooa on.H| vvo. mmwo. Hoa.l om.5u v5u. ~m5. coNc.I N~.mn mow. man. m~.~ oA.N mNo.I MO5. ammo. v.~a m5wo.l coo. do.ol a. o. n. n. ac. dc. m5. 0. w. 00 mo. doc. no. ~.HAI mN.oI H.AAI H.~an .oo~+ .oou+ .ooa+ .em+ .oal .omu .oom+ .uOu :00» noon. coca uOu canduun>a can” scan no cauquAOum .ououuo- unaccouon. vOOu new o~nc-a>c need cash uo sanguOQOMA uuudcco than ~QCOwu uqvouu uOu o~n¢-a>o wand cash no scauuoaoum aquaccouoa succuuau nan» cu cash uOu ouch vasoooac a» ouaunauauoun vOOu ou cash no Cocoa-on no ouch h» nuawnduauoum adduccouom auscuuac luau ou roan no unconnou uo ouch au naaunduuuoum vOOu 0» cash no ounce-on uo vaoruvuzu a» awaanduauOum .v.~.n>¢4d .n.n.n>aqa .n.n.n>‘qa .~.n.n>‘qa in.scn><4a .~.H.n>44o .H.H.m>¢aa “Honda anommmm Anommzm Anomzma av no 5. av no vv nv cam anon Scum ounuucaoo uncouom moa.~ .n~\u nov~o. .uaucOn -uoa\.Hoo oom.mnm .NAuCOu uuoa\u ov.m« u Godddwn coon. a coaasab .me.n a codauwn a5.- a coaasan Tax moo.“ on~a> cam once mmh — cumm— U‘ZLUQ— 9¢ ~mx¢0hd \a Iauuouwuu nuanEHOuuom oaaa> ounm osau> :3“ unOB can anon scum cocano acouuom cauuucauoo uOuOEdu-m coo-ca Hflughdh ..v.ucoov .HH.HHH Onndh 205 .mcflxomuu mowumm 05w» mo neMIMOImmoscoom mo chammofi u was GOOM mo mowum umxume n nmmm coflumfidmsoo coca mufimmo Hum amusvasoeummcoc n umzmom oEoucH manomommec nuance Mom amusuasoeumm H «anUm moscm>mu um: canon mcflumxume mo Hmumcucfi wasp u mmzmam mmscm>ou ammo umc amusuasowumm mo Hmnmouce 08w» n zomam conch oSHm> Hmunuasoauum mo Hmummuafl mafia u m<>9¢ monomxo amusuHsOAumm mo Hmumouce mafia u mxmomc . ume mm maum? w Ammmav can coHumazfiwm Hmwhlum m «0 cam on» HMHMHW macaw” \m 206 other hand, flattens the whole curve with much greater con- sequences. 'Apparently, bush thresholds are of little conse- quence in the model.‘ Perennial and food thresholds can be expected to be more crucial since productive uses are being compared, e.g., replanting a perennial against continuing in traditional production. This will be investigated in the next chapter. The proportions of cultivable bush land available for perennial commodities are quite sensitive (Run 47). Proportions available for food, on the other hand, are re- latively insensitive, except for the market price of food. In this case, the perennial sector proportions (Run 48) are relatively more sensitive than those of the food sector (Run 49). This, coupled with the results of Runs 28-35 might suggest the usefulness, for the purposes of this model, of obtaining accurate land use surveys. Price Parameters Sensitivity tests were conducted on twelve para- meters of the price generation component of the southern model: five commodity marketing costs, two marketing profit margins, four export commodity FOB prices, and the rate of change of the agricultural wage rate (Table III.12). Marketing costs appear relatively insensitive (Runs 50-54) . Of the five tested,the marketing cost of food is :he most sensitive. Higher food producer prices resulting g. P-“ ...... _ r .y - . __ .4. W. p— ' “' '1‘; m“. 207 from the lower marketing costs (Run 54) result in increased production which in turn leads to lower market prices (PRFD) and higher incomes (ATRCN and PCDINA) and value added (ATVAS). Cocoa marketing costs (Run 50) are more sensi- tive than those for oil palm products (Runs 51 and 52), particularly for agricultural net revenues (ATRCN) and nmrketing board net revenues (ATRMBS) since cocoa accounts for a greater proportion of these output variables than do palm products. For example, in the last year of the base run, cocoa accounts for about 17% of agricultural net revenues while palm products contribute 12 1/2% (and food makes up about 68%). As for marketing board revenues, the main factor explaining cocoa's sensitivity relative to oil palm is that palm oil exports (through the marketing board) decline during the simulation run and eventually disappear. Marketing profit margins of rubber and foodl/ are also rather insensitive, food being the more sensitive of the two. The more unfavorable food price to farmers (Run 54) reduces production, raises market prices and depresses value added and income, as might be expected. A trace increase in exports and marketing board revenues results from the more favorable position of export crops relative to food. See Chapter 10. 1/ Marketing profit margins for cocoa and palm products are ruyt tested here since these are marketing board policies. Am ..__“. SJ .0 1‘ v.fL ‘1' ”a; one. ”i m. “urn-A l 208 The rate of change of the agricultural wage rate (PLR) has negligible effect, the largest output deviation occurring in agricultural net revenues. Experience with adjusting the model to evaluate policies indicates, however, that the response to production campaigns, particularly the 1/ replanting of perennials, is quite sensitive to PLR '—‘J Higher wage rates lessen the relative profitability diffe- rential of the more labor intensive modern alternatives ‘ 9'"? ..-—V ....—n— -*_- over current traditional production. This is related to .Lr)... _ _ the sensitivity of the response thresholds of traditional '_ \ perennials and food (mentioned above in the discussion of Runs 42 and 43 [Table III.11] and investigated in the next chapter). In general, the export price trends (WPR(i)) appear rather insensitive (Runs 56-49). However, the sensitivity of these parameters is underestimated by the tests performed here because world prices in the model are determined by recorded prices from 1953-1970; so it is only for the last 15 years of the simulation run (i.e., 1971-1985) that the Since this is true for all four of We WPR(i) are operative. them, we can nevertheless make comparisons among them. can see that changes in the export prices of cocoa and palm products are more sensitive than rubber price changes. I; 11/ This test was not made in the sensitivity runs for either this or the next chapter. 209 o~.~u o~.~ nocc. no.n novo.| ~m.nl ~o~.o vvo.a NNM.I -.Ht 5ouo. o~.~ Nae. vNN. Nae. omoo. cv.~| mwn. ov.N om~.u mom.» m~5.t mvo. NmNO. ~m~c.| ~v.~u an.~1 o~.m om.«n -.nu can. -.n mv~.n vnv.0 wwm.n ~m.~ ano.u ova. No5o.o aan.u 5nno. Hod. omno.| m5oo.l omm.l Hoe. m~.H mo. OH. ca. mo. 50. 50. 5d. ed. no. mo. m5c. ca. 0H. NH. .o~+ .co~+ .cml .omt .om+ o.nv+ o.nv+ .ons .u> -.uancae\uc couch one) puuzuaauwuoa no accord mo 000: Aoouun no newuuoa ocuno chance uqup& new uuuxuqfi cook .00qu «0 cowquQOua. chance uw uncun ocauox tuna among: .00qu no cOauHOQOHQV nuuou ocwuox nude 000m .oouua «0 cauuuoaoun. nuuoo ucwuox nun! henna: .00uua no cauuuoa tang. canon ocwuoxunfl Hocuox Edam Aouaun no COwuuoa noun. uuooo ucwuoxuos ”“0 Edam AoUMun «0 :ONuHOQOuQ. uuaou ocauox nqu .0000 me Amontmum .vomtmmm AmoIBmOU Avolbmou Anothmou A~czsmoo Advlbmoo 5m om mm on nm an an on :3“ ”USE ROBE ousuuocoo ucoouom mo~.~ .nu\u nov~o. .uxucou -uoa\.Hau oom.mnm .uanCOI uuoe\u ov.m~ u codaawn moon. u noduawn vmv.n u cauauwn m5.ua u coaasan moo.~ 2:2, :3. 0.0m mmh fi\‘ chla— O‘ZhUm—‘ (Znouad mm!¢9<_ ZUKFC _ m<>9< — mxxOh‘ \m thfluuhu OOCQEMOUHQA 03~n> :5: Oman 05~a> cam puck 65¢ GOIQ UCOONUQ c0uuwcauoo uouoaduam vouooa MOJIEIMIQ .HovOI caucuses on» no nuouoaduun toque «a nanny auu>auuucon no nuns-oz .N~.Hwn CHAIF 210 .ocuxoauu acquo- old» «0 uququuauocoooo uo eunuch! coca uo onwun uoxuql nodunlsncou coco qumao non ~¢u=u~20«uoacoc ofioucu odouuomauv quqaao non Hausu~50uuou nusco>ou ac: punch ocuuoxuqfl no anyways“ ofiuu nonco>uu naau an: unusuasoquua no Hauooucu oeuu cocoa oa~n> unmanageauoa «0 aauoouc« mafia uuuonxo Hau5u~:0«uoa no anuooucu 05¢» mmb Damn u‘zuum (ZHOUA mntxh¢ 2019‘ m<>b< I mxuofl< ”one uo~&n«ua> orb ..moouo can c0«ua~=£«n unoauan - u0 one or» an one nonaa> \u Ava. n~m.c ~o~.: .o n5a.n .o o5n.n om~.n ouo.u Hoe. ~o.: .ooaa- o5o~ nouua «chum tuna) nonosu no octane no ouau ~a:0«uuon0um oomo.n can. H~.~ “mm. mmu. ”no. «oo. «o. .ooo+ o5aa houn- oowun vane) Hooker Hana no ensure no oucu auscuuuoaoum 5o~. no.~n mmm.o -.«u ~an.u mov.u goo. Ho.u .ooauu o5oa ucuuo ooaun pauoz aao Edna no oocoro no ouou HocOquOQOum come. one. ao.~ «no. man. o~.~ aoo. moo. .oov+ o5ma sebum acqun pane) noooo no oucczu uo ouch auteuuuoaoum Avoxmz Amoco: Auozmz «some: do ow an on and neon [cum ounuuaaoo ucoouoo no~.~ .n«\~ HQVNO. as: coco .u>a:0n .u>0:0- u a u u o=~m> 03~a> Scum noduscwuoo -uon\.soo uuoaxu coasaub cosusan codasan caisson use once can boos oocozo souoEouaa oom.nnm ov.n~ coon. ewe." ap.- meo.~ accuses 03H.) 63“ 0.6m amb— amdmfiw » 0<2h0m _ (Zuoum— mm11h<fl ZU¢P

h< — mx¢OL< l5, lflwNOUth OUCQahOuNOA \e pounce uouoEdu-a C51 ..1.ucoo. .-.-_ uanafi 211 Again, this is due to the relatively smaller role played by the latter. The palm oil world price (Run 57) would pro- bably be more sensitive than it actually is if palm oil exports didn't decline to zero with increasing domestic demand. Summary %r We have seen how sensitivity tests provide essential information for model building and validation by flagging ; possible programming and modeling errors and by contributing “ AUJ.I‘.._" to an understanding of the model itself as well as of the system it is simulating. Sensitivity analyses may also be used to examine potential policies and to suggest priorities for data collection. Analyses of runs testing 61 selected parameters were presented in detail to illustrate these capabilities. Simulation Time Cycles Two superimposed time cycles are used in the south- ern model. One time increment, denoted DT, is the principal computation cycle, i.e., the distance between mesh points of the numerical solution. The other increment, DTX, is the land allocation decision cycle. DTX is generally larger than DT in order to conserve computer time executing the long and complex decision mechanisms. Thus, the model is generally run with DT=.25 and DTx=l.0; that is, decisions 212 are made once a simulated year$/, while other computations are made four times a year. The model uses Euler's single step explicit method to solve differential equations (the initial value problem) numerically. Briefly, Euler's method seeks to solve a differential equation u’(t) f(t.U) u(to) = uO . by defining mesh points tk' k=0,...,N and sequentially solving at the mesh points U = U + hf(tk,U k+l k k) ' If the method converges, we would have lim max Iuk - Ukl = 0 h+0 OikfiN where uk=u(tk) is the "true" solution at tk and Uk is the approximate, numerical solution generated [53, pp. 75-76]. (h=DT in the model.) Generally, convergence depends on the nature of f, but in a simulation model, f(-,-) is usually unknown; all we know is the value f(tk'Uk)' The most that can be said about f is that it is bounded. An attempt will be made here,with the results of a series of runs wherein DT and .i/ Hence, land use transition rates are assumed constant for a year. arm "m firm 213 DTX are varied, to test the sensitivity of the computer model's behavior to changes in the simulation cycles DT and DTX and to give an indication of whether Euler's method converges to a solution for the underlying mathematical model. Since the more rapidly f changes with t the worse the approximation for a given h (i.e., DT), the eight test runs are all made under one of the policy situations des- cribed in Chapter 10l/. and macroeconomic growth rates changing much more rapidly than in the base run (which merely projects current po- licies and trends), we can get a better indication of the sensitivity of the model to the computation cycles. Two sets of runs were made. (The results of both are tabulated in Table III.13.) The first keeps the two increments, UT and DTX, equal and decreases them succes- sively from .5 to .01 years. The second series of runs keep DT fixed at .1 years and varies the decision cycle, DTX, from 1.0 to .1 years. Four of the output variables of Table III.13 are plotted (Figures III.1 and III.2) against DT on semi-log l/ Specifically, Run 8, Table IV.1. The major differences from that run are that policies here begin in 1953 in- stead of 1971 and the run is for 32 years instead of 42. In addition, the southern submodel is here operating independently of the rest of the Nigeria model. Thus, with land transition rates “:3 -"’. __f_. 1.!" A 3" 8:. . 214 PM I. NJ .mcqunuu uoHuou 02H» mo uHuIMOImnoccoom no cascade I was coon mo ocean aoxuus I coma .cOHumESmcoo wean uuHmco non HuucuH50Hummc0c I Udzmom. osoocH oHnunomch uuHmao Hon HnucuHsOHuuo I azHoom osco>0u um: canon mcHuomee mo HoumoucH 03H» I mmzmac ossu>ou sumo um: HousuHsUHumu mo HmummucH cEHu I zumaa cocoa 05Hu> HousuH50Huon mo HuuuoucH 05H» I m¢>8¢ muuomxo HmuauH50Humu m0 HammoucH 02H» I mxm0h¢ uncoHuHchoo mHndHuu> NHm.H Ho-o. oemm. oo.mH vHom. HN~.¢ om.MH m5o.v .o- H. H. 5Hm.H m5mmo. onm. «H.o~ mm5m. ~Hm.¢ oo.vH «vo.¢ .5NH N. H. vo~.H ovawo. ommm. mm.mH vomo. oo~.e no.MH mo5.v ~.o5 m. H. H¢N.H hmmmo. Nvmm. 55.mH mHmm. mm~.e mo.MH om5.v m.Hm .H H. mm~.H HNNNo. vmmm. om.mH ommm. «mH.v em.MH M55.e .ooHN Ho. Ho. oom.H Homuo. ovmm. o5.mH m~5m. mmH.v em.MH mHo.e .mmv mo. mo. NHm.H Homwo. ovmm. oo.mH «How. H-.e om.mH m5o.v .omw H. H. Hem.H MHNNo. mmmm. Ho.o~ ooo5. v5~.v ~5.MH 5oo.m m.mo mm. m~. oHv.H mvmmo. momm. oe.o~ Hmm5. mmm.v 5m.MH mum.m m.mv m. m. .HmIcom Iu0m\.Hmu .uhIson u u u u xeo I .nH\u coHHHHE Iuom\u coHHHHo coHHHHo coHHHHo coHHHHo Amocooomo so was ammo odzmom «zHoum amazed zumsd m4>s¢ mxmomd oEHa com .xaa can an mandamuocH 08H» :0 mummy huH>HuHmcom mo muHammm .MH.HHH OHQMB 215 scales to emphasize changes in the outputs for proportional changes in the time increments. (The graphs are for the first set of runs, so DT=DTX.) In general, we see dimi- nishing returns for proportional decreases in DT. This implies the numerical approximations are approaching a so- lution. It also implies increasing costs in computer time per unit improvement in the approximation. Figure III.3 indicates how the computer run time increases with propor- _— ...—.-w -...— tional decreases in DT and DTX. The change in the price of food (and hence, re- \‘ ? ”-..?! - lated variables such as value added and food consumption) changes direction when DT = DTX = .01 (Table III.13). The somewhat uniform behavior (i.e. showing diminishing returns throughout the decrease in DT) of the other variables may indicate that the exceptions are due to modeling or pro- gramming errors. Similarly with the substantial qualitative change in behavior when DTX # DT (the lower half of Table III.13). Comparing Figures III.1 and III.2 with Figure III.3, we might subjectively estimate .1 as an "optimal" value for DT. For DTX, .5 would seem reasonable. However, it is of extreme interest to reduce computer time as much as possible and still maintain a reasonable approximation; particularly considering the desirability of making large numbers of runs for policy analysis (and Monte Carlo analyses--Chapters 10 and 11). Thus, the Nigeria model 216 .mmHo>0 coHHMHsEHm uanmMMHp How Am¢>9 can AmmeMdv manomxm HmusuHsoHHmm m0 mcoHusHOm oumEonumms H.HHH ousmHm IXBQHBQ . , o.H m mm. H. mo. Ho. I 1 nl H . 1 H H H H H H H H H H H m.m I5.v o.m $4 5.m#. Im.v m.m¢fi lo.m m.MHI IH.m o.vHI IN.m H.vH% #W.m AsoHHHHn me God A m4>sa A .HH.o we mNmOhfl 217 .mmHowo coHHMHsEHm ucmnwmme Mom Aammmo poem mo mOHHm uoxumfi can Amanomo oEoocH oHnmmommHo muHmmo mom mo mcoHusHom mumeonummd m. HHH wuson +xaauan o.H m. mm. H. mo. Ho. H H 1 H H H H H H H H H 1 H H N n ommo.1 Io.mH HNNo.I o.mH NNNo.r owoN mmmo.. ~.om Hmmo.r H.o~ mwmo.r .m.o~ H. oH\uv . A.u»Icomu0m\uc chum dzHaUm 218 .mmHoho coHHMHsfiHm ouch no mco mcHhHm> cmr3 moEHu can coHHMHssHm m.HHH ousmHm § 8 . . . o.H+XBQ m. mm. H. mo Ho Lcoo 400m IoomH IoooH AH . use cabs omNI Iooom XBQHBGB OOMT Icocm a . I . HH.uBvaBQB xBQIBQB 219 as a whole and the southern submodel in particular use M = .25 and DTX = 1.0. P A R T IV TOWARDS A SOLUTION Introduction The objective of the Nigerian Simulation Project, as specified in its USAID contract, was to investigate the fea- sibility of applying the systems science-simulation approach to the problems of development planning. With that in mind, the models developed by the project group--including the southern regional agricultural submodel of an agricultural economy characterized by competition between annual and peren- nial crops--are specifically oriented to policy development and analysis. Chapter 10, in reporting and analyzing the results of a series of policy runs, illustrates how the model could be used in an actual planning situation$/. The chapter also indicates roughly how we might address considerations of the sensitivity of simulated policy projections to data uncertainty. The dissertation concludes (Chapter 11) with a discussion of needed improvements and extensions of the cur- rent model and of the form an implementation and institution- alization of the model might take. l/ In fact, the analysis was made following limited inter- actions with Nigerian policy makers and agriculturalists and later fed back to them. 220 CHAPTER 10 Policy Formulation A system simulation model may be used by policy makers in two principal ways. One is to sharpen his in- tuition and add to his understanding of the real-world system he is concerned with. As discussed in Chapter 9, this may be undertaken with sensitivity analyses. The second application——the formulation of development policies-- 'will be discussed in this chapter. Policy making is a process immersed in uncertainty because it concerns the future. Development policy making is submerged to uncertainty's darkest depths due to the immensely complex (and thus still imperfectly understood) process of economic development. Not only is there uncer- tainty concerning future states of the environment (e.g., weather, world demand for export commodities, international and domestic political alignments) but there is also un- certainty about the future behavior of the time-variant and nonlinear domestic economic system, particularly its response to policy stimuli. System simulation, by modeling specific causal and structural relationships and by pro- jecting time paths of behavior, provides the flexibility necessary to deal with this complexity and uncertainty. 221 222 Once the political process has established the goals of development or the direction development is to take (Chapter 1, above), policies must be formulated for the attainment of those goals. (This process also involves political considerations.) As discussed in Chapter 9, it is highly desirable to develop policies which are relative- ly insensitive to a range of conditions reflecting the uncertainty both of future weather or world market situa- tions, for example, and of the quality of data inputs to the model. As was suggested above, Monte Carlo techniques may be used with the simulation model to enable that kind of analysis of policy options. Since much work remains to be done to provide the model with a Monte Carlo capability (see Chapter 11), this chapter presents an analysis of the results of a series of deterministic policy runs followed by a coarse illustration of policy sensitivity tests. Policy Experimentation Following initial interactions with Nigerian policy makers and experts, a series of seventeen policy experiments were defined and run with the total Nigeria model. Although this dissertation is concerned with the southern regional agricultural submodel, all 17 runs are reported for both regions and the national level. I feel this is justified on two counts. First, the policies tested have national implications, and interregional 223 (North-South) and intersectoral (agricultural-nonagricul- tural) interactions are important contributors to policy consequences. More significantly, however, the organiza- tion of the 17 runs (described below) and of the analysis is in a form particularly relevant for, and useful to, policy makers. As such, a complete presentation (as opposed to covering just the southern-related policies) provides a useful illustration of the application of the system simu- lation model reported here. With some adaptation, the southern (and northern) model can be implemented indepen- dently; however, at present and for Nigeria, their linkage is necessary. Run Definitions and Organization Policy experiments were conducted with 17 simula- tion runs which cover the time period 1953-1995 (Table IV.1). The model is constrained to approximate real con- ditions from 1953-1965 using observed FOB (export) and ;producer prices for that period. The results analyzed here are f0r the period 1970-1995, with policy implementation beginning in 1971. The year 1970 is thus considered the starting time with simulated "initial" conditions. Proé jections are carried as far as 1995 in order to give the long run diffusion responses to the production campaigns time to exert their major impact. With simulation, it is easy to build up the complexity 224 Table IV.l. Policy simulation runs. Run Run No. Sets Run Definition 1 all Standard Run--no modernization of production; normal export taxes and marketing board surpluses. 2 2, 3 Export taxes and marketing board surpluses cut-off at year 1970. 3 2, 3 Export taxes and marketing board surpluses phased-out from 1970—1980. 4 l Tse-tse fly-eradication program from 1971- 1981. 5 2 Production campaigns in cotton and groundnuts from 1971-1981. 6 2 Production campaign in food grains from 1971- 1981. 7 2 Combines Run 5 and Run 6. 8 3 Production campaigns in cocoa new planting, cocoa replanting, rubber replanting and palm replanting from 1971-1981. 9 3 Production campaigns in cocoa new planting, cocoa replanting and palm replanting from 1971-1981. 10 3 Run 8 plus modernization of palm and rubber processing. 11 4 Combines Run 7 and Run 8. 12 4 Run 11 with production campaign in food roots in the Middle Belt from 1971-1981. 13 4 Run 11 with a further improvement in food grains technology after 1980. 14 4 Combines Run 11 and Run 2. 15 4 Combines Run 11 and Run 3. 16 5 Run 11 with half the campaign budget. 17 5 Run 11 with twice the campaign budget. 225 of the combinations of policies tested. Starting with runs to evaluate single policies or programs (e.g., rubber re— planting), we may successively add other policies and programs (e.g., reduce marketing board and export taxes) to investigate interactive effects. In addition, a flexible output format allows us either to look at the behavior of aggregated macro-economic variables or to zero in and in- vestigate the responses on a more micro level. The policy runs are organized to take advantage of these capabilities. The 17 simulation runs are grouped into five sets (Table IV.l) which examine increasingly complex interactions at progressively higher levels of industry and geopolitical aggregation. All five sets include Run 1, the base run, as a standard point of reference. The base run projects likely performance under Current policies, with no programs to modernize production and with export and marketing board taxes maintained at current levels. The tsetse fly has a dramatic impact on the area where cattle can graze in good health and the corresponding size and productivity of the Nigerian cattle industry (and the income accruing to Northern Nigerians). In the first set of runs, Run 4 investigates the results of a tsetse fly eradication program budgeted for £3 million over ten years. (An eradication cost of £100/sq. mile is assumed.) Interactions among cash crops (cotton and ground- nuts) and food crops in the North are focused on in the 226 second set of runs, Runs 2, 3, 5, 6 and 7. Runs 2 and 3 compare the effects of cutting off export and marketing board taxes in 1970 or phasing them out over a tenfyear period. In the remaining runs of this set, these taxes are maintained at recent levels (25 percent for cotton and groundnuts) while various combinations of production campaigns are tested. The total budget for the production campaigns is assumed to be £40 million spread over a 10— year period. (See Figure II.12.) This budget pays for extension salaries, subsidies and overhead expenses. Run 5 simulates programs to increase cotton and groundnut pro- duction via extension efforts to introduce new seed varieties and improved cultural practices, improving groundnut and cotton yields to 1000 and 600 lbs./acre, res- pectively. In this run, groundnuts get 2/3 of the budget, while cotton gets 1/3. The same end (improved cash crop production) is sought in Run 6 via a food grains moderni- zation program (to hopefully release land for cash crop expansion). If food production is being modernized, the model provides for cotton yields to increase as the labor pressure is eased. This reflects cotton being planted earlier in the season. New technologies in food grain production are assumed to increase yields 2 1/2 times. Here, all £40 million go to food grain programs. All three programs--cotton, groundnut and food grains--are 227 then combined in Run 7, where the budget is split 40 percent, 20 percent and 40 percent to groundnuts, cotton and food, respectively. Agricultural policies and programs aimed at the southern ecological region are examined in simulation Runs 2, 3, 8, 9 and 10. Runs 2 and 3 again compare the conse- quences of cutting off export and marketing board taxes or, alternatively, phasing them out. Normal levels of market- ing board taxes are assumed to be 20 percent for the three c0mmodities handled by marketing boards (cocoa, palm oil and palm kernels), while export taxes for those three and rubber are 20 percent, 15 percent, 15 percent and 15 per- cent, respectively. Runs 8, 9 and 10 investigate production campaigns in the perennial crops and efforts to improve the processing methods for oil palm and rubber products. The production campaigns assume a budget of £40 million over 10 years to pay for extension salaries, subsidies and overhead expenses. Run 8 involves a modest cocoa new planting program and replanting programs for cocoa, palm and rubber. The budget is split among these programs 10 percent, 30 percent, 40 percent and 20 percent, respectively. Of the 40 percent in the palm replanting program, 25 percent is used in the areas where palm competes with rubber, and 75 percent is applied to areas where palm has no perennial competitors. .Run 9 attempts to highlight the interactive effects of the 228 oil palm-rubber competition (in comparison with Run 8) by not conducting the rubber replanting program and devoting that portion of the budget to palm replanting. The assumed yields at maturity (in lbs./acre-year) for new planted cocoa and replanted cocoa, palm and rubber are 950, 850, 6700 and 1000, respectively. The model provides for these yields to gradually increase 20% as farmers gain experience with the new methods of cultivation involved in modern production. Finally, Run 10 adds investment in modern processing facilities for oil palm and rubber products to the pro- grams of Run 8. For palm this means Stork hydraulic presses, while for rubber it means crumb factories. The investment rate is established at £100 thousand and £200 thousand for palm and rubber respectively, until a prespecified level of transformation has been reached (50 percent for palm and 100 percent for rubber). While rubber processing is being transformed from sheets to crumb, the model simulates a gradual increase in the domestic industrial demand for crumb rubber up to 50 percent of production. While the first three sets of runs focus on industry- or region-specific policies, the fourth set of runs, Runs 11, 12, 13, 14, and 15, examines aggregate and interactive effects of agricultural development policies and programs in both the North and the South. Run 11 combines Runs 7 and 8 so that the following production campaigns are carried crut simultaneously at the same budget levels (£40 million 229 in each of the North and the South) and the same commodity proportions as specified above: modernization of cotton, groundnuts and food grains in the North, and new planting of cocoa and replanting of cocoa, palm and rubber in the South. Run 12 speculates on the impact of modernizing food production (roots and tubers) in the Middle Belt area of the North in addition to the modernizationprograms dis- cussed above. In this way, we can specifically investigate the implications for regional specialization, i.e., the South specializing in perennials and relying on the North for food. The word "speculates" was used above since the modernization of root and tuber food production depends on the development of the requisite technologies, which de- velopment is not presently on the horizon. Another speculation is made in Run 13. Running the programs specified in Run 11, a further doubling of food grains yields is assumed to diffuse over a period of four or five years after 1980 as a result of new techno- logies which may be developed in the next ten years by national and international research stations. Thus, :modern food yields after 1980 are assumed to be potentially five times the current traditional yields experienced in northern Nigeria. This experiment investigates the poten- tial effects on exports (due to cash crop interactions), food prices and consumption. Finally, Runs 14 and 15 combine the production 230 campaigns of Run 11 with the export and marketing board tax policies of Runs 2 and 3, respectively, i.e., the alternatives of cutting off and phasing out these taxes. The last set of runs, Runs 11, 16, and 17, examines the relative consequences of alternative levels of the campaign budgets (RMAX in Figure II.12). In this way, we can address the question of whether it would be worthwhile to intensify (or de-emphasize) modernization promotion efforts. That is, would likely gains be worth the added expenditures? Or, would the savings from decreased ex- penditures (saying nothing about alternative uses for the resources) be worth the projected production losses? Run 1, the standard run, has zero budgets, of course. Run 11 has budgets of £40 million each in the North and South, allocated among the programs, as indicated above. Run 16 halves this budget, while Run 17 doubles it, always with the same proportional allocations to the specific campaigns. The following sections analyze and graphically portray the results of these 17 runs. Policies Related to the Cattle Industry Run 4 simulates a lO—year tsetse fly eradication program budgeted at £3 million. This analysis does not consider other livestock programs or their potential inter- actions with other agricultural policies and programs due 231 1/ to limitations of the current model— . Animal populationsZ/, sales and resultant incomes all rise as might be expected (Figures IV.l and IV.2). Fly- free grazing land (Figure IV.3) experiences a dramatic in- crease, and the general range conditiong/ improves substan- tially over the base run (Figure IV.4). In every case, however, the gains attributed to the fly eradication program in Run 4 are temporary in the sense that these performance variables, after an initial increase, return to the same trends as experienced in the base run, although at a higher 13331. By 1995, the slopes of the results of Run 4 are all either the same as the slopes of Run 1 results or are approaching these slopes. Thus, the animal population (Figure IV.l) increases rapidly as new grazing areas are opened up. Once these new areas have reached their animal capacity, male and female populations grow at the same rate as in the base run. This causes l/ The study by Kellogg in 1971 [26] examines some ad- ditional considerations on mortality loss, marketing costs, etc. which could be incorporated into the model for a more comprehensive analysis of this program and others related to the cattle industry. 2/ The initial (1970) cattle p0pulation assumed in the model is about five million head (Figure IV.1). Although this figure.is somewhat below current estimates of Nigeria's cattle herds, the relative results of Runs 1 and 4 are still valid. 2/ "Range condition" is defined as an index of range land grass yields and reflects the effects of overgrazing. That is, its value at any time during the simulation period (1970-1975) is the ratio of grass yields at that time to grass yields at the initial time (1970). 232 sales and incomes (Figure IV.2) also to experience the same growth rates as in Run 1 after the initial spurt. The amount of fly-free grazing land experiences a dramatic increase from 1975 to 1985 as a direct result of the eradication program (Figure IV.3). After 1985, however, grazing land declines at the same rate as in Run 1 due to the expansion of crop lands. Similarly, the decline in range condition due to overgrazing (Figure IV.4) is slowed substantially as new areas are opened up and the grazing pressure eases. By 1995, the cattle population is grazing even these new areas to capacity, and the range condition continues to decline at the same rate as in the base run. The conclusion to be drawn from this is that the fly eradication program has merely "bought time." The dete- rioration of overgrazed ranges has been delayed, not halted (much less reversed). The loss of grazing land to crops continues in Run 4 at the same rate as in Run 1. The anie mal population growth rate (and hence the growth in beef and milk supplies) is the same after the eradication pro- gram as before. This is not to say there shouldn't be a fly eradi- cation program. This program does have substantial short run results. However, the time gained by it could be used to carry out programs which will have more long-lasting results. Indeed, other programs, such as grazing reserves, might not even be feasible without the prior elimination of the tsetse fly. Cattla Population (union toad) 233 m mamas 3,0 __ 1. Continuation of proaaat ttaoda and poliaioa (tho baaa m). 4. Fly Indication prawn. 3.0 P. 2.’ ... Ru 4 II! 1.0 P M 1 a it I 01910 1911: 19100 1910: To!“ xiii—— Fig. 11.1 Cattla population of salad (no ad 1.100 (FY). 1970-1993. with ad without a fly atadioatioa PW.- Cattlo Incona (nillion ilyr.) 234 III “III!!!” 24 L- 1. Continuation of praaont tronda ad poiicioa (tho baao ta). 4. Fly oradioation pronta. Ia ‘ 22 20 18 16 _ 14 .- 12 .. 10 P l o I l l L l l 1910 1975 mo 1!” 1990 1995 '1!- IV.2 Cattlo iaooa (ton ainai aaloo an) ad nilk M. 1910-1995, with ad without a fly otadioation pron-a. Grazing Land (nillion acraa) 235 In! DIFIIITIOIS 1. Continuation of praaont tranda and policiao (tho baoo ran). 4. Fly otadication prograa. 40 _. Run 4 30)— 20 _. Run 1 10 _. i 0T 1 1 1° 1 l 1970 1975 1980 1903 1990 1 :13. IV.3 Ply-tron [toning 1and, 1970-1995. with and without a fly otadioation stout-n. Range Candi tion (proportion) 236 1.0 hill 03erle l. Continuation of proaant tronda and policioa (tho baao run). 4. Ply oradication program .9 L .8 *— Run 4 .7 '— llun 1 Ji- 0" 1 L l L L 1970 1975 1900 1905 1990 1995 Fig. 19.4 Raga condition indax (tho ratio of raga lad graaa yialda at a point in tia to than yiola at tho initial tia, 1970). 1970-1995. with and without a fly oradication pmra. 237 Northern Regional Policies The set of runs which investigates the consequences of policies and programs relevant to northern Nigeria includes Runs 1, 2, 3, 5, 6 and 7 as defined above and in Table IV.l. Briefly, these runs respectively project present trends and policies (the base run), cut off market- ing board and export taxes, phase out marketing board and export taxes, implement production campaigns in cotton and groundnuts, implement a campaign to modernize food grains production, and examine production campaigns in all three commodities--cotton, groundnuts and food grains. As expected, the elimination of taxes stimulates agricultural production and incomes. Value added in agri- culture improves slightly over the base run (Figure IV.5), as do exports (Figure IV.6)l/. The more immediate stimulus of cutting off taxes (Run 2) initially causes higher exports and value added than Run 3 (phasing out taxes), but also a slightly higher food price (Figure IV.9) for the nonagricul- tural population. Disposable agricultural worker incomes (Figure IV.7)Z/ markedly increased over the base run due in part to the higher producer prices for cash craps and to i/ The large negative foreign exchange shown in Figure IV.6 is due primarily to projected import demands of the textile industry being charged to cotton exports. In addition, about 10-20 percent of the indicated imports is beef for consumption. -3/ Disposable income in Figure IV.7 (and Figure IV.15) includes wages earned but is net of agricultural sector debt service and interest. 238 slightly higher food prices£/. The major contributor to increased incomes, however, is the greatly increased (over the base run) cash food sales to the South to meet the higher agricultural and non- agricultural demands for food. Southern agricultural EEEE food demands increase as the agricultural sector reduces its desired level of subsistence in response to higher cash incomes resulting from the export crop tax reductions. In addition, Southern nonagricultural food demands rise due to the rise in nonagricultural income resulting from the greater demands for nonagricultural goods and services ge- nerated by the increased agricultural income (called multi- plier effects, below). The long run results of Run 2 are similar to those of Run 3. After 1980, when marketing board and export taxes are zero in either policy situation, food consump- tion by the nonagricultural population (Figure IV.10) shows a substantial rise as the increased agricultural incomes from Runs 2 and 3 begin to have their multiplier effects on nonagricultural incomes. Later, higer food prices cause nonagricultural food consumption to approach the same level as in the base run. Figure IV.10 indicates steadily falling nonagri- cultural food consumption in all runs (as do Figures IV.17 l/ Food acounts for about 90 percent of agricultural value added in the North. ' 239 and IV.2? below). These results must be interpreted with caution. They represent only staple food consumption, and do not incorporate other sources of nutrition such as fish, meat, fruits and vegetables. As nonagricultural incomes rise, we might expect to see an increasing substi- tution of these items for the staples treated in the model. The modernization of cotton and groudnut production (Run 5) substantially improves the performance of all the variables observed compared to both the base run and the runs eliminating taxes. Foreign exchange increased the most (Figure IV.6), about 30 percent over Run 1. Since food crops rather than export crops dominate northern agri- cultural production, other variables, such as value added (Figure IV.5), income (Figure IV.8) and, hence, food con- sumption (Figure IV.10) show a less dramatic increase. Marketing board revenues (Figure IV.7) show a 150 percent increase by 1995. Run 6 examines a program to modernize food grains production. Indeed, foreign exchange and marketing board revenues do pick up (over the base run) as land and labor are released for cash crop production. The difference is less pronounced at the end of the run (1995) than earlier in the simulated time period as the initial reduction in total food land is gradually reversed to meet the subsis- tence demands of the expanding agricultural population. Throughout the time period 1970-1995, exports and marketing 240 board revenues in Run 6 are below those of Run 5 where cash crop production is directly transfbrmed. This can be explained by the slower diffusion of food modernization (compared to cash crop modernization diffusion) which is built into the model. A larger promotion effort (budget) would stimulate a quicker response to food modernization and, hence, a larger effect on cash crop production. I In Run 7, promotion efforts are conducted in cotton groundnuts and food grains simultaneously. Most output variables compound the increases of Runs 5 and 6 over the base run; the results in Run 7 are more than the mere ad- dition of these increases. Marketing board revenues (Figure IV.7) provide a striking example of this. Revenues in 1995 in Run 7 are 200 percent greater than Run 1 while revenues in Runs 5 and 6 are 150 percent and 15 percent greater, respectively. This is due to the fact that cash crop production, which has expanded onto former food land as a consequence of food modernization, is itself modernized in Run 7, further augmenting the positive results of Run 6. In addition, and more significantly in the long run, the modernization of food in conjunction with cotton and ground- nuts allows more timely planting of the cash crops, result- ing in even higher yields for the modern varieties than would otherwise be obtained. Food prices are lower in Run 7 than in any other run. This effect is more than offset, however, by the Vail. Addad (Iillion t/yr.) 241 tun DEFINITIONS Continuation of proaont trund- and policioa (hao run). Cut off not-hating hoard ad anport tom. 3. Photo out urinating board and orport tanoa. 13¢!) )— 5. Hodorniao cotton and groumhut production. 6. Modomiao food lraino production. 7. Hod-min cotton. .romdnut and food grain production. H 8 1 .~ :- 1 l l J l 1910 19 7S 19cc 1905 1990 1995 fig. ".5 Total valua addod in ariculturo in tho lorth. 1970-1995. ador varioua policy conditioua. Mricultural Exports (nillion I/yr.) 242 Run 2 fl“ 3 50 U Iuna 5.7/ Inn 6/ -50 .—. [UN DEFINITIONS -100 — l. Continuation of proton: tronda and policioa (hoaa m). 2. Cut off narkoting hoard ad oxport taxoa. 3. Photo out n:rkcting board and -150 '— export tan 5. Hodornito cotton and groundnut production. 7 6. Modorniao food graina production. 7. Hodorniaa cotton. groundnut and food [raino production. -200 .— Run 5 -250 — -300 - Iau 2.3.6 450 l l l l l 1910 1975 1950 1985 1990 1995 Pin. IV.6 turnip onchanga fro. unrthoru agricultural oxporta (includin; iaorta oi outta and boot). 1970-1995. Indor warioua policy audit Harkoting hoard lawcnuea (nilliona ilyr.) 70 60 lot) 243 RUN DEFINITIONS ' FE} l. Continuation of proacnt tronda and policioa (haao run). 2. Cut off narkoting board and oxport ta" Run 7 3. Phaao out narkcting board and oxport taxoa. 5. Hodotniao cotton and groundnut production. 6. Hodorniro food Iratna production. 7. liodornito cotton, Izroundnut and food gralna production. 3. he? “...—.1 .... ...-a. 4*“ 1.... a—H-p— ‘1?" _. . Run ) 20 10 /'Run3 [11142.3 1 * l l J 0 1970 1975 19” 1985 1990 . 1995 Fig. IV.7 Total narhoting hoard not rawonuoo tron uorthorn co-oditioo, 1970-1995, undor varioua policy conditiona. Diapoaablo Incoa pot Horkcr (I'luorkur-yr.) 244 h _ Runs 5,] I’lllNuun 1.3 1,6 30 *— 25 ‘- NUN DEFINITIONS 1. Continuation of praoont tronda and policioa (haao run . 2. Cut off norkcting hoard and oxport 15 a. 3. Phaao out narkating board and axport taxoa. 5. Nodarniro cotton and groundnut production. 10 __ 6. Nodornita food graina production. 7. lbdorniao cotton, groundnut ad food graina production. 5 I— 9 I I I I I 1970 1975 l900 1905 1990 1999 fig. IV.8 Diapooahlo incoa par agricultural workor in tho North, 1970-1995. Indor varioua policy condition. Price of Food (£l1h.) 245 IUN DEFINITIONS '015 —' l. Continuation of proaont tranda and policioa (haaa run). 2. Cut off uarhoting board and axport Run 2 taxao. I. 3. Phaoo out narhoting hoard and ’raunl 3.5 01“ __ oaport tanaa. Run 1 ’ S. Hodorniao cotton and groundnut production. Run 6 6. Hodorniao food graina production. 7. Nodorniao cotton. groudnut ad food graina production. Run 7 .013 1.5.6.7 .012 .011 .010 .009 do T I I l I i 1970 1975 1900 1985 1990 1995 Fig. IV.9 Narhot prico of food in tho North. 1970-1995, undor warioua policy conditioua. Caloric metion pat Capita (thouaand calorica/peraon-yr.)_ 650 — 640 030 020 246 M DEFINITIONS 1. Continuation of proaont tronda and policioa (haac run). Cut off narkoting board and oxport tanao. Phaao out not-hating board and oxport tanaa. Nodorniao cotton and groundnut production. Nodorniao food graina production. Hodorniao cotton. groundnut and food graina production. 610 I" m 5,6,7 ./ ' la 1 000 '— 590 ’— lun 7 son "" tuna 5.6 - l '2 L 1 1 l l 19 70 1975 1900 1905 1990 1995 '18- “.10 Caloric coaation (of ataplaa) par capita of tho northorn nonagricultural population. 1970-1995. ador varioua policy conditiona. 247 :increased productivity of food so that value added and in- <:ome are slightly higher in Run 7 than Run 5. The lower :food prices coupled with increased nonagricultural income result in higher nonagricultural food consumption (Figure IV.10). Southern Regional Policies The set of runs which investigates the consequences of policies and programs relevant to southern Nigeria includes Runs 1, 2, 3, 8, 9, and 10 as defined earlier and in Table IV.1. Briefly, these runs respectively project present trends and policies (the base run), cut off market- ing board and export taxes, phase out these taxes, implement production campaigns in all three perennial commodities (cocoa, palm and rubber), implement production campaigns in cocoa and palm only, and implement the same programs as Run 8 simultaneously with investments to modernize and transform palm and rubber processing capacities (to Stork presses and crumb factories, respectively). Run 10 also assumes the domestic demand for crumb rubber increases gradually to 50 percent of production. The most striking observation that can be made about Runs 2 and 3 (cutting off and phasing out taxes) is not that the long run results are virtually identical, for taxes are eventually zero in both cases. Nor is it that incomes, value added, exports, etc. are initially higher than the other runs and consistently higher than the base 248 :rnin--the reduction in taxes represents an immediate increase in producer prices, whereas there is a delay involved for tihe perennial modernization programs to show results. This Cieday is due to the natural gestation and maturation lags c>f the perennials and the longer lags before the innova- 1:ions are diffused beyond the direct promotion results. trhe most striking observation concerning thd behavior shown in Runs 2 and 3 is that value added, exports and in- «come (Figures IV.1l, IV.12 and IV.15) are relatively higher initially in Run 2 than_in Run 3; while later in the simu- lated time period (after about 1978), they are relatively higher in Run 3 than in Run 2, finally approaching the same steady state levels in both runs. Run 2 should indeed have higher results initially since producer price increases are immediate. The short term supply (harvest) response is sharp initially, and then tapers off, ultimately returning to normal levels as farmers gradually come to regard the higher prices as "normal." Exports begin to increase again after 1980 (Figure IV.12) as the long term supply (plant— ing) response to the higher prices becomes increasingly dominant, finally tapering off again as acreage has expand- ed to its limit (as in the base run) and production from aging traditional trees falls. In Run 3, prices rise steadily over a lO-year period while taxes are being phased out. Thus, the harvest response is lower than in Run 2. However, it lasts longer 249 since the new price (achieved when taxes have finally been eliminated) is not seen as "normal” by the farmers until ' Zlaiter. Therefore, while exports in Run 2 taper off, the luearvest and planting responses reinforce each other in Run 3. Eventually, however, the acreage limits are reach- caca, the natural aging process decreases yields, and the JJong run results of Runsx2 and 3 are virtually the same (Figures IV.ll, IV.12, IV.14, IV.15). Although long run exports, when taxes are removed, aare virtually the same as in the base run (due to capacity .limits and aging traditional trees), the higher prices Ikeep long run value added and income per worker (Figures vall and IV.15) higher than the base run. Per worker income falls during the latter part of the runs because the labor force is growing faster than income. The increased agricultural incomes, via multiplier «effects on nonagricultural incomes, cause a higher con- Isumption (in Runs 2 and 3 than in Run 1) of staple calories be the nonagricultural population through most of the simulated time period (Figure IV.17). As incomes stabilize in the long run, however, the higher food prices associated 'with Runs 2 and 3 result in lower nonagricultural staple food consumption. Comparing Runs 8 and 10 (production campaigns in the three major perennial commodities without and with modernization of palm and rubber processing), some 250 iJnteresting observations can be made. Value added (Figure IV.11) and marketing board revenues (Figure IV.13.) are Iiigher in Run 10 than in Run 8 due to the increased techni— <:a1 efficiency of oil palm and rubber processing facilities. VVhile palm oil exports are also substantially improved (Figure IV.14), total exports (Figure IV.12) are lower due 1:0 the assumption in Run 10 that the domestic demand for :rubber increases to 50 percent of production over a 15- jyear period, thus reducing rubber exports (which don't pass through a marketing board, thus not diminishing marketing board revenues). Indeed, exports arg_initially higher in Run 10 while domestic rubber demand is still low. In spite of this increased production, incomes in Run 10 are lower than in Run 8 (Figure IV.15). The reason is that palm oil processing with the Stork hydraulic presses, 'while technically more efficient (i.e., more oil is extracted per pound of fruit), is economically inefficient. That is, the increased processing costs outweigh the revenue from increased production, thus making palm processing unpro- fitablel/. The centralized crumb rubber factories, on the other hand, prove to be substantially more efficient-- economically as well as technically--than the traditional y The transformation of processing takes place in the model irregardless of its profitability. It is carried out solely by an exogenous (policy) investment. The model's rudimentary processing component would have to be expanded to more realistically simulate investment decisions (Chapter 4). Valut Added (N11110:: ilyr.) 251 900r- RUN DEFINITIONS 1. Continuation of prooont tronda ad policioa (baao an). 2. Cut off narhoting hoard ad oxport taroo. 3. Fhaao out (ovar ton yaara) r m 10 narhoting hoard and onport taaoa. . 800- 8. Now plant cocoa and roplant cocoa. ' “n 9 pain and ruhhor. 1! 8 9. Now plant cocoa and roplat cocoa “a ad paln. 10. Now plant cocoa. roplant cocoa. pain and ruhhor and nodarniao . 2 3 pala and ruhhor procooaing. ' Run 1 700*- 600%- Run 1 500 — la 2 \ \Run 3 400 - \ Iuna 8.9.10 I... L i .1 I I I I I 1970 1973 1900 1905 1990 1995 Fig. “.11 total waluo addad in agriculturo in tho South. 1970-1993. ador wariouo policy caditioaa. Agricultural Exporta (Million i/yr.) 252 RUN DEFINITIONS 250 _. 1. Continuation of proaont tronda and Run 9 policioa (haao run). 2. Cut off oarhoting board and oxport Run 8 tarot. 3. Phaao out (owar tan yaara) Run 10 narkoting board and oxport tau. 8. Now plat cocoa ad roplat cocoa. pain and ruhhor. 9. Now plant cocoa and roplant cocoa and pain. 10. Now plant cocoa. roplat cocoa. paln ad ruhhor and nodarniao 200 .— paln ad ruhhor procuring. IsoI" lluna 1.2.3 100I 0L 1 1 l l l 1970 1975 1900 1985 1990 i 1995 Fig. IV.12 Foraign orchaga iron aouthorn agricultural oaporta. 1970-1995. Indor warioua policy conditiona. Narkoting hoard Iawonuoa (Nillion ilyr.) 253 Run 9 INN DEFINITIONS w I— l. Continuation of prooont trada and m 10 policioa (haao run). 2. Cut off narkoting hoard ad oaport M 3 tarot. 3. Fhaao out (our ton yoara) 35 __ oat-hating hoard ad axport tau. 8. Now plant cocoa ad roplat cocoa. polo and abhor. ‘ 9. Now plat cocoa ad roplat cocoa ‘ and pain. 10. Now plat cocoa. raplant cocoa. 30 __ paln ad ruhhor ad oodorniao paln and ruhhor procaaaiug. 25 r- Run 1 20 I— ,/\ u i.- m 3.9 10 - hu: 3 / 5 - la 2 \luno 2.3 o \ L l L l 1970 1973 19” 1909 1990 1993 Fig. IV.13 l'otal oat-hating hoard not rowaua tron aouthorn coaoditioa. 1970-1995. adar variou- policy conditiono. Falo Oil Exports (Nillion t/yr.) 15 10 -10 -15 -20 r I9 70 254 / \m :0 \ \\ E / m DEFINITIONS 1. Continuation of proaont tronda and policioa (halo rm). 2. Cut off oat-hating hoard and oxport taut. 3. Fhaoo out (owor ton yoara) oarhoting board and orport tanao. 8. Now plant cocoa ad roplant cocoa. palo and ruhhor. 9. Now plat cocoa ad roplant cocoa 7 ad polo. 10. Now plat cocoa. roplant cocoa. polo ad ruhhor and oodorniao polo ad abhor procoaaing. /Run1 2.3 l l l L 1 1975 man 1905 1990 1995 Fig. “.14 Foroia orchaga tron palo oil orporta. 1970-1995. ador varioua policy conditiona. Diapoaahlo lncooa par Norhar (Ilworkcr-ycar) 255 EON DEFINITIONS 1. Continuation of proaant tronda and policioa (haao run). 2. Cut off oarhoting hoard and export taaaa. 3. Fhaao out (owar ton yoarn) oarhoting hoard and axport taxca. M 2 8. Now plant cocoa and roplant cocoa. ///F' polo and ruhhor. 9. Now plant cocoa ad roplant cocoa /' Inn 3 ad polo. 10. Now plant cocoa. roplant cocoa, pain and ruhhor and oodorniao polo-and ruhhor procoaaing. 30L. Inna 8.9 Iona 8. 1 10 25 \ 10 g 3 " 8.9.10 nun 2 'un 1 20*— i d3? 1 l L I L 1970 1973 1980 1985 1990 1995 Fig. IV.13 loal diopooahlo incooo par agricultural worhor in tho South. 1970-1995. undar varioua policy conditiona. Frico of Food (II/1h.) 256 .020 ‘— .019 F— .018 '— M9 .017 '— .016 F" 1. RUN DEFINITIONS Continuation of proaont tranda and policioa (haao run). 2. Cut off oarkoting hoard ad oaport .015 — (m. 3. Fhoao out (ovor ton yoara) oarhoting hoard ad aaport taaao. 8. Now plant cocoa ad roplat cocoa. polo ad rahor. .014 r- 9. Now plant cocoa and roplat cocoa ad polo. 10. Now plat cocoa. roplat cocoa. palo ad rtbhor ad adorniao palo _. and ruhhor procaaaing. .013 .012 .011 I- AL. ,1 I I I e I L 1970 1973 19m 1985 1990 1999 Fig. IV.16 lbrhot prion of food in tho South. 1970-1993. adar warioa policy caditiooa. Caloric ConIqution Per Capita (1.000 calories/person-yr.) 257 010 '- 600 580 570 $50 560 530 520 510 Fig. - riunlo m2 F‘ / Ru 3 /- n ’ / _ 4 BUN DEFINITIONS __ 1. Continuation of prnaant tranda and policioa (haaa run). 2. Cut off Iarkoting board and export taxaa. 3. Phaae out (ovar tan yearn) r- narhating hoard and export tanaa. u 8. New plant cocoa and roplant cocoa. Run- 8'9'1 pain and ruhhor. 9. New plant cocoa and roplant cocoa __ and paln. 10. Jan plant cocoa, roplant cocoa. Run 1 paln and ruhhor and nodarniaa pal- and ruhhor procaaaing. 'una 2.3 .Jv T I L I I I 1970 1975 1930 1985 1990 1995 IV.17 Caloric canon-ption (of ataplaa) par capita of tho aouthorn nonagricultural population. 1970-1995, undar varioua policy conditions. 258 sheet—making facilities operated on the village level. Run 9 was an experiment to investigate the conse- quences of increasing the palm replanting effort at the expense of rubber in the crop sector where the two peren- nials compete. Indeed, palm oil exports do improve substan- tially over Run 8 (Figure IV.14). Value added and total exports are also higher in spite of the still traditional rubber production. It is interesting to note that value added, exports, marketing board revenues and income per worker all are lower in Runs 8 and 9 than in the base run for about the first six to eight years of the simulated time period (1976-1978) before rising to substantially improved levels. This is due to the replanting programs removing trees from production and the gestation lag which occurs before the new trees come into production. Nonagricultural food consumption is higher in Runs 8, 9 and 10 than in the other runs (Figure IV.17) due to the multiplier effects of increased agricultural incomes (Figure IV.15) on nonagricultural incomes and due to slightly lower food prices (Figure IV.16). Policies Viewed on the National Level The fourth set of runs, Run 1, 11, 12, 13, 14 and 15, examines the results of agricultural development poli- cies and programs at the national level. Briefly, Run 1 projects present trends and policies (the base run); Run 11 259 implements production campaigns in cotton, groundnuts, food grains, cocoa, palm and rubber; Run 12 implements a program to modernize food roots in the Middle Belt in addition to the above programs; Run 13 investigates the effects of, in addition to the programs of Run 11, the diffusion of a further doubling of food grains yields beginning after 1980; Run 14 implements the programs of Run 11 with a cut—off of taxes; and Run 15 does the same as Run 14 except with a phase-out of taxes. ‘ Coupled with the modernization programs, the eli- mination of marketing board and export taxes substantially enhances the results of the modernization programs in the presence of these taxes. Figures IV.24 and IV.25 indicate that, while both total exports and total imports increase in Runs 14 and 15 compared to Run 11, exports experience a relatively greater rise, leaving Nigeria with a more favor- able balance of payments. Similar increases are seen in other variables, such as GDP (gross domestic product, assuming marketing board and export tax revenues are not put to productive use), value added in agriculture, and agricultural exports (Figures IV.18 through IV.21 and IV.23). Nonagricultural food consumption is higher in Runs ll, 14 and 15, with modernization, than in the base run (Figure IV.27). This is due to the multiplier effect of increased agricultural income on nonagricultural income, 260 i.e., increasing agricultural demand for consumer goods from the nonagricultural sector. Run 12 was an attempt to speculate on the conse- quences of increased production of food root crops in the Middle Belt (assuming improved technology to be available).. The indications are that the South would tend to specialize in exports while importing food from the North. Shipments of food increase about 56 percent by 1995 over Run 11. However, this results in much lower food prices (Figure IV.26) rather than the substitution of perennial production for food production; Southern agricultural exports remain virtually the same as Run 11 (Figure IV.21). This can be attributed to the current model's limitations, specifically the one which constrains the transfer of food land to perennial production (Table 11.1, Chapter 3). Without this restriction, we would see a move to export speCiali- zation in the South in the presence of a secure food supply from the North. The lower food prices do lead to a dra- matically higher level of food consumption by the nonagri- cultural population (Figure IV.27). An interesting observation can be made concerning agricultural value added and gross domestic product (GDP) (Figures IV.18, IV.19 and IV.23). Such a large pr0portion of value added and GDP is derived from food production (about 80 percent for agricultural value added and 30 percent for GDP) that these variables at current prices 261 are depressed in Runs 11 and (particularly) 12 due to lower food prices (Figure IV.26). In "real” terms (i.e., relative. to food prices in the base run), Runs 12 and 11 would show even greater improvements over Run 1, with Run 12 probably taking the lead. Modern food grains yields in the North were gradually doubled in Run 13 over a four to five-year period after 1980 (i.e., to five times the current traditional yields) to in- vestigate the consequences of the introduction and diffusion of new technologies expected to be developed during the 1970's. The results show that exports (Figure IV.20) and marketing board revenues (Figure IV.22) do improve subs- tantially over Run 11 after 1980. Value added also increases slightly (Figure IV.18). However, by the end of the simu- lated time period, the results of Run 13 and Run 11 become quite similar. The initial increase in cash crop acreage, resulting from labor and land freed from subsistence food production, is later reduced as the population continues to expand and more food land is required. Value added in Run 13 (Figure IV.18) eventually falls below that of Run 11 because of the somewhat lower food prices. The effect on southern exports is nil (Figure IV.21), while the lower food prices cause southern value added to fall slightly and nonagricultural food consumption to rise. Note that value added in the North rises more than twice as fast as in the South (Figures IV.18 and IV.19). Valuo Add-d in Northarn nut-mur- human an.) 262 m Domino-Is 1. Continuation of prooont trondo ad policioa (hao run). W 11. Production cqaiao in cotton. proadnuta. food graino. cocoa pain and ruhhor. ‘ 15 12. Production main in food 1 ’ rooto in tho Niddlo Iolt. in addition to tho pron- of la 11. ”ML 13. Dublin; adorn food grain yioldo aitor 19m. in addition to tho progr- 1‘. Cutting on narhatin. hoard ad oxport tanoa, in addition to tho progr- of m 13 Run 11. 1100'- 15. Phaoin. out narhoting hoard ad M 1 I onport tanoo, in addition to tho progr- of la 11. . 12 900- no .- / la n 500 '- \- la 15 300 ‘- Av at L l l l l 1970 ‘1913 19') 1903 1990 1995 Fig. IV.18 Total oalno addod in northorn agriculturo. 1970-1995. ador various policy condition. valuo Addod1n Southorn Agriculturo (Killian ilyr.) 263 RUN DILHNI‘I'NN‘S 11.15 I. Continuation of prooont tronb and policioa (haoo rm). 11. Production mains in cotton. 800‘- groudnuto. food praina. cocoa. pal- ., 11 ad ruhhor. 12. Production main in food rooto Run 13 in tho Hiddlo Bolt. in addition to tho program of In ll. 13. Douhling adorn food graino yioldo aftor 19cc, in addition to tho m 1 700(- prograoa of In 11. 16. Cutting of! narhotina hoard ad onport tauo. in addition to tho progr- oi la 11. 15. Phaaing out narhoting hoard ad oaport taco. in addition to tho prooraa of Run 11. Run 15 600‘. la 1 50m- Iun u / 40°F / Ian 11.12.13 300 - J. 0L 1 l I J l 1970 1973 19” 1905 1990 1995 Fig. IV.19 total Voluo addod in aouthorn agriculturo. 1910-19”. ador variou- policy conditiono. Inrtharn Agricultural motto Olillion 2hr.) 264 so )- Ia 13 o ". -50 b I. ornament 16.15 1. Continuation of praoant trando ad -100 _ policioa (haoa ta). 11. Production again in cotton. proadnutn. food graino. cocoa. pa1n ad rahar. 12. Iraduction c-aia in (and rooto in tho Iliddla halt. in addition to 4,0 _, tho pron. at In 11. 13. Donhlin. nodnrn (and praino yiala altar man. in addition to tho ... 12,13 propr- ot la 11. 1‘. cutting oil narhatin. hoard ad 3. u aaport tanna. in additia to tho .2” __ pron- of In 11. 13. bail. out narhotin. hoard ad apart tanno. in addition to tho propr- oi la 11. -230 '- non" ha 1 - 1 l A L l l 1910 1913 19” 1903 1990 1995 Fig. IV.20 loraia anchmn iron not-thorn agricultural aaporco (including iaorto of cotton ad haai). 1970-1995. adnr variouo policy conditiono. Southarn Agricultural Inporto (Killian ilyr.) 265 Ill Dill! 1710.8 1. Continuation of prnoant trada ad policioa (haoa run). 250*- 11. Production caaaigno in cotton. groudnuta. food graino. cocoa. in tha lliddla halt. in addition to tho prograo of In 11. 13. Doubling nodarn food groino yialda altar 1930 in addition to tho progr- oi In 11. u. Cutting of! lactating hoard ad onport tanao. in addition to tho progr- o! la 11. 200 _ 15. Phaing out narhoting hoard ad onport tanno. in addition to tho progr- paln ad ruhhor. m “'15 12. Production caaaign in load rooto luno 11.12. 13 of I. 11. Inn 15 150 '- ——lun 1 14. 1” 0T 1 1 l l l 1970 1973 19') 1905 1990 1995 Pig. IV.21 Poraign anchagn iron aouthorn agricultural arporta. 1970-1993. ador varioa policy caditiono. 266 .. 13 ll. annuals . 12 l. Continuation of proaant trondn ad " 11 100 "' policioa (hano run). 11. Production caniao in cotton. 12. Production maign in food rooto in tho Iiiddla halt. in addition to tho progr- of an 11. 13. Doubling nodarn food groino yialdo aitar 1900. in addition to tho . prograo at In 11. 1‘. Cutting oii narhating hoard ad aaport tanno. in addition to tho progr. oi Inn 11. 15. Phaoing out narhoting hoard ad onport tanon. in addition to tho progr- oi ion 11. so u I llarhoting Ioard Invanuaa (Killian ilyr.) I /- 1o . 15 l 1 1970 1915 19” 1935 ’ 1990 1995 Pig. IV.22 Total anthotiog hoard not rooanuno tron northnrn ad aouthorn co-aditiaa. 1910-1993. adnr oarioa poiicy conditionn. 0 ‘ Grooo Donnotic Product (Hillion t/yr.) 267 RUN DEFINITIONS ‘ 1. Continuation of prooont trondo and ‘ 15 5000 L. policioa (hana run). 1 ' 11. Production canpaigno in cotton. groundnuto. food groino, cocoa. pain and ruhhor. 12. Production calpaign in food rooto in tho Niddla Bolt. in addition 'unl 11.13 5500 _. to tho prograna of Inn 11. 13. Doubling nodarn food groino yialda altar 1980 in addition to tho progrann of Run 11. 11. Cutting of! aarkoting hoandand ' 1 oaport tanaa. in addition to tho 4000 __ prograno of Run 11. ‘ 12 15. Phaoing out narkating hoard and export tanon. in addition to tho prograno oi Run 11. 3500 *- l t 3000 t- 2500 *- \ tun 15 2000 -' 1500 " A» o’[_ l, L l .1 ,L 1970 1975 1980 1985 1990 1995 Fig. IV.23 Croao donnotic product (anon-ing narhoting hoard and aaport tarot are not put to production uno). 1970-1995. undnr variouo policy conditiono. Exportn (liillion l/yr.) 268 - no 14.15 M13 M12 1’°q" Punt 11.13 1000"‘ lunlb 9oar- m DIPIN 11'1“!» 1. Continuation ol prooant ttnndn ad policiao (hano fill). 11. Production cqaigno in cotton. m... groundnuto. lood graino. cocoa. paln ad ruhhor. 12. Production caaaia in load rooto in tho Hiddla halt. in addition to tho prograa ol la 11. 13. Douhling nodarn lood groino yioldn altar 1900 in addition to tho prograa ol Run 11. 700’ 1‘. Cutting oll narhating hoard ad onport tan. in addition to tho prograa ol Run 11. 15. Phaoing out narkoting hoard ad oxport tan. in addition to tho prograa ol Inn 11. 03' l l 1 .1 . l 1910 1915 1910 1915 1990 1995 Fig. IV.2‘ I'otal onporto (agricultural ad nonagricultural). 1970-1995. ador vation policy conditiono. Inporto (Million i/yr.) 1. 11. 12. 7w _ 13. 16. 15. 1970 269 ID” DEFINITIONS Continuation ol praoont tronda and policioa (haoa run). Production canpaigna in cotton. groundnuto. lood groino. cocoa. pain and ruhhor. Production canpaign in load rooto in tho Niddla halt. in addition to tho prograno ol Run 11. Doubling nodarn food groino yioldn altar 1980 in addition to tho prograno ol Inn 11. Cutting oll narhating hoard and anport taxno. in addition to tho prograno ol M 110 Phasing out narkoting hoard and oxport tancn. in addition to tho progrann ol Run 11. 1 1 1 1975 1980 1985 Pig. IV.25 total inporto. 1970b1995. undnr variouo policy conditiono. 111 1990 ‘0“. 1‘015 a 11.13 Run 12 1995 Price ol Pood (l/lh.) .016 .013 .012 .011 .010 .007 P 1970 1. 11. 12. 13. 1‘. 15. 270 RUN DNPINITIONS Continuation ol pronont trendo and policioa (bane not) . Production canpaigna in cotton. groundnuto. lood groino. cocoa. paln and rubber. Production caapaign in load rooto in tho Niddla halt. in addition to tho prograan ol Run 11. Doubling nodarn lood groino yioldn altar 1980 in additi prograno ol Bun 11. Cutting all narhoting board and export taxoo. in addition to tho progrann ol Run 11. Phaning out narhating board and export taxeo. in addition to the progrann ol Run 11. “\w 1 1975 on to the Run 1‘ 1111 1980 Run 1‘ Run 15 'un 1 Inn 11 'un 13 11.13 12 1 11 1 1985 1990 1995 ' Pig. IV.26 Narhat price ol lood in the North. 1970-1995. ador variou- policy conditiono. Caloric Conaunption Per Capita (1000 caloriao/paroon-yr.) 590 580 570 560 550 560 530 520 510 13. 1‘. 15. J oT I 1970 Pig. IV.2? Caloric conauaption (ol otaploo) ol tho aouthorn nonagricultural population. 271 Run 12 RUN DEFINITIONS Continuation of pronont trends and policioa (bane run). - Production cqaignn in cotton. groadnutn. lood groino. cocoa. paln and rubber. Production caapaign in food rooto in the man. 1.1:. in addition to tho ' 11-“115 prograno ol Run 11. Doubling nodarn food groino yioldn altar 1900 in addition to the prograno ol Nun 11. Cutting oll narheting board and export taxno, in addition to tho prograno ol Inn 11. Phaaing out aarhating board and export taaoa. in addition to tho prograno ol Run 11. Run 1 1 1 1 1 111 1975 1900 1905 1990 1995 1970-1995. under varioun policy conditiono. 272 This is due to the much more dominant role food plays in northern agriculture. In the base run, food accounts for over 90 percent of value added in the North and only about 75 percent in the South. Rising food prices and steady or i falling export prices account for the rapid rise in north- ern value added compared to the South. Varying Production Campaign Budget Levels The fifth set of runs, Runs 1, ll, 16 and 17, in- vestigates the relative effects of various levels of pro- duction campaign budgets. Run 1 is the base run where no campaigns are carried out. Run 16 spends £20 million on five programs in the South--30 percent to each of cocoa replanting and palm replanting where palm doesn't compete with other perennials (essentially the eastern states), 20 percent to rubber replanting, 10 percent to cocoa new planting, and 10 percent to palm replanting where palm competes with rubber--and £20 million on three programs in the North--40 percent to each of groundnut and food grains modernization and 20 percent to cotton modernization. Run 11 budgets £40 million in each region for the same programs in the same proportions, and Run 17 doubles the budget again to £80 million, still for the same programs and in the same proportions. Exports (Figure IV.28) and marketing board revenues (Figure IV.29) are the variables which most directly reflect increased export production resulting from the modernization Agricultural Exports (nillion I/yr.) 200” mar -10\J '— -200 "' .100 1 I 1 0 20 ‘0 00 Caapaign Budget (Idllion l) Pig. IV.28 Agriculturaloxporto in the North (including haal and cotton iaporto) (an) and South (38). in 1995. under varying production canpaign hudgoto. Tota1 Marketing Board lovonuoo (nillion Ilyr.) 274 1:0 )— ‘0 I— J. T I I L 0 20 ‘0 00 ania budget (nillion l) Pig. IV.29 Total narhating hoard not ravenuaa lron northern ad aouthorn audition in 1995 under varying production cqain hudgntn. Nodern Annualo Lad (nillion acres) 275 (X of total budget) 2 7.0__ Cotton ( 01) Groundnut (402) 0.0 '- 5.0- Pood (402) (“0*- 3.0“- 1.0— 1.0" l l 1 0 20 60 N Caaaign Budget (nillion i) Fig. IV.3O Hodorn anualo cotton. gro'adnut ad food land in 1995 under varying production calpaign budgeta. Modern Perenniala Land (thousand acreo) 276 (1 of total budget) 20011?- R1’ (301) 1750)— 1501(- 1250*- 1000*" C (301) C (1055') 750*" ' R (101) " (202) 500” 2 I 1 1 l 0 20 £0 80 Caaaign budget (nillion i) Pig. “.31 Nodern perennialo lad in new plated cocoa (NC). roplated cocoa (RC). roplated paln where no other perennial conpetition (RP). replanted pain where ruhhor conpetition (NPR) and replanted ruhhor (III!) in 1995 under varying production caaaim hudgeto. 277 programs. Interestingly, they indicate diminishing returns for larger campaign efforts. Thus, increasing the moderni- zation budget from £20 million to £40 million increases foreign exchange and marketing board revenues by about £70 million and £14 million, (or £3.5 and £.7 per pound of increased budget), respectively. A further doubling of the effort (i.e., another £40 million) would only return an additional £75 million and £17 million in foreign exchange and marketing board revenues (or about £1.9 and £.4 per pound of increased budget), respectively. Figures IV.30 and IV.31 portray the acreage of each crop in modern production in 1995 resulting from various levels of production campaign budgets. All commodities exhibit the same diminishing returns in foreign exchange and marketing board revenues discussed above. Conclusions The major conclusion to be drawn from the above results is that a technological transformation of agricul- tural export crop production is necessary for sustained growthl/. Other development policies show only short run benefits which are eventually eaten up by continued popu- lation growth, by activated land constraints and by declining l/ This conclusion is of course dependent on the model's validity and is limited to the policies and programs tested. It is not inconceivable that there may be some other route to sustained growth than the one indicated here. 278 yields of aging perennials. This was true of the tsetse fly eradication program, where initial gains were later lost to a growing cattle population and to expanding crop acreages. It was also true of the elimination of marketing board and export taxes, where land constraints and declin- ing yields in the South eventually nullified positive results of the higher producer prices. And it was also true of the food grains modernization programs in the North, where an expanding population eventually reversed the gains made in the increased availability of land and labor for export crop production. Only production campaigns to modernize the production of export crops with the introduction of high—yielding seed variates and improved cultural practices had beneficial consequences which were maintained in the long run. Other conclusions can be made from the analysis concerning interregional and intersectoral interactions. North-South shipments of food do play a substantial role in supplying the southern population, and the indications are that there exists a potential for regional specializa- tion, wherein the northern Middle Belt area (where roots and tubers--the primary components of southern staple consumption--can be grown) would grow food for a South which would specialize in export perennial crop production. Interactions between the nonagricultural and agri- cultural sectors are also strong and indicate that 279 agricultural development can also lead to growth in the nonagricultural sector. For example, rising agricultural incomes mean an increasing demand for nonagricultural con- sumer and investment goods which means more employment and higher incomes in the nonagricultural sector. This in turn means greater nonagricultural demands for agri- cultural products (food and raw materials) and thus more agricultural income. And so it goes. This is the multi- plier effect referred to in the analysisl/. A final observation that can be made from the above policy analysis concerns the production campaign budget levels. Specifically, they show diminishing marginal returns. That is, as the campaigns are intensified (the budgets are incremented), resulting increments in output criteria (such as exports) become less and less. Policy Sensitivity Each of the three southern regional production campaigns examined in the last section (Runs 8, 9 and 10; Table IV.l) were tested for sensitivity to 29 land alloca- tion parameters. Many other parameters could have also been investigated, including those tested in Chapter 9, but the 29 were chosen for illustrative purposes because they are directly related to the policies under consideration. l/ See [4] for a fuller discussion of this phenomenon. 280 The consequences of parameter variations on the results of the three policy runs are examined in terms of three out- put criteria--accumulated agricultural exports (AFORXS), accumulated agricultural value added (ATVAS), and accumu- lated marketing board revenues (ATRMBS). The policy runs used here are exactly the same as Runs-8, 9 and 10 of the last section with one major excep- tion-~here, the southern submodel was run independently of p the rest of the Nigeria model and thus without interregional and intersectoral interactionsl/. The results reported here (Table IV.2) are thus somewhat distorted in the absence of shipments of food from the North. For example, the 1995 price of food in the base run (Run 1) of the last section was .0193 £/lb. (Figure IV.15), while here it turned out to be .0519 £/lb.! Similar exaggerations occur when comparing the price of food in Runs 8, 9 and 10 here and in the last section. Nevertheless, if the results given below are not comparable with those of the previous analysis, they are comparable among the three policy stipulations here and thus serve their illustrative purposes. The results are tabulated in Table IV.2 for AFORXS, IATVAS and ATRMBS, respectively. A quick look at the table will show that variations in the proportions of traditional l/ The current model does not provide for these interactions to be exogenously supplied when a regional submodel operates alone. Such provision is on the agenda for further development. 281 1 , . .., . .-. cone. node. oaoo. ~¢.o~ nv.- o~.- voo.n can.n mos.n n. noon. whom. muom. ~o.o~ vv.- on.- mum.n cmw.n mom.n n. -vo. nave. n-w. on.o~ sv.- nu.- -a.n ~oo.n ova.n .oom abode. caNNo. cameo. no.0” no.- o~.- ouo.n mah.n ~H5.n moo. page. chum. anew. an.o~ .nv.- >~.- coo.n has." ouh.n «co. coowa. eo-w. «snow. ~a.o~ av.- nn.u~ ouw.n ~0n.n aau.n moo. anon. have. omco. ~o.o~ mm.- on.~u a~o.n nao.v nmo.n ~oo. cwono. «Nana. enooo. no.o~ on.- no.- coon.n once." e~n5.n moo. «ado. «haw. Adoo. no.o~ nv.- mo.- aoo.n nah.m Hos.n do. vnmo. mnvo. ovwo. an.o~ Ho.o~ hh.o~ anhm.n .mao.n canm.n moo. «emu. ~vmo. omoo. mo.o~ n~.- oo.- umn.n mom.n ~vh.n moo. moan. cram. -oo. Hm.o~ nv.H~ o~.- mmo.n nmh.n con.n I ll...1rl. .1 I1 ca m 0 ca a o em a a o=~c> l l l ::m \oncam >0aaon Ixomcam >ow~oo \oncsz >0w~ce omom .u cohaann. .mm:¢e<. Au coaaawo. Am<>aav .u acquaan. .mxx0h4. nonco>o¢ onoom ocwuoxuox . noon< o=~o> “onsuasouuv< houndxm Honou~39ano< b! L canouwuu oucoELOuuoo no. no. .omh v00. v00. .00. voo. coo. No. coo. Ho. .uOuuom Edam. Sana ocwucoaaou uOu vaccnoucu cocoon Ion xuauoaouauono oooou ocwunoanou new ouoznouzu onconn Ion auaannauauouo ..uhnucooo\nouoe. aoco«o«uuo noduoa Icon ucooo couucouxm .ouoo\nuwcs .Oucwv .nOuoom Cognac. Edna ocaucoaa an: new nooosouon codesuuuo .onuo \nua::.Oucuv nooaou ocwucoao 30: new nouofionoa acansuuuo .ouooxnuucn .Oucao Annuuom Egon. Edna onwucoan Jon new nouoeouon counsuuwo Aonuo \nuac: .Oucu. oooou mcaucoaa he: now wouozouoo caunnuuuo .ouuo\nuwns .Ouca. .uouuom nonnnmv Band mcaunoanou uou uouoaouod enunnuuao .ouoo \nuwcs .Oucwv non noon ocwucoadou new nouoeouoa cooosuuuo .ouuo\nuacs .Oucwv Annuoow Edna. Sand ucwucoaoou new nouoeouoa onwuouuwo Aouoo\ouwcs .Oucw. cacao monocoadou nan nouofiouom scansuuuo A~.~.B¢=h -.~UBB:P Luau .oanoDnU Aavmoano AmvaDHU Anymoanu ...mlsnaao an.~vbnauu .~.~vbDDHU A~.NVFQDHU can noon 4 ad ca 03~o> cam umOP coauzcnuoo nouofiouoa nouuoe CODOEoooa C3“ .ncouunsuwn >Ua~oa ooucu have: homo» auw>wuwncon auuuoa no nuasnom .~.>~ canoh 282 mono. moaw. mama. «nan. vouo. mafia. undo. oonw. «cow. noon. vaao. homo. chum. chao. vhuo. cmsn. «mow. vhaw. moan. vhuw. momm. Nwmm. mode. vhao. «How. Nucw. «moo. room. maom. Nuow. ncam. Once. owmm. omhm. “How. haow. aa.o~ ua.on oa.o~ onH.~N mn.o~ om.o~ on.o~ eoc.- oo.- ma.o~ am.cN «Ho.a~ nv.- mv.aN n'.~N emo.- hn.- nv.- mm.HN onv.- «h.AN um.H~ nv.~N onv.- o~.AN o~.- «N.- ooh.- n~.- o~.H~ Nv.- oov.«~ on.a~ hm.- o~.~N aom.~N muo.n moo.n ~co.n eNAm.n onhw.n nm0.n avow.m who.n -o.n mvm.n vao.m ohw.n hoh.n hoh.n huh.n ava.n anch.n hoh.n emw@.n hon.n Hwo.n ouw.n Non.n hon.n veh.n van.n vch.n oncm.n oomo.n vor.n aoo@.n Hao.n me.n nom.n non.n oaw.n 6°. 00. mou. a0. mv. mv. .I'I'Ilill II (IIIYII-OA .:0«u030un. .uOuoom Eden. E~oo ocwucoam non uOu ecuouoa0nn sudalnoaaa>o was; .cOADQEouov ooooo vcaocoad non new coauu0doun auwaunonno>a one; naouccouoa unwucoaa in: new noon ucsoo Ieao shenanounoona odouccouon ocuucoad Ion new ouou ucsoo Iran auwnanouquCQ naoqccoCOQ ucaucoaa to: Can oncodnou no ouon huauanounuoum naouc IcoMOQ onuucoad Io: new naoznoucu oncoon Ion aunaanouauoua .uOuoom noonsa. Egon ocaucoaoou uOu oncoanou «o coon auaaannuououa neonsu onwunouaou uOu oncomnon no ouau soaaaneuauoua «unuoom Edam. sand ocwucoanou new oncomnou no ouch auaaanouauona ooooo unaucoHnou nan uncommon no when suaaanounooua Auouoom Cannon. Sand ocuucoanou uOu oaosnouzu cocoon Ion auaaanuonuouo nonndu mcwucoadon new vaoznnucu cocoon Ion suaaanauauoua .~.~.F>(AU .~.~.s>¢au A~vn¢a .~.sxo .~.na=m .mvnzzh ...“.aozm an.nvammm .~.~.aa=m AH.~Vfim=m .v.~.a¢=s An.uvau=a nu «N aw ON «a ma ha 0« ma va nu «a on a -\Mucax sundae ca o ncnm hoqaoo ca Ixa o was: soaaoa Au acaauwn. .mmtx84. nonco>o¢ ouoom acauoxuoz .u codaaun. Am<>hdv nonn< on~o> unusuusouuo< Au cohaauov nuuoaxm Housuasoquo< .mxm0h<. ohuouwuo oucoEMOuucm oouo> com neon on~o> HOOP cauuucuuoo nouoflonoo nuance unannouoa A.v.ucoov .N.>H Danoh 2133 .~.>H manna cw one macauacwuoc can >Owaom \m .csu noon EOuu oouoouoou muasmou mouoowpcn vmflw. made. Nada. mafia. made. mafia. «haw. vsao. mnaw. mnam. vsao. vbaw. Naom. NHow. Naow. «Moo. «How. Naoo. Hw.om Hw.om mm.on Hw.o~ Hm.o~ Hw.o~ vv.- nv.HN vv.H~ mv.HN mv.a~ mv.a~ a~.HN m~.- on.H~ mN.H~ m~.HN m~.- vow.n mmo.n mmo.m mmw.m mmw.m mmm.m moh.m hoh.m wwh.m hw5.m nah.m hoh.m von.n vor.n vor.m «on.n con.n vow.m a. ACmesu Iuwo. Anchoom non Inna. Egon ucwucoad no» new newun0doua xuwaaooawo>o ocoa Acofimouuwov nonosu unaucoaa no» new noduuoaoum aunaaanou>m cane Anodnsuuwo. Anchoow Sandy Edna mcaucnad non u0u noduMOQOud auflawnoaao>o pong AcoamSuuwov noooo azaucnaa Ion new ceauuoaoum xuaafiooawo>o pcoq Acoauoe IOuQ. .uOuoom non Innmv ano ocaucoad Ion uOu c0auu0d0ud auaawooaao>o coca ACOADOEouQV nonnau moaucnam Ion qu ceauuoaoum auaaanmaam>o scan Av.~.e>aao A~.~Ve>om oucom moauoxuoz AmmZMde Au :Owaawnv Am<>B amusuasUano< Au Sofiaawnv Amxmomflv muuonxm unusuaoofiuv< ofiuouwuu oucoEuONuom czan> cam omnm ooao> com umwfi coauacaumo thOEnuom pounce Houosouca cam A.p.ucoo. .~.>H wanna 284 perennial lands have negligible effect on any of the three output variables in any of the policy situations (Runs 22-29). Similarly, the discount rate for evaluating the profitability of replanted perennials is the most sensitive parameter tested (Run 20). Diffusion parameters for replanting perennials (Runs 1-4) and the parameters regulating the replanting pro- fitability response rates (Runs 14-17) are also relatively sensitive. We can see that for a few of the sensitivity runs (marked with a "*" in the table), the relative order of the output variables in the three policy situations has changed from the order of the base values. For example, in the base runs (i.e., the policy runs with no parameter changes), agricultural exports are ordered (from highest to lowest) as Policy 9-Policy8-Policy 10. In Runs 2 and 4, on the other hand--where the diffusion response parameters for replanting palm in the Palm and Rubber Sectors, respectively, are tested --the order is Policy 9-Policy lO-Policy 8. The implication "*n is that the parameters whose test runs are marked with a in Table IV.2 are the most cruciall/ for the evaluation of alternative policies. Thus, efforts to improve estimates of their values would apparently be justified. The three policy situations examined are relatively stable in the face of parameter variations. Runs 5 and 20 generate the largest deviations from base values of 1/ Of the 29 tested here; others, not tested, may be similarly important or even more so. 285 agricultural exports and marketing board revenues under all three policy conditions. Runs 2 and 20 give the largest deviations of value added under the three policies, except for Policy 9 where Run 15 replaces Run 20. These deviations are tabulated in Table IV.3 as percentages of base values. Value added varies less than 2 1/2% in either direction in all three cases, while exports and marketing board reVenues vary less than 6 3/4% and 7 l/2%, respectively, in either direction. In addition, the relatively few cases of a reordering of policy results (marked by "*" in Table IV.2) suggest stable policies. Table IV.3. Greatest deviations of three output variables from 29 parameter variations under three policy situations (percent of base values). Policy Output Situations , . ' . . Variables Policy 8 Policy 9 Policy 10 Agricultural Run 5 6.72 6.53 6.63 Exports (AFORXS) Run 20 a -5.42 -6.45 -4.69 Agricultural Value Run 2 -2.44 -2.42 -2.11 Added (ATVAS) Run 20* 2.35 1.31 1.54 Marketing Board Run 5 7.43 ‘7.18 7.10 Revenues (ATRMBS) Run 20 -5.24 -7.08 -4.59 * Except Policy 9, where Run 15 is tabulated. 286 Summary This chapter has presented a detailed analysis of some agricultural development policy options which have been under consideration in Nigeria. The analysis was organized to illustrate how a system simulation model such as the one presented here could be used as part of the development-planning and policy-formulation process. We may conclude that while detailed considerations of policy sensitivity and stability in the face of uncertain para- meters must await the development of a Monte Carlo capa- bility in the model, the present model can provide at least some useful information in this regard. Of particular significance is the model‘s ability to project the conse- quences of a variety of policy combinations whose inter- active and dynamic effects may then be analyzed. CHAPTER 11 Summary and Conclusions This study concludes with a summary of the foregoing chapters, and conclusions are drawn concerning the practical utility of the present model. This is followed by a dis- cussion of further work which can and should be done on the model if it is to be successfully and usefully implemented. Finally, a brief sketch is given of the form such an imple- mentation would take. Summary Agricultural development is viewed as a complex process involving the dynamic interactions of economic, political and social subsystems. Necessarily simplified analytical models have been found wanting in comprehensive- ness and detail to be of significant use for either expla- nation or prediction of system behavior. Analog simulation models which might have been sufficient in this regard were too cumbersome and impractical [21]. Since Forrester's introduction of industrial dynamics techniques in 1961 [16], much work has been done on the modeling of industries and regional and national economies (e.g., [22, 33, 36]). With this background, and building upon the foun- dation laid by the Consortium analysis of Nigeria's 287 288 agricultural sector [24], a research team at Michigan State University, under contract to the United States Agency for International Development, developed a digital computer system simulation model of Nigeria's agricultural economy with links to the nonagricultural sector (Figure 1.1) [35]. The Nigeria model includes two regional agricultural sub— models, a nonagricultural submodel and components which model the demography of Nigeria and the interregional trade in food. The agricultural economy of southern Nigeria, as well as that of many other tropical areas, is characterized by competition between perennial and annual commodities for scarce productive resources. The southern regional sub- model presented in this dissertation considers five commod- ities: cocoa, oil palm, rubber, food and tobacco. Because of the importance of tree crops in the South, perennials are modeled as dynamic populations distributed over time and productivity (Chapter 2). Eight perennial populations are defined, four traditional and four modern. The productivity dimension of each population is lumped into five production cohorts (Figure II.3)--gestation, rising yields, maximum yields, declining yields, and old age. The maturation time through each cohort is assumed to be a random variable following a gamma distribution (Figure II.4) modeled deter— ministically as a series of distributed delays (Chapters 2 and 3). 289 Land use transition rates are based on perceived relative profitability differentials of the alternatives available in each of four ecological zones. Decisions are influenced by government promotion efforts, if any, and by farmer-to-farmer diffusion (Chapter 3). Given technological coefficients and the allocation of land, production, pro- cessing and marketing are carried out for cocoa, oil palm, rubber, food and tobacco. Supplies are price responsive in two ways: by a short run harvest response and by the longer run land allocation decisions (Chapter 4). Prices of export commodities are derived from exogenous world prices and national tax policies, while endogenous demand—supply rela- tionships determine domestic prices for food and palm oil (Chapter 5). Finally, the agricultural sector budget is accounted, and output criteria are generated (Chapter 7). There are three direct policy entry points in the model: commodity production campaigns can be specified, marketing board and export tax policies can be regulated, and income taxes can be levied (Chapter 6). The model's applicability to policy formulation was demonstrated in Chapter 10, where the results were analyzed of a series of 17 runs examining progressively more complex combinations of policy options which have recently been considered in Nigeria. The major conclusion drawn from these runs, given the model's assumptions, is that a technological transformation of agriculture (incorporating both improved inputs and improved cultural practices) is necessary for 290 substantial and sustained economic growth. In attempting to come to grips with the uncertainty arising from the necessary use of some poor and questionable data, an investigation was made in Chapter 10 into the stability and sensitivity of policies to variations in the' values of selected parameters. While the results suggest relative policy stability for most of the parameters varied-- that is, little deviation, in general, in the absolute and relative levels of output criteria under the various policy conditions examined-~changes in some of the parameters, particularly those affecting the supply and demand of palm oil, caused appreciable output deviations and even a re- ordering of output values in the three policy situations considered. In any case, many more such tests would be necessary to more fully treat the data uncertainty problem. This might be done by running the model in a Monte Carlo mode (discussed below), where many parameter variations would be treated simultaneously and stochastically and output statistics would be generated. Sensitivity analyses, discussed in Chapter 9, may serve three purposes. First, they provide an indirect way to test policy options. One or several parameters could be changed to reflect a particular policy goal and the conse- quences thus simulated. Secondly, sensitivity analyses may indicate logical or theoretical inconsistencies in the model and may also add to one's understanding of and insights into both the model and the corresponding real system. This 291 application of sensitivity tests was illustrated in Chapter 9. Finally, the results of sensitivity tests can suggest data collection priorities by indicating those parameters which are of greatest consequence to the performance of the model. For example, the results of the tests reported in Chapter 9 show that initial land usage patterns and para- meters affecting the supply and demand of palm oil and food are quite sensitive, suggesting the value of collecting data in these areas. Data needs of the model are discussed in Chapter 8. Tuning the model to track recorded time series is presented as one approach both to treating parameters for which no (or only poor) data exist and to assuring some correspondence to the real system. General validation procedures then interact iteratively on a continuing basis with the model- building process by evaluating the model's behavior and assumptions against theory, empirical evidence and know- ledgeable intuition. Conclusions From the sensitivity and policy analyses of Chapters 9 and 10, we can conclude that, although the model as presented here needs further work, it can, even in its present form, provide important contributions to three broad aspects of the development-planning and policy-making process: understanding the socio-economic system, formulat- ing development policies and focusing research activities. 292 These aspects are somewhat overlapping; for example, both research and an increased understanding of the problem cer- tainly contribute to improved policy formulations. Understanding the System Detailed analyses of the behavior of the model (the simulated system) under a range of assumptions (particularly data) and policy conditions provide a comprehensive view of the complex and dynamic socio-economic system under study. This, combined with the model-building process itself-- particularly the identification of causal and structural relationships--can contribute substantially to an improved understanding of and sharpened intuitions regarding the development process in general as well as the particular socio-economic system itself--Nigeria's in this case. This was demonstrated in Chapter 9 where sensitivity tests pin- pointed sensitive parameters and where the analyses carried out to explain the consequences of parameter changes high- lighted complex interactions of the simulated system. Insofar as the simulated system faithfully represents relevant behavioral patterns of the real system, this height- ened understanding can be a valuable asset in reducing some of the uncertainty policy makers necessarily face. Policy Formulation A more direct input to the policy-making process is the capability of the model to explore the consequences and implications of a wide range of development policy Options. 293 We saw in Chapter 10 how the model projects time paths of relevant output variables under alternative and increasingly complex combinations of policies. Thus, using the same data available and used for more traditional (e.g., paper-and- pencil) type projections, the model takes account of many more complex policies and interactions than can be done by hand or with a desk calculator. In this way, a good deal of the uncertainty concerning the system's response to various policies can be reduced. Another important application of the model to policy formulation is in dealing with the uncertainty inherent in the quality of the available data. Sensitivity tests were conducted in Chapter 10 where key parameters were varied in each of three policy situations. While those few runs could hardly be called a complete analysis, they do illustrate how the model can be used to evaluate the sensitivity of policies to data uncertainty. This is information essential in the search for stable policies, that is, policies which will have the intended results even though projections were based on poor data. Research Activities A third contribution the model can make to develop- ment planning is as a focus for research activities. There are primarily three ways in which use of the model can provide a central theme to coordinate and guide research. First, sensitivity analyses will suggest data collection priorities to improve the available estimates of the most " “3.. oa' was!“ - 294 important parameters and coefficients of the model. In some cases, new survey and estimation methods may have to be devised to accomplish the task. For example, tests in Chapter 9 indicate the sensitivity of the parameters con- trolling the rates of innovation and other information diffusion among farmers. New techniques may have to be found to estimate these parameters. Another area of research which the model's applica- tion will motivate is investigations into structural rela- tionships among and the behavior of component elements of the socio-economic system. These efforts will be necessary to continually improve and keep up to date the model's assumptions and representations of the real system and to keep it relevant to the needs and concerns of policy makers in a changing world. Finally, technological research may be suggested by policy runs which speculate on the likely consequences of the introduction of an innovation which may not actually be developed at the moment. Of course, the projected conse- quences would have to indicate that the expense of under- taking such research and development is warranted. In summary, a system simulation model such as has been presented here can be a useful and valuable tool in the battle against uncertainty in the development-planning process, providing a comprehensive view of a complex, dynamic system while at the same time facilitating policy experimentation and motivating research. Such models are 295 characterized by a high initial cost (reflecting the costs of data acquisition and modeling) but a relatively low recurrent (user) cost as the model is used to explore a myriad of policy options. Improvements and Extensions of the Model A simulation model of human systems can never be "completed". This is particularly true if the model is to be applied in practical policy-making situations. Aside from the truism that "you can't model everything," data can be sharpened, structural and causal relationships must be continually verified in a changing world, and even the prob- lem definition which delimits the model and specifies its constraints may have to be revised from time to time in re- sponse to the evolving needs of planners and policy makers. The latter case could require a major model expansion or re- emphasis. It is an economic truism that any modification of the model, including the improvements and extensions dis- cussed below, will incur costs for modeling and programming which will have to be weighed against the expected returns of increased model flexibility and relevance before a deci- sion is made to go ahead with the modification. A number of areas in the current southern model can be identified as needing further attention to improve the model's performance. These are discussed below as "improve- ments". Preliminary experiences with the southern model, operating as part of the total Nigeria model, have suggested possible extensions to enable it to better address some of 296 the major problems of economic development. These will also be discussed. Improvements There are several aspects of the southern model which need further development and verification. First, it is not certain that the model of the domestic palm oil price mech- anism (Equation 5.4) adequately or even realistically re- presents the actual operation of that market. In particular, the link between the domestic market price and the marketing board price is not clear. Since the competition for palm oil between foreign and domestic markets makes this a fairly sensitive commodity in the model, further research and eventual modification of this aspect of the model may be indicated. A second area that could call for further work is the treatment of the modernization of processing. As pointed out in Chapter 10, the model currently simulates the trans- formation of agricultural processing irregardless of the profitability of the supposedly "modern" technology; all that is necessary for modernization to be carried out is a policy of exogenous investment in modern capacity (Equation 4.15). Thus, in Run 10 of the 17 runs analyzed in Chapter 10, oil palm processing was converted from hand presses to Stork hydraulic presses even though farmers were losing :money on it. If policy makers and planners feel this is an area which they would like to investigate more fully, then revisions of the model will be necessary. 297 The land use alternatives specified in each of the four ecological zones (or crop sectors--Figures 1.3 and II.2) may also do with some confirmation. Table II.l lists the potential alternatives omitted from consideration in the model. These omissions are based on assumptions concerning the relative significance of the alternatives and on consi- derations of model simplification and efficiency. However, further evidence may indicate a greater importance for some of the omitted alternative land uses (e.g., food land being planted in traditional perennials), in which case the model will have to be modified. Related to this possible shortcoming of the model is the question of whether the entire set of "logical alterna- tives" in Table II.l is too restrictive. There is currently in Nigeria interest in the possibilities of introducing and expanding the production of other tree crop commodities, e.g., kola and coffee, in areas where cocoa is marginal. If the model were to be developed further to handle such addi- tional perennials, however, it may also be necessary to re- define the ecological zones in which land allocation decisions take place (Figure II.2). A major feature of the model which needs theoretical and empirical verification is the land use decision mechanism (Chapter 3). One question arises concerning the realism of - relating all decisions--even those pertaining to traditional land uses--to a diffusion curve (Equation 3.8) which is usually considered descriptive of the diffusion of innovations. 298 Another aspect of the decision mechanism which is un- realistic is the effective lack of constraints on land allo- cations. First, the capital constraint on land use decisions (Equations 3.13 and 7.12) is virtually inactive in the model and does not effectively represent the actual constraints Nigerian farmers seem to be facing. Additional research is necessary to better understand the nature of this problem before further modeling work can be done on it. It may well be that this phenomenon cannot be handled meaningfully until‘ the model can deal with the question of income distribution, discussed below. A second constraint, one which is not in the model at all, is the availability of labor. Based on pre-civil war conditions, the model assumes there will be no shortage of agricultural labor; any such shortage in the indigenous southern population will be met by seasonal migration from the North. Actually, the availability of agricultural labor i§_a problem in Nigeria today, and in other developing countries as well, so that the assumption of no labor con- straint is a serious limitation of the model. Thus, it may be desirable, if the model is to be implemented, to give high priority to modifying the model to realistically reflect actual labor constraints on land allocation and production decisions. A less serious shortcoming is the lack of constraints on other inputs, primarily fertilizers and other chemicals and seeds and seedlings. If it is felt the availability of 299 these inputs is a real problem to be assessed, it wouldn't be too difficult to enable the model to do so. Two examples of other structures of the southern model which may bear further verification are the subsistence level adjustment mechanism and the use of exponentially weighted price averages. First, it may be questioned whether Equations 4.1-4.3--in assuming the functional relationship shown in Figure 11.9 between food market stability, food price level and cash crop income on the one hand and, on the other, the level at which the agricultural population will want to feed itself--rea1istically, or even adequately, determine the agricultural subsistence level. Secondly, further information may indicate weaknesses in the assumption that, in making their decisions, the ex: pected prices that farmers project are exponentially weighted averages of recent prices (Equation 5.8). Research findings may even suggest promising alternative formulations. Another question which might be raised concerns the use of exponen- tial price averages, instead of the price in a reference year, as a base for determining the harvest supply response (Equation 4.6). Finally, this model, and indeed any model, may always be improved by improving the data that go into it. As has been discussed, the model itself may help in this endeavor by indicating those parameters to which the simulated behavior of the model is most sensitive. 300 Extensions There are two categories of possible extensions of the model, both of which would add to the model's relevance and usefulness to development planning and policy making. The first involves enabling the model to address some of the major practical and theoretical problems of economic develop- ment. The other category of model extensions is of a tech- nical nature and would increase the model's flexibility to deal with a wider range of planning needs. In the initial, problem definition phase of the Nigerian Simulation Project, interactions with Nigerian researchers and officials helped identify areas of concern to agricultural development planners which the model could relevently address. Some of these included: 1) extension efforts to increase export and other cash crop production, which would thus improve both government's balance of pay- ments posture and cash incomes to the private agricultural sector; 2) marketing board pricing policies, where there was a question of trade-offs between public revenues (which could ostensibly be used to finance development projects) and private income; 3) promotion of improvements in and modernization of the cattle industry (e.g., tstse fly eradi- cation and the creation of grazing reserves) to increase production and consumption of beef and milk; and 4) efforts to increase food production to maintain and improve the nutrition of the agricultural and growing urban pOpulations. I I. Illiii 301 The last item is one direction in which the model might be extended further. In placing emphasis on export production, food is treated in a very aggregate way. Non- staples are not considered at alll/, while staples are ag- gregated into a composite (defined in Chapter 3), and their nutritional value is treated solely in terms of Calories. On the other side of the coin, the model determines only the population's demand--urban and rural, cash and subsist- ence--for staple Calories (assumed to be about 80% of total caloric needs). Other nutritional factors, such as proteins and vitamins, are ignored. These limitations of the model were cited in Chapter 10 to explain the apparent unfavorable nutritional future of urban Nigeria projected in the policy runs analyzed in that Chapter (Figures IV.10, IV.16 and IV.27). Currently in Nigeria, however, and in many other developing countries as well, the problems of nutrition are increasingly in the forefront of policy issues [38]. If these concerns persist and deepen, and if it is thus deemed worthwhile to expand the model, perhaps substantially, to assist in the formulation of policy solutions, the model could be extended to treat individual food crops and a ‘wider range of nutritional indicators. l/ Domestic palm oil consumption is computed, but only as it competes with exports. It is not considered for its contribution to nutrition. Similarly, beef and milk are viewed from the standpoint of production; consumption demand is not treated endogenously in the model. 302 Another concern of economic development, a problem often made more acute by the development process itself, is the issue of the distribution of income [11]. At present, the model distributes income between the agricultural and nonagricultural sectors, between traditional and modern sectors within the nonagricultural economy [ 4], and geo- graphically by region and ecological zone within the agri- cultural sector (Chapter 7). However, as discussed above and in Chapter 7, it may be desirable to also distinguish, within the agricultural sector, between large farmers with the educational and material resources to take full advantage of modern agricultural technology and small farmers barely above subsistence and struggling to enter the cash economy. To the extent that the inclusion of this distinction would enable the model to more realistically simulate the production and consumption decisions of the agricultural sector, the model's applicability to the analysis of policy consequences would be enhanced. In addition, this dimension of income distribution would be an important output criterion for evaluating alternative policies. Further research on the linkages between income distribution patterns and agricul- tural decision making is necessary, however, before the lnodel can be extended to include this phenomenon. A third possible problem area which would call for Ian.extension of the model, and one of growing concern to :researchers and policy makers (e.g., [18]), is the question (3f rural-urban migration and urban unemployment. This problem, 303 like income distribution, also seems to accompany develOp- ment, and it may be an even more crucial issue for its implications for social and political stability. However, although some significant theoretical and empirical research has been conducted in this area, there is yet no general agreement on the principal motivations and mechanisms govern- ing rural-urban migration. Is it rural-urban wage differen- tials? Or education? Or rural unemployment? Or is it the bright city lights? Perhaps some combination of these and other factors all play a role and, if so, what is that combination and how do they work together to motivate or inhibit rural-urban migration. Although questions such as these should ideally be answered to provide a theoretical and empirical foundation for building realistic models, the problem will not wait. Thus, it may be necessary to con- struct an interim model, or alternative models, which may be used temporarily to deal with the problem. Indeed, such models will probably even prove useful in an iterative process of developing and testing theories of migration. 4 A final development problem which the model might be extended to address is inflation. Not only is inflation of particular concern to developing countries for its effects on investment, consumption and terms of trade but also, if it continues rampant and uncontrolled, for its likely con- .sequences for economic, social and political stability. ‘This is another area toward which, in spite of the lack of :rtrong theoretical agreement on causal relationships and 304 dynamic behavior, modeling efforts may have to be directed. We have discussed extensions of the model which may be indicated to increase its relevance as an aid in dealing with the problems of economic development. There are also a few extensions, technical in nature, which can add to its range and depth of application to policy formulation. One such extension has already been discussed in Chapters 8, 9 and lO--running the model in a Monte Carlo stochastic mode rather than deterministically. In this way, probability distributions (reflecting data uncertainty) would be specified for key parameters, initial conditions and coefficients of the model; a number of simulation runs (on the order of a hundred) would be made, each drawing samples from these distributions; and output statistics would be generated. As discussed in earlier chapters, such Monte Carlo runs could be useful both to deal with data problems and to evaluate the relative stability and sensi- tivity of policy alternatives in the face of uncertainty. However, there are a number of problems which must be evaluated and solved before a Monte Carlo capability for the model would be feasible. First, there is the problem of defining the parameter probability distributions. This is not insurmountable. Indeed, it has already been done for the northern regional submodel [35, Chapter 4]. There is another potential difficulty, however, which may prove rmore intractable in terms of statistical methods and complicated computer programming requirements: it may not 305 make sense to sample from all the probability distributions independently. In particular, we might require the model to maintain for each sample a "reasonable" goodness-of-fit of time series tracking (Chapter 8). That is, althOugh indivi- dual parameters and initial conditions may vary, they should all vary in such a way as to maintain internal consistency so the model still simulates the same system. A third problem of using Monte Carlo techniques-- the computer execution time necessary to make hundreds of simulation runs--may be handled by the second possible technical extension of the model to be discussed, namely, the use of response surfaces. A response surface is an explicit functional relationship between a vector of relevant output variables and the parameters and initial conditions which have been given probability distributions. Thus, samples from the distributions would be "plugged" into this vector function to determine an observation of the output variables, bypassing the need to make simulation runs of the model. Response surfaces can also be used for policy analysis if policy parameters and variables are included among the independent variables of the function. A look at the generalized response surface function will suggest a limitation of the method: where Y = a vector of output variables at time t a vector function "2| II 306 a = a vector of parameters 8 a vector of initial conditions n a vector of policy instruments. The problem is that a different surface would have to be generated for each point in time which may be of interest as a terminal time. Ideally, a dynamic surface would be generated as an explicit function of time, i.e., Y(t) = F(a,B,n,t). Another difficulty is the generation of the response surface itself. In preliminary work in this area, Turnquist and Manetsch, working with the cattle component of the. northern submodel, used Monte Carlo simulation runs to generate output observations to which they fitted multi- variate polynomials [51]. They found there was a trade-off between the computer time saved in using the surface and the time required to generate it in the first place, so that, given the computer time required to fit the surface, the simulation run time would determine whether it is cheaper to generate a response surface or to use Monte Carlo runs of the whole simulation model. In connection with the problem of generating the surface, a new surface would have to be generated every time the model itself was modified! As a final extension to be discussed here, it could be technically feasible to enable the model to operate in an optimization mode, perhaps by using gradient search tech- niques on response surfaces. However, it is questionable whether this would be a relevant tool for the policy maker. 307 Without common denominators for the many and varied goals of deve10pment, an objective function may not exist. It has been suggested [46] that decision making in general (i.e., not just for economic development) is more a process of ' "satisficing" than of optimizing. That is, decision makers seek satisfactory results within acceptable limits. Uncer- tainty about available alternatives and about the likely consequences of alternatives and the decision maker's igno- rance of his own subjective welfare function make optimization virtually impossible. Implementation The theme of this dissertation has been more than the presentation of a system simulation model and of results of model tests. I have continually emphasized how the model could be of use to planners and policy makers as a tooland methodology with which to get a handle on hundreds of complex interactions in order to project consequences of policy options and to sharpen insights into the socio-economic system of interest. I conclude here with a brief discussion , of where this approach would fit into the policy-making process. Figure IV.32 is a schematic representation of policy making as a problem-solving processl/. At the top is the problem definition phase. The diagram emphasizes the l/ This discussion is drawn and extended from concepts pre- sented in [ 1] and [29]. The diagram is adapted from Ladipo's paper. 308 Conceptualization of Need%= Normative Information Pool Decision-Making Interaction Loop Positive Information Pool Specification of Goals ("Goods" and 'Bads') Specification of Releu vant Policy Variables, Performance Variables, Constraints, etc. ~%Mathematical Modeling 'L___mp__eme .1 Computer I I 1 ' | fiodeI Re '1 and Val inement idgtion Model Application (Policy Simulation) | ’Formula ion off '| P01; 7 Policy Implementation Out (EPolicy Consequencegy' put o I I l l I I I I -I Figure IV.32 System simulation and the policy-making process. Problem Definition Phase 7" I I System Simulation_,._ Phase Policy Formulation and Implementation Phase I l H'— l I 309 interactions and resources that come to bear in defining the problem. The actors consist of decision makers, members of their staff, and outside consultants and researchers-~each with a conceptualization of the problems and needs of society. This conceptualization is based on cultural background and norms and on positive information about contemporary condi- tions. The interaction loop is the center of the process, where the actors exchange views and information on perceived needs and suggested prescriptions. This creative interaction concretely specifies the goals to be attained, defines the problem in terms of constraints, controllable inputs, environ— mental inputs and relevant output criteria, and finally identifies a collection of relevant policy issues to be explored. The problem definition phase also requires nor- 'mative and non-normative (positive) information on the state of the system (economy, society, environment). These infor- mation pools are continually being modified and expanded as new information is sought and acquired in light of the agreed- upon goals and objectives. Such information may then suggest modifications in the goals or later stages of the policy- making process. The system simulation phase has been the subject of earlier chapters of this paper. Usually, it is missing from the process, its place taken by paper-and-pencil projections, recursive or linear programming techniques, or merely intuitive and seat-of-the-pants methods of analyzing and 310 evaluating potential policies. Perhaps the most important feature of this process is the continual iterative feedback from each stage through the interaction 100p where decision makers, consultants and staff members evaluate what has been learned and, if necessary, modify earlier stages. For example, on the basis of model testing, another pass through the modeling stage may be called for. Or, experiences with applying the model to analyze alternative policies may suggest changes in the goals or in the set of relevant policy variables, which might then require additional modeling. In addition, events (including the con- sequences of earlier policies) continue to take place in the world and may generate new ideas and perceived needs which will be conceptualized by the actors in the policy-making process and fed into the process from the top (Figure IV.32). The final point to be made here concerns the relation- ship between the model and the decision maker. The policy decision maker, in evaluating simulated results, must be aware of the assumptions and simplifications built into the model, and he must appreciate limitations that exist vis-a-vis the questions the model is capable of addressing. Further- more, the model described is principally an economic model which will indicate the likely economic consequences of alternative policies; it was not designed to directly answer social or political questions. The policy-making process must still be responsive to the political pressures and social interests which are indispensable components of that 311 same process. In short, a simulation model, while potentially an integral and important part of the decision-making process, will not replace the decision maker. It will, however, give him more information, help to identify new and economically feasible policy options, and sharpen his intuition, thus making for better decisions. BIBLIOGRAPHY "10. 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