The area eme is rare 6 have beer. It analysis, than Urba CorIsllmers It ] Effects i] elastiCitj it is alsc long‘run E meHts, the dologiCal 031$ vErSuS illusion, a L‘- (fl) ABSTRACT f KOREAN RURAL DEMAND FOR FOOD AND ITS 1/ l‘. (:igfk A SHORT AND LONG RUN ANALYSIS OF THE X . IMPLICATIONS TO AGRICULTURAL POLICIES BY Jongtack Yoo The desire to investigate the rural demand for food in Korea emerged from the fact that relevant research in depth is rare and conventional static models for demand analysis have been inadequate. It seems less attention has been paid to rural demand analysis, because of the fact that it is more complicated than urban demand analysis. One complication is that rural consumers are also producers of most food products they consume. It has been asserted that long—run elasticities or effects in economic relationships are greater than short-run elasticities or effects. On the other side of the argument, it is also asserted that short-run effects are greater than long-run effects. In relation with these contradicting argu- ments, the other problem areas in both theoretical and metho- dological aspects in empirical demand analysis are instantane— ous versus lagged adjustment, money illusion versus no money illusion, and other statistical problems such as aggregation bias and serial correlation. n~.< .1?“ . .r \f, I“ go“ . y 4 ‘v. v x‘— A c' model wa S lnvestlga annual da for ten f fzr two m fied acco iata, thr< and barle; It u facis have Of fCOd st @677.an r91 FUCessEd firming ch in interpr iistrisute gave Consi Eda; the Of barley- 1 . Ther. and long 1'] Jongtack Yoo A dynamic demand analysis by using a state adjustment model was undertaken. The basic idea of the model was to investigate if consumers adjust their consumption according to psychological inertia (habit) or according to the physical inventory level. In this study, data were grouped into quarterly and annual data. With quarterly data, a state adjustment model for ten food items and a second-order distributed lag model for two major grains were specified for farm groups classi- fied according to the size of land holdings. With annual data, three systems of equations for the demand for rice and barley-and-wheat were established. It was found that rice, meat, dairy and processed foods have stronger habit forming aspects than other types of food studied. The adjustment coefficient in the rice demand relationship was the largest next to that of the processed foods. This indicates the degree of the habit forming characteristics of rice and will give a new direction in interpreting static demand analysis. The second order distributed lag model for rice and barley—and-wheat also gave consistent results with those of the state adjustment model; the lagged effects for rice were greater than those of barley-and-wheat, and for other foods, they were negligible. There was no uniformity about the magnitude of short and long run effects. For rice, meat, dairy products and processed foods, the long run effects were greater than the short I increas< greater As coeffici value fo that the S'n'itCh t: coefficie fistinguj The were less effiCient illusion 1 fer the f,- In t b~r7 Y1 C«&E) wel. an ' interp r ay‘all/Sis; Jongtack Yoo short run effects in absolute terms indicating a possible increase in the demand if income effect is positive and greater than price effect. As to the differences among farm groups, the adjustment coefficient for the largest farm group showed the smallest value for rice(relative to the other farm groups), indicating that the more wealthy families have more opportunities to switch to other foods. The differences in the adjustment coefficients among the farm groups on other food followed no distinguishable pattern. When undeflated nominal data were used, the results were less satisfactory, particularly in cases of income co- efficients which were mostly negative. A sort of money illusion was interpreted as a rational consumer behavior for the farmer. In the simulation model, a "three-mode" control method and various levels of government purchase prices of rice and barley were tried. Despite severe fluctuations of the results, an interpretation was established on the basis of the previous analysis; demand for rice would increase moderately or remain stable while demand for barley-and-wheat would decrease. The unstable results were attributed to unstable error terms in the estimated equation system and to exclusion of urban demand and supply response. Relevancy of the characteristics of foods and its importance to policy issues have long been recognized. In I’ viii‘" ' Jongtack Yoo view of rural consumers' habit formed for rice, the policy instruments such as the purchase price mechanism may be limited. Consequently future policy should place more emphasis on the rural poverty problem in general. In addition, efforts should be made to lower prices for which rural demands are elastic, such as processed foods and dairy products. Though there were some encouraging results, there are many areas that should be refined and investigated. They include handling of nonlinear constraints, developing con- sistency checks with budget constraints and nutritional requirements, making inter-group comparisons of income elasticities, testing the validity of the permanent income hypothesis, and developing more stable and accurate simulation models. 1:}. A‘ u m u 1 . . 1.! 7 ll AS} RUE ir A SHORT AND LONG RUN ANALYSIS OF THE KOREAN RURAL DEMAND FOR FOOD AND ITS IMPLICATIONS TO AGRICULTURAL POLICIES BY Jongtack Yoo A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1975 ’t‘M‘. .V g“, _. . I \ Dr. John and patie stage of would ha I \ obert Cr and Dr. v ACKNOWLEDGMENTS I would like to express my sincere appreciation to Dr. John N. Ferris for his valuable guidance, counseling' and patience during my graduate program and at the final stage of the thesis writing. Without his help, this work would have been almost impossible to finish in time. I would also like to thank Dr. Glenn Johnson, Dr. Robert Gustafson, Dr. Thomas Manetsch, Dr. G. E. Rossmiller and Dr. William Haley for their kindness and encouragement during my entire academic program. Dr. Clyde Greer of Montana State University is also one of the unforgetable figures. My thanks also go to the United States and the Korean Governments for granting me an unusual chance for higher education. Mr. David T. Mateyka of the USDA and the staffs of the Ministry of Agriculture and Fisheries of Korea, who took the burden of hard work during my absence, also deserve deep appreciation. My wife, Chungja, deserves special thanks for her patience and hard work to make both ends meet throughout the seemingly endless educational process. One of her close friends, Haeja Lee, also deserves many thanks for the many nights of typing drafts. ii GREEK l I. INTROD Needl SCOpI Obje» 11- LITERAT Theo: TiI Fis K0} Ne: Relat III. ANALyT; Basic Ste K TABLE OF CONTENTS CHAPTER I. INTRODUCTION . . . . . . . . . . . . . . . Needs for the Research . . . . . . . . Scope and Methodology of the Study . . . Objectives of the Study . . . . . . . . II. LITERATURE SURVEY . . . . . . . . . . . . Theoretical Aspects and Empirical Works Tinbergen's Model . . . . . . . . . . Fischer's Model . . . . . . . . . . . Koyck's Model . . . . . Nerlove's Model . . . . . . . . . . . Related Research in Korea . . . . . . . III. ANALYTIC APPROACH . . . . . . . . . . . . Basic Model . . . . . . . . . . . . . State Adjustment Model . . . . . . . . Nonlinear Least Square Method . . . Constrained Least Square by Linear Approximation . . . . . . . . . . Quadratic Programming . . . . . . . Long-Run Coefficients . . . . . . . Special Cases . . . . . . . . . . . Estimation . . . . . . . . . . . . . Projection Problem . . . . . . Additive Versus Nonadditive Model . Rational Distributed Lag Model . . . . Aggregation Bias . . . . . . . . . . . . General Consideration . . . . . . . . Aggregation Bias . . . . . . . . . . . IV. SIMULATION MODEL: A CONCEPTUAL FRAMEWORK Economics and Control Theory . . . . . . Economic Applications of Deterministic Models . . . . . . . . . . . . . Characteristics of Models . . . . . . Feed Back Control . . . . . . . . . Optimal Control . . . . . . . . . . Adaptive Control . . . . . . . . . . iii GAMER EC A51; v. ESTIIIII IMPL Esti Da Va He: Polic VI' CONCLUS APPENDIX CHAPTER Page Economic Applications of Stochastic Control MethOdS O I O O O O O O O O I O O O O 6 9 A Simple Simulation Model . . . . . . . . . . V. ESTIMATION AND SIMULATION RESULTS AND POLICY IMPLQT IONS O O O C C C O O O O O O O O O O C 7 3 Estimation Results . . . . . . . . . . . . . . 73 Data . . . . . . . . . . . . . . . . . . . . 73 Variable Definition 2 L . . . . . . . . . . 74 Equations and System of Equations . . . . . 76 State Adjustment Model . . . . . . . 76 Rational Distributed Lag Model of Second Order . . . . . . . . . . . . . . . . . 76 Equation System for Rice and Barley-and- Wheat with Annual Data . . . . . . . . . 76 Auxiliary Equations . . . . . . . . . . . 77 General Procedures of Estimation . . . . . . 77 Estimation Results . . . . . . . . . . . . . 80 An Overview . . . . . . . . 91 Second Order Distributed Lag Model . . . . 101 Annual Demand Equations for Rice and Barley-and-Wheat . . . . . . . . . . . . 102 Simulation . . . . . . . . . . . . . . . . . 115 Comments on the Simulation Model . . . . . 127 Policy Implications . . . . . . . . . . . . . 128 VI. CONCLUSION . . . . . . . . . . . . . . . . . . . 139 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . 149 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . 160 iv 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. 5.9. 5.10. TABLE 3.1. 3.2. 5.1. 5.10. LIST OF TABLES AND FIGURES Adult-Equivalent Scales . . . . . . . . . . . . Examples of Lag Distribution . . . . . . . . . Estimation Results of Reduced Form Equations of Demand for Rice (qij) for Each Group . . . Derived Structural Coefficients for Rice (qi.). Estimation Results of Reduced Form Equation of Demand for Barley-and-Wheat (q2.) for Each Group I O O O O O O O O O O O O J O O O O O O O Derived Structural Coefficients for Barley- and-Wheat (qzj) . . . . . . . . . . . . . . . Estimation Results of Reduced Form Equations of Demand for Miscellaneous Grains (q3j) . . . . Estimation Result of Reduced Form Equations of Demand for Pulses (q4j) for Each Group . . . Derived Structural Coefficients for Pulses (q4j).................... Estimation Results of Reduced form Equations of Demand for Potatoes (qu) for Each Group . . Estimation Results of Reduced Form Equations of Demand for Vegetables (q60), Meats (q70), Fish and Marine Products (q80), Dairy Products (q90), and Processed Foods (qOO) at National Level in Expenditure Terms . . . Derived Structural Coefficients for Miscellaneous Grains (q30), Potatoes (q50), Vegetables (q60), Meats (q70), Dairy Products (q80), Fish and Marine Products (q90) and Processed Foods (qOO) at National Average . . . . . . . . . . . . . . Page 34 53 81 83 84 85 86 87 89 9O 5.11. 5.18. 5.19. 5.20. 5.21. 5.22. 5.23. Estimated Coefficients of Income and Price for Various Foods (National Average Reduced Form Equations; Unrestricted) . . . Depreciation Rate (c) and Adjustment Coefficients (bl) (National Average) . . . . Short- and Long-Run Coefficients and Short- Run Elasticities at National Level . . . . . Estimation Results for Rice (q10) and Barley- and-Wheat in the Second Order Distributed Lag Model . . . . . . . . . . . . . . . . . . National Average Demand for Rice (qu) and Barley—and-Wheat (q20) with Annual Data: ZSLS (Lowest Inventory Level Used) . . . . . Auxiliary Equations for Projection and Simulation . . . . . . . . . . . . . . . . . National Average Demand for Rice, 0(10), and Barley-and-Wheat, Q(2), (Annual Data): Simultaneous Equation System (ZSLS) with the Lowest Inventory - Adult Equivalent Scale (AES) . . . . . . . . . . . . . . . . . National Annual Average Demand Equations System for Rice and Barley-and-Wheat with Change in Inventory Level . . . . . . . . . . . . . Income and Price Coefficients of Annual Model with Per Capita and Adult-Equivalent Scale. . Generated Control Parameter Values of KP, Simulated K I K. o o o o o o o o o o o o o o o o o r 1 Results of Rice Demand and Sales . . Simulated Results of Barley-and-Wheat Demand and Sales . . . . . . . . . . . . . . . . . . . . Simulated Results of Rice and Barley—and-Wheat Demand with Fixed Rate Changes in Real Purchase Prices . . . . . . . . . . . . . . . Price Response to the Government Rice and Barley Purchase Prices (Partial Analysis) . . Possible Results from Various Level of Government Purchase Prices (Partial Analysis) . . . . . . . . . . . . . . . . . . vi 92 94 96 103 107 108 109 110 111 117 119 120 124 131 133 521 521 FIGURE 2L 22. 23. 11. (J. 11. i3. 5.4. Adjus Rat Selec Urbanq Demanc Engel Possit Tote A Bloc Bari Pric Lag Di: Ave: Lag Di (Na Simula Sch Variou of FIGURE 2.1. Adjustment Coefficient (b ) and Depreciation Rate (c) for Each Farm roup . . . . . . . Selected Statistics for Each Farm Group . . . Urban-Rural Demand. . . . . . . . . . . . . . Demand Curves for Rice . . . . . . . . . . . Engel Curves of Rice . . . . . . . . . . . . Possible Relationship between Individual and Total Lag Distribution . . . . . . . . . . A Block Diagram for Rural Demand for Rice and Barley—and-Wheat and Government Purchase Prices 0 O O O O O O D O O C O O O O O O I Lag Distribution for Rice Demand (National Average) . . . . . . . . . . . . . . . . . 5.2. Lag Distribution for Barley-and-Wheat 5-4- Various Experimental Government Purchase Prices (National Average) . . . . . . . . . . . . Simulated Results by using "Three-Mode" Control Scheme . . . . . . . . . . . . . . . . . . of Rice (GPl) and Barley (GP2) and Results vii 136 138 21 24 24 59 72 104 105 121 125 CHAPTER I INTRODUCTION Needs for the Research In empirical demand analysis, we usually adopt a static approach, the basic proposition being that demand is a well defined function of current prices, income and other determin- ants given a nonmeasurable ordinal utility function and rational consumer behavior. This static reversible demand curve is the basis of using the traditional concept of price elasticity [E1].1 Since price elasticities have been key elements in formulating and evaluating a government's price policy, these elasticities have been calculated and used for forecasting possible outcomes of the policies without giving much consideration to the basic propositions upon which a demand function is based. The major problem areas in both theoretical and metho- dological aspects in empirical demand analysis, as this researcher perceives, are, among other things, definition of consumption--actua1 use and inventory, short- versus long-run elasticities (whether it is a decreasing or increasing function of time), instantaneous versus lagged adjustment, homogeneity 1 graphy. Bracketed number refers to items listed in the Biblio- (no money illusion) versus inhomogeneity (money illusion) con- dition, and other statistical problems such as aggregation bias and serial correlation. Contrary to supply analysis or theory of the firm, it seems less attention has been paid to demand analysis in terms of above problem areas, particularly in the Korean food market- ing research. In View of general consensus that most develop- ing countries need more basic research than developed countries, a balance of research activities is desired in the sense discussed above. Consequently, most agricultural market equilibrium models are some variant of Cobweb or harmonic models with dynamic supply functions and simple static demand functions. Even though such a pattern in research activities is rather understandable in view of distinctive nature and importance of supply and production, it is clearly an oversimplification of the real world to assume perfect knowledge and instantaneous adjustment in demand functions. There is no general agreement or rule about the distinc- tion and magnitude of short- and long-run elasticities of demand functions. It has been a common practice to apply an intuitive rule that the long run must be greater than a year [T17]. This length of run, however, must be carefully examined according to the various products, particularly in the case of food products, since the frequency of consumer's purchasing varies from several times a week to several times a month or a year. Particularly, rural consumers have less frequent shopping trips due to either institutional or technical regidities. It is recognized, however, that the choice of subperiods in such details can not be incorporated into the analysis due to the limited data. It is, though, relevant in making correct inferences. Furthermore, there is an argument that it is impossible to measure short-run demand elasticities [N5] despite the fact that short-run elasticities are more relevant and important in analyzing the distinction between actual con- sumption and consumer inventory in case of nonperishable agricultural products. In conjunction with short- and long-run elasticities and lagged adjustment, there is an unsettled argument about the appropriateness of the permanent income hypothesis in an individual commodity demand function. The hypothesis may be relevant to discern change in consumption behavior whether it is due to change in taste and preference or due to income (permanent or transitory) change. The-implications of the permanent income hypothesis in relation with rural demand are twofold; first, it is often argued that farmers have variable income compared to urban wage earners and this fact leads to lower income elasticity of demand for food of urban wage earners. It is expected under the permanent income hypothesis that permanentcom- ponent varies less for farmers than for urban wage earners given tastes and preferences [N4]. It is of interest to find contradicting empirical results in Korea. Daly found rural income elasticity of demand for rice is higher than that of urban demand [810, D1]. Gustafson, et al [610] in the case of rural food demand and Hayenga et al. [H4] in the case of rice demand also found similar results as Daly's. Secondly, an inertia in consumption can be inter- preted as consumer behavior of adjusting consumption in line with permanent income rather than transitory components of income [H9]. In making inferences on the Korean rural demand for food, it may be a matter of judgement of a researcher which aSpect should be emphasized more--permanent income hypothesis or inertia, along with the question of more variablility of farm income. Can we hypothesize that, when farm house- hold income rises, consumers will not immediately attain the higher level of consumption and when income falls they would maintain the level of consumption at their higher income level? Can it be explained by inertia in adjusting food consumption? Existence of money illusion is also argued in the aggregate consumption function as well as in a demand func- tion for an individual commodity. This argument, however, has rarely been empirically tested and left to further investigations [P4], particularly in demand analysis [B9]. Along with the relative magnitude of the short- and long-run elasticities, the money illusion problem has an important bearing in the methodological approach in projecting a much longer period demand pattern. Most FAO and other long-run demand projections (i.e., [Fl]) simply drop the price variables by assuming constant priceswhich amount to zero long-run price elasticities, or which amount to an assump- tion of no money illusion. It is in contrast with an OECD long-run projection [01] which includes price variables implicitly by using a concept of "composite elasticity", which is comparable to "total elasticity" concept [B1]. A study done by Ferris and Sorenson [F2] also includes prices in long term projections. Nutritional aspects were not considered as an important economic problem in neoclassical economic theory partly because of possible characteristics of public goods and subsequent externalities. Though considered in terms of characteristics of goods and consumer technology [L1] and hedonic price indices [68, R4], empirical applications in the context of.nutrition and human resource development are rare. Rural demand analysis seems to be much more complicated than urban demand analysis, mainly because of the fact that rural consumers are also producers of most food products they consume. But most related research has emphasized the urban demand analysis, regarding rural demand as a residual and consequently agricultural price policy has been analyzed with respect to urban demand. The other policy implications of these problems are tantamount. Seasonal and secular price movements, gross farm income, short term outflow of certain agricultural products from consuming areas to producing areas, possible reduction in the consumption of certain farm products, desired level of prices for the economy as a whole, rural migration, and others are directly or indirectly related to rural demand for food. In this sense, Tolley's remark [T15] is quite appro- priate: In view of the fact that. . .future shifts in demand will be principle determinant of what is desirable and possible in [Korean] grain policy, there should be no hesitancy in pur- suing grain demand analysis.2 Scope and Methodologypof the Study The scope of this study includes 10 food items listed in the Farm Household Economy Survey. They are rice, barley- anddwheat, miscellaneous grains, pulses, potatoes, vegetables, meats, dairy products, fish-and-marine products and other processed foods. The first five foods were analyzed in terms of national averages and also for five farm groups classified according to farm land holdings. The last five food items which are reported in expenditure terms were analyzed at the national average level only. 2Tolley, G. S., ibid., p. 13. The basic model adopted in this study was the state adjustment model developed by Houthakker and Taylor, the details of which are explained in Chapter III. The funda- mental idea of this model is to investigate whether con- sumers are adjusting their consumption according to physical stock (inventory adjustment) or psychological inertia (habit forming). To investigate further lagged effects, a second order rational distributed lag model was used where appro- priate. For projection and policy simulation, a very simple simulation model was used. Objectiyes of the Study The first set of the research objectives was to find the validity of the following hypotheses in the rural demand for food analysis and see what kinds of effects emerge from these hypotheses: l. The long-run effects or elasticities are greater than short—run elasticities which are asserted in most economic textbooks. 2. Consumers are free of money illusion and consequently real elasticities are equal to nominal elasticities. 3. There exists a lagged consumption adjustment phenomenon which would differ among different products. 4. Food consumption is a function of permanent income rather than transitory income. Income elasticity is different among different farm groups in the sense that the income elasticity of the lower income group would be greater than that of higher income groups. Secondly, it was hoped to develop tools or models for the following subject matters: 1. Short- and long-run projections of rural food demand patterns. Degree of aggregation bias in the food demand function. Thirdly, it was intended to investigate the following policy implications: 1. Level of the government purchase prices of rice and barley and their impacts on rural demand for rice and barley, inventory and market sales. A possibility of induced change in the consumption of grains either through market or nonmarket mechanisms. Other related policy problems such as off-farm employment, rural-urban migration and size distri- bution of land. CHAPTER II LITERATURE SURVEY Theoretical Aspects and Empirical Works Norris [N6] differentiates demand theory into long and short run. Short run refers to a period fo time when no changes in income and in established consumption rates occur. The important variables are purchases, savings and stocks of the goods. Long run refers to the period when consumers re-evaluate their commitments and change their habits accord- ing to the change in income. In the short run, purchase patterns can vary, even though the consumption pattern remains stable. The difference between the changed pattern and the stable consumption pattern is the change in the inventory level. Thus Norris' definition is synonymous with the usual distinction between static and dynamic demand. One of the most serious defects of the standard approach in demand analysis is its static nature, which is not essen- tially changed by an arbitrary inclusion of lagged variables. An explicit dynamic demand theory has been given by Tintner and by Mosak in the form of maximization of utility over time [T9, T10, T11]. Stone [8111 with wide applications, Nerlove [N3, N4], and Houthakker and Taylor [H9] in the form of a state adjustment hypothesis using nonadditive and additive models. 10 It is, however, well known that there is no general rule or agreement about the distinction of the length of run, particularly in the case of demand analysis. Marshall [M5] identifies long run as a long period of time which is "normal" as distinguished from "secular" change which refers to gradual change over time caused by changes in the state of arts, population, tastes, etc. To have a well defined demand function it is usually argued that the length of run should not be so short that the desire for variety cannot be satisfied nor so long that the utility function changes [H6]. “Mighell and Allen [M9] describe the long run demand curve as an "irreversible adjustment path" compared to "reversible" adjustment of the short run demand curve. This is corresponding to the irreversible supply function argu- ment according to asset fixity notion of Johnson, G.L. [J3, J4], asset in demand theory being tastes and preference or habits depending on different notions of rigidity and adjustment of consumption behavior. Chernoff [C2] bases the distinction on the technological and institutional rigidites and treats only the permanent component in the long run relationship. Wold and Jureen [W3] argue that in empirical demand studies trend free data will result in short-run elasticities trend data will give those of intermediate range and the combination of trend, lag in price and adjustment in quantity demanded would produce the long-run elasticities. 11 Friedman [F9] maintains that the ceteris paribus condi— tions are not substantive but methodological and that the long- run elasticity is greater than the short-run elasticity. The similar conclusions about the magnitude of elasticity for the different length of run are found in Stigler [S7], Nerlove [N4], Shepherd [$52 and Weintraub [W2]. The common reasoning of the similar conclusion is based on lagged adjust4 ment in consumption behavior due to institutional [N4], technological [N4, 82, S7], psychological or habit [N4, S7] and uncertainty [N4] factors. Samuelson [$1, 82], employing the result of the Le Chatelier principle that the change in volume with respect to a given change in pressure is greater when temperature is permitted to vary in accordance with the conditions of equilibrium, also concludes that the long-run demand elas- ticity is greater than the short-run elasticity. Empirically Pasour and Shimper [P3] attempted to compare the two elasticities and concluded that for commodities demanded for actual consumption unlike the demand for changes in storage the long-run demand is more elastic. The first serious attempt to measure the difference between the short- and long-run demand elasticities was made by WOrking [W4] in which he found the long-run (5-10 years) demand elasticity for meat is more elastic than the short-run (one year) elasticity. He uses the model b2Ib3 P = onb1(100q/Q) (lOOc/C)b4 12 Where: P = Given year's deflated price index of the commodity = Average consumption of preceding 10 years Per capita consumption of the given year H a K) II - Income index 0 I Consumer price index¢for the given year C = Average consumer price index for preceding 10 years and the long-run elasticity (Elr) and short-run elasticity (Esr) are E = l/b lr l Esr = 1”’2 As was discussed by O'Reagan [02] and Kuznets [K13], improper functional form and wrong derivation of elasticity (elasticity does not always equal the inverse of flexibility or vice versa)detracted from the validity of his work. Tomek and Cochrane [T16] argue that the long run price elasticity for a product represents a complete quantity adjustment to a given price change where the determinants of the demand are constant, and that the long-run adjustment period is the dated time required for this complete adjust- ment to take place. Thus, they confine themselves to a static demand function in making the distinction. Using a modified version of Nerlove's distributed lag model and following Fox [F7] and Foote [F11], they formulated a short and long-run adjustment model: qt = bOr + blrpt + (1-r)qt_l + bzryt + b3rp t . . . «Hawaii... J. .u......a.......1..=1 \ ‘. . 13 Where: q, p, p' and y are quantity, own price, other price and income, respectively. r is elasticity or coefficient of adjustment 0 i r i l blr is short-run elasticity b1 is long-run elasticity. It seems that their model (also Nerlove's) necessarily leads to a conclusion that long-run elasticities are greater than short-run elasticities because 0 i r i 1. They also calcu- lated the adjustment period (n) by assigning an arbitrary proportion of consumption adjustment (say, 95 percent) such that (1 - r)n : .05 Don Paarlberg [Pl] also claims that the long-run price quantity relation is far different from the short-run rela- tion, and in the long-run for many farm products a higher price means lower gross income to the farmers and sellers as demand becomes elastic. Nerlove and Addison's work on food demand in the U.K. [N5] provides the same result. At the other extreme, the short-run elasticities are argued to be greater than the long run elasticities. That is, elasticity is a decreasing function of time. Conceptually it was asserted by Shepherd [SS] in the case of demand for storage and Breimyer [B6] who cites inflexible characteristics of demand in modern society as the main reason. Empirically 14 it was found by Tomek [T16], Breimyer [86] both in the case of meat and Pasour [P12] in the case of apples. In between these two extremes, there is an argument that the elasticity with respect to time may be U shaped [M3, P3]. The reasoning rests on the different types of reaction of consumers according to different purposes of consumption (actual use or storage). As to the formal proof of the belief that long-run elasticity is greater than short- run elasticity, Subotnik [512] concludes that there is no reason to believe that it is true regardless of the situa- tion. Long-run elasticity may be greater than short-run elasticity when the substitution effect of the last commodity that enters into the long-run consideration is negative and when the real income effect for the last commodity is small.1 Griliches [G9] points out that it is not obvious in theory if all long-run responses should be larger than short-run responses: This is clearly wrong for inventory models and other speculative situations. Brandow [BS] states that, in principle, demand may be elastic over a longer period than shorter period with some exceptions, in contrast with Houthakker and Taylor [H9] who argue that3 1For mathematical proof, see Subotnik, A. [812], p. 554. 2Griliches, z., p. 137. 3Houthakker-Taylor, p. 2. 15 For habit-forming commodities, the long-term effect of a change in income is larger than the short-term effect, and their consumption is less dependent on income change than are purchases of durables. Brandow uses a lag model to distinguish the short-run and long-run elasticity such that for a short run, .. -_— * - .. Pit Pit-l r(P it-l Pit-1) + Cl(qit qit-l) + C2(qjt - qjt-l) + o o o For long run, * = Pt a + blqit + bijt + . . . where P; is the price which, in the long—run, is consistent with the values in year t. He found that the long- and short-run price flexibilities were approximately equal in case of meat demand. Further he notes that though not conclusive, demand elasticities should not be required to satisfy the homogeneity relation exactly. By this he seems to implicitly assume an existence of money illusion in demand functions. Usual approaches to incorporate dynamic elements in demand analysis can be divided into three broad groups: The first is to add a trend term to the static demand equations. The second introduces trends into the parameters of the classical static demand equations (i.e., Stone [810]). The third is to use distributed lags in demand equations. In this third category, there are wide varieties of forms and 16 underlying assumptions of the distributed lags: (1) no specific assumptions are made with regard to the forms of distributed lag (i.e., Tinbergen [T8] and Alt [A8]). (2) specific assumptions are made about the general forms (Fischer [F3, F14] and Koyck [K12]), and (3) specific forms of distirbuted lag depending on the causes of lags (Nerlove [N4] with pure quantity adjustment and Hick's notion of an expectation [A9, C1, H7] model, and Houthakker and Taylor [H9] with quantity adjustment with respect to physical and/or psychological stocks). The general forms of demand equations with various distributed lags are briefly listed as follows: Tinbergen's Model L12) ll bo(§/&) I§bi)(§/E) 0 t1! ll Fischer's Model 1) qt = a + 6m b(u) p(t—u)du log normal time path N N 2) qt = a + b(Z (N-i)Pt_i/Z (N—i)) short cut method 0 o Koyck's Model _ w m qt — a + bOPt+ blPt—l + . . . + bk-lPt-k+l + bkg d Pt—k-m Let k = 0, then 17 qt = a(1-d) + bop + dqt-l o < d < 1 and (31 II S]? bO(p/q) Elr — bogd‘“ (E/c'i) = (bo/(l-dH (Eva) Nerlove's Model at: * Qt FXt and X* are vectors of quantity adjustment and expected prices and income, respectively. With appropriate transformation, the above equation will become Qt = AX + BQ t t-l ' CQt-z Mundlak [M12, M13] presents the procedure for comparing the long- and short-run elasticities applying to the theory of firms. As to the relationship between the permanent income hypothesis [F9] and demand for individual commodities, there have been considerable arguments in both theoretical and methodological aspects. Nerlove [N4] argues that the notion of permanent income hypothesis, if used in demand analysis, implies that the distributed lag is only in income and it should be for each commodity and for total consumption. One practice in empirical demand study has been to calculate income elasticity from cross section data and insert it into 18 time series analysis [B8, 88, T12, W3]. This pooling method is sometimes argued to be inconsistent with the permanent income hypothesis because the two are different concepts [N4]. Absence of money illusion amounts to the zero degree homogeneity condition and is a rational human behavior assump- tion in traditional demand theory. Because of this assump- tion, real prices and income are used in demand equations [T18]. Bronson and Klevorick [39] suggest using a money illusion index such that: C/Pa = f(Y/Pa) in an aggregate consumption function to see if money illusion exists: if a = 1 it does not; if a = 0 it does. If there is no money illusion effect, real elasticity is equal to nominal elasticity [W3]. As noted earlier, Brandow argues that the homogeneity condition of elasticities (sum of elasticities are zero) should not be required exactly, "though not conclusive " [B5], which implies that price and income should not be deflated. Usual approaches to the analysis of demand for stocks have been one of three types: capital goods and investment approach [P2,G7], production and consumption gap approach [B7, T1] and simple time lag approach [P3] and Houthakker and Taylor's approach [H9], the last of which is explained in Chapter III. 19 Related Research in Korea Among the numerous studies and surveys on Korean food demand, only a few research efforts which seem to be relevant are reviewed briefly. No research distinguished explicitly between short-run and long-run demand analysis. Further more, most studies emphasized urban demand analysis. The Grains Policy Task Force's report [R2] for policy alternatives on rice, barley and wheat dealt essentially with short-term (4 months) demand analysis. It was based on the elasticities for June-September period by using monthly data and a constraint of constant total consumption assump- tion such that 30 total _ 3 an _ . = V‘ .Xapi'o l 1'2'3 1 3:1 and assuming the rice price and quantity and wheat quantity fixed in a basic model of Q = f(P,Y). The assumption of constant consumption during the period did not account for consumer inventory. Furthermore, the report did not include rural income in the demand equation under an assumption of constant rural income during the four-month period. This assumption nay imply that rural income is rather stable during a short- term period as compared with urban wage earners, or that rural income plays a rather minor role in determining demand. 20 In view of its analysis for short-term policy alternatives, dropping the rural income variable may not be such a critical matter. But the relative stability of rural income compared to that of urban income during the June- September period is doubtful because of its strong seasonal pattern and, if rural income response in its demand for grains is significant, it would be better to include it in the analysis. The other interesting point in the report is an assump- tion of higher rural grain prices than urban consumer prices which is often found in the real situation. This fact alone puts an upward pressure on urban consumer prices because grain movement from production areas to urban consumption areas would be discouraged, or in some cases, the flow would be reversed. As introduced earlier, Daly, R. F. of USDA [Dl] con- ducted both Korean urban and rural demand analysis for rice with annual data and found that price and income responses of rural consumers are higher than those of urban consumers such that Elasticities4 Rice/Rice Rice/Barley Rice/Income Urban -l.15 .358 .014 Rural -4.40 1.32 .68 4 Daly, R. F0, ibid., p. 30-31. 21 He noted that this is a general phenomenon in a sub- sistence economy. He attributed chronical shortage of rice to a lower rice price along with very elastic rural demand. He further explained the possible direction of supply and demand by using a graphical approach recognizing the limi- tations of statistical analysis as in Figure 2.1. Price Urban Rural I I demand RD;/’ demand I l (RD ) 0 I I / / / I ' / / l l / / RD2 I I ’ / I I / / / / l I P1 / / I I A I I / / ////' / l I I/ ' I ’ I I Q Q Q ' ' 1 2 3 Q4 . L 0 I I I Quantity 01 O O Oi and 05 reflect the rural demand shifts QZQ4 = def1c1t at RDo and P1 0104 = def1c1t at RD1 and P1 0304 = def1c1t at RD2 and P1 Figure 2.1. Urban-Rural Demand. It is apparent from Figure 2.1 that a higher price will reduce deficits or even create a surplus which is con- sistent with basic economic theory, and also clear that the 22 more elastic (price) the rural demand the greater the deficit at lower prices. He did not explicitly analyze what causes the demand shift when he matches a positive demand shift with a lower price and a negative shift with a higher price; that is, Oi axis when P1 and 0% axis when a higher price. As usually the case in demand analysis, traditional demand shifters, income and population, may be insufficient to explain underlying consumption behavior and demand shifts. Moon's [M11] study on rice and barley price policy is also a short-term analysis based on monthly or quarterly data. The main characteristics of his study as far as the demand for grains is concerned were that: 1. Rural demand and sale and urban demand functions for rice and barley under a free market system are specified such that q . = f(Pu., Puj, P y ) for urban demand u1 1 u ui q f(Pr., Prj' stockt_1, yr, p 1 qi sold) ri ri for rural demand. where q, p, and y are per capita monthly consump- tion, monthly prices deflated and income deflated (rural income is from other than qi), and sub- scripts u, r, i, and j denote urban, rural, own and other grains, respectively. 2. To incorporate "consumer's taste and preference" in the urban demand equation, he used an additional variable of multiplicative form, Pui yu 23 3. Another set of rural demand equations and "market transaction" equation were used to analyze policy alternatives such that qri = r(Pri' prj' yr, rural pop., domestic production) Pi = m(Puit-l' Puj' y“ urban pop., total supply of grains) where quarterly data were used. The second equation is essentially an urban demand equation. 4. "Satiety points" where a certain level of price or income does not affect the consumption of rice were introduced such that, from the first set of the equations, dq/dp lys = 0 or dq/dyu IP;i = 0 for urban demand. It seems that there is little logic, as far as economic theory is concerned, to have two different sets of equations and to include a multiplicative variable which is only use- ful to derive, what he calls, "satiety points." In addition, there is a technical difficulty that may lead to a misleading inference. His argument can be explained simply by the following Figures 2.2 and 2.3. Demand curves do, d and d l 2 depending on various levels of income, and e0, el and e2 represent the relationship are Engel curves corresponding to various price levels. Then, contrary to his argument that increasing income could 24 P do(Y=Yu*) d q > * * / 2w- y“ ) elm< e2‘P>P*> P .1. ////// _ * 1 \ /\ eo(p—p ) ' dl(y y*. This would lead to a surprisingly different policy conclusion contrary to his previous con- clusion which was the same as Daly's; above certain levels of income, lower prices would reduce rice consumption with a demand curve d2; rice would be a Giffen good while its Engel curve has positive slope when p > p*. To avoid this contra- diction, his demand curve should be contrained within the range of p 2 p1, q 3 ql, do and d1. Gustafson et al. [6101 analyzed the demand for nonfood and food using household expenditure data and imposing homo- geneity (degree one) condition with respect to expenditure, income and price. They suggested further research to combine the cross section and time series analysis for both urban and rural demand, and to analyze more about the aggregation bias and single equation bias of estimates. The imposed homogeneity (degree one) with respect to expenditure is same as homogeneity (degree zero) condition with respect to quantity demanded. 25 They indicate that income elasticity for farmer's food demand is greater than that of nonfarmers (1.02 versus 0.32) and that there has been a downward trend in food consumption unaccountable for by changes in price, the most likely ex- planatory hypothesis being a change in tastes due to urban- ization and increased mobility. They also note that undeflated income, expenditure and prices would not give a good result because of a highly inflationary situation and high correlation among indepen- dent variables (with quantity or expenditure as dependent variable). Daly [D1] argued that the analysis using unde- flated prices and incomes with the price variable dependent seemed most logical and somewhat more significant statis- tically in Korean rice demand analysis. These two opinions are not contradicting because they are dealing with different dependent variables. Gustafson et al. pointed out, on the other hand, that deflating by a general price index tends to result in a very high negative correlation between deflated price of food and deflated price of nonfood depending on data. Though it seems not obvious intuitively, it may be true if a general price index could not deflate both prices equivalently. Hayenga et al. [H4] conducted a single equation analysis of total, urban and rural demand for major grains, meat, fruits and vegetables by using four different sources of aggregate data: Ministry of Agriculture and Fisheries, 26 Economic Planning Board of Korea, FAO of UN and Farm House- hold Economy Survey data. They implicitly regarded the coefficients as long-run coefficients. They also suggested that regional demand and inventory analysis be conducted. Variables included in each commodity equation varied; mostly quantities, prices and income, prices being sometimes omitted due to the lack of appropriate data. Their work was a good example of how usual regression analysis with different source of data could result in vastly different inferences. Among the coefficients they found some of them are as follows: Rice Barley Price Income Price Income Urban -.760 -.035 -.9481 -l.3lll Rural -.l43 .296 -.300 - .363 1For both barley and wheat. As in most findings, rural income response on rice demand is positive and urban response is negative. But price responses are smaller in rural than urban areas. They attribute greater price responsiveness of urban consumers to the alternative substitutes available to the urban consumer and exposure to the greater variety of food consumption patterns than in rural areas, and smaller price responsiveness of rural consumers to less market-orientedness of farmers and to the characteristics of being producers and 27 consumers simultaneously. This is quite a different observa- tion from others, particularly from Daly's. Probably it may be desirable to disaggregate farm groups into some detail and see if they respond in different manners. The Korean Agricultural Sector Study (KASS) [Kl] deals with rural food demand as a residual and calculated rural per capita food consumption, qt, by using (1 + E Yt ' Yto + E Pt ' Pto y P ) yto P to qt = qto where Ey’ Ep, y and p are rural income elasticity, price elasticity, gross nominal rural per capita income and average price, respectively and subscript to = 1970. BY and Ep are calculated outside the simulation model, and some of them seem to be adjusted according to various sources of information including researchers' judgement. Some of the price and income elasticities that are listed in KASS Special Report (Table 3.10, pp. 3-16, No. 9) are shown below: Rural Urban Price Income Price Income1 Rice .0 .06 - .4 -l.0 Barley 0 - .20 -1.0 -1.0 Wheat -1.0 .20 - .6 1.5 Pulses 0 .80 - .4 .8 Vegetables 0 .40 - .8 .4 Beef -1.0 1.7 - .48 1.7 Fish - .7 .35 - .7 .35 1Urban income elasticities are time—varying such that EY(t-DT) = Eyt°(qt-qt_DT)/(qt - qto) where DT 18 a simulation time interval. 28 One of the interesting points is that most of the elasticities of rural demand are smaller than those of urban demand, and some are set at zero. A joint study report of Yonsei University of Korea and USDA [G1] utilized cross-sectional data from 1964 and derived three sets of projection parameters for food demand: adult-equivalent scale, total expenditure elasticities for foods and average adult consumption of selected foods. At the time of this study, the full text of the report was not available. Thus some of the major findings are only listed: food consumption patterns have been changing due to urbanization and industrialization; expenditures for grains other than rice are inversely related to income; the lowest income households consume relatively less rice and more barley; the growth rate in food demand in urban areas is twice that in rural areas. The Agricultural Economics Research Institute (AERI) of Korea conducted studies on the prices, marketing channels and consumption of rice and barley particularly in the Seoul area by using time series data and by exploring some new cross-section surveys [A4]. They also undertook a number of other studies on the supply of and demand for rice [A3]. In the case of demand for rice and barley, they assumed rice price elasticity being -.5 and the income and population effect .50 without explanation [A4]. The other study simply calculated various constant elasticities by inverting the flexibility model of basic demand equations. 29 Tolley [T13, T14] emphasizing demand for rice as an; important factor in the short-run rice price policy, used the upper and lower limit of various elasticities to predict the range of possible outcomes, and he listed annual and seasonal price stabilization, economic efficiency and equity as policy goals. Other agricultural market surveys include the joint survey of the National Agricultural Cooperatives Federation (NACF) of Korea and International Marketing Institute of the United States for rice, beef, sweet potatoes, ramie and apples [Nl], a study on canned foods [A2] and a survey on Honam rice [K10]. They are based primarily on time series and some on limited cross-section surveys. As has been briefly discussed so far, most studies have been conducted with traditional static demand equations and some with simple distributed lag models. Since there is no such thing as the elasticity and because of difficulties of measurement it is too much to expect consistent estimates from various researchers. An effort should be made, just the same, to develop a reliable estimation process for the structure of food demand. To do this we must recognize the trade offs between data available, economic theory and statistical methods. CHAPTER I I I ANALYTIC APPROACH As was found in the previous chapters, there is no unique method of differentiating the short- and long—run demand analysis and hence static and dynamic demand. Not even a consensus about the magnitude of respective elasti- cities or coefficients is found among economists. Specifications of the model have been heavily depen- dent upon a oriori belief that the long run effects or elasticities are greater than those of short run. Employing a priori belief in the specification of model is an important .method in empirical study of economic phenomenon. Without sound theoretical or a priori knowledge, model building of socio-economic reality is usually thought to be infeasible. There is, however, another method--the "black box" approach [M3, N2]. The basic approach is to start with no knowledge about the system. In this study, both approaches were employed. As far as the relative magnitude of the short- and long-run effects of the change in prices, income and other variables is con- cerned, no a priori knowledge or propositions were incorpor- ated in the model specification, even though there was one defect in conjunction with the relative magnitude which is 30 31 discussed later. On the other hand, the relevant variables and other basic economic behavior were based on theory and real-world observations. Basic Model The "state adjustment and nonadditive" model formulated by Houthakker and Taylor was used, with some modifications and addition. The model was basically formulated with speci- fic propositions about the consumption behavior and form of distributed lag. It was postulated that the effect of past behavior can be represented by the current values of certain "state variables",1 an example of which is inventory level, either physical or psychological. The dynamic process is then that of adjustment in physical or psychological stocks (i.e., stock represented by the past habit of eating). It is "state" adjustment rather than "flow" adjustment of A. R. Bergstrom [H9] or Nerlove [N4]. In the "flow" adjustment model, the dynamic aspect of consumption is viewed as an attempt of a consumer to bring his actual consumption closer to some desired level.2 1"State variables" are defined as those variables that are affected by past history [M3, N2]. 2In "flow adjustment" model, state variable is replaced by q and equation system consists of dq/dt = 0(q*-q) and q* = a + by where q* is long run level and q is desired level [H9]. 32 It is a "nonadditive" model in the sense that it does not exactly fit classical static consumer theory and that budget constraints are not introduced in the estimating procedure.3 One of the advantages of this approach is that physical inventory levels do not necessarily appear in the final equation system. It seems desirable to incorporate possible consumption behavior arising from the "subsistence" nature of small farmers, particularly, in the case of basic foods. In cases where price and/or income do not significantly affect consumption level, it can be interpreted either as a habit forming effect and inertia to adjustment or as the existence of a subsistence level of certain commodities. State Adjustment Model Using the Houthakker-Taylor's proposition, the following basic demand equation for a quarterly model was formulated for an individual farm household: qijt = bijo + bijlsijt + bij2 th Z b133 Pit + b134DV2 Where: q = per capita demand rate in either quantity or expenditure term. 3Additive model uses a quadratic utility function, u(q,s) a + s'b + l/2q'Aq + q'Bs + l/Zs'Cs and a budget constraint, =q' p'q y, where primes denote transpose. 33 stock, habit or consumer inertia to adjust. U) ll y = gross household income per capita prices DVZ, DV3 and DV4 = quarter dummy variables. Subscript i = an individual food (i = 1,. . .,10: rice, barley and wheat, miscellaneous grains, pulses, potatoes, vegetables, meats, dairy, fish and marine products and processed foods. j = household according to farm size (j = 0,. . .,5). The division of farm household groups into five according to farm size is to facilitate aggregation of rural demand function which will be discussed later in this chapter. Per capita figures were used rather than per household, even though it is difficult to regard children as decision makers in purchasing and consuming certain goods. Utility of dependent or other family members is more or less dictated by adults who actually purchase and cook foods. Moreover, the number of consumers of different commodities will certainly differ. A good example of this case is education expenditure; it may be assumed that quantity demanded by persons above about thirty years of age is negligible. There are some commodities, on the other hand, that can not be consumed by individuals, of which an example is housing expenditure. In this sense, Stone's "equivalent-adult scale" [Sll] seems to make sense. This scale is a weighted sum of the numbers in different age and sex groups. Since, however, "equivalent-adult scale“ should be 34 different among different commodities, there is room for arbitrariness. Particularly, in the case of food consump- tion that is under consideration in this study, it seems that such a different refinement of adult scale may not be necessary and that the per capita unit might be enough. Despite this consideration, the scale was tried for annual data using some of the scales from the relative weights of the working class in the United Kingdom developed by Stone [88]. Such scales are shown in Table 3.1. Stone's scales do not include the age group over 66 years, the scale of which is assumed to be between under 14 years and 15-17 years. Table 3.1. Adult-Equivalent Scales Age Group Male Female Under 14 0.52 0.52 14 - 65 1.00 0.90 Over 661 0.65 0.65 1 This corresponds to Stone's scale of 5-13. Rate of change in stock (physical or psychological), s, can be expressed by ds __E = - 3.2 dt qt cst where c represents constant proportional depreciation or 35 consumption rate out of the stock and, for convenience's sake, subscripts i and j are deleted, and dummy variables are omitted.4 Solving Equation 3.1 for st, then 1 <10 1 s = ——(q - b - b y - E b. P. ) - ——-e 3.3 t bl t o 2 t i=1 13 1t bl t Substitute st into Equation 3.2: ds <10 t _ c _ _ _ cg 62‘ ' qt ' 5" (qt bo bzyt .E bi3Pit) + b t 3‘4 1 1—1 1 Differentiate Equation 3.1 with respect to t; Emigwifimb 3311.th 3,5 dt ldt Zdt i3 dt dt Substituting Equation 3.4 into Equation 3.5, then dqt dyt dt ' blqt ' C(qt ' bo ' bzyt ’ £bi3pit) + b2dt dp. de 1t t + Zbint + Cet + dt dyt dpit = cbO + (bl - cht + bzaz— + zbi3at + Cb2Y1: det + Zcbi3pit + cet + a:- 3.6 4 Full model is shown in Appendix. 36 For discrete approximation, Equation 3.6 can be reduced to the following Equation 3.7 by using trapezoidal rule.5 The usual approach of using finite differences to replace deri- vatives is less accurate. + 2A. P. + 2A. P. 1 1 2Yt + A3Yt-1 4 t 15 1t-l + V 3.7 This reduced equation was used for estimation. Since most of the data cover the period from 1964 to 1972, all of the variables in equation 3.7 cannot be used, particularly in the case of annual data and prices which are either inac- curate or Iacking. In those cases, appropriate adjustments are made. When dummy variables are used, the reduced form coefficients are just c times structural coefficients with appropriate adjustments (see Appendix). If qt is the rate of consumption per unit of time, dt, then, JEEET is the corresponding total consumption per t unit of time, DT.6 The relationships between b's and A's are as follows: h0 = Ao(2-b+c)/2c 3.8 h1 = (-2+Alc+2Al+c)/(1+Al) 3.9 h2 = A2(2-b1+c)/(2+c) 3.10 5For derivation of Equation 3.7, see Appendix- 6If quarterly data are used, DT = 1/4 and the values of A's in Equation 3.7 will be different (see Appendix). And DT shall not be confused with DT used in the simulation model in Chapter IV. 37 h2 = A3(2-bl+c)/(c-2) 3.11 bi3 = Ai4(2-bl+c)/(2+c) 3.12 bi3 = Ais(2-bl+c)/(c-2) 3.13 and C = 2(A3+A2)/(A2-A3) = 2(Ai4+Ai5)/(Ai4-Ai5) , 3.14 Since above Equations 3.8 through 3.14 are over identi- fied, following constraints are given: A. for i g ,. . .,10 3.15 = A3 14 AZAiS In solving the estimation problem with nonlinear con- straints, there have been three methods: (a) "nonlinear least square" method [K6], (b) "constrained least square" by linear approximation of nonlinear constraints suggested by Houthakker and Taylor [H9], and (c) quadratic programming method [B4, H1, W1, TS]. Nonlinear Least Square Method Minimize S = 2 [q - ° - q - D Y t 2-(b1-c) 2-(Sl-C) t-l 2 2-(El-C) t (c-2) _ (2+c) _ 2 2-(bl-5T Yt-l 2b ‘ b 2b132116133) pit i3 (c-2) 2 5:51:37 pit-l] 3'16 with respect to all b's and c. 38 Then the resulting estimates are equivalent to the maxi- mum likelihood estimation (MLE) method. It is, however, not guarnateed to generate global optimum values. Also computa- tion are much more complicated because of various combinations of unbounded values of parameters which give most difficulties. Constrained Least Square byLinear Approximation Form a Lagrangian equation L = 2(qt - A - A o ’ Alqt-l Zyt ’ A3yt-l _ZA13pit ’ 2 ZAi4pit_l) - zzAiIAZAiS A3Ai4) 3.17 where A's are Lagrangian multipliers. Differentiate 3.17 with respect to A's and 1's, then we obtain a system of equations such that 8L 8L ‘——— = 0 and ——— BAi Ski = 0 for i g 1,. . .,10 3.18 Solving for A's in terms of 1's gives the following system of equations: 0 (xi) = AzAis — A3Ai4 1 i 1,. . .,10 3.19 Next step is to approximate 0(11) by a linear system of functions 9L(Ai) which is done by solving each equation for two arbitrary 11's and by evaluating 9(11) if it is zero. This procedure continues until it converges. As in the cases of alternative methods, convergence is 39 not always guaranteed because exact functional forms of Equation 3.10 are unknown and nonlinear. Quadratic Programming The problem formulation is the same as the previous methods. There are various kinds of algorithms and opera- tion research techniques; gradient projection method, separ- able programming by piece-wise linearization. Powell's algorithm, complex methods and others. However there is no best algorithm; it dpends on the nature of the problems at hand and trade-offs. In this study, constraints are linearized, which will be discussed in Chapter V. Long-Run Coefficients The short- and long-run effects of change in price and income were derived in the following manner. The coeffié cients of structural Equation 3.1, b's, are interpreted as those of instantaneous adjustment or short-run effects given other variables including the state variable. The long-run coefficient of prices and income, which correspond to entire changes and shifts in demand associated with a once and for all change in the state variable, s, is ng:§:~, for g # 1, that is shown in Equation 3.23. In the long run, it is postulated that the rate of change in stock, 3, in Equation 3.2 is zero such that g? = q* .. (33* = 0 3.20 40 where * denotes long-run level. Then 5* = q*/c 3.21 Substitution into Equation 3.1 gives *= * q bo + (bl/c)q + b + 2b. * * 2Yt 13pit 3'22 ignoring other terms including error terms. Hence assuming bl # c q* bo(c/(c-bl)) + b2(c/(c-b1))y; + Zbi3(c/(c-bl))P;t 3.23 and (n a- ll bo/(c-bl) + (bz/(C’b1))Y§ + 2(bi3/(c-bal;t 3.24 Then bg(c/(c-bl)) is interpreted as the long-run coefficients. To see the relationship between qt, St’ q* and s* and the meaning of b1, the following manipulation is done: From Equation 3.1 and 3.3. _ = - * bl(st s*) qt (bo + bzy; + XbiBPEt + bls ) 3.25 Replacing yt and Pi with y* and P; from Equation 3.22 t t' the term in the parenthesis in the right hand side of Equation 3.25 is just q*. Hence - * = — * . b1(st 3) qt q 3 25 41 where b1 may be termed the coefficient of adjustment, the notion of which is different from Nerlove's concept. If b1 is negative, purchases or consumption are above their long-run equilibrium level and the inventory, 5, is below its long-run level. It is also the case when the former are below their long-run level and the latter is above its long- run level. Durable goods will give rise to this case given tastes and income. The larger the stock at the beginning, the less consumers will buy. If b is positive, the two 1 deviations (deviation of qt and s from q* and s*, respectively) t have the same sign; if current inventory is below the long- run level, consumers will buy less, and if it is above the long-run level they will buy more. A plausible explanation of this case, contrast to durable goods, will be habit forming phenomena. For example, prolonged habit of eating rice which implies larger inventory in terms of this model, either from tradition or prestige, will lead to larger consumption above the long-run equilibrium, other things being equal. There are several advantages in formulating the model in this way compared to Nerlove's model. As briefly dis- cussed earlier, Nerlove conceptualizes several forms of a distributed lag depending on various assumptions. The most complex model includes all of the major assumptions, which are (a) current price and income affect long—run equilibrium level of consumption, (b) uncertainties about prices and 42 income do exist, and (c) institutional and/or technological rigidities in consumption exist. Assumptions (a) and (b) lead touse coefficients of expectations, E, and assumption (c) coefficients of adjustments, R, as discussed in Chapter II. Both of the coefficients or elasticities are bounded between 0 and 1. The reduced form equations arising from these assumptions are usually in the form of Q = nlxt + an t + n30 3.27 t-l t-2 Then the short-run coefficients or elasticities matrix, "1, is represented by nl=RFE < I‘ 3.28 where the long-run effects are denoted by F. It is clear from Equation 3.28 that the long-run effect, P, is necessarily greater than the short-run effect, "1, of the change in the independent variable matrix X since 0 < R, E < I. As indicated earlier this approach results from a restrictive a priori knowledge about the relative magnitude of the short- and long-run effects. It is also clear that bl in the state adjustment model corresponds to coefficients of adjustments, R, in Nerlove's model. The meaning and scope of b however, is less res- ll trictive than R, since b1 can take any value except some special cases which are discussed later. As indicated earlier, 43 one of the defects in the state adjustment model is that it does not count existence of uncertainties in price and income explicitly. The economic meaning of the coefficients of expectation and adjustment is well documented (Arrow and Nerlove [A3], Nerlove [H7], Cagan [Cl], Friedman [F9], Hicks [H7), Griliches [67]). In general they are thought to be functions of consumer's economic horizon that is supposed to be affected by social unrest, government price control, degree of price fluctuations and other factors; the more violent and rampant they are, the smaller the coefficients will be. If we interpret b1 and c prOperly, we could remedy a certain aspect of defects in the state adjustment model; a defect of which is exclusion of uncertainties in explicit form. Incidentally, even the combination of the partial adjustment (R) and adaptive expectation (E) could not accomodate the kind of uncertainties with unknown distribu- tion as discussed by Knight [K7]. It is possible to incor- porate traditioal coefficients of expectation into the state adjustment model. But this leads to extremely complicated estimation problems with nonlinear constraints of high order. Actually b1 and c represent all factors of consumer inertia and adjustment in accordance with price and income expectation which is clear from the lagged terms in the Equation 3.7 if we employ the conventional approach of using lagged terms in behavioral equations without specifying exact relationships or distributions. 44 Since it is perceived that the distributed lag model seems to conform to a priori beliefs, another form of dis- tributed lag, "rational distributed lag", which is discussed in the latter part of this section, was tried to compare the results with the state adjustment model. We will discuss some implications of special cases. Special Cases The occurances and implications of special cases would depend on the way of transforming the equation, Following Houthakker and Taylor, Equation 3.7 takes different forms such that qt _ A0 + Alqt 1 + Aszt + A 3yt-l 3’29 ignoring other termsftm expository purposes. Then A0 = Zboc/(Z-(bl-c)) 3.30 A1 = (2+(b1-c))/(2-(b1-c)) 3.31 and A2 = b2(2+c)/(2-(b1-c)) 3.32 which are the same as in Equation 3.7, but ' __ _ _ o A 3 — b2c/(2 (b1 c)) 3 33 and Ayt = yt - yt_1 3.34 which are different from those in Equation 3.7. 45 And, similarily, all the coefficients of lagged terms will be multiplicative of c/(2-bl+c). Manipulation of Equation 3.7 in this fashion will make interpretation of some of the special cases different as in cases (b) and (G). Since it seems less meaningful to create more special cases, the treatment of functional forms in this study did not follow the Houthakker-Taylor method. For example, from Equation 3.29, when c = 0, A' = 0, but A2 # 0. Then 3 the coefficient of the lagged term, takes two different Yt_1. values, since AZAyt = Azyt - AZYt-l' Let us examine some of the special cases. (a) A1 = l implying that bl = c7 In this case, long term interpretation breaks down as far as the model is concerned since all the coefficients in Equations 3.8 through 3.14 are not defined. This is true because complementary and particular solutions of Equation 3.7 contain A: and l/(l-Al), respectively.8 Then there will be no distinction between the short-run and long-run effect since, as t + w, A: remains constant which is also clear from Equation 3.23. It is suggested by Houthakker and Taylor to transform Equation 3.7 as follows: 71f A1 = 1, then (2+bl-c)/(2-bl+c) = l which results in b1 = c. 8A general form of first order difference Equation 3.7 is qt = IoAI + f(t)/(l-Al) where I0 is determined from initial conditions and f(t) represents the rest of the terms. 46 qt - qt-l = A0 + A2yt + A3yt-1 3’35 ignoring other terms again. (b) c = 2 or -29 When c = 2 all the coefficients of the lagged terms will become zero. This is a case of a static model. When c = -2, the coefficients of current independent values will become zero which will be a special expectational behavior. According to Houthakker and Taylor the case when c = 2 arises if a commodity is bought once a year with a life time of one year and if DT = 1. This line of explanation is plausible if the consumer has no specific concern about the characteristics of such a commodity or if static assumptions hold. In contrast to the previous case, when c = -2, the demand relationship might be governed completely by the past history or habit. (c) c = 0 Then the definitional Equation 3.2 reduces to ds/dt = qt 3.2' and the long run level of q* will become zero. This implies that there is no "feedback" from the past habit, or that there is no desire on the part of the consumer to achieve q*. This case might be that of inferior good according to Houthakker-Taylor. 9When quarterly data are used, it is adjusted with l/DT (see Appendix). 47 Estimation In principle, it is necessary to have both supply and demand equations and to estimate them simultaneously because price and quantity are jointly determined. Unfortunately, however, the simultaneous estimation procedures have seldom given us convincing results in demand analysis [H9]. This may be due to difficulty of deriving appropriate and consis- tent supply equations and due to the fact that, in case of agricultural products, supply is almost predetermined within a given period. Thus in this study it was unavoidable to use single equation estimation procedures without specifying the supply functions. In some cases as discussed in projection and simulation techniques, a simultaneous system was tried by treating some of the independent variables as endogenous variables. But it should be noted here that this is not a true simultaneous system in the sense that supply and demand are jointly determined in the conventional approach. It will serve as an instrument to facilitate projection and simulation. A related problem is autocorrelation which occurs in in almost all distributed lag models.lo Error term, et, 10In contrast to Griliches' [H4], Houthakker and Taylor argue that, "Autocorrelation has been detected much less with the dynamic model than with the static model. This is primarily because the dynamic model is a more adequate specification" [H9, p. 35]. Equation 3.1 and V V 48 t are not the same. Vt is defined by (2+c)e - (c-2)e _ = t t l 3.36 t (2-b1+c) Depending on the nature of e t' variance and covariance of V have different values. t Fi then Vt will serially correlated: rst let et m N(O,oz) which is non-autocorrelated, 11 E(V V ) = E (2+c)et - (c-2)et__1 . (2+c)et_1 - (c-2)et_2 t' t-l 2 - b + c 2 - b + c l l 2 (c - 4) 2 (2-bl+c)2 o 3.37 which becomes zero when c = 2. . _ 2 Secondly, 1f et — et-l + Vt and Vt W (0,0 ), then 2(4+c2)oii+ (c2 - 4)o2 where Oij 15 the covariance between et and et_1. Thus the Durbin-Watson statistic, A A 2 2(V - V ) M. = H} 2 t 3.39 XV should be adjusted in both cases such that when 3.37, E( D.W.) 3.40 II? N I O O I A 11 Subsequent derivations are from Houthakker and Taylor [H9, pp. 35-36] with notations changed. 49 and when Equation 3.38, (4+cz)oi. - (4-c2)02 2 + 2 3 3.41 E(D.W.) (4-c2)oij - (4+c2)o2 Projection Problem Projections, in general, can be made either by solving difference Equation 3.7 or by substituting corresponding values. Usually the former method yields more error because of rounding. The most troublesome problem is how to derive the cor- responding independent variables for projections. For this reason, the quarterly model was not used for projection purposes. Only annual demand equations for rice and barley and wheat were simultaneously estimated using a two stage least square estimation procedure. These equations were used in a policy experiment by using a simulation technique that is discussed in Chapter IV. Additive Versus Nonadditive Model The decision whether to us the nonadditive state adjust- ment model rather than the additive state adjustment model was a matter of trade-offs. While the nonadditive model does not have to assume an explicit utility function other than utility being a function of quantity, can be estimated by single equation estimation procedure, and also does not require the estimation of marginal utility of money, this 50 model does have some defects. They are that estimates may be biased even with smaller mean square error (MSE) when estimated by single equation procedures, that identification problem in the depreciation rate, c, forces the ratio of the short and long-run effect, c/(c-bl) in Equation 3.23, to be the same for all independent variables in an equation and that it does not satisfy budget constraint. The additive model, on the other hand, is free of these defects. But a "quadratic utility function" is arbitrarily defined and this forces the model to estimate marginal 12 utility of money that is subject to change depending upon the form and monotonic transformation of a utility function.13 Even though the estimates of simultaneous equations are not biased compared to those of the nonadditive model, their MSE are greater. For policy formulation and projec- tion purposes, the decision of choosing between smaller MSE and an unbiased estimator has not been of unanimous agree- ment among economists. According to Mincer-Zarnowitz criteria [M10], the goal of forecasting is the minimization of MSE which is expressed by 12Since quadratic utility function is defined as (q,s) = q'a + s'b + l/2q'Aq + q'Bs + l/25'Cs, derivation procedure of final equation by using Lagrangian equation with a budget constraint, p'q = y, can not eliminate the multiplier, A, which is marginal utility of money [H9]. l3Monotonic transformation of a utility function does not change final demand equation and preference ordering but changes the value of marginal utility of money. 51 (At - Et)2 MSE = zw— N 3.42 where At is actual value of forecasted variables, Et is forecasted value, N is the number of observations. Theil [T5] uses U as a statistic to measure the goodness of fit of forecasting which is defined as _ 2 1/2 (£(Ei Ai) ) U ___ 2 2 3.43 F—zni + f—ZAi If U is zero, it implies perfect forecast. The choice between unbiasedness and smaller MSE depends upon circumstances and loss function of user of the projections. It seems that if we are generating a large number of projec- tions across the economy it would be more important to have unbiased estimates than those having smaller variance. Rational Distributed Lag Model If the number of observations is small, as may well be in the case of annual data, and if these successive past observations are not collinear, then the weights with which past and present values are combined can be estimated directly by least squares. When, however, the observations increase, as in the case of quarterly data, it may become necessary to make some reasonable assumptions about lag distributions. In general, these assumptions include popular geometric, arithmetically declining [F3], Pascal [Kll] of which inverted v lag and polynomial interpolation distribution 52 are the cases, and rational distributed lag distribution [T5]. The adaptive expectation [Cl] model that attributes the lags to uncertainties and the partial adjustment model that attributes the lags to technical, institutional or psychological inertia [N3] usually adOpt an assumption of geometrically declining weights of past impacts. A doubt was raised by Griliches [G9] about its generality. He points out that because of wide spread availability of quarterly and monthly data, the assumption that the largest response occurs immediately after the beginning of the adjustment period seems to be quite restrictive. The other distributions, however, are not free of difficulties. For instance, those using the polynomial distribution must decide the degree of polynomial a priori which is not always well established. The rational distributed lag form also requires such assumption. In any case, distributed lag models suffer from "theo- retical adhockery." Examples of various lag functions are given in Table 3.2. Admitting its theoretical adhockery, Jorgenson's rational distributed lag was used in the rural demand specification, and results were compared with those of a lag distribution arising from state adjustment assumptions. One of the benefits of using a rational distributed lag is, as he indicates, that it makes equations estimatable in 53 Table 3.2. Examples of Lag Distribution 1 l A(L) T(L) Distribution (l-r) (l-rL) Geometric Distribution (l-r) (l-rL)n Pascal and General Distribution (l-rl)... (l-rzL)(l-r3L)... Rational Lag Distribution 1In y = b A(L) x where L is lag operator (L is a lag t T(L) t n ' operator such that Lyt = yt-l" . .,L = yt-n) A(L) and T(T) are finite polynomials of rational generating functions and r is root(s) of polynomial(s). ta sense that number of unknown parameters can be kept as small as possible. Another is that the approximation of an arbitrary lag function is possible to any desired degree of accuracy. The class of rational distributed lag function is defined by the condition that the sequence of the coeffi- cients of Wi in s + w‘s2 + . . . 3-44 W(S) = wo + W1 2 on where Zwi = l which describes the form of lag distribution has a rational generating function of Wi which is denoted by W(S) where m a + a s + . . + a S _ A(S) _ l ’ ' ’ m = W(S) — ifi§7" 56_:_BI§+" . .' + angfi W(L) 3.45 and S is auxiliary dummy variable. W(L) is a short hand notation for a power series or polynomial in lag operator L 54 (rational generating function). Then yt, a dependent variable, can be expressed by Equation 3.46 with some dependent vari- ab1e(s), x such that t, A(L) x 3.47 yt = bW(L)xt = bT(L) t With this concept in mind, let us specify the struc- tural or original equation14 as Q* = b + b + b + 2b. P? + b DV2 + b DV3 t o 1 1 * * 12Y1t 22Y2t 3 t 4 5 + b6DV4 + et 3.48 where stars denote the long-run level and also indicate that there exists a rational lag distribution in the variables. Let us specify a second order rational distributed lag model such that ignoring other terms _ * * qt — W(L) (bO + blzylt + b22y2t + Zbi3pit) 3.49 where (ak+3 + ak+4L) W(L) = A(L)/T(L) _ _ (l AiL)(l 12L) for each k = 0,2,4 3.50 where a's are defined in Equation 3.51. Then the final form will be 14Terminology differs depending on starting point of logic. Jorgenson treats Equation 3.49 as the original or structural equation. The reason for treating Equation 3.48 as the original is to distinguish between the short and long run. 55 qt = a0 + alqt-l + azqt-z + a3Yit + a4Y1t-1 + a5y2t + a + a DV2 + a DV3 + 2a. P + zaiBPt-l 9 10 6Y2t-1 17 t + allov4 + vt 3-51 which will serve as an equation to be estimated, and where 2 (1 11L)(1 12mgt (1 (Al + 12)L + AAZL )qt = qt ' alqt-l ‘ a2qt-2 3'52 Where: a1 = 11 + 12 3.53 a2 = -11A2 3.54 What are the relationships between W(L)b, or the coefficients of Equation 3.51 and those in Equation 3.48? In Jorgenson's original article [J5] and Griliches' survey article on distributed lag models [G9] they do not explore these relationships in terms of short and long run. As briefly noted in Chapter II, Tinbergen [T8], Fischer [F3, F4] and Koyck [K11] developed a device to distinguish the short- and long-run effects of price changes. According to Tinbergen, the short-run coefficient is just that of current price and the long-run coefficient is the sum of the coefficient of the lagged price variable as well as current price. Fischer defines them similarly using both log normal and arithmetically declining lag. 56 Koyck's method is also similar to the previous method except in the case of long-run coefficients; the long-run coefficient is defined as the coefficient of current price multiplied by lagged power of weight of each period which is summed over the relevant lag period. The common practice of their approach is to sum the coefficients of all lagged independent variables with different summing methods. The other point is that they use one equation to distinguish the short- and long-run effects. Given an equation of certain distributed lag form, find the relationship. The basic approach used in this study as far as the rational distributed lag model is concerned was the same as Tinsbergen and Fischer's method for the short-term effect. But for the long-run relationship the structural coefficients were treated as the sum of total weights which is explained below. Let us look at the time path of a transitory change in independent variables on all future q, assuming that all current values of all variables are l and all lagged variables are zero. Then weights15 at t time period, rj, are given by r0 = a3 3.55 r1 = a4 + alqt = a4 + alro 3.56 r2 = alr1 + azqt = alr1 + azrO 3.57 15 The derivations of weight and wi are from Griliches [G9]. 57 r + a r 3.58 r. = a r. + a r. 3.59 To derive wi's, which describe the form of the lag and gives the relative influence of differently lagged values of independent variables on current qt, first we find the sum of rj such that 2r - b 2w - b — (ak+3 a ak+4) 3 60 j ’ h i ‘ h ’ 1 - a1 = a ’ 2 since Zwi l by definition for h = 2,. . .,6 and k = 0,2,4, ignoring other terms. Normalizing Equation 3.60 such that Zr. 3 + = 1 3.61 ak+3 ak+4_ l - a1 - a2 then we have the following relationships: wO = ro(1-a1-a2)/(ak+3 + ak+4) 3.62 wl = rl(l-al-a2)/(ak+3 + ak+4) 3.63 wj = rj(1--al-a2)/(ak_'_3 + ak+4) 3.64 Following the guideline defined previously, we may formulate the relationship between the structural coefficidents 58 that are assumed to be long-run coefficients and those in the final equation as follow by using rj: Letting A = l-al-az, then b12 = (a3 + a4)/A b22 = (a5 + a6)/A bi3 = (317 + ai8)/A b4 = a9/A 3.65 b5 = alo/A b6 = all/A vt = et + alet-l + azet-z Specifying the relationship in this manner may not be very appealing, mainly because of no clear-cut mathematical linkage between the "structural equation", 3.48 and the Equations 3.49 or 3.51. However, it seems to be a matter of assumption and of interpretation of b in Equation 3.60. h Interpretation of long-run effects as an accumulation of the weights of transitory change in the independent variables on future quantity consumed may be a reasonable one as is expressed by Equation 3.60. In this study, logical consis- tencies were checked with the empirical results from the state adjustment model. The usefulness of wj is in describing the lag form. Figure 3.1 shows the relationship between the individual lag distribution and the total lag distribution. The total lag distribution is supposed to show the impact of change in all independent variables on the current dependent variable. 59 ‘\ T(L) Figure 3.1. Possible Relationship between Individual and Total Lag Distribution. Depending on the individual lag distribution, the total lag distribution can be a convolutionary shape. Aggregation Bias General Consideration Aggregation is usually thought to be satisfactory by the analysts to the extent that they believe the cost of incorporating detailed information outweighs the reliability of the results from them. Thus the cost and reliability are two important factors that should be taken into account in disaggregation and aggregation. In the case of Korean rural demand analysis it was assumed that there have been less reliable results in the usual aggregated models and the cost involved in the dis- aggregated approach is far less. The division of farm 60 households into five according to the size of land holdings seems to be reasonable in view of cost. Aggregation is said to be "consistent" [G4], when the more detailed data do not give very different results from those of aggregated information. There are some doubts about the validity of a micro- model that heavily depends on more detailed information than a macro-model does. Peston [P5] argues that any micro theory to explain the same universe as macro theory would be either useless or wrong, if the latter were valid. For example, if household consumption depends not only on its own income but also on the distribution of income, then a micro demand analysis that neglects this latter dependence will suffer specification error, and the predictions based on this micro-model or disaggregated model will be less accurate [G11]. If the behavior of the independent variables is not known, the assumption of consistent aggregation imposes severe restrictions on the usefulness of individual micro functions [G4]. But, if it is known, i.e., income distribu- tion is constant or changes systematically, then this re- striction will be less severe even if we include this variable in individual equations. There are two useful theorems developed and proved by Green [G4] which are condensed into following Theorem 1 without showing proof: 61 Theorem 1. It is necessary for consistent aggre- gation, when the optimal conditions are such that the marginal rates of substitution between any two commodities are same for any two groups, that (a) for each group, each set of points in the commodity space at which marginal rates of substitution are constant, is a straight line, (b) for a given set of marginal rates of substi- tution, the straight lines for all groups are parallel, and (c) the Engel curves for all groups should pass through their respective origins. In reality it is difficult to believe that those consistency conditions are given in Theorem 1 are all met. For an example, it may be true that each individual or group of rural households has a certain minimum level of consumption below which his or its utility function is not defined. In this study, it was assumed that these consistency conditions were not satisfied. It was also recognized that insistence on the impossibility of aggregating any two variables would destroy all marginal analysis in economic theory. Thus it was assumed that there is a degree of disaggregation or aggregation at a certain level that is legitimate. The purpose of this section was to show aggregation bias in a demand equation when it is specified with average (arithmetic) per capita or per household data. Additional assumptions for this purpose were that the parameters estimated from the demand equation specified with original 16This also applies to aggregation of production functions. It is of interest to note that Klein [K4, K5] argues that only technical relationships should be taken into account in aggregation. 62 per capita data not averaged arithmetically at the national level are true parameters and that the functional form is linear. Aggregation Bias Let the demand equation with original demand equation for each farm group be: qj = aj + bljxlj _ ijXZj 3.66 where x denotes any independent variables, ignoring other terms and subscripts, and also let the equation be estimated from arithmetic average data used in most empirical studies. = I l- a + blxl + bzx2 3.67 Where: ("i = Q/N i = X/N Q,X,N = total quantity demanded (Zq.) , independent variables (2x. ) and total namber of households or number of roups, respectively. Then, under the consistent aggregation assumption, the following relation should hold: a' = a. N J/ bl = blj/N and 3.68 ' = b2 ij/N Aggregation bias is, then, any deviation from Equations 3.68. The exact relationship of bias is derived by Theil [T4] and Green [G4]. CHAPTER IV SIMULATION MODEL: A CONCEPTUAL FRAMEWORK Economics and Control Theory The methods of control theory developed in electrical and communication engineering have been increasingly wide- spread in empirical studies of economic theory. In the fields of macroeconomics, the applications of control theory and optimization techniques include, among others, a growth model of a national economy, and an economic planning model focusing on the sectoral allocation of investment over time and short-run fluctuations of general price level and employment. In microeconomics, the applications have been in such areas as consumer choice over lifetimes, theory of firms and resource development, though these applications have been less attractive than those in macro models. In the past, estimation procedures for determining the coefficients of the economic models have dominated econometrics. Recently, many efforts have been directed toward the simulation and optimization of given models, either deterministic or stochastic. We have seen that the capability for projection or prediction from the economic model is quite limited because 63 64 of the inability to conceive fruitful categories of general- ization with which to bring intellectual order into the real world and also because of the inability to formulate "high-level hypothesis" that can digest all the useful real world data [H5]. Actually there is no way of avoiding the conditional- probabilistic nature of projections of economic phenomena. Researchers, thus, have to make reasonable assumptions about structural relationships not only between the past and present but also between the sample period and the predic- tion period. When structural changes are expected to occur during the latter period, the problems confronting the researchers are to specify the change and to establish the new structure. Two distinctive models have been used for economic applications: (a) deterministic and (b) stochastic control models. Underlying deterministic control models is the assumption that there is a unique value of a variable at each stage of process (single valued function). It can either be static or dynamic. Stochastic control models involve multi-valued functions [M14] including parameter estimation or adjustment at each stage of process. Economic Applications of Deterministic Models Most of the economic applications briefly cited above belong to deterministic models. They are macro stabiliza- tion models [P8, A5, H8, P9], economic growth models 65 [P8, K9],models for firms [S4], and sectoral models [R3]. Characteristics of Models Feed Back Control Given a linear controllable system specified by dX/dt AX(t) + BU(t) 4.1 Where X, U, A and B denote an nxl state vector, a mxl control vector, nxn parameters and nxm parameters, respec- tively, with initial condition being X(to) = X0, then a feed back control problem is to find the control vector, U(t), as a function of state vector, X(t), such that certain prOperties like stability and/or steady state error are attained. The class of feedback controls generally includes the proportional, derivative and integral controls such that U(t) = CX(t) + Ddx/dt + Ff;x(r)dr 4.2 in time domain, or U 1'1 E(S) = kp + kr(s) + S— 4.3 in 3 domain where E denotes the difference between desired system output and actual output [M4, P8]. The purpose of the control scheme is, then, to determine the unknown coefficients C, D and F or kr' kp and ki’ More are dis- cussed here because it is relevant with the simulation model in this study. 66 Proportional Control: C or kp It is a correcting action for the desired level to be made proportional in magnitude and opposite in sign to the error, E, in a system output. The ratio of the policy variables and error, u/E, may be called a proportional correction factor which is a measure of the strength of the policy or control. As an example, a proportioal correction factor of 0.5 would mean that if system output is 2 percent below (or above) the desired value, the government would attempt to manipulate policy variables by an amount of equal to 2% x 0.5 = 1% (or minus 1%) of the actual system output. There are some defects despite its simple form and ease of application. First, complete correction of an error is difficult to obtain because of the error inherent to the prOportional policy measure in a finite time horizon. Secondly, it tends to cause a cyclical fluctuation in the time path of system output, that is, the greater this fluctuation, the stronger the policy and the longer the time lag will be, even though it is smaller than that of an integral policy measure. Derivative Control: D or Kr It is used to reduce oscillations of system output by adjusting control variables to the derivative of error. Note that when dE/dt = 0 it gives zero control variables. Thus it will not work for the targets that are constant 67 step functions for a long time period and at the same time when error does not change. Thus usually rate control alone is not used. Integral Control: F or Ki An integral control policy is that the policy variables are adjusted proportionally in magnitude and opposite in sign to the cumulated error up to that time. Integral correction factor is defined the same way as proportional correction factor except that error is integrated. Even though we can avoid the first defect of a pro- portional control policy, cyclical fluctuations will become greater, and the longer the error continues, the larger the control‘variable will become which is usually upper bounded. For this reason the integral control method alone also is rarely used. In the case where desired policy target is a ramp function, proportional policy measure does not track the target very well. More than that there is usually an upper limit on the policy variable. Alternative measure is to combine proportional and integral policy measures to reduce the tracking error. But the introduction of integral policy measure will often increase oscillation. If deri- vative or rate control measure is combined, it would dampen oscillation. 68 Optimal Control Optimal control requires a performance criterion in addition to Equation 4.1 such as profit, utility or other objective functions. Given a performance criterion opt. J = {E f(x(t), u(t))dt 4.4 subject to X(t )eS fl u(t)tU for all t x(t)eX then optimal control problem is how to determine u(t) as a function of time (open loop), or a function of X(t) (closed 100p) such that Equation 4.4 is optimized subject to given constraints. The work done in this area for economic applications include Tinbergen [T6], Theil [T5], Fox et a1 [F8] and Chow [C3] . Adaptive Control These methods are designed to analyze the various implications of a broad class of admissable controls which may include various sub-optimal (satisficing) controls such as evluation of alternative learning processes, comparisons of alternative approximations to the complex model and sequential analysis of system behavior assuming a priori 69 Baysian probability distribution of unknown parameters. They are principally governed by the flow of information. The work and economic applications include Theil [T2] and Zellner [22]. Economic Applications of Stochastic Control Methods Since most deterministic models have stochastic counterparts, most of previous applications include sto- chastic parts. Some of the characteristics of the stochastic control methods are parameter and state estimation and control to optimize the expected value of some performance criterion. A Simple Simulation Model The purpose of the simulation in this study is not to give an answer to the question of "how to do", but to give policy makers an information about "how much", given the model. The answer to the former question is out of the scope of this study. In this sense, it may not be a realistic approach. But certainly it can serve as a basis of normative judgements which are unavoidable in policy formulations and implementations. It is a deterministic control model with dynamic elements using the econometric model specified in the previous chapter. It is also a very simple and basic feed back control scheme with very limited numbers of state, 70 policy and performance variables. It is kept as simple as possible not only because of limited data but also because of a desire to see the workability of the feed back control model for a rural demand system. The desire to develop a rural demand simulation model has been augmented by very interesting and stimulating ideas of Dr. T. Manetsch of Michigan State University. According to him, domestic and world-wide food crises may result in the following major consequences:1 a. Migration back to rural area b. Decrease in food supplies, particularly grains, to urban areas c. Suffering of the lower income groups, particularly those that have no ties with rural population. d. Farm supply may not respond to price or income changes significantly e. Inevitable government intervention in the form of food rationing both in consumption and marketing of certain farm products. His draft paper contains detail model components such as birth and mortality ratios which depend on the nutritional intake level, private and public stocks of foods, population in age, sex, migration from and to rural area, and other factors. An easy and simplest way to . incorporate this idea might be to manipulate relevant 1It is summarized from"A Model Builder's Diary"[§ig.] by T. Manetsch. 71 parameters in the model with proper assumptions. For example, such parameters will include the coefficients of population and migration rates. To use econometrics in simulation models, we can either transform the equation system into "state variable form" [P9] or use the equations directly in simulation. It seems that it is a matter of technique in claculations. In this study estimated equations were used directly. The scope of the commodities included in the simulation model is limited to rice and barley-and-wheat with annual data. 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I -:I- .- _“ anIIIII. x _ 63.3 2... c- w 36 $6 I 3L . mumcuuam . _I »u . e muqm unassum>oo CHAPTER V ESTIMATION AND SIMULATION RESULTS AND POLICY IMPLICATIONS Estimatipn Results Data Most of the data used in this study were from the Farm Household Economy Survey published annually by the Bureau of Statistics, Ministry of Agriculture and Fisheries (MAF) of the Republic of Korea. Other data were from the Monthly Statistical Review of the Bank of Korea and the Statistical Yearbook of MAF. The Farm Household Economy Survey started in 1962. But comprehensive data are available only from 1964. In this study the data covered the period of 1965-1973 for quarterly and annual data. In analyzing the state adjustment model, annual data which include only 9 observations were not apprOpriate to be used. Thus for the state adjustment model and the second order rational distributed lag model, only quarterly data were used. For simple simulation and projections, annual data were used. For rice, barley-and-wheat, miscellaneous grains, pulses and potatoes, actual quantity data were used, while for vegetables, meats, fish-and-marine products, dairy' 73 74 products and processed foods, expenditure data were used. For the first five food items, demand equations were specified for the nationalaverage and each farm group, while for the last five food items, only national average demand functions were specified. The annual simulation and projection model which con- sisted of a system of equations was also specified with national average data. The adult-equivalent-scale was tried for annual data only. Variable Definition qij = ith food consumed by jth household (R/per capita) H. II 1 = rice, 2 = barley-and-wheat, 3 = miscellaneous grains, 4 pulses, 5 = potatoes, 6 = vegetables. 7 = meat, 8 = dairy, 9 = fish-and-marine products, 10 = processed foods C: ll 0 ll national average per household 1 = farm with less than 0.5 cheongbo 2 = farm with 0.5 - 1.0 cheongbo 3 = farm with 1.0 - 1.5 cheongbo 4 = farm with 1.5 - 2.0 cheongbo 5 = farm with over 2.0 cheongbo y1 = gross farm income of jth group (Won per capita) y2 = gross nonfarm income of jth group (Won per capita) s = stocks in terms of nonmeasurable psychological habits (or inertia) SI = lowest actual monthly stocks or change in inven- tory during a year for food (g/capita) 75 y = gross household income when quarter, net when annual data (=ylj + y2j - Taxes)(Won per capita) p = price (index) (1965 = 100) P0 = production FPPI = farm purchase price index (1965 = 100) UV = Quarter Dummy Variables If 2nd quarter DV2 = 1, otherwise 0 If 3rd quarter DV3 = 1, otherwise 0 If 4th quarter DV4 = 1, otherwise 0 GPl = Government purchasing price of rice (won/80kg) GP2 = Government purchasing price of barley (Won/50kg) PM = Total number of farm households TM = Percentage of nonfarm workers to total members of family DL = Average land holdings of jth group (cheongbo/ household) 1 = Liter (unit for measuring grains)l T Calendar time (1,. . .,9) SSFh = Number family members per sex and age group h = 1, number of family members under age 14 (total) h = 2, number of family members 14-64 (male) h = 3, number of family members 14-64 (female) h = 4, number of family members over 65 (total) SF = Number of family members per household. 112 N .798 kg. for rice, .549 kg. for barley and .765 kg. for wheat. 76 Equations and System of Equations State Adjustment Model 1. Structural Equation qt = bO + b + b + b3Pt + b DV2 + b DV3 + b DV4 lst 2Yt 4 5 6 +8 I t 3.1 2. Reduced form equation to be used in estimation qt = A0 + A1qt-1 + A2Y1: + A3yt-l + ZAi4Pit + ZAiSPit-l I + A6DV2 + A7DV3 + ABDV4 + Vt 3.7 Rational Distributed Lag Model of Second Order qt = a0 + alqt-l + ant-Z + a3Y1t + a4Y1t-1 + aSYZt + a6Y2t-l + £ai7Pit + zaiSPit-l + a9DV2 + aloDVB + allDV4 + Et 3.50' Equation System for Rice and Barley-and-Wheat with Annual Data Qlt _ a10 + a11Yt + a12P1t + a13P2t ta = a20 + aZlyt + a23P2t P1t - a3o + a3ISI1t + a33GPl + a34GP2 5.1 P2t = a4O + a428I2t + a43GPl + a44GP2 SIlt- a50 + a51P1t + a52P2t + a5313011: + a5413921: + assT SI2t' a60 + a61P1t + a62P2t + a63PQit + a64PQZt + a65T Yt’ a7o + a7lPlt + a72P2t + a73PM + a74TM T”: aso + a81Yt + aazT 77 Auxilia§y5Eguations PQl = B + B T 10 ll PQZ = B20 + 321T PM = 830 + B31T SF = B40 + B41T 5.2 SSF1 = Bso + 351T SSF2 = B60 + B61T SSF3 = B7o + B71T SSF4 = 380 + B81T General Procedures of Estimation Several functional forms with arithmetic linear, double logarithm and semilogarithm forms have been tried. It was found, in general, that the logarithmic transformation did not significantly improve the equations. Consequently arithmetic linear forms were adopted in most cases. This form is also convenient for calculating relevant structural coefficients. The models with quarterly data were estimated by OLS. As indicated earlier, it was almost prohibitive to use the simultaneous system procedure because of a large number of variables. A "stepwise-delete-and-add" procedure with an F value of .15 was used to observe the behavior of the coefficients. After this procedure, variables were selected in the light of economic theory, statistical properties, the characteristics of the model at hand and judgement of 78 this researcher. Some of the variables need to be mentioned specifically. The separate income variables, farm income (ylj) and nonfarm income (Y2j)’ were tried to see how the rural consumers respond to the different sources of income. It was felt that since the farm income comes mainly from crop production which is also a major source of food consumption, rural consumers may not respond to the income change in the same manner as urban consumers do. The income response was expected to be negative as it was found to be in many cases. Nonfarm income was considered as a proxy variable to relate the rural consumption pattern to a possible exposure to nontraditional food consumption--factors that might induce an "eye-opening" to wider "choice set." It was also expected that rural consumers would respond positively to nonfarm income change in contrast to farm income change due to a possible psychological influence stemming from a freer 'decision to dispose of their products for consumption. As expected, in most cases, the coefficientturned out to be positive and its absolute magnitudes or elasticitieSIwere greater than those of farm income; thus, on balance, the net effect of total farm household income was positive. Despite this "elegancy", there were some problems; increased numbers of constraints, unexpected and unexplain- able results in some cases, and large standard errors. Thus, after due considerations about the trade offs, it was 79 decided to combine two sources of income into a single variable. Separate sources of income will be mentioned only when it seems to be appropriate. Considering the characteristics of the rural consumers, production (PQ) was excluded in demand equations. There are some studies which include production in rural demand equations as in Fox [F7] and Moon [M11]. But the inclusion of production in the demand equation seems to make the nature of the demand equation rather ambiguous by making the demand equation a combination of supply and demand. This procedure also results in high positive correlation (about .7 to .9) of production with farm income, though it is a relevant variable in rural consumption decisions. Thus, in final equations, production was excluded. Quarter dummy variables are included regardless of their significances, for quarterly consumption levels are thought to be different and also they would represent some other influences that are not explicitly included in the equations. After the selection of variables and forms of equations, a new OLS estimation procedure was conducted. With these initial results, parameter constraints were imposed as discussed in Chapter III and briefly described in this chapter. Other than equality constraints, the selection of parameters to be fixed was based on the significance level, theoretical and empirical meaningfulness and linearity. For the second order rational distributed lag model and the 80 annual model, no constraints were imposed. For the second order rational distributed lag model, initial results from "stepwise-delete-and-add" procedures with OLS were used. Since it was found that for most food items other than rice and barley-and—wheat more than two-quarter lag effects were not significant, the model was applied only to these two foods. Despite its limited application, it is hoped that the rational distributed lag model would serve to show the performance of different "models." For the annual model, the two-stage-least-square (ZSLS) method was used to estimate the system of equations summarized at the beginning of this chapter. It should be noted here that, because of a small number of observations (9) the number of predetermined variables to be used in the equation system has to be less than 9. Otherwise, ZSLS turns out to be the same as OLS. Estimation Results The final results of reduced form equations and derived structural coefficients for the quarterly model are tabulated in Table 5.1 through 5.10. The numbers in parentheses are standard deviations. 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Less but relatively stable and significant results were found in the case of pulses. This might char- acterize the Korean rural economy. The expression that "cooked rice and soy sauce" are enough for dinner or lunch, has been a common belief for the farmers or for urban poor people. Income effects of most foods are positive except in the cases of barley-and—wheat, miscellaneous grains, and vegetables for national average level demand equations, as are shown in Table 5.11. The negative income effects of barley-and-wheat seem to be less obvious when the importance of wheat for various uses is considered. It seems that the data reported in the Farm Household Economy Survey give much more weight to barley when they aggregate barley and wheat into a single food item "barley-and-wheat." If this is the case, then the negative relationship seems to be realistic, considering its minor role in food consumption compared to rice and possible access to other foods such as rice, meats, dairy and others as income increases. For miscellaneous grains and vegetables, 92 Table 5.11. Estimated Coefficients of Income and Price for Various Foods (National Average Reduced Form Equations; Unrestricted) Foods Income Price Rice .00112 -.l99 Barley-Wheat -.00016 -.242 Miscellaneous Grains -.00017 .0178 Pulses .00017 -.0196 Potatoes .0002 -.031 Vegetables -.00016 --- Meats .00018 -.0075 Dairy .0006 --- Fish and Marine Products .00002 --- Processed Foods .0000? -—- as income increases would also have the opportunity to substitute higher quality food for miscellaneous grains and vegetables. The price effects for miscellaneous grains turn out to be positive in all farm groups' demand equations. Are they Giffen goods? It is too early to conclude that they are. Other than basic food grains, particularly rice and barley-and-wheat, lagged effects beyond two quarters seem to be negligible. This may suggest that prolonged habitual inertia are stronger and rural consumers' expectation about price and income remain longer for rice and barley-and-wheat. 93 The depreication rate, c; (the coefficient of "Psycho- logical stock") shows positive signs for rice, barley-and- wheat, pulses, vegetables, meats, dairy products and pro- cessed foods and negative signs for miscellaneous grains, potatoes, and fish-and-marine products in the case of national average level. The proper interpretation of the meaning of this coefficient, c, is not given in the Houthakker and Taylor model except that it serves as an intermediate role to derive b1 and other structural coefficients. If we rewrite Equation 3.2 in a discrete approximation form such that = l qt Ast + cst 3.2 then we can interpret that, if psychological stocks are constant, the higher (and positive) is c, the more they consume, other things being equal. For example, the value of c for rice is larger than that of barley-and-wheat as shown in Table 5.12. According to the implication of the state adjustment model,’the negative sign of b implies that the consumption 1 pattern of a food is above long-run equilibrium level if its inventory (or psychological inertia) is below its long-run equilibrium, or that the consumption pattern is below the long-run equilibrium if its inventory (or psychological inertia) is above their long-run equilibrium level. The more inventory to begin with, the less will consumers buy, or the other way around. If bl is positive, the two deviations 94 Tab1e_5.12. Depreciation Rate (c) and Adjustment Coefficients (bl) (National Average) Foods c ’ b 1 Rice 7.82 3.64 Barley-Wheat 2.51 - 4.98 Miscellaneous Grains -l44 -37 Pulses 1.1 - 5.59 Potatoes - 1.6 - 3.24 Vegetables .69 - 8.5 Meats 8.74 .79 Dairy Products 4 .79 Fish and Marine Products - 12 - 5 Processed Foods 48 10 between the short-run consumption level and psychological inertia and between long-run consumption level and psycho- logical inertia have same sign, implying that it has a habit forming effect. As shown in Table 5.12, the signs of bl for rice, meats, dairy products and processed food are positive, and others are negative. Thus the former group of foods may be said to have habit forming effects, while the latter have inventory adjustment effect as can be seen in usual durable goods analysis. In the case of rice, there were strong elements of habit forming phenomena as noted earlier. Other cases may not be intuitively appealing. One may 95 argue that every food has both habit forming and inventory adjustment elements. That may well be true. The point is, which element is stronger? The purpose of the state adjust- ment model is to identify this relative stronger or weaker element. Viewing this way, the positive sign on meats, dairy products and processed food have stronger habit forming elements. As to the magnitude of the coefficients, rice is the highest among this group except that of the processed foods. Here it should be noted that the commodity definition of processed foods reported in the Farm House- hold Economy Survey is not given. Judging from the data on quantity consumed and expenditure, it seems that it does include not only those from commercial channels, the processed foods proper, but also includes those made at home such as noodles and rice cookies. Thus, it may be safe to say that the processed foods are really another form of composite foods consisting of all grains. Other derived coefficients are shown in Table 5.2 for rice, Table 5.4 for barley-and-wheat, Table 5.7 for pulses and Table 5.10 for the rest of foods only in cases of national average levels. The short and long run struc- tural coefficients of income and prices and conventional short-run elasticities, all at national average levels, are summarized in Table 5.13. It is found that long-run coefficients are greater in absolute value terms than short-run coefficients for III III III oooo. Amo.m o oooo. mooom ommmmooum III III III III III III muoscoum mswuszocMInmflm III III III maoo. Aao.o o Hoo. muosooum snows oooo. I loo.HIo Hooo. I oHooo. loo.a o oHooo. momma III III III moooo. Ammo.HIo mooo. I mmHnmummm> % ooo. Ammo.HIo ooo. I mooo. I Ammo. o mooo. mmoumuom moo. I loo.HIo moo. I moooo. loo. o omooo. mmmasm mooo. “omo. o moo. ooooo. I Aomo.Io «Hooo. I madame . msomcmaaoomwz NH. I loam.HIo 5mm. I ooooo. I Aoooo.Io omooo. I ummnzIochsmHumm oom. I Aooo. IV mma. I oaoo. Aooa. o oooo. moom mmfln—HO mmfluflo mmmiwcoq IwumMHm cam uuomm csmmcoq IwumMHm cam uuonm mom—”Hm mEOUC H MUOOW Hw>mq Hancoumz um mmwpfloflummam csquHoam can musmaoflmumoo admImGOQ.©cm quonm .MH .m OHQMB 97 rice, vegetable, meats, dairy products and processed foods. For fish-and-marine products, no significant results are found. The long-run coefficients of other foods are less in absolute value terms than those of short-run coefficients. Interestingly enough, short-run coefficients of potatoes and vegetables change signs from the short-run relationship {mm to the long run. It seems that current potato consumption will reverse its direction with respect to both income and prices, thus, in the long run it would be another inferior goods. The sign shift of the vegetable demand relationship with respect to income, from negative to positive, may be explained by the possibility that poor farmers can not now afford to buy vegetables due to immediate needs for (and/or stronger habitual inertia attached to) other foods; but if income increases enough, they might be able to demand more vegetables. This can be done either by withholding produced vegetables from the markets or by increasing purchases. Incidentally, farmers' actual cash expenditures on vegetables are larger in prOportion (about 24.5 percent of total impli- cit expenditures, compared to 1.8 percent for rice and 6.4 percent for barley-and-wheat)at 1973 annual national average figures. In interpreting long-run coefficients, care should be taken. As defined earlier in Equation 3.2, the long run is defied as DJ ('1' I O S D; d' 98 that is; it is defined as that point where there is no further change in the psychological stock level (or consumption habit is constant). It does not say anything about the magnitudes of the explanatory variables. For example, itwas found that in the case of national average rice consumption per capita, long run coefficients are greater than short-run coefficients as shown in Table 5.3 - Thus we can infer that as long as current rice con- sumption habit prolongs, the long run value of each coeffi- cient will be multiplied by 1.933 which is derived from Here again, the problem is to what specific time period does the long run refer. As far as the model is concerned, there is no specific time framework given except the defini- tion; the long-run equilibrium. This is one of the reasons why the long-run relationship is not used for numerical Projections. This may be one of the weaknesses that economists have to face. But at least one can make inference about the future direction. It can be expected that in the case of highly infla- tionary Situations, undeflated data, particularly prices, would give some biased results in statistical analysis. In th :13 study it was found that with undeflated data. (Fri egg and incomes), the signs of own price have shown 00 . . . . . T7“":“ect direction in many cases. But thlS is not the case 99 for the income variable. Since quantity of food consumption is relatively stable with respect to nominal prices and incomes it can be easily expected that the income effect would be negative. This was also indicated by Gustafson [GlO] . For instance, nominal income effects on rice consumption turnedout to be negative for all groups except for national averages which is hardly explainable with economic theory for normal goods. Apart from this methodological problem, there seems to be a problem of money illusion. Under economic theory, if both prices and incomes are increasing in same proportion, quantity demanded will remain at the same level as before the changes. This is the homogeneity condition in mathema- tical terms. This condition, however, may not strictly hold in the real world. First of all, all prices are not changing in the same proportion as income. For rural consumers, this fact alone gives some constraints on their consumption in two aspects; first, since more income is expected from higher prices, their consumption of foods produced by their OWn hands will be restricted, other things being equal; Secondly, rise in nonfood prices would add psychological influences to their food consumption, the net influence of prices of foods and income change being somewhat to dis- C C C . our-age food consumption, ceteris paribus. Viewed this way, negative nominal income effects are C Ompletely rational for the farmers in contrast to urban 100 consumers. In other words, money illusion which is discarded in neoclassical economic demand theory may be a result of rational consumer behavior. The degree of negative nominal income effects has shown to be stronger for rice. Inter- estingly enough, for barley-and-wheat, nominal income effects have shown positive signs for all farm groups including national average level. Other food demand equations revealed little significant differences between the two contradictory results. Recognizing that money illusion may be a rational behavior for rural consumers (farmers), the characteristics of an individual food in terms of habit inertia and his- torical patterns also have to be taken into consideration in general, which also served as an important role in choosing parameters to be constrained. Thus it was decided to use deflated data rather than undeflated data. According to Nerlove [N3], a test of the permanent income hypothesis can be accomplished by examining whether the distributed lag is significant only in the income variable and/or whether distributed lags are the same for each individual commodity. Since total consumption function is not estimated, it may be inappropriate to test permanent income hypothesis by the significant level of the coeffi- cients of lagged income variables. Following the Nerlove procedure of testing the hypothesis, there is no lagged income variable appearing in the equation system, implicitly implying that the corresponding coefficients are zero. 101 Without going through all the details of testing procedure, it seems that the results from this study are not convincing. But at the conventional 5 percent significance level, most of the coefficients of lagged income variables turned out to be insignificatn except in cases of rice (qll and qu), barley-and-wheat (q21 and q24), potatoes (q54), vegetable (q60) and the fish-and-marine products (q90). For rice, rural poor consumers in the group of farm size with less than 1.0 cheongbo may spend more as their transistory income increases compared to the upper income group. But again, without further investigation, existing results do not give any further conclusions. In this sense, this study failed to reveal correct premises. It was also found that consistent aggregation was difficult because the sample sizes were different among different farm groups. Moreover different functional forms added to the difficulty in checking the aggregation bias. Despite these difficulties, an attempt was made to see how biases might be found. In many cases, coefficients of the national average demand equations were not consistent with those derived by averaging each farm group's coefficients. §gpond Order Distributed Lag Model As indicated earlier, no significant coefficients could be found in demand equations other than for rice and barley- and-wheat. Thus only two equations at the national average 102 level with quarterly data and with two sources of income were analyzed. Relevant coefficients are shown in Table 5.14. Following the procedure described in Chapter III, lag dis- tributions of four important variables, farm income, nonfarm income and two prices are graphed in Figure 5.1 and 5.2. Since the solutions of both demand equations have complex roots,1 the system is oscillatory and has a negative lag distribution, but it converges as time approaches infinity. It is clear from the figures that the lagged effects of each variable in the rice demand function are longer but smaller than those in the barley—and-wheat demand function. From this we can infer that rural consumers attach more importance to rice than barley-and-wheat. The smaller magnitude of oscillation may also imply its relative stability and prolongedness in terms of psy- chological inertia. This also seems to be consistent with the previous results and with the finding that lagged effects beyond one quarter are not significant for other foods. The only significant coefficient of two-period's lagged quantity for other foods is in the case of the demand for pulses for farm size less than 0.5 cheongbo. Annual Demand Equations for Rice and Barleyfand-Wheat Three systems of eight equations were tried-—one with the lowest monthly actual inventory level during the year, 1It is because -4(a9) > (a1)2 103 ST: fimoJ Ago; Ammo; $8.. 88.. 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H+ H+ .H.m musmwh OOHm NO OOHHm Mom HI mumuuwsq V<<< ¢ HMGOAUMZV ummszItchamaumm “om nodusnauumfio mmq .~.m gunman mumuumsv om ummnSIGCMI>wHumm mo ooflum “Oh HI om oH I D > \I I I‘ It < < < o mumuumaw om coflusnwuumwo mmq GEOUGH EmeIcoz Mom H... coausnwuumov mmq H+ mowm mo moflum Mom mnmuumsv om ow\) oH _\I/ . IICIIWC cofluonfluumoo mod wEoocH Emma mom mumuumsv om om OH H+ ' I ( G a I ‘ :ofiusnflhumwm and Ff H+ 106 the second with the change in ending inventory in terms of calendar year and the third with the adult-equivalent-scaled variables. The results are summarized in Tables 5.15 through 5.18. The reason why the lowest monthly inventory level was chosen is based on an assumption that farmers may attach {A more importance on the lowest inventory level in making consumption decisions rather than the change in inventory. It may make no difference between the lowest inventory and change in inventory level. Let us assume that one household has a large inventory and another has a smaller inventory from the beginning but the changes in inventory level are the same for both households. The fact that the former will leave still larger ending inventory than the latter seems to influence consumption differently. One short- coming of using the lowest inventory level, however, is that it does not satisfy the indentity: Production = Consumption + Sales + Change in Inventory 5.3 which will be used in simulation model. To remedy this shortcoming, change in inventory level from previous year's ending inventory to current year's ending inventory level measured in December was used. In this case, there are two alternative ways of incorporating the identity relationship 5.3. The one is to regard sales 107 Table 5.15. National Average Demand for Rice (qu) and Barley-and-Wheat (q20) with Annual Data: ZSLS (Lowest Inventory Level Used) Constant Net Income Rice Price Barley-and- Deflated by Index Deflated Wheat Price FPPI by FPPI Index Deflated (Won/capita) (Percent) by FPPI (Percent) Y P1 P2 A(lO) A(ll) A(12) A(13) :22 010 155.622 .0031 -2.110 1.38 .67 (.0013) (1.149) (.70) A(20) A(Zl) A(22) A(23) 020 114.52 -.00063 --- -.l49 .65 (.0004) (.179) Lowest Gov't. Gov't. Inventory Purchase Purchase Level Price of Rice Price of (l/month) (Won/80kg.) Barley Deflated (Won/60kg.) Deflated A(30) A(31) A(32) A(33) Pl 4.64 -.254 1.543 5.701 .95 (.171) (.354) (1.279) A(40) A(41) A(42) A(43) P2 -2.4 -.35 1.63 5.5 .97 (.13) (.35) (.95) P1 P2 A(50) A(Sl) A(52) Lowest Inventory -49.196 .599 .28 .56 of Rice (.85) (.78) 511 A(60) A(61) A(62) For Barley and Wheat -29.77 1.51 -.96 .42 512 (.90) (.83) P(1) P(2) Off-Farm Total Workers/ Number of Total Family Rural (Percent) Household TM PM A(70) A(7l) A(72) A(73) M74) R2 D.w. Y -234237.58 447.57 15985.94 11076.93 .07 .90 1.7 (202.64) (20655.92) (5404.28) .05 Y Time A(80) A(Bl) A(82) TM 2.282 -.00006 .184 .56 1.6 (.00005) (.1) 108 Table 5.16. Auxiliary Equations for Projection and Simulation Constant Time R2 Rice Production 299.81 9.45 .65 i/Household (14.79) (2.63) PO (10) Barley-Wheat 159.75 -2.53 .28 Production (z/Household) (8.72) (1.55) PQ (20) Number of Rural Households 2579718 -13215.4 .51 PM (4937.6) Number of 6.354 -.075 .98 Family/Household (0.02) (.004) SF to market as residuals, the other is to make the changes in inventory as residuals. Both have rationale. The first might be based on an assumption of more emphasis on food consumption per se and the second on farm income attainable from selling their products. In this study, the former method was chosen . The results show little differences from the quarterly model. Signs of the coefficients of prices and income were the same; the income effect for barley-and-wheat being negative. Results show that government purchase prices of rice and barley have significant and positive effect on both prices and income. 109 Table 5.17. National Average Demand for Rice, C(10), and Barley-and-Wheat, 0(m», (Annual Simultaneous Equation System (ZSLS) with the Lowest Inventory - Adult Equivalent Scale (ABS) Data): Constant Net Income/ Price Price of R D.W. Capita Index Barley- (Won/AES) (Percent) Wheat Deflated (Percent) Deflated Y1 P(1) P(2) C(10) C(11) C(12) C(13) Q'(10) 208.901 .0031 -2.682 1.701 .60 '2.46 (.0013) (1.533) .951 C(20) C(21) C(22) C(23) , Q'(20) 160.638 -.00057 --- -.306 .70 2.05 (.0004) (.201) Lowest Gov't. Gov't. Stock Purchase Purchase During Year Price of Price of Rice (SI(10) Rice (Won/ Barley Barley-Wheat 80kg.) (Won/50kg.) (SI(20) (l/Month) C(30) C(31) C(32) C(33) P(1) 5.241 -.192 1.536 5.66 .95 2.49 (.134) (.362) (1.3) C(40) C(41) C(42) C(43) P(2) -.016 -.003 .016 .055 .97 2.84 (.00097) (.0034) (.0092) P1 P2 C(50) C(51) C(52) S’I(lO) -62.603 .821 32.24 .55 2.31 (1.11) (102.46) C(60) C(61) C(62) S'I(20) -37.08 2.032 -133.623 .43 2.16 (1.185) (108.93) P1 P2 Off—Farm Total Land Worker/ Rural Distributim Total House- (Cheongbo/ Family hold Household) (Percent) TM PM DL A(70) A(7l) A(82) A(73) A(74) A(75) Y' ~699652.82 486.55 65944.17 31455.24 .223 3390.468 .78 2.8 (749.59) (97878.91) (23535.15) (.18) (51113.29) Y' Time C(80) C(81) C(82) TM 2.41 —.00005 .195 (.00005) (.109) ‘M firm". - M‘ 110 Table 5.18. National Annual Average Demand Equations System for Rice and Barley-and-Wheat with Change in Inventory Level Constant Y P1 P2 R2 D.W. A(lO) A(ll) A(12) A(13) 010 129.88 .0023 —1.252 .929 .76 1.88 (.00097) ( .715) (.458) A(20) A(21) A(22) A(23) 020 116.54 -.00054 --- -.193 .66 1.82 (.0004) (.171) Change in Change in Rice Inven- Barley- tory (E/Year Wheat per capita) Inventory (i/Year/ capita) SIl SIZ GPl GP2 A(30) A(3l) A(32) A(33) A(34) P1 16.017 -.037 --- .014 .0402 (.031) (.003) (.0125) .94 2.62 A(40) A(4l) A(42) A(43) A(44) P2 -l.634 --- .114 .0105 .062 .91 2.45 (.133) (.004) (.016) P1 P2 Rice Barley- Calendar Production Wheat Year (i/Capita/ Production Year) (fi/Capita/ Year) P01 P02 '1‘ A(50) A(Sl) A(52) A(53) A(54) A(SS) SIl 336.26 4.402 -7.1 1.63 -4.07 -18.29 .75 2.01 (5.65) (5.2) (.77) (2.26) (13.79) A(60) A(61) A(62) A(63) A(64) A(65) 812 246.11 1.389 -1.504 -.115 -1.177 —5.92 .68 2.62 (2.025) (1.874) (.276) (.811) (4.94) P1 P2 Off—Farm Number of Employment Rural (Percent Household Total Family) TM PM A(70) A(71) A(72) A(73) A(74) Y -472087 497.06 352.56 20334.1 .149 .83 2.46 (272.28) (308.11) (9582.9) (.09) Y T A(80) A(81) A(82) TM 2.22 -.00006 .176 .56 1.62 (.00005) (.098) 111 s!- i There was little difference between the respective coefficients in the per capita model and the adult-equi- valent-sca led model; coefficients of income were almost the same, but those of prices were greater in absolute value terms for the adult-equivalent-scaled equations (AES) than for the per capita equations (PC). This relationship is shown in Table 5.19 which is abstracted from Table 5.15 and 5.18. Table 5.19. Income and Price Coefficients of Annual Model with Per Capita and Adult-Equivalent Scale Net Income Price Price Index Deflated Index of Barley- by FPPI of Rice and-Wheat (Won/PC,AES) Deflated Deflated (Percent) (Percent) Rice Per Capita .0031 -2.11 1.38 (.0013) (1.49) (.71) Adult-Equivalent . 0031 -2 . 68 l . 71 Scale (.0013) (1.53) (.95) Barley—and-Wheat Per Capita -.00063 --- -.l49 (.0004) --- (.179) Adult-Equivalent '-.00057 --- -.306 Scale (.0004) --- (.201) As expected, the income coefficients were of about the same magnitude because both quantities and income were d“3flated by the same scales, respectively, but prices were n0t- Apart from this methodological difference, we faced 112 choice of "correct" parameters. Though it was crude enough to scale quantities and income with .52 for age group under 14, with 1.0 for male adult and .9 for female adult both between 14-65 and with .65 over 65, we recognized that there were certain differences of quantities and income that go into decision making process for consumption depending on the age and sex structure of a family. If this is the case, we are under-estimating price coefficients when we use ordinary per capita variables. Thus in the actual policy making stage, this point should be taken into consideration. Differences in the absolute magnitudes of coefficients of estimated equations between the quarterly model and the annual model, were not apparent in this study. But, given the same variables, quarterly coefficients were smaller than those of the annual model because of DT = .25 which entered into the calculation process of deriving structural coefficients. Another plausible expanation for small quarterly coefficients may come from the permanent income hypothesis [A1, H9]. This point is also important in making correct inferences and for the policy making process. In the simulation model and projection, change in inventory level instead of the lowest level of inventory was used and the system of equation was re-estimated by using ZSLS. The results of the estimation are shown in Table 5.18. Demand equations were not much different from 113 those with the lowest inventory level and government pur- chasing prices of rice and barley did affect prices and income significantly. Since identity relationship 5.3 holds, equations for inventory change can be rewritten as follows: PQ1 - Ql - SALES = A(SO) + A(51)Pl + A(52)P2 + A(53)PQ1 + A(54)PQ2 + A(55)T 5.4 Substitution of demand equation, 01' and rearrangement of terms disregarding other terms for convenience's sake gave 5* the following market supply equation; SALES m — A(50) - [A(Sl) - A(12)]Pl - [A(52) - A(13)]P2 (Rice) 5.5 Similarily, for barley-and-wheat, SALES m - A(60) - A(61)P1 - [A(62) - A(23)]P2 5.6 (Barley-and Wheat) From the above equations, it is clear that for the market supply equations to have positive slopes with respect to their own prices, A(12), the price coefficient of rice demand equation, and A(23), the price coefficient of barley- and-wheat equation should be greater, algebraically, than A(Sl) and A(52) respectively. Using the estimated results from the Table 5.21, equations 5.5 and 5.6 become 114 SALES % - 336.26 - 5.7Pl + 8.4 P2 5.7 (Rice) and SALES m 246.11 + 1.7P2 + 1.7P2 - 1.39P1 5.8 (Barley-and- Wheat) Surprisingly, the rice market supply equation had a negative slope while barley-and-wheat had a positive one. Since they are only partial equations which do not count for other terms and because of large standard errors of A(Sl) and A(52), it is not conclusive at this point whether we can accept the results. Total effects were analyzed in the simulation model. According to the results at hand, all show that rural income per household is positively correlated with the re- maining total number of farm households in all three equation systems (.7, .223 and .149) though two systems result in larger standard errors. With small number of observations, it is too early to conclude urban migration is harmbul to the rural economy. But it is suggested as a topic for further policy analysis [H3]. Off-farm employment rate, TM, shows positive correla- tion with income when TM is an explanatory variable but negative when it is a dependent variable. With more off-farm employment opportunities, more income is expected. On the other hand, increasing income seems to discourage seeking off-farm work, 115 Simulation The equation system used in a very simple simulation model was based on the systems of equations 5.1 through 5.2. The model was applied to only rice and barley-and-wheat. This is mainly because the most important policy variables that can be identified and that are available are the govern- ment purchasing prices of rice (GPl) and barley (GP2). These two policy variables clearly have given a tremendous impact to rural economy. To simulate the block-diagram model in Chapter IV with a three-mode feed back control technique, it was necessary to find a linearized and discrete approximation of control equation such that 'c n f(ERROR) f(Desired Sale [DSALI - Actual Sale [ASAL]) ERRORt - ERRORt_1 Kp ERRORt + Kr[ DT T 7 + Ki (2 ERRORt) 5. 0 Where Ut is policy variable matrix such that U = [cpl t L§P2_ and KP' Kr' and KJ.- are proportional, derivative and integral policy modes, respectively. The second term of equation 5.9 is linear approximation of d(ERRORt) and the third is that dt 116 of f(ERROR)dt. ERROR is a matrix defined as DSRDRt - ASALR _ t ERRORt ‘ DSRDBt — ASALBt 5'11 where ASAL is an implicit actual marketed quantity of rice and barley-and-wheat per household. It is implicit because it does not account for amounts not marketed but consumed for various purposes other than direct human consumption. Thus this figure does not necessarily match actual quantity ‘tifll. 0'. -' '-.". marketed which is reported in various sources, and exceeds the actual quantity marketed.' Then ASAL = Production [PQ] - Demand [Q] - Change in Inventory [81) 5.12 The desired quantity of sale DSRD is assumed to take the following equational forms DSRDR = 1210.4 (1 + .05 /T) , 1964 i T 5 1973 5.13 DSRDR = 1689.69 , T > 1973 5.14 DSRDB = 350 (1 + .03 JE) , 1964 3 T 3 1973 5.15 DSRDB = 510.72 , T > 1973 5.16 where DSRDR and DSRDB are desired quantity of rice and barley- and-wheat to be marketed per household, respectively, and the initial values of which are actual implicit sales in 1965. Upper limits which are set about 10 percent higher than the peak sales during past 10 years are given, con- sidering reasonable ranges of production and demand. 117 Coefficients, .05 and .03, are derived from rates of popula- tion growth (assumed to be around .02) and other additional factors such as urbanization, production and governmental demand increase. One of the difficulties in this discrete version of the three-modes control equation was to find out correspon- r' ding control parameters KP, Kr’ and Ki' A simple but costly method is to run the simulation model during the sample period many times with various alternative values of these parameters. Other methods would be computer optimization techniques such as COMPLEX or Bard's computer version of Newton-Gauss method [K2]. In this study, a less costly and less elegant method is used. Relevant data were generated by using assumed DSRD quantities and actual implicit sale quantities. Then an ordinary least square (OLS) method wasused to generate KP, Kr’ and Ki outside the simulation model, assuming that policy makers have had such control schemes in mind during the sample period and simulation period. The generated parameter values are shown in Table 5.20. "Adjusting Factors" are the constant term in OLS estimated equation. Table 5.20. Generated Control Parameter Values of Kp'Kr'Ki K K K. Adjustin p r 1 Factor 9 _; (Constant) GPl 3-mode .171 -.373 1.04 2888.11 GP2 3-mode -.025 -.l43 1.30 618.5 118 Along with these parameters, and alternative arbitrary ~values of them, the model has been run by incorporating a time delay (DELAY) in market sales. Unfortunately due to the nature of the equation system which uses the estimated parameters, arbitrary variations of parameter values have given unacceptably large errors: Thus after many trials it was decided to use a simultaneous-equation solution type simulation with fixed parameters with a few adjustments. The results of the simulation are given in Table 5.21 and 5.22 g and Figure 5.3. The value of DT, simulation period, is chosen as l, on the following ground despite possible larger simulation errors due to the large value of DT. (1) Parameters are estimated with annual data, thus if we use, for example, Q.DT (rate) variable rather than Q (stock) in the simulation, the extrapolation exceeds far beyond the sample range, thus resulting in larger errors. These errors have been larger, particularly due to the simultaneous nature of the system. (2) One possible way of constgpcting rate variables is to divide all dependent variables by multiplying DT and later to sum or integrate them. But this would give the same result as using DT = 1. (3) Government decisions on the level of purchase prices are assumed to be made annually, which is the most usual case. Thus, it seems to be reasonable to base the 119 1" .AmmmaIemmao ceaumm :Oaumassam mcauso mcamum>Imsau was as use .AmomaImmmao ceaumo waaEMm mcauso vc.a n as can mm.I u as .ama. u Qua o.maa cmoo moma mam aov comm mama m.oaa moon omm mom mmaa mmmm coma m.aaa mama moma one «mm momm mama m.ooa omen mom com maaa ammm mmma a.aaa omoo ovva mom mmo mmmm amma m.voa mmmm amm mmm oaoa vmmm coma m.aaa mmmm mama om amp momm mmma a.aoa momm maoa mav coo mmmm ohma o.maa acmm mmma memI omm nmmm mmma o.ooa mmmm mmoa mmv who mmmm omma a.maa mmvm vmma mva vmaa «mmm . mmma a.am ooam moma cam mme momm omma o.aoa a.aaa mama aooa mama mmm ma aom mmm. moam mmmm mmma o.mm m.mma aooo mmma omma «mmI nmmI own now mmam mmam mmma m.om m.moa ommm mom mmm omm mmo amm omm nmam onmm amma m.om m.om mmom mmma mmaa m mo I mam omo moam coma omma a.mm m.om anon mmaa ovaa maa oma mmm mmm vmom amam moma v.ooa m.mm comm moma ovma oomI momI mmo mmm vvcm moma coma m.om m.am mmom mmaa mooa cm I mmaI ohm wom aacm maam mama n.moa a.am mmmm mmm moaa mam wma mmm mmm mmma mmam coma m.aoa o.ooa omam mmma oama ommI mva com com mvma omoa moma IIIIIIIammm\wIIIIII IIIammm\mxoo\cozII I IIIIIIII IIIIIII caosomso=\a IIIIIIIIIIIIIIII cwuuassam omumassam toumassam concassam omumaasam oouuasEam uo no we no no no pmumsaumm amouom ooumEaumm amouod owumEaumm amsuod omumsaumm amount ovumsauuu amsuufi coudaauum anauod moauo ommtousm muoucw>ca moaum umxumz moam u.>oo mamm uaoaamEH ca mozmno vcmsuo acavoscoum H00” no 2855: .a oo.a + at a a» mommmoo mm.u u momma ama. u awe can vmma umuwm mm.mmma .mmma aaucs amx mo. + av v.cama n mamm omuamwo “umaom can panama 00am no nuasoom vuuuaaaam .a~.m manna 1J20 momanama. coauom aoauoanaao mcauso maamuo>Iosau no: as non .AmamaImmma. coauom oameom «no mcauso a.a I as can oa. I an .ao.I I mxa aam amm mmmI moo oam mmma a.ooa aaaa oom momI mmm omm ooma m.om omm omm mmmI mmo amm moma m.mm maaa mom mmmI mma mam mmma o.ooa omoa mom mmmI aoo mmm aoma a.am mooa moo momI oam mam ooma a.moa amaa omo mmmI mmo amm mama o.mo oom . mom amaI amo oom mama a.aaa oama mom mmmI moo mom aama m.om _ mom oom ma I omo moa . mama o.oaa mmma aam mamI mam oma mama m.oa moa oom mm I mam oma oama a.aoa ammo mom aom mom ma I oo I omo moo . maa maa mama m.ooa meaaa amaa moo omo oo I ooaI ooo aao moo moo mama m.mm a am mom amm mam ma om moo moo omo ooa aama m.om m.om mma mam amm mm a I mmm oom omo mmo oama m.om. m.om oam aom mom oa I am amm mam omo mam mmma m.mo . m.ao mam man moo oa I ma oom mom mom mam omma o.mm a.am omo mom omm m mm I mom aam mmm aom aoma a.mm m.ooa mmm oam mmm mm ao aom mom omm mam mmma a.am o.ooa mooa mom maa mma omm mmm amm aom mam mmma IIIIIIIamam\oIIIIII IIIaaam\mxom\cozII IIIIIIIIII oaonom=o=\aIIIIIIIIIIIIIIIIII III counanEam counanaam touoasEam nonmaoEam Umumaoaam wouuasEam HO HO HO HO HO HO ”Oudfiwu um Hdaauofl ”mug—59mm Hflfluud Oflfigwumm HflaauOto nomad—Emu mm Han—90¢ Cflugwumm Hflfluud Ufludfiwumm HGOUOC umxun! ovaam ouunousm muouco>ca unuszImoauau moauom u.>oo oaom uaoaamaa ca omcmnu panama scauoououm now» u IIIIwWIII an mommm a a.a + .u mommmc o oa.I u momma ac.I I mac can .mama umuum ma.cam .nmma aaucs am\ no. + a. omm n mamm omwamoo "moamm can nausea amoerochmoaumm no muasmmm uoumaoeam .mm.m manna 121 . Production ,._a~——"""'—"—_———- Projected 2000) ‘ Desired 1500:’/’fl_’_fl_~_'___//’ sale 1000' A A . 'I' \\ ,\ f‘ .A‘. l: \ mlnd ' I \ ." "I x’ I \‘ W [I \ l/ .\ f.- (V, j a mam“ ; 1‘] ,t . . . i’ ’ \ SlJTllllath“’““- 500+ r 1965 70 1975 80 1985 (A) Ri cc Demand Change in GPl a.d GP2 80 1985 (B) Change in government real purchase price of rice (GPl) 1000 F and barley (GP2) aaaaaaaaai__~___‘§~___'Production \ Projected 500 ‘ \-w%a ._ . Desired Sale ( ”mww M“\ammg/‘\3/'1Myuand OUxxvaifih Simulated ..... _L l l I 1965 70 75 80 1985 (C).Barley—and-Wheat.Demand Figure 5.3. Simulated results by using "three-mode" control scheme. 122 model on this fact, even though there is no technical dif— ficulty to incorporate this decision rule in the model with fine time series (i.e., DT less than 1). It was also decided not to incorporate the time delay factor, mainly because the data used in this model are 255 post values reported at the end of the year. It is possible '5“ to assume certain quantities which are in the input channels 3 which will be marketed in the future. But considering the ) fact that the purpose of incorporating this simulation model II. ...~ . is restricted to rural demand analysis and projections, no further elaborations were attempted. According to the results as shown in Table 5.21 and 5.22, the projected demand for rice in 1984 is 1177 l/house- hold in 1974 to 1177 2/household in 1984 for rice and from 292 2 in 1984 to 576 i in 1974 for barley-and-wheat. The fluctuation may have originated from decision functions that were set to adjust government purchasing prices annually in such a way that the proportional control parameter Kp is increased upward holding other control parameters constant during simulation period (1973-1985). Also, since the model with a "three-mode" control scheme is more or less of academic interest and may or may not represent a realistic version of government policy, an intuitive but more realistic version of simulation model was tried. The policy variables used were the same as before but with a decision rule to increase or decrease purchasing 123 prices at a certain fixed level annually. During the past ten years, the farm purchase price index (FPPI) has risen about 25 percent annually, while government purchase prices of rice and barley have been increasing annually about 38 percent and 34 percent in nominal terms, respectively. Thus these are reasonable assumption based on past experience. Ir“ To experiment, extreme values were chosen. Four of the alternative policy measures were chosen and their results are shown in Table 5.23 and Figure 5.4. The first column Q'I'XI" av-DQ‘ '. of Table 5.23 shows the possible trend of demand for rice and barley-and-wheat when the rice purchase price, GPl is assumed to be increased initially 40 percent in 1974 over that of 1973 in real terms and increased 5 percent annually there— after; while the barley purchase price, GP2, is to be decreased initially 20 percent below the 1973 purchase price in real terms and decreased 2.5 percent annually thereafter. According this fixed rate increase or decrease in purchase prices, rice demand is projected to be 886 l per household in 1975, 902 l per household in 1979 and 928 g in 1983 and 587 2 in 1984. Demand for barley-and-wheat is prOjected to be 434 2 per household in 1975, 390 g in 1979 and 414 2 in 1984. Despite this large increase in the rice Purchasing price and drastic decrease in the barley pur- chasing price, market price rice increased only about 20 percent and barley-and-wheat price decreased only about 6 Percentzin.real terms from the 1965 base period. 124 r: II omo o I ooo o I oao mmo oao mom ooma mmm omma mom mmma omm mmm oom mmm moma oao om omo maa mmo oom omo amo, moma com omoa mam mooa omm mom mom mam aoma moo amm mam mmm mmo aom mmo moo coma omm moma mom coma . omm com cmm mom mmma moo omm moo omm ooo aao , moo mom mmma mmm omma woo mmma mom mmm mao omm mmma ooo omo moo omo. mmo omo aoo mmm omma ooo mmaa moo mmaa moo aam 1o omo coo mmma omo omm amo mom mmo moo mmo mom omma IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIoaonomsom\a IIIIIII IIIIII IIJHIIIIIIIIIIIIIIIII poms: nouns umooz poms: Imoaamm 00am Imoaamm 00am Immaumm 00am Immaumm 00am mmI I ma mm.mI I ma mmI I ma mm.mI I ma woa u as mm u an woa u an mm u an can umwszImoaumm ocm umonBImoaumm How ommouooo moo aom unmouomo w cm moan aom ommoao I moan How wmmmuo Isa wmm amauaca Isa woo amuauca Ham» a m a omcmnu mo mmumm amused mum mu can a muons as H + avmom u mom can A9 a + aomomm u amo “mooaum mmmnousm ammo ca mmmcmsu ovum omxam Spas oomEmo ummozIoGMImoaumm can 00am mo muaommm ooumasEam .mm.m manna oco Aamuo moan mo mooaum amoroxsm ucoE2u0>oo acocos_uooxm macauo> "0...! 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