—_ —— —_ — __ — — __ — Labor Aiiocation and Productivity for Upland Rice Farms: Sierra Leone, 1974-1975 by E. Chinwe Spears LIBRARY Michigan State University , ' LABOR ALLOCATION AND PRODUCTIVITY FOR UPLAND RICE FARMS: SIERRA LEONE, 1974/1975 By E. Chinwe Spears l PLAN B PAPER Submitted to l Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1977 / 14/" 52 a / "'1 ’4‘ ll. 7 Ill-f in.) TABLE OF CONTENTS LIST OF TABLES . . . . . ............. . ....... iii LIST OF FIGURES ......................... v CHAPTER I. INTRODUCTION ....................... 1 Agriculture in the Development Process . . . . . . . . . 2 Purpose and Scope of the Study ......... '. . . . 4 Data Source ....................... 5 Data Collection . . . .‘ ...... . .......... 5 11. LITERATURE REVIEW ..................... 8 . . Recent Studies ..................... 10 III. PROBLEM SETTING ...................... :16 Physical Environment .................. 16 Rice Production in Sierra Leone ............ ’. 18 IV. DATA ANALYSIS ....................... 23 Farm Characteristics and Labor Utilization ....... 23 V. PRODUCTIVITY ANALYSIS ................... 31 Production Function Theory ............... 31 Regression Analysis Theory ............... 36 rFitting the Production Function ............. ‘38 _Equating Marginal Value Product and Marginal Factor . Cost ...... ‘ ......... . ......... 55 VI. SUMMARY AND CONCLUSIONS . . . . . ....... . . . . . . 61 BIBLIOGRAPHY ................. . . . . . . . . . . 67 ii TABLE I. 10. 11. LIST OF TABLES Farm Characteristics of Resource Regions, 86 Upland Rice Farms: Sierra Leone, 1975/76 ............ . . Labor Inputs and Yields in 86 Upland Rice Farms, Sierra Leone: 1974/75 . . . . ................. Regional Comparison of Labor Contribution By Class, 86 Upland Rice Farms, Sierra Leone: 1974/75 . . . . . . . Monthly Use of Labor Inputs in 86 Upland Rice Farms: Sierra Leone, 1974/75 ........ . ......... Hours Worked Per Adult Female Per Month Per Season, 86 Upland Rice Farms: Sierra Leone, 1974/75 ....... Hours Worked Per Adult Male Per Month Per Season, 86 Upland Rice Farms: Sierra Leone, 1974/75 . . . . . . . Regression Coefficients (bi' 5), Their Standard Errors (obi 's), and Level of Significance, 86 Upland Rice Farms: Sierra Leone, 1974/75 ......... . ........ Regression 1: Regression Equation and Correlation Coefficients for 86 Upland Rice Farms: Sierra Leone, 1974/75 ......................... Regression 1: Input Categories and Output (in Logarithms and Antilogarithmic Form), Regression Coefficients (bi' s) and Marginal Products of the Inputs, 86 Upland Rice Farms: Sierra Leone, 1974/75 ....... . .......... Regression 2: Input Categories and Output (in Logarithms and Antilogarithmic Form), Regression Coefficients (bi' s) and Marginal Products of the Inputs, 86 Upland Rice Farms: Sierra Leone, 1974/75 .............. Regression 3: Input Categories and Output (in Logarithms and Antilogarithmic Form), Regression Coefficients (bi' s) and Marginal Products of the Input, 86 Upland Rice Farms: Sierra Leone, 1974/75 ........ . . . . . iii Page 24 25 26 27 28 29 45 47 49 50 52 TABLE . ‘ Page 12. Comparison of the Estimated Regression Coefficients (bi's) and the Standard Regression Coefficients (bi*'s) Required to Yield Minimum Marginal Value Products . . . . ...... 58 iv LIST OF FIGURES FIGURE Page 1. Sierra Leone Rural Enumeration Areas and Urban Areas . . . . 2. Areas Nhere Different Types of Swampland are Concentrated in Sierra Leone, Urban Areas and Location of Enumeration 19 Areas . . . ........................ CHAPTER I INTRODUCTION Sierra Leone is a West African country bordered by Guinea to the north and west and by Liberia to the southeast. Land area is approxi- mately 27,925 square miles, lying between 6°55' and 10° north latitude and 10°16' and 13°18' west latitude.1 The country lies completely in ‘ the tropical zone and can be divided into three different ecological regions: the interior hills and plateaus: the coastal plain and; the colony peninsula.2 ' The population of Sierra Leone is approximately 2.8 million people. Agriculture is the dominant sector in Sierra Leone with an estimated 75 percent of the papulation being engaged in subsistence farming and prodUcing 32 percent of the gross domestic product. Sierra Leone is a major rice producing country and thus rice has an important role in the economy. Rice produces about 45 percent of the agricul- tural value added. Additionally, rice is an important staple food with estimates of 240 pounds of rice per capita being consumed per annum in rural areas and 150 pounds per capita in urban areas. Since this is the case, National DeVelopment Plans have empha- sized the development of this sector. The most recent Plan, in a ISaylor, R. 6., The Economic System of Sierra Leone. Duke University Press, Durham,_T967. 2 Jarrett, H. R.. A Geography of Sierra Leone and the Ga . London: Longmans and Green, 1954, p. 10. mb1a. 1 discussion of the basic features and elements of the Plan, states: Top priority has been given to agriculture, the growth rate of which is projected to increase from an estimated 1.6 percent during 1963/64-1970/71 to 4.6 percent. . . . Apart from acceleration of overall economic growth, rapid expansion of output in the commodity producing sectors will contribute to important objectives of the Plan rela- ting to income distribution, foreign exchange, and the creation of conditions for sustained long-term economic growth. Further, the Plan contained an overall framework for the develop- ment of the agricultural sector and a section specific to rice produc- tion.4 A major goal of the Plan is to increase rice production to self-sufficiency. With 81 percent of Sierra Leone's farmers growing at least one rice crop per year, the importance of rice in the economy and in the Development Plan can.hard1y be denied. ' Agriculture in the Development Process From the introduction, it is safe to assume that Sierra Leone is a country intent on developing and has the characteristics common to the majority of the developing countries in Tropical Africa. These include: - 1. Real income is low, although there may be sectors in the urban area which have high incomes; 2% Low income means low productivity and the implications of low productivity are: ' a. Unless a country has high foreign exchange earnings, most foodstuffs must be produced domestically; 3The Government of Sierra Leone, "National Development Plan, 1974/75-1978/79," Central Planning Unit, Ministry of Development and Economic Planning, Freetown, 1974, p. viii. . 41bid., see pp. 125-137. 3 b. Farms are likely to be small in size; c. The labor to land ratio may be high; d. Because the productivity of labor is low, the marginal product of labor is also low; e. Traditional agriculture prevails.5 The descriptive section of this paper will show that most of these points are true of Sierra Leone. Additionally, the agricultural sector is expected to contribute greatly to the economic development of their countries. Myint suggests that the agricultural sector is expected to contribute to development in the following ways: 1. By increasing domestic food supply; 2. By providing a growing market for domestic manufactures; .3. By contributing to domestic savings and capital formation; 4. By providing foreign exchange through agricultural exports.6 Given the necessity of developing the agricultural sector so that it may contribute in the manner suggested by Myint, policy-making and planning are required. Although policy and planning have taken place, it has been done without a great deal of information about the sector whose development is being considered. Information gaps to be considered are: I l. The general insufficiency of knowledge about traditional agriculture, with some specifics being: a. Resource allocation; 5Morgan, T., Economic Development: Concept and Strategy. New York: Harper, 1975. pp. 35 ff. 6Myint, H., “Agriculture and Economic Development in the Open Economy," Agriculture in Development Theory. Reynolds, ed., New Haven: Yale University Press, 1975. pp. 328 ff. 4 b. The decision-making process; c. Technical coefficients, i.e., input-output data. 2. Productive techniques which would affect the input-output ratios, i.e., cause an upward shift in the production function. 3. The barriers to the adoption of new techniques. 4. The means by which these barriers might be removed. Purpose and Scope of the Study The problems of planning due to lack of information can only be solved by research based on primary data. A basic objective of this Study is to add to the information pool. In attempting to reach this Objective the fellowing areas will be covered: . 1. Labor resources for Sierra Leone upland rice farms. 2. Use of labor over a crop year. 3. Estimation of production functions for selected inputs, including labor‘and an evaluation of the relative importance of the factors. 4. Allocative efficiency will be tested. This paper has six chapters. Chapter two reviews literature which is relevant to rice production in Sierra Leone. Chapter three is descriptive of the physical environment and the upland rice farm attivities in Sierra Leone. Chapter four describes farm character- iStics, labor resource availability and the use of labor over a crop .year. Chapter five is more analytical in nature, containing the 'theoretical framework, an estimation of production functions for %elected inputs, including labor, and an evaluation of the relative 5 importance of the inputs. Also included in this chapter is a test .for allocative efficiency“ The final chapter will summarize the results and discuss the possible implications for productivity improvement. Data Source Data used for this study were collected in crop year 1974/1975 fer the farm management compdnent of the African Rural Employment Project.7 The data were collected by an integrated twice-weekly enumeration of a sample of rural households over a period of twelve months beginning January 1974. The sampling procedure was as follows:8 a. The country was divided into nine agricultural resource regions. ‘ ’ b. Three census enumeration areas (consisting of 80-100 house- holds) were chosen at random from each region (excluding I urban areas). c. Twenty households were chosen at random in each enumeration area to give a total sample of approximately 500 households in about 25 enumeration areas (see Figure 1). Data Collection 4' . The research program had been divided into five integrated micro- level studies. For the purpose of this study it is the farm level 7Byerlee, o. and Eicher, 0.x. "Rural Employment, Migration and Economic Development: Theoretical Issues and Empirical Evidence from Africa." African Rural Employment Paper No. 1, East Lansing: Depart- ment of Agricultural Economics, Michigan State University, September, 1972. 8Byerlee, D. and Eicher, C.K., 1972, 0p; cit., p. 42. ,Q—O-O_o-o-O‘ I J J J- I I J Wfrgifi 0 20 4O 60 Boxulometars /' £1111an Tum 11-. 5444111.: llMfifl'c ERMMI rattan Areas ,...-- ,.., 1. ,' ' Al \. ’o ‘ Sinhumo \ I ‘- /‘ "\ 7 .oKobolo \. I. 1‘ \ - AI 2 1 J Komouoso finds“ ‘3 K. "k I Kondombm \ mass 5 f ,1 ‘ “o..1N22 ONOnz .uumnoca acmeonOEO NONON :Ouwcm< we“ co “cocoasou NONEOOOOOE scam ago No» mNmNNONmO New» OONO ON ONNOONFOO even were agape: "oucmmm NON O NO NNN OO NP NO NO , NO NN NO NO NO ‘ OOLNN ONN O O N O N ON NO NO NO NO NO ON ON_OO NON N O O O NO NN OO NO No mm NO ON mNNemN NNN OO NO ON NO ON ON NN OON ONN NN ON ON ONO: . NN NONONN OLONNOON N NNN O ON NN N NO NO NN N. N_ NN ON NN OOLNN ONN -- -- N -- N ON ON NN ON OO ON N ONOOO NNO F N N N NN NO ON OO NN NNN OO O ONOOON NON NN NN NN N OF N_ O O_ N NO NO NO ONO: mp cwmwm no: .0 ONO N ON _N N O ON N ON NN NNN O. OO OONN: ONN NO ON N -- N ON NO NO OO NO NN NN ONNOO ONN ON ON N NN O ON NO NO ON ON O NN ONOOON ONO NO NO NN N O NN . OPN ON NN NO OO OO ONO: . NN OOOONNNON .O OON NN OO ON N NN NO ONN ON ON OO NNN NON OOLNN NON O N NN ON ON ON NON NON ONN OON NO. NO ONNOO ONN N N NN ON N. OO. ON. ONN OON ONN NO NO ONOOON NON. ON NN NN O N OO ON, NON ONN NON NON ONN . ONO: . .m..~ “2..me :mepgoz .m NOO ON NON NO NO NO ONN ON O NO ON OO NN OOLNN ONN N N N N ON ON ON ON ON ON N_ O ONNOO NNO N N N ON NO NO NO ON NP. OO NN O ONOEON ONN ON ON NO NN ON NON. ON NO NO NON ONP NO ONO: .fl op umaou ccmcuaom . WWW ON ON ON -- -- ONN ON ON NNN OON NO N Oats: N NOO MN NW Ow NN N NN ONN NNN NON OON NO NN ONNOO NNO O O O N NO ON OO NNN NNN NN ON ONOOON NO NO ON NN O NN NON NON NON OON NNN NN ONO: NOON LON 1O, zll,la, O, O z Oi, .h. OO NONONOON ON mesa: Ono uco cm cameo cu. N No mmcsomwmmmm>0, which in turn implies that the second derivative aYzlaXiZ exists and is negative. If the algebraic form of Y = f(Xi) is known, the following can be derived: 1. the average product of Xi, 2. the marginal product of Xi, 3. the maximum level of Y that can be attained, 4. elasticity of response with respect to Xi. In the case of multiple inputs, the above measures are derived by holding all variables fixed except for the variable to be examined. In addition to the factor-product relations, we can examine factor- factor relations. These consist of: l. the family of isoquant equations, 2. the marginal rate of substitution of Xi for xi, 3. the elasticity of substitution of X, for Xj, 4. the family of isocline equations, 5. the ridge line equations, 6; the optimum combination of inputs, 7. the optimum level of output.36 Isoquant equations are loci of input combinations that yield a fixed level of output. These equations are obtained by rearranging the response function to give one input as a function of the other with output regarded as fixed. For various levels of output, this function h“ 36Dillon, J.L., The Analysis of Resonse in Crop and Livestock fflroduction, Oxford: Pergamon Press, 1968. 33 will give a family of isoquant equations. j gives the rate at which Xi must be substituted for Xj if X.j is decreased by an infinitesimal amount and the level of Y is to remain unchanged. The marginal rate of substitution of Xi for X The elasticity of substitution of Xi for Xj is defined as the relative change in Xi divided by the relative change in Xj if Xi is substituted fbr Xj while Y is unchanged. This elasticity is a pure number and can be interpreted as the percentage change in X, needed to maintain Y at the unchanged level while changing Xj by one percent. Isoclines are defined as the loci of all combinations of Xi and Xj which have the same marginal rate of substitution. They constitute paths up or down the response surface joining points of equal curvature on the isoquants. The family isocline equations is derived by solving for the change in Xi divided by the change in Xi and equating to the marginal rate of substitution of Xi fer Xj which specifies a particular isocline. _ Ridge lines are two special isoclines for which the marginal rate of substitution of Xi for Xj is equal to zero or infinity. The significance of ridge lines is that they mark the boundary between rational and irrational combinations of inputs. The optimum combination of inputs are those Quantities of. inputs that will produce a given output at minimum cost. In order to determine these quantities, called the least-cost combination, one must know the relative prices of the inputs and their marginal rate of substitution. The least-cost combination is achieved when thetuarginal rate of substitution of X1. for xj equals the price ratio of Xi to Xj. 34 The optimal level of output (Y) occurs when the marginal products of all inputs (MPx ) equals the inverse price ratio (Pxi/Py)' For ‘ i example, if the function is (a) Y = f(x1’ xj) maximum output is Specified by: (b) 11’: PyY - (Pxi X,i + ij Xj) where fl'= maximum output P O price Maximization of n with respect to Xi and Xj requires simulta- neous solution of two equations. (c) duvetx. = 0 1 (d) our/0xj o to find the combination of Xi and Xj that gives the desired level of Y. The required second order conditions fer a maximum is automatically , satisfied through the assumption of diminishing returns. The first derivatives ofequation (b), equations (c) and (d) can be rewritten as: aY/axi = Pxi/Py ' aY/OLXJ. = PXj/Py The above relationships would satisfy the aim of describing the reSponse process. Another possible purpose of response analysis would be that'bf pr0blem solving. This approach is geared to changing the response result, by controlling input levels, in order to achieve some specified result. Johnson expresses the relationship between positive and normative knowledge: 35 . . . objective knowledge of the normative can be pro- cessed with objective knowledge of the positive to reach objective prescriptive knowledge. The normative knowledge in this case is reflected in prices, the positive in the marginal rate of substitution of the inputs and 'the prescriptive knowledge sought is the optimal level of output (sometimes called profit maximization). The following preconditions for maximization must be established prior to attempting maximization: 1. A common denominator among the goods and the bads involved; 2. Interpersonal validity of that comnon denominator; 3. Establishment of the second order conditions necessary to insure the existence of a maximum in the common denominator; 4. Agreement on the decision rule to use.38 ' A . For use in production function analysis, these preconditions are met in the following way: 1. The use of money as the common denominator via the pricing of inputs and output; 2. It is assumed that money is an interpersonally valid common denominator, i.e., the value of money is the same for all persons;* ' 1 3. Second order conditions are established by an underlying assumption of production function theory, i,e., the 37Johnson, G.L., "Contributions of Economists to a Rational De- cision Making Process in the Field of Agricultural Policy." Abbreviated version of a paper presented at the International Agricultural Econo- mists Association Meeting. Nairobi, 1976, p. 4. 381bid., p. 5. *Generally, economists confine themselves to only Pareto better changes in which case an interpersonally valid common denominator is not needed . 36 principle of diminishing returns is operative; 4. The decision generally used is that of profit maximization which states that profit is maximized if the marginal value product of the factor is equal to its marginal cost. Regression Analygis Theory Crop response functions are typically estimated from experimental data or from cross sectional data by multiple regression using the principle of least squares estimation. Multiple regression is a method of analyzing the collective and separate contributions of two or more independent variables (Xi's) to the variations of a dependent variable; (Y). The principle of least squares estimation involves minimizing the sum of the squared deviations of'the observed from the predicted values. Regression techniques are a well developed theory and require no restatement. ’ When using regression techniques, the resulting estimates are often tested against null hypotheses. The standard error of the regression coefficients and their respective t values are examined for significant difference from zero at a percent level. One percent or 5 percent levels are those most commonly used. The application of this test was designed to prevent two types of errors called Type I and Type II errors: Type I error: to reject Ho but H0 is true. Type II error: to accept Ho but H0 is false. The levels of significance mentioned above refer to Type I error, i.e., the error of calling a true hypothesis false. In the majority of experimental work and hypothesis testing, consideration is given I 37 only to the Type I error. The seriousness of committing either one of these errors is dependent on the problem being studied. Statistically it is possible to set any desired levels of protection for both types of error but the number of observations to give this protection is often very large. In the case of most practical work, the number of observa- tions is given and it has been demonstrated in statistical research that if the level of protection fer a Type I error is lowered this automatically increases the level of protection for a Type II error, and vice versa. To use this test for the fitted production function the formulation would be: Ho: 81 = O . Ha: Bi f 0 This statement of the null hypothesis means that there is no relatidn- ship between x, and Y. A Confidende intervals are often used in addition to testing a null hypothesis. The confidence interval can be estimated using the same information as used to test the null hypothesis and is estimated for the purpose of producing an interval which would contain the true Value of the parameter with some given level of probability. If the test statistic falls within this interval the null hypothesis is accepted. If, as often happens in fitted production functions, the regres- sion coefficients are not significantly different from zero, the implication is that an increase in the input with which that regres- sion coefficient is related will not contribute to an increase in output. Similarly, the test statistic for the regression coefficient 38 nay'fall within the confidence interval and one would be convinced that the null hypothesis should be accepted. For the purpose of productivity analysis the testing of the regression coefficients in a null hypothesis is of limited usefulness. In the discussion of production function theory one of the relations which could be examined was the optimum levels of inputs to attain some level of output. A better method would therefore be to test the regression coefficients necessary to give a minimum set of returns. This type of test would better evaluate the allocative efficiency which 'would be a concern in productivity analysis. Fittinggthe Production Function From the 145 farmers interviewed for the upland rice sample, 86 usable records were obtained. The entire Northern Plateau (Region 7) and the Riverain Grasslands (Region 4) were not included in the analysis because: 1.’ Output data were incomplete for Region 7 and; 2. For Region 4, deletion of farms with missing data made the remaining number too small to represent the region. The variables selected from the output data are: Y = output: in bushels' hale labor: hours X x .0. 11 II 2 female labor: hours x 11 3 child labor: hours hired labor: hours - cropped land: acres R UT 1 39 X6 = bush age: years X7 = seed: pounds X8 = capital: Leones Output -- 22 x 22 feet yield plots were laid out at the time the fields were measured. The farmer cultivated the plots in the same way as the rest of the field and at the time of the major harvest. The yield plot was harvested by the farmer in the presence of the enumerator. Labor =e measured in actual hours. This input was disaggregated into four Classes: Male: over 15 years of age Female: over 15 years of,age . Child: 10 to 15 years of age Hired For purposes of aggregation, as when computing total family labor ihpUts, manLhour equivalents were computed by applying weights of 1.0, 0.75 and 0.50 to male, female, and child labor, respectively. The weights reflect the relative wage rates on a national basis. Land =~ because of a shifting cultivation, each field was actually measured in each enumeration area. p zBash =='the age was measured by the number of years since the iaha~nas previously cropped. ESeed'v- measured in pounds for the total acreage. iCapital r- measured in Leones (Le. 1.00 = $1.10 U.S. in 1974/75) Hh'tePMS 0f Current depreciated value. The estimated annual capital 1 i=1 increasing returns to scale are exhibited. The marginal productivities of the input categories (Xi) may be calculated directly from the exponents by using the formula: ( 1 b1? 3 MPP = x1 xi where Y, the estimated output, is the antilog of log Y in equation (1) and X1 is the quantity of the input under consideration (1 e l, . . ., n). ' are: 43 The strengths of the Cobb-Douglas function for this type of study Its simple functional form is computationally economical; It yields statistically significant estimates of the coefficients without imposing excessive demands for large samples. It provides important information such as the extent to which a factor's marginal productivity declines as the level of input increases, given the quantities of all other factors of production; measures of returns to scale; and for the variables included, it is necessary to estimate 41,42 relatively few parameters. This gives a considerable advantage over other types of functions in costs ‘of computation as well as in minimizing the loss of degrees of freedom. The limitations of this type of function are: 1. 2. The elasticity of each factor is constant, and All elasticities of substitution of Xi for Xj are constant regardless of the size or ratio of the factors. These properties are derived from the fact that the function is linear f in the logarithms which is the property which makes it possible to fit the function statistically by linear multiple regression. Many of the types of factor substitution found in agriculture are not of 41 Yotopoulos, P.A., and Nugent, J.B., Economics of Development: Empirical Investigations, New York: Harper and Row Publishers, 1976. 42 The number of parameters for the equation is one more than the total number of variables. 44 constant elasticity. This makes special adjustment or rejection of observations necessary where the use of one or more observations is quite small. Shaw and Wright suggest that such adjustment or rejection must be on a subjective basis and they discuss briefly the consequences 43 of adjustment or rejection of observations. Griliches, in later articles also discusses the consequences of exclusion of observations.44 The values of the parameters of the Cobb-Douglas function were obtained using ordinary least squares technique. The first fitted Cobb-Douglas function in logarithmic form for the selected sample is: (4) log v = .444 + .094 log x1 + .058 log x2 (.098) (.073) + .096 log X (.103) - .015 log x (.020) (.109) - .063 log X6 + .049 log X7 + .049 log X8 ' (.114) (.133) (.071) + 1.058 log X 3 4 5 The bi's in the equation are the elasticities of the dependent variable (Y) output in bushels, with respect to the independent variables (Xi's)2 The value of these bi's indicates the percentage change in output associated with a one percent change in the respective input category, holding all other inphts constant. The constant log a is the intercept on the log Y axis. The regression coefficients (bi's), the associated standard errors (Obi)’ and the level of significance are shown in Table 7. Land showed the only significant difference from zero at a low level, 43Shaw, H.R., and Wright, P.A., "Alternative Methods of Farm Management Analysis,“ Canadian Journal of Agricultural Economics, Vol. 3, No.1, 1955, pp. 74-75. . 44Griliches, 2., "Specification Bias in Estimates of Production Functions,“ Journal of Farm Economics, 39:8-20, 1957. 45 Table 7. Regression Coefficients (b.'s), Their Standard Errors , (ob 's), and Level of Sign1fiance, 86 Upland Rice Farms: Sie ra Leone. 1974/75 Input . b ob Significance Category i i Level Male Labor .09402 .09791 .359 Female Labor .05764 -07268 .430 Child Labor -.01492 .02027 .464 Hired Labor .09588 .10278 .358 Land 1.05767 .10921 .000 Bush -.06310 .11443 .583 Seed .04855 .13349 .717 Capital .04924 .07135 .492 the one percent level. The other inputs ranged in signifianct differ- ence from zero from the 35 percent level to the 72 percent level. . More important than the percentage level at which there is significant difference from zero for the purpose of economic analysis is the sum of the regression coefficients (bi's) which was 1.325, indicating increasing returns to scale. This sum of the coefficients was tested to determine whether significantly different from one. There was significant different from one at the one percent level; therefore, the indication of increasing returns to scale was accepted. The implication is that an increase in all inputs of one percent would lead to'a 1.325 increase in output. It should be noted that although this indication of increasing returns is accepted, it is with qualifications. These estimates are based on averages and therefore it can not be assumed that increasing returns to scale apply to individual farms. The inplication would be that farm size would be increasing. The average farm size in Sierra Leone is less than 6 acres with a range of 1 acre to 21 acres which 46 indicates relatively few large farms; therefore, while increasing returns to scale is statistically significant, this result is questionable on the basis of general evidence about Sierra Leonean agriculture. The simple correlations among the logs of the input categories are shown in Table 8. Land (X5) showed the highest correlation with output. The multiple correlation (R) was .82. The coefficient of determination was .69, while the adjusted coefficient (R2) was .66. Using the adjusted coefficient gives an indication that 66 percent of the variation in the logarithm of the dependent variable (Y) output, was associated with the independent variables included in the equa- tion. The unexplained variance of 34 percent may be attributed to 45 other inputs and institutional arrange- variables such as the weather, ments which are difficult to quantify. The effects of such non-included variables on the log of the output are assumed to be randomly distri- buted. 'Because of the difficulties involved in measuring adequately some of the input (and in defining what is a input46), a second function which omitted the input category of bush was run in an attempt to obtain g better fit with greater confidence in the meaning of the regression coefficients. The logarithmic form becomes: 45The upland rice yields are about 60 percent of those reported in earlier surveys due mainly to the pattern 0f rainfall that prevailed in Sierra Leone in the 1974/75 crop season. See Spencer and Byerlee, pp, £15,, p. 54. 46Bush age may not be a suitable variable as is, i.e., as a mea- sure of soil fertility. If bush were multipled by acreage it would have given total land availability but this would not be an appropriate mea- sure as the aim was to estimate a coefficient for land actually under cultivation far the crop year. 47 .Pm>o~ ucmwgwn p an» an ong seem ucmgmmeeu A—ucmquecmem P a . m.. mm a cue: .usnuao A>v meaoegm> pcmvcwqmu as» co mweuefi xv ea ecm> acmccoamuce on» on uuoamac oeummem use men mucm eueemwou copmmwgmwg ones can. eem. Pmm.- ammene «me. emu»- nee. mew. ma=_e»lm Fee "we epp mop mop owe meo was. eaten eaaeeeem meo. ace. moo.- wmo.p moo. meo.- mmo. coo. mmucmeuemmoou cowmmmcmoa mm~.. aem. ecu. mew. woe. ~m_. mam. .mm. >........eeaeeo.ll em". meo. eeN. epm. ewe. emp. oeo.- ex........epeeau opp. oee. New. meN. men. mPN. ex..........eaam mom. oeNJ Nee. emo.- 0mm.. ex..........em=m man. Now. New. eem. mx..........e=ee . moo. Pew. mam. ex...aonee eaae: amp. ewe. mx...aonee ep_eu map. ~x..goam4 apnea; ._ Px....coee4 a_ez m e . _ m N _ "meeaeueccaoo eoeeepaacou mx Nx ex x x x. x x movemepmum emacosmeqaam ee.o u we ee.o u we . . mm o u e ex mo_ meo. + Nx eo_ eeo. +.ex.eo_ nee. - mx.eoe mmo.~ + ex ea. eee. + mx.eee mpo. - ~x eoe wee. + _x no. eeo. + eee. u e no. me\eae_ .aeoae escaFW ."meaea woe: campus cw you mucmeuewmoou coeuoemsgou use savanna“ coemmmcmmm “— coemmwcmmm .m m_nuh 48 (5) log Y = .433 + .074 log X1 + .065 log X2 -(.0l5 log X3 (.093) (.071) .021) + .09l log X + l.049 log X + .049 log X (.101) 4 (.107) 5 (.132) 7 + .048 log X (.071) 8 The modified equation had an adjusted coefficient of deter- mination (R2) of .66 which is identical to the initial equation. The sum of the coefficients (bi's) increased by .036 or a 2.7 percent increase to l.36l. A comparison of Table 9 and Table 10 shows insignificant changes for most of the regression coefficients (bi's). A noticeable change occurred in the regression coefficients for male labor and female labor. The male labor coefficient decreased by 21 percent while the female labor coefficient increased by l2 percent. This phenomena is! discussed by Griliches in the article previously cited.47 In summary, if one accepts as a plausible assumption that there is correlation to some extent between the excluded variable and the included variables, the exclusion will bias the estimate of at least one of the coeffi- cients upward and in this particular function because the sum of the coefficients was larger than one, there will be an overestimation. A' third function aggregated labor into a single input category. This was accomplished using the weighing system previously specified which gives homogeneous man-hours. The rationale for the estimation of this farm follows frOm the general rule of classifying input categories, i.e., combine good substitutes and measure according to —__ 47Griliches, 92, 313,, pp. lO-l3. 49 xm.x eoem. _ex.me mmm.m . meo. xN.e meuw.x ex no. m_xo. xex.me mwm.m eeo. N~.mex xex~.m xx xe.ex- exmm.w- xex.me mwm.m . meo.- we.x expo.~ ex o~.xm xeee.xx xex.me mmm.m mmo.x m~.e mmee.x . mx eo. exec. xex.me mum.m moo. . ex.mmm momm.e ex e~.- xeeo.- xex.me . mem.m mxo.- em e_ exme.~ mx we. once. xex.me mmm.m mmo. mm.emm xemx.e Nx No. _ emoo. xex.me . mwe.m eeo. e~.mmmx xmmx.e xx ex ex . > m P wm e m xyommumu e>z ea: eexxeee x ex e eexeeee .m ex eeeex mxxexex..a= _xaez me x x max we ex ex me, seeeeeeo pep=< moeepc< 1. page“ mxxexee .e ems eeeaem "meeea eeee eeexee em .2 ~32. 51 the common denominator which makes them good substitutes and/or good complements. The form with labor inputs aggregated becomes: (6) log Y = -.352 + .322 log Xi + l.024 log X (.l38) + .050 log X8 (.064) 5 + .00l log X7 (.104) (.l28) Table ll shows the results. In terms of R (.83), R2 (.69), R2 (.67), and the Zbi's (1.397), regression 3 does not differ signifi- cantly from regression 2 in which the labor inputs are disaggregated. The decision as to the final form of the function and the specification of the variables should be based on more than arbitrary choice. The justification for choosing to use the disaggregated form, equation (5) is as follows: male'labor, hired labor, female labor and child labor are complementary. 0omplementary as used here does not imply complementarity in the economic sense which involves propor- tionality between the inputs. Rather, the term is used in the sense that there are certain tasks for certain labor classes which are more or less institutionalized. These socio-cultural constraints also prevent the labor classes from being good substitutes for all farm tasks. For example, although women are capable of many of the less arduous bush clearing activities, in fact, they do not engage in such activities even when it leads to the employment of hired labor to accomplish these activities. Therefbre, when evaluating allocative efficiency by comparing the marginal value product of labor to the market wage rate, it seems appropriate to do so with disaggregated marginal value products of labor. As with equation (4), equation (5) contains only one independent variable, land (X5), which is significantly different from zero at the 52 P mmn.P Pmmm. me.¢¢ Non.m omo. Fm.m mama.— MWx Poo. Nooo. xmm.ee Nex.m xoo. . N~.mex xex~.m xx ee.em eeex.o_ . xmm.ee Nee.” eeo._ m~.e eNee.x mx emo. eeoo.. xmm.ee . me.m «mm. mx.~em~ xmmm.x xx ex e» > no w ww e . zeommumo e>z eez eexxeee x x e eoxeeee .w eex eeeex m5\e~mp .m om; mggmwm "wagon muem acmeaz om .muza:H on» mo muuzuoem Fecemcm: use Am. av mucmeoeemmou coemmmemmm .AeLou ueezuegmmopeuc< vcm mscueemmog :ev uaauao wee moxcoumpeu annex .m coemmmcmom .ee venue ' gi va )5 ‘01 53 one percent level. This significance of only one variable could be interpreted in various ways. One coald hypothesize that: l. there is high correlation between land and the other variables. If a high correlation existed, the extent could be ascertained by examining the correlation coeffi- cients shown in the simple correlation table. A correla- tion coefficient greater than |0.8| between a pair of independent variables is usually taken as evidence of high multi-cOllinearity. This does not appear to be the case. 2. land is the most important factor in the productive process. This statement is, of course, true but is not a sufficient reason for the lack of significance of the other inputs. 3. the level of aggregation, e.g., the labor inputs are aggregated for the entire year, may have an effect of the resulting coefficients. This indication of seasonality will be discussed more fully at a later point. 4. in addition to possible seasonality, there will be un- explained variance. The marginal physical products (hPPxi) of the input categories (Xi's) were calculated directly from the exponents using the formula given in equation (3). The marginal value products represent the value of the marginal physical products at the per unit cost of Le. 5.00 which was the minimum government price per bushel during the l974/75 cr0p season. The marginal value product for male labor (XI) of Le. .0l3 is below the value of Le. .02 Specified by Spencer and Byerlee as the 54 hourly return to labor.48 Of special interest is the marginal value product fer female labor (X2) which at Le. .016 is higher than fbr males although not significantly so. The going wage rate for women is .75 percent of the male wage rate but in so far as can be determined from this data, the value of female labor is the same as the value of male labor. This has implications for the weighing system which was used here. The utilization of a conversion scale, whereby women have been weighed by 0.75 may be inappropriate. In recent studies Spencer and Tollens have used a weight of 1.0 for women hased on the belief . that women are as efficient as men in the types of farm work performed by women and that any conversion of female and child labor 49,50 b to man labor units is arbitrary. . The negative value for child labor (X3) is not startling. While child labor may be used for such tasks as bird-scaring, the quantity of labor used is small and the negative sign would indicate that there is a substitute for child labor. Since it is known that females also perform this task, female labor may substitute for child labor. The calculated marginal value product of land (X5) appears to be very high but whether in fact it is high will be determined by the equating of marginal value product and marginal factor cost. The capital (X8) marginal value product may be realistic or it may not. It is entirely dependent on the source of the capital. If the farmer 48Spencer and Byerlee, 99, 213,, p. 59. 49Spencer, 33. 915.1972, p. 15. 50Tollens, E.F., “Problems of Micro-Economic Data Collection on Farms in Northern Zaire." African Rural Employment Working Paper No. 7, Department of Agricultural Economics, Michigan State Univer- sity, East Lansing, Michigan, 1975, p. 18. 55 borrows at an established credit institution (bank) the interest ' rate will be approximately 11 percent. If borrowing from a local lender, the range of interest may be very wide. The same is the case when borrowing.from relatives and friends. (Equating Marginal'Value Product and Marginai_Eactor Cost Theoretically the farms should make use of the inputs at the level where the marginal value product of each input is equated with the marginal factor cost of the input (MVP = MFC). Rather than test the regression coefficients against the null hypothesis, the estimated regression coefficients (bi) shown in Table 5 were compared with the coefficient which would be required to yield marginal value products equal to a set of minimum expected returns. This calculation was done for'the labor and land inputs although in Sierra Leone, as in many African countries, it is difficult to value land because there is no’ land market. Similarly, the true opportunity cost of capital is difficult to establish since there is usually a fragmented capital market. The minimum expected returns are: Male labor per hour -.10 Le. Female labor per hour .075 Le. Child labor per hour .050 Le. Hired labor per hour .10 Le. Land per farm 5.00 Le. l. The minimum expected return on male labor was based on the national average hourly wage rate for Sierra Leone during the 1974/75 crap year. 56 2. The minimum expected return on female labor was based on the national average hourly wage rate. This rate was generally 0.75 percent of the male wage rate. 3. The minimum expected return of 0.50 fer child labor is based on child labor being calculated at 50 percent of an adult male. 4. The hired labor rate is normally the same as the first three categories, dependent upon sex and age. However, for reasons of simplification, all hired.labor was converted to man-hour equivalents using weights of 0.75 and 0.50 fer female and child labor, respectiVely. The rationale fbr this is that the quantity of female and child hired labor was not sufficient to justify a separate category within the regression on one hand but on the other, was sufficiently: significant such that it could not be ignored. 5. Land return is the amount given as rent for the entire farm. Most land is communally owned in Sierra Leone and this type of ownership has not been a serious constraint to rice production. The family communal system of land ownership has precluded the development of an effective _ market for agricultural land. Additionally, there is a land surplus. Token fees are sometimes paid by a small proportion of farmers and it is this token fee which is being used here. The regression coefficient which will yield a minimum return will be termed the standard regression coefficient and designated bit This bi* was obtained by solving for equation (7): (7) , b.* = where MVPXi is the expected return; Xi and Y are from equation (5). Table 12 shows the results of the calculations. Table 12 also shows the t-test which was used to test whether the estimated regression coefficient (6i) was significantly different from the standard regression coefficient (bi*) required to yield a minimum return. The t-value was derived using the fbllowing equation (8): E. - b*. (8) t = 1 1 obi The results indicate that the estimated regression coefficients (gins) fbr the labor classes of male, female and hired labor were significantly different from the standard regression coefficients (bi*'s) at the 5 percent level. Taken at face value this would indicate misallocation of these resources. There are several hypotheses one could suggest to explain these results. ’ 1. The result may reflect that the wage rate is inappropriate ' for use in this context. It has been suggested that since the demand for wage labor is seasonal, it may be artifi- cially high, that is, not reflect the year round cost of labor. 2. Measurement problems--when a farmer is asked the amount of time spent on his upland rice farm and he gives a number of hours, these hours may be recorded without qualification. 58 meo. we meo. en eeeexx_eexm eez meo.x woe. exm. mxe. eeo._ me eeeexexeexm mm~.~ Pox. eme.x- xe~.P .mo. ea eeeexeeeeem eez oxm. . omo. xmo. - exo. mxo.- me eeeexexeexm emo.e xxo. xee._- eom.. moo. Ne eeeexexeexm Fee.m Nee. Nex.~- exm.~ exo. .e wuwwmwmewmwm maea> a uummnwum «ea . em «we em en mo pm>mg mucmcmwmwo on» was Am. muuauoea maem> Pmcemeez Sneeze: upwe> o» umgezoma Am.«env mucmeuemmmou coemmmxmom oceucmpm my manoeuemewou :oemmocmma.cmaesepmm on» yo comeceasoo .mp mPnMP f 59 No consideration as is given to the "arduousness and urgency? of the task being performed. These, taken together with his health and environmental factors will result in sub- stantially different rates of work for the same task. What this means in a practical sense is that the farmer may take an entire day at a task on one occasion but complete the same task in a matter of hours on another occasion.. The implication for productivity analysis is that the labor input will be overestimated in terms of hours productively engaged and the results would make it appear that produc- tivity is quite low. Seasonality--one of the weaknesses of fitting an annual function is that it does not allow for the introduction of time, i.e., in this case the year is condensed into a point in time. But most agricultural work is highly seasonal, reflecting the effect of climate on the biological processes in agricultural production. This means that the demand for labor for a particular enterprise will also be seasonal, displaying wide fluctuations, while the supply of family labor is relatively evenly distributed throughout the year. During these slack periods, the productivity of the family labor is very low and one could say, does not effectively contribute to out- put. However, since hired labor is used only in those particular seasons when required, their productivity would be expected to be high. Further, if productivity analysis were done only for the seasons when there was hired labor present, we could expect to find that family 60 labor productivity was also high. As hired labor is used mainly in . periods of high productivity, the higher marginal value productivity estimates for hired than family labor is reasonable. CHAPTER VI SUMMARY AND CONCLUSIONS This paper attempts to add to the body of knowledge about tradi- tional agriculture among upland rice farmers in Sierra Leone, the farm characteristics, labor utilization, and possible constraints to in- creased productivity. Characteristically, an upland farmer cultivates about 6 acres per year but when taking the bush fallow system into consideration, he has access to about 50 acres. The upland farmer uses traditional methods and'tools, i.e., does not make use of fertilizers or machinery, con- sequently his capital input is quite small. Labor, then, is the primary input with family labor the primary source. Hired labor is used in all regions and comprises 22 percent of the total labor input. This is 2 percent higher than reported by 51 and may be attributed to the high use of hired Spencer and Byerlee labor (35 percent) in the Southern Coast which is characterized by the unusual,demographic features of small household size (5.4) and high net out-migration rates (over lleercent). The remaining 78 percent of the labor input which is the family contribution nay be broken down as follows: males - 46 percent; females - 26 percent; and child - 6 percent. It is worth noting that Moa Basin had a much higher incidence of the use of female labor at 51Spencer and Byerlee, op, cit., p. 28. 61 62 40 percent more than the other regions. The average male labor input, combining both family males and hired males, was 1,330 hours per year or 110 hours per month. This is a deceptively low figure. When looking at the peak month, it is seen that male labor inputs are 229 hours.- A similar analysis holds for female labor. The yearly average is 506 hours or 42 hours per month but in the peak month female labor contributes 107 hours. The output of rice from the farms averaged 780 pounds per acre, varying from 497 pounds in the Scarcies to 1,174 pounds per acre in the Northern Plains. It was noted that the rainfall pattern had contributed to a 60 percent lower yield than normally expected. Relating man-hours to yield, an average labor input of about 62 hours was required to produce one pound of rice. The range was from a low of 36 hours in Moa Basin to 88 hours in the Southern Plains. Cobb-Douglas functions were fitted for three equations. The initial Cobb-Douglas, using eight independent variables was not analyzed because it was felt that bush as neasured in years between cultivation periods was an inappropriate measure of soil fertility, i.e., not really an input. . In the second regression equation with seven independent variables, four labor classes, land, seed, and capital, the marginal value products were calculated. The male labor value of 0.013 Le. was less than previous studies have found. This may be due to rounding differences. Female labor value was higher than male at 0.016 Le., a somewhat unexpected result. However the value was not significantly higher which implies equality. This suggests that within the sex- related tasks, the female is as productive as the male. Hired labor _ W— ' —A-— —--' fl _ .. ' 63 had a value three times that of male labor which may suggest that -there are variations in the quality and intensity of labor, i.e., paid labor is more effective than family labor. Child labor was not significant and could very easily be substituted for by female labor. .Nothing conclusive was said earlier in the text about the marginal value products of land, seed, and capital because no land market exists, seed is retained from the previous year's crop, and the capital market is highly fragmented. 'However, after determining the bi? required to equate the MVP and MFC of land, it was discovered that bi and bi* were not significantly different. This implies allocative efficiency in the use of land. A third function with labor aggregated into an homogeneous input yielded regression coefficients which were not statistically significant from zero and the equation had the same explanatory power as the dis: aggregated labor equation, therefore the second equation was used for further analysis. The standard regression coefficients required to yield a minimum expected return were derived by which to test the estimated regression coefficients. The results indicated that, if no error had been made in the estimation, the utilization of labor resources was not at the effi- cient level of organization. .However, the hiring of labor during the planting and harvesting seasons even on the smallest farms makes it difficult to accept these results. When taking into consideration that the measurement of labor use was for the entire year and therefbre does not say anything explicitly { about the existence of excess labor or labor shortages at particular seasons during the year, one feels that the calculated marginal value 64 products may be misleading, i.e., too low for the labor inputs. Another consideration is the validity of equating the family year round productivity with a seasonal wage rate. A more detailed analysis of regional and seasonal productivities would be required less one make such sweeping generalizations as to cast doubt on the whole analysis. However, based on the information available, it may be concluded that the use of non-family labor is an important factor during the peak season and helps to relieve labor constraints at that time. But in Sierra Leone, a class of landless laborers has not yet arisen, con- . sequently the time non-family labor would be most in demand coincides with the period when this labor must also devote more time to their own farms. Therefore, not only the extent to which a family can afford to employ non-family labor but the availability of this labor at the appro- priate time is of importance. Njoku and Karr52 have suggested that one possible way to increase upland rice production in Sierra Leone is to increase the labor availability by adjusting agricultural prices, thereby providing increased employment opportunities in the agricultural sector for the rural to urban migrants. This possibility should not be casually dis- missed; thowever, evidence both in Sierra Leone and other countries suggests income may not be the most important variable in the decision to migrate to an urban area; further, the net rate of out-migration is not very high in Sierra Leone. Another suggestion is that perhaps the output of the current labor force can be increased by shifts, i.e., redistribution of labor ”mom and Karr, 9.2- _c_j_t_., p. 297.. 65 within the agricultural sector. The feasibility of this suggestion is dependent on many factors. For example, if the peak season for upland rice farmers coincides with the slack season for farmers using other modes of production (such as mangrOve swamp or inland swamp rice) or for (farmers with other crops and this does not conflict with their other off-farm activities, with economic incentives, this seasonal migratory employment pattern may be helpful. , . In addition to increased output due to labor availability, labor productivity must be considered. Productivity increases can be obtained . by using non-traditional inputs. Among the conventionally suggested inputs are tractorization, combine harvestors, improved seed varieties, fertilizers, pesticides, water control, small mechanical aids and more efficient hand tools. With respect to tractorization, Spencer and Byerlee53 point out that the use of tractors in Sierra Leone was only possible with heavy government subsidization. That is to say, without the subsidy, it is not economically feasible to use tractors. Additionally, while tractor cultivation may relieve constraints at one point, the labor con- straints are often transferred to other periods such as the time of harvesting. The use of the combine harvestor is possible only on farms of a much greater acreage than the average farm size for the Sierra Leone upland rice farms. Further, Winch has reported that in Ghana the increased output was only 17 percent for the large farms using combine 53Spencer and Byerlee, 92, 913,, p. 66 harvestors while the labor displacement in man-hours was very high.54 A more fruitful avenue to increased productivity would be the use of small mechanical aids, more efficient hand tools, improved seed varieties, fertilizers, and pesticides. A discussion of the require- ments for the introduction and adoption of these non-traditional inputs in Sierra Leone is not within the scope of this study but will be further pursued in a later study. 54Winch, F.E., “Costs and Returns of Alternative Rice Production Systems in Northern Ghana: Implications for Output, Employment and Income Distribution." Unpublished Ph.D. Dissertation, Michigan State University, East Lansing, 1976, p. 136. BIBLIOGRAPHY BIBLIOGRAPHY‘ Byerlee, D. and Eicher, C.K. 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