T HE algebraic production function is the classical method of specifying physical relationships between inputs and output. The traditional approach in determining coefficients for an aggregate production function has been a direct least-squares estimation, usually based on time-series data. An important problem that develops is highly correlated "independent" variables. It is not possible to obtain reliable estimates of the parameters in a production function such as (1) (if n is more than two or three) because of the high correlations between the inputs X i .l Therefore, output is usually regressed on a limited number of highly aggregated variables; i.e., output Y is "described," but the structural validity and usefulness of the parameter estimates is questionable.A second approach-the use of factor shares as production elasticitiestrades the intercorrelation problem for the dubious assumption that economic equilibrium prevails.t Use of production coefficients derived in such a manner to determine optimum resource allocation and output is anachronistic.The approach used in this paper is an attempt to combine favorable features of the two approaches described above.
RationaleThe factor share is defined as the ratio of expenditure on a resource to the value of output. If equilibrium quantities of all resources are used, then the factor share and elasticity of production are equal, as shown below. The factor share is (2) by definition:
PiXI(2) F, = --.
P 7YIn equilibrium the marginal product of XI is equal to the factor-product price ratio, as in (3): 1 Simple correlation coefficients between the nine input categories used in this study (there are 9!/2!7!=86 correlations) were .78•.88•••.•.99. The matrix of sums of squares is then so nearly singular as to give highly dubious results.I For published work on factor shares see
Second thoughts about the assigned title of this paper (Rural Development Research—One Perspective) prompted a change — there is a not too subtle implication that the “one perspective” may not be the correct perspective. Also, I had envisioned assimilating a number of perspectives attributable to others into my own – and at least attempting not to miss the target altogether. However, such would be a rather placid and inappropriate approach to the topic. Consequently, I propose to confront the topic of rural development research more directly, scrutinizing it as closely as possible, and attempting to make a contribution to a better understanding of the problems facing rural development researchers and those concerned with action programs in “rural development.”
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