WHEAT: Productivity and Expectations
This chapter is concerned first with the estimation of the relationship between on the one hand, output per acre on our sample wheat plots and, on the other, the levels of inputs and some characteristics of cultivators; and then with the interpretation of the results of that estimation. We shall be paying special attention to the estimated value marginal productivities of various inputs compared both with the costs of those inputs and with the views of cultivators as to the effects on yield of varying input levels. In § 8.1 we set out our choice of model and explanatory variables. The correlation matrix of our selected variables is presented in § 8.2. We shall be particularly interested in two features of that matrix. First, the relationships amongst the 'good practice' and associated variables introduced in the preceding chapter and, secondly, an analysis of variance for variables associated with tenancy.
Our main regression results are presented in § 8.3. The comparisons of estimated productivities with prices are contained in § 8.4. Cultivators' views on productivities are compared with our estimates in § 8.5 and we attempt to use our knowledge of plots and cultivators to understand residuals which are left 'unexplained' in the regressions. We draw some conclusions for economic theories of input choice in § 8.6, paying particular attention to choice under uncertainty. We speculate on possible practical improvements in cultivation technique in § 8.7. Concluding remarks are presented in § 8.8. There is an appendix on alternative functional forms.
We wish to understand the variations across plots in the yield per acre of wheat. We shall be using the techniques of regression, with output per acre as the variable to be explained, and the inputs employed together with certain measurable characteristics of cultivators as explanatory variables. Our task in this section is to explain our selection of the models we use in the regressions.
A standard approach to the analysis of production is to present the output of a farm or firm as a function of the three classical factors of production: labour, land, and capital. The detail embodied in our data permits our analysis to be rather more subtle. Thus, for example, instead of using a variable 'labour' we employ measures of the specific tasks performed by labour which constitute the direct inputs into production-the number of ploughings, the number of irrigations, whether or not the plot was weeded, and so on. This more detailed approach involves certain problems in defining tasks and we return to this issue below.
We are not here concerned with the output of the farm as a whole but with the output from a particular plot. One would expect two identical plots with