Appendix 6: 



Preliminary Findings of the 



Production Function Estimates 



The main data source for the production function analysis in the 

 text is Hayami and Ruttan's (1971) sample, extended to cover ob- 

 servations for 1968 and including an agricultural research vari- 

 able. The natu'al level at which to estimate the production func- 

 tion is the farm level. But, data on numbers of farms are available 

 only for 1960. Alternatively, on the assumption of linear 

 homogeneities, the function can be estimated per unit of labor. 

 The difficulty here is that labor force data (males) are not on actual 

 labor input but on the available labor. Appendix table 6.A tests 

 estimates of the production function at the sectorial aggregate 

 level, the farm level, and at the per capita— i.e. per laborer— level. 



A comparison of aggregate level to a per- farm regression does 

 not reveal large differences. The labor coefficient in regressions 5 

 and 6 seems to reflect errors in the assumption of linear 

 homogeneity of the production function; therefore this specifica- 

 tion is rejected and not utilized in the text. 



It should be noted that, with the inclusion of the Research vari- 

 able, the Fertilizers variable declines in size and significance, the 

 same being true about the Schooling coefficient (its estimate in a 

 regression without research is not reported here). These two vari- 

 ables, together with the Technical Education variable, served in 

 the original Hayami and Ruttan analysis as proxies for human 

 capital and research. These proxies are effectively replaced by a 

 genuine research variable, the Fertilizers variable again being sig- 

 nificant in the combination of time-series with cross-sectional 

 data. 



The meaning of these results is that, given research, fertilizers 

 application does not contribute significantly to the explanation of 

 productivity differences between countries, but it does contribute 

 to explaining the overtime shifts in productivity. The schooling 

 variable, i.e. schooling in the country at large, is evidently not a 

 good one for measuring the quality of the farm labor force. 



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