80 A^riciiliural Research and Piodiiciiviiy 



where 



y. Total agricultural product in country,/ year t{j= 1 36)(/ 



= 1 for 1955,5 for 1960, 10 for 1965, 13 for 1968) 

 X A vector of inputs^ 



A'l Land 



Xj Labor 



X3 Livestock 



X4 Fertilizers 



X5 Machinery 



x^ Technical education 



x-7 Research, knowledge 



<y.j Country-specific 'Mevel" coefficient 



7y Country-specific time-trend coefficient 



/( ) Cobb-Douglas function. 



The specification in 5.1 is quite general. The olj coefficients are 

 the estimates of the countries' productivity levels. The 7/ is an 

 estimate of the country's specific time-trend coefficients, within 

 country productivity changes. 



Regression estimates are presented in table 5.1. Regression 1 is 

 estimated on the assumption that there are no country or trend 

 effects, i.e. aj — yj — for all./; in regression 2, 7/ = 0; in regres- 

 sion 3, ay = 0. In regression 4 the estimate of equation 5.1 is 

 unrestricted. 



The regression coefficients in table 5.1 are the elasticities of 

 production, proportional to the marginal products of the factors. 

 The estimated elasticities vary a great deal between the regression 

 in the table. This should not be unexpected, as the coefficients are 

 measured from variations in different directions: in regression 1, 

 the elasticities are estimated from both within and between coun- 

 try variations (fitting a line to all four points:^!, «2. ^i- b-^ln figure 

 5.1), while the estimates in regression 4 are restricted to within- 

 country variation, with the country-specific time-trend 

 7- allowed for. 



2. See notes to appendix table 6. A for detailed description of variables 1-7 and 

 sources of data, and appendix 5 for a discussion of alternative specification of the 

 research variable x-/. 



