74 A^riculiiiral Research and Product iviiy 



of three parts: (1) direct contribution of indigenous research to 

 productivity — indicated by the coefficient of A'(Oin tables 4.2 and 

 4.3; (2) the accelerating effect of own work on borrowing, i.e. the 

 contribution of a unit in the exponent of the borrowing function; 

 (3) the contribution of research in one country to productivity in 

 others, i.e. the marginal contribution of a unit of borrowed 

 knowledge, i5(0, times the transferability factor, which indicates 

 how many such units a paper produced in one country can be 

 turned into times the borrowing factor 1/(1 + ae~!^P). Estimates 

 of these three components are listed in table 4.4. 



In the linear model the indigenous slocks were deflated both by 

 area and by the regional deflators. Estimates for both cases are re- 

 ported in the table. The unbiased estimate of y in the double-log 

 model is its geometric mean. Accordingly, marginal contributions 

 are usually calculated, for such models, at that point in the sam- 

 ples. But the geometric mean will generally differ from the 

 arithmetic mean, the difference being a measure of the dispersion 

 of the variable.' ' Yields per unit of land vary much less than the 

 stocks of knowledge, which start from small numbers for 1948 

 and grow to 1968. A better representation of the "typical coun- 

 try" is therefore given by the arithmetic averages. The estimates 

 for the double-log model were therefore also calculated at these 

 points of the sample. 



Since the logistic borrowing function is nonlinear, the esti- 

 mates in columns 2 and 5 were prepared by calculating the 

 marginal contribution for each point of the sample and averaging 

 (arithmetically or geometrically) these values. The average bor- 

 rowing factor values used in columns 3 and 6 were calculated in 

 the same way.'^ 



The estimates in the last line of table 4.4 are probably the most 

 "reasonable." They are based on a double-log model that incor- 

 porates the assumption of diminishing marginal products. The 



1 1 . The ariihmelic mean of the pair (5,495) is 250, the geometric average is 49.7. 



12. The average values for the borrowing factor 1/(1 + ae'i^P) are 



Wheal Maize 



The linear model .442 -507 



The double-log model .229 102 



