62 Aariculniral Research and Produciiviiy 



belongs to region /. The pool of specific knowledge from which a 

 country borrows, by hypothesis, is 



Rift) = R.{t)-r..K.{t); (4.6) 



that is, it is the stock of regional knowledge less the country's own 

 contribution (figure 4.1). 



To formulate the borrowing activity, a logistic ''borrowing 

 function" was specified 



B.U)= ^ [R..{s)l{\^-ae-^Pf'^)]ds (4.7) 



1} Jo '-^ 



where 5.(0 is the borrowed stock and a, j3 are parameters (figure 

 4.2). Borrowing is defined as a flow and is accumulated to a stock. 

 The borrowed stock of knowledge in a country is the weighted 

 sum of the stocks borrowed from the different regions, with the 

 regional shares, r.., as weights. 



B.{t) = Xr.fi.. it) (4.8) 



The parameter lAl + Cki), the intercept of the borrowing func- 

 tion (figure 4.2), indicates the amount of borrowing a country can 

 do in the absence of indigenous research. In the limit, as p^°°. 

 the country borrows all of the regional pool. In the regressions, o: 



and j3 were estimated by searching for the value that yielded the 

 highest /?2 



Production conditions are quite diversified, even in the smaller 

 countries; thus the measure of knowledge should be corrected to 

 take account of this factor. Two deflators were used to this end, 

 and the numbers of publications in a country were divided by 

 these deflators. The first is the average crop (wheat and maize) 

 area in the country over the sample period, a. in country 

 j (appendix 2, columns 3,8) 



^iy=^- (4.9) 



The use of this deflator implies that crop production conditions 



I 

 I 



