84 Agricithiiral Research and Proiliiclivily 



(publications) by 4 percent, which will, in turn, increase produc- 

 tion by .04 X .04 = .0016 — or 16^ for every $100. The marginal 

 benefit-cost ratio for research outlays is therefore 16/8 == 2.0. 



Two factors make the benefit-cost of 2.0 a lower bound: (1) the 

 research elasticity used in the calculation is the lowest in table 

 5.1; (2) the estimate is based, implicitly, on the assumption that 

 knowledge affects productivity only over the sample period. The 

 present value of future effects is not taken into account. (To the 

 extent that knowledge depreciates, the estimated elasticities in ta- 

 ble 5.1 are lower than the true coefficients of net knowledge in 

 production.) 



Country-Specific Estimates 



The introduction of the country-specific trend coefficients in 

 regression 3 in table 5.1 contributes significantly to the regression 

 {F^Qi = 6.398), though its effect on the estimated elasticities is 

 smaller than that of the country intercepts. 



The complete model with country-specific intercepts and 

 trends is estimated in regression 4 of table 5.1, the country- 

 specific variables contributing significantly to the explanation.'* 



The country-specific estimates of the productivity levels and 

 trend variables are summarized in tables 5.2 and 5.3. The coun- 

 tries are ranked in table 5.2, according to the order of the country 

 intercept estimated in regression 4 of table 5.1. The table should 

 be read as follows. From an identical collection of inputs, the 

 Netherlands' output of agricultural products will be 210 percent 

 that of Germany (chosen as a benchmark with e"^ = 1.00). Tech- 

 nological change in the Netherlands changed over the period 

 1955-68, at the pace of .6 percent per annum. The Netherlands' 

 rank is twenty-fifth in terms of this trend parameter. 



The countries' intercepts reflect not only genuine differences 

 in efficiency of production and use of resources but also 

 systematic errors in the measurement of inputs and output. This 

 last component may be responsible for the very high coefficient 



4. ^72 ^ 8.376 for ihe addition of trends to a regression with country-specific 

 intercepts. 



