On production functions, technical progress, and time trends

This paper extends the works of Fisher (1971), Simon (1979), and Nelson and Kang (1984) on econometric estimation of aggregate production functions. It explores through Monte Carlo simulations why the estimation of the aggregate Cobb-Douglas usually yields good fits, parameter estimates consistent with actual shares of capital and labor, and approximately constant returns to scale. Our results suggest that: (i) spuriousness is, at most, a secondary explanation for the high R2 value found by many researchers; (ii) the Cobb-Douglas form with a linear time trend will work well for actual economies as long as the variation in the growth rates of the wage and profit rates does not exceed a certain threshold; (iii) the marginal productivity condition for labor will, in most cases, explain wages well; and (iv) successful Cobb-Douglas production function estimations carry no implications for such issues as technical progress, the degree of returns to scale, competition, and profit maximization.