Why do Aggregate Production Functions Work? Fisher's simulations, Shaikh's identity and some new results

The literature on aggregation has shown that the conditions for successful aggregation of micro production functions into an aggregate production function are far too stringent to be believable (Fisher 1969, 1971). Despite this, aggregate production functions continue being used. The reason is that they seem to 'work'. This happens, however, because underlying every aggregate production function is the income accounting identity that links input and output, i.e. output equals wages plus profits. A simple algebraic transformation of this identity yields a form that resembles a production function (Shaikh, 1974, 1980). This paper uses Monte Carlo simulations to study two questions. First, how much spuriousness can help explain the relatively good fits of the Cobb-Douglas production function? The simulations show that the contribution of spuriousness to a high R 2 is minor once we properly account for the fact that input and output data used in production function estimations are linked through the income accounting identity. It is mostly the link through this identity that explains the results. Secondly, we study how much factor shares have to vary in an economy so as to render the Cobb-Douglas production function with a time trend a bad choice for modelling and estimation purposes. We conclude that the Cobb-Douglas form is robust to relatively large variations in the factor shares. What makes this form often fail are the variations in the growth rates of the wage and profit rates.