A New Method for Specifying Functional Forms of Production Functions

E23

We propose a new method for specifying the functional form of production functions. We start from the well known fact that the size of firms follows a power-law distribution; namely, each of output Y, capital K, and labor L follows a power-law distribution with a different exponent. We then examine how the functional form of these density functions for the size distributions are related to the functional form of production function, and use that relationship in specifying the functional form of production function. Specifically, given the density functions for K and L, which are observed from the data, and a functional form of production function, we compute a density function for Y. We then compare this theoretical density function for Y with the empirical one. We repeat this procedure until we reach a functional form of production function in which theoretical and empirical density functions for Y coincides. Applying this method to the firm level data for 25 countries, we find that, for most of the countries, the theoretical density function for Y coincides with the empirical one when we adopt the Cobb-Douglas production function. We also find that firms located at the upper tail of the distribution for Y tend to havean extraordinary large value for K or for L, but not for A (i.e., total factor productivity), which is inconsistent with the view that high growth of Y is associated with high growth of A.