Testing cost vs. profit function

Abstract

The empirical literature on estimation of production technology mostly focuses on estimation of dual cost functions. Estimation of a profit function is not that common. Here, we formally test whether the production technology should be represented by a cost or profit function. We also derive elasticities associated with the long-run profit function from the estimated cost function.

Notes

¹ An alternative approach is to test whether a factor should be treated as fixed or not (Kulatilaka, 1985).

² A more thorough discussion on the properties of restricted profit and cost functions and their relationships can be found in, e.g. McFadden (1978.

³ Further description of the salmon farming data and the industry can be found in Tveterås (2002a), Kumbhakar (2001 2002a).

⁴ The instruments when conducting the test include exogenous variables (input prices, time dummies, regions) in the model, the output price and interactions of output price and exogenous variables in the model.

⁵ We also conducted two other Hausman tests where the null hypothesis in which output in the cost function is exogenous. The first test allowed only ln y to be endogenous. Since the value of the test statistic (that is distributed as χ²(1)) is 1.52 that has a p-value of 0.217, we cannot reject the null hypothesis at the usual levels of significance. In the second test all variables containing y were allowed to potentially be endogenous. The value of the test statistic is found to be 7.74 for which the p-value (for a χ²(15) random variable) is 0.934. Thus, we failed to reject this null hypothesis as well. These tests show that endogeneity of output is not an issue in the salmon farming industry.