Stochastic specification in random production models of cost-minimizing firms

We examine the implications of additive, homoskedastic errors for models of firmʹs cost-minimizing behavior. The premise is that some factors unobservable to the econometrician are known to the firm and must satisfy the theoretical restrictions imposed by cost minimization. We analyze additive homoskedastic errors for both the input demand model and the cost share model. We find that this simple error structure is inconsistent with rational behavior if some part of the stochastic component is known to the decision-maker. Input demand models violate nonnegativity and cannot represent homothetic technologies. For cost share systems, nonnegativity is also a potential problem but, surprisingly, concavity can be easily satisfied. An empirical application assesses the practical significance of these results.