Parametric production frontier functions are frequently used in stochastic frontier models, but there do not seem to be any empirical test statistics for the plausibility of this application. In this paper, we develop procedures to test whether or not the parametric production frontier functions are suitable. Toward this aim, we developed two test statistics based on local smoothing and an empirical process, respectively. Residual-based wild bootstrap versions of these two test statistics are also suggested. The distributions of technical inefficiency and the noise term are not specified, which allows specification testing of the production frontier function even under heteroscedasticity. Simulation studies and a real data example are presented to examine the finite sample sizes and powers of the test statistics. The theory developed in this paper is useful for production managers in their decisions on production.