Valid tests of whether technical inefficiency depends on firm characteristics

We wish to test whether technical inefficiency depends on observable characteristics of the firm. We consider a two-step procedure in which the second step is a regression of estimated inefficiency on firm characteristics. A valid test of the hypothesis of no effect requires an adjustment to the variance matrix of the estimates. Unfortunately the adjustment is not distribution-free. We show that this test is the LM test in the exponential case. We also consider tests based on nonlinear least squares, which do not require a distributional assumption. The size and power of these tests are examined in simulations.