On the Use of Artificial Regressions in Certain Microeconometric Models

<italic>Conditional moment tests</italic> check to see whether or not population moment equalities, implied by the null model specification, hold approximately in the sample. Asymptotically valid conditional statistics can easily be calculated from the output of a so-called <italic>outer product of the gradient</italic> (OPG) artificial regression. However, several studies have now found that this OPG variant exhibits extremely poor finite sample behavior and that significant improvements can be made by employing the efficient variant. In the light of such evidence, this paper develops new artificial regressions that can be used to calculate the efficient variant of the test statistic. These artificial regressions can also serve several other purposes, including the construction of Hausmantype tests of parameter estimator consistency.