Published online by Cambridge University Press: 11 February 2009
Conditional moment tests check to seewhether or not population moment equalities, impliedby the null model specification, hold approximatelyin the sample. Asymptotically valid conditionalstatistics can easily be calculated from the outputof a so-called outer product of thegradient (OPG) artificial regression.However, several studies have now found that thisOPG variant exhibits extremely poor finite samplebehavior and that significant improvements can bemade by employing the efficient variant. In thelight of such evidence, this paper develops newartificial regressions that can be used to calculatethe efficient variant of the test statistic. Theseartificial regressions can also serve several otherpurposes, including the construction of Hausmantypetests of parameter estimator consistency.