On the Use of Artificial Regressions in Certain Microeconometric Models
针对条件矩检验中OPG人工回归在小样本下表现差的问题，提出了能计算高效检验统计量的新人工回归方法，还可用于构建参数估计量一致性的Hausman型检验。
Conditional moment tests 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 outer product of the gradient (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.