ON THE CONDITIONAL LIKELIHOOD RATIO TEST FOR SEVERAL PARAMETERS IN IV REGRESSION
研究了工具变量回归中检验多个内生变量系数是否为零的问题，通过条件化方法使似然比检验相似化，并推广了迭代条件化论证以简化统计量的分布计算，为m=2的情况给出了解析结果，对更大的m提出了模拟方法。
For the problem of testing the hypothesis that all m coefficients of the right-hand-side endogenous variables in an instrumental variables (IV) regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument. To exploit this fact requires knowledge of the relevant conditional cumulative distribution function (c.d.f.) of the LR statistic, but the statistic is a function of the smallest characteristic root of an ( m + 1)-square matrix and is therefore analytically difficult to deal with when m > 1. We show in this paper that an iterative conditioning argument used by Hillier (2009) and Andrews, Moreira, and Stock (2007 Journal of Econometrics 139, 116–132) to evaluate the c.d.f. in the case m = 1 can be generalized to the case of arbitrary m . This means that we can completely bypass the difficulty of dealing with the smallest characteristic root. Analytic results are obtained for the case m = 2, and a simple and efficient simulation approach to evaluating the c.d.f. is suggested for larger values of m .