2015/05/25 by Humberto Moreira, Moreira, Humberto, Marcelo J. Moreira +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Monetary Policy and Economic Impact #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1505.06644
openalex publication_date 2015/05/25 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
This paper considers two-sided tests for the parameter of an endogenous\nvariable in an instrumental variable (IV) model with heteroskedastic and\nautocorrelated errors. We develop the finite-sample theory of weighted-average\npower (WAP) tests with normal errors and a known long-run variance. We\nintroduce two weights which are invariant to orthogonal transformations of the\ninstruments; e.g., changing the order in which the instruments appear. While\ntests using the MM1 weight can be severely biased, optimal tests based on the\nMM2 weight are naturally two-sided when errors are homoskedastic.\n We propose two boundary conditions that yield two-sided tests whether errors\nare homoskedastic or not. The locally unbiased (LU) condition is related to the\npower around the null hypothesis and is a weaker requirement than unbiasedness.\nThe strongly unbiased (SU) condition is more restrictive than LU, but the\nassociated WAP tests are easier to implement. Several tests are SU in finite\nsamples or asymptotically, including tests robust to weak IV (such as the\nAnderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews'\n(2015) PI-CLC tests) and two-sided tests which are optimal when the sample size\nis large and instruments are strong.\n We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests.\nDropping the restrictive assumptions of normality and known variance, the\ntheory is shown to remain valid at the cost of asymptotic approximations. The\nMM2-SU test is optimal under the strong IV asymptotics, and outperforms other\nexisting tests under the weak IV asymptotics.\n