Simple and trustworthy cluster-robust GMM inference

Abstract

This paper develops a new asymptotic theory for two-step GMM estimation and inference in the presence of clustered dependence. The key feature of alternative asymptotics is the number of clusters G is regarded as small or …xed when the sample size increases. Under the small-G asymptotics, this paper shows the centered two-step GMM estimator and the two continuously-updating GMM estimators we consider have the same asymptotic mixed normal distribution. In addition, the J statistic, the trinity of two-step GMM statistics (QLR, LM and Wald), and the t statistic are all asymptotically pivotal, and each can be modi…ed to have an asymptotic standard F distribution or t distribution. We suggest a …nite sample variance correction to further improve the accuracy of the F and t approximations. Our proposed asymptotic F and t tests are very appealing to practitioners because our test statistics are simple modi…cations of the usual test statistics, and critical values are readily available from standard statistical tables. A Monte Carlo study shows that our proposed tests are more accurate than the conventional inferences under the large-G asymptotics.

Asymptotic theory for the inference of the latent trawl model for extreme values

“…We extend the asymptotic convergence in distribution of single-stage and two-stage estimators from Newey and McFadden (1994) and Hwang (2021) to weakly approaching sequences of distributions. As explained in Section 3, p. 2142, Newey and McFadden (1994) As described above, asymptotic normality results from convergence in probability of the Hessian, convergence in distribution of the average score, and the Slutzky theorem.…”

“…We introduce a regularity assumption on the latent trawl set to allow the application of the central limit theorem from Hwang (2021). It unfolds as follows Assumption 2.…”

Cluster-Robust Inference: A Guide to Empirical Practice

“…Hansen and Lee (2019, Theorem 12) provides a similar result for GMM estimation, which is also very widely applicable. More recently, the fixed-G approach discussed in Section 4.2 has been applied to GMM estimation by Hwang (2021). It leads to a novel inferential procedure that involves modifying the usual asymptotic t and F statistics, but it requires that cluster sizes be approximately equal.…”

Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters

“…However, as emphasized by Ibragimov andMüller (2010, 2016), Bester, Conley, and Hansen (2011), Cameron and Miller (2015), Canay, Romano, and Shaikh (2017), Hagemann (2019aHagemann ( ,b, 2020 and Canay et al (2020), many empirical studies motivate an alternative framework in which the number of clusters is small, while the number of observations in each cluster is relatively large. For inference, we may consider applying the approaches developed by Bester et al (2011), Hwang (2020), Ibragimov andMüller (2010, 2016), and Canay et al (2017). However, Bester et al (2011) and Hwang (2020) require (asymptotically) equal cluster-level sample size, while Ibragimov andMüller (2010, 2016) and Canay et al (2017) hinge on strong identification for all clusters.…”

“…For inference, we may consider applying the approaches developed by Bester et al (2011), Hwang (2020), Ibragimov andMüller (2010, 2016), and Canay et al (2017). However, Bester et al (2011) and Hwang (2020) require (asymptotically) equal cluster-level sample size, while Ibragimov andMüller (2010, 2016) and Canay et al (2017) hinge on strong identification for all clusters. Our bootstrap Wald test is more flexible as it does not require equal cluster size and only needs strong identification in one of the clusters.…”