Fixed-smoothing asymptotics in the generalized empirical likelihood estimation framework

This paper considers two-step e¢ cient GMM estimation and inference where the weighting matrix and asymptotic variance matrix are based on the series long run variance estimator. We propose a simple and easy-to-implement modi…cation to the trinity of test statistics in the two-step e¢ cient GMM setting and show that the modi…ed test statistics are all asymptotically F distributed under the so-called …xed-smoothing asymptotics. The modi…cation is multiplicative and involves the J statistic for testing over-identifying restrictions. This leads to convenient asymptotic F tests that use standard F critical values. Simulation shows that, in terms of both size and power, the asymptotic F tests perform as well as the nonstandard tests proposed recently by Sun (2014b) in …nite samples. But the F tests are more appealing as the critical values are readily available from standard statistical tables. Compared to the conventional chi-square tests, the F tests are as powerful, but are much more accurate in size.JEL Classi…cation: C12, C32

Section: Resultsmentioning

confidence: 85%

AsymptoticFandttests in an efficient GMM setting

Hwang

Sun

2017

“…The proof of part (a) is essentially the same as the proof of Proposition 7. The only di¤erence is that the second term in (46) will not be present for the centered two-step GMM estimator^ c 2 : The proof of part (b) is similar. The proof of part (e) is similar to that of Proposition 6(e).…”

Section: Design IIImentioning

confidence: 83%

Simple and trustworthy cluster-robust GMM inference

Hwang

2021

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.

“…For this reason, Assumption 5.2 (b) does not follow directly from standard textbook arguments. Nevertheless, su¢ cient primitive conditions can be found in Zhang (2016), who considers the …xed-smoothing asymptotics under strong identi…cation for generalized empirical likelihood estimators, which include the CU-GMM as a special case.…”

Section: Testing Hypotheses On Subsets Of the Parametersmentioning

confidence: 99%

Asymptotic F tests under possibly weak identification

Martínez-Iriarte

Sun

Wang

2020

This paper develops asymptotic F tests robust to weak identi…cation and temporal dependence. The test statistics are modi…ed versions of the S statistic of Stock and Wright (2000) and the K statistic of Kleibergen (2005), both of which are based on the continuous updating generalized method of moments. In the former case, the modi…cation involves only a multiplicative degree-of-freedom adjustment. In the latter case, the modi…cation involves an additional multiplicative adjustment that uses a J statistic for testing overidenti…cation. By adopting …xed-smoothing asymptotics, we show that both the modi…ed S statistic and the modi…ed K statistic are asymptotically F-distributed. The asymptotic F theory accounts for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators, which the asymptotic chi-squared theory ignores. Monte Carlo simulations show that the F approximations are much more accurate than the corresponding chi-squared approximations in …nite samples.