Asymptotic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>F</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si216.gif" display="inline" overflow="scroll"><mml:mi>t</mml:mi></mml:math>tests in an efficient GMM setting

Hwang, Jungbin; Sun, Yixiao

doi:10.1016/j.jeconom.2017.02.003

Cited by 18 publications

(23 citation statements)

References 26 publications

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“…hold jointly under small-G asymptotics. Here, M N (0; V) denotes a random variable that follows a mixed normal distribution with conditional variance V: The random multiplication term (1 +B 0 qS 1 qq B q ) in(22) re ‡ects the estimation uncertainty of CCE weighting matrix on the limiting distribution of p n(^ c ): The small-G limiting distribution in(22) …”

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confidence: 99%

Simple and trustworthy cluster-robust GMM inference

Hwang

2021

Journal of Econometrics

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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.

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confidence: 99%

Simple and trustworthy cluster-robust GMM inference

Hwang

2021

Journal of Econometrics

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“…The fixed-smoothing asymptotic distributions are nonstandard in both kernel and OS cases. For the OS case, Hwang and Sun (2017) show that a modified Wald statistic is asymptotically F distributed and that a modified t statistic is asymptotically t distributed. More specifically, the modified Wald and t statistics are given by…”

Section: The Test Proceduresmentioning

confidence: 97%

“…More recently, researchers established fixed-smoothing asymptotics in a general two-step GMM framework. See Sun and Kim (2012), Sun (2013Sun ( , 2014b, and Hwang and Sun (2017). The key difference between first-and two-step GMM is that in two-step GMM, the HAR variance estimator not only appears in the covariance estimator but also plays the role of the optimal weighting matrix in the second-step GMM criterion function.…”

Section: Introductionmentioning

confidence: 99%

“…These two commands automatically select the testing-optimal smoothing parameter. We also provide another pair of commands, gmmhar and gmmhart, that implement the fixed-smoothing Wald and t tests in a two-step efficient GMM setting, introduced in Hwang and Sun (2017). Under the fixed-smoothing asymptotics, Hwang and Sun (2017) show that the modified Wald statistic is asymptotically F distributed and the modified t statistic is asymptotically t distributed.…”

Section: Introductionmentioning

confidence: 99%

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Heteroskedasticity- and Autocorrelation-robust F and t Tests in Stata

Sun

2018

The Stata Journal: Promoting communications on statistics and S

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In this article, we consider time-series, ordinary least-squares, and instrumental-variable regressions and introduce a new pair of commands, har and hart, that implement more accurate heteroskedasticity- and autocorrelation-robust (HAR) F and t tests. These tests represent part of the recent progress on HAR inference. The F and t tests are based on the convenient F and t approximations and are more accurate than the conventional chi-squared and normal approximations. The underlying smoothing parameters are selected to target the type I and type II errors, which are the two fundamental objects in every hypothesis testing problem. The estimation command har and the postestimation test command hart allow for both kernel HAR variance estimators and orthonormal-series HAR variance estimators. In addition, we introduce another pair of new commands, gmmhar and gmmhart, that implement the recently developed F and t tests in a two-step generalized method of moments framework. For these commands, we opt for the orthonormal-series HAR variance estimator based on the Fourier bases because it allows us to develop convenient F and t approximations as in the first-step generalized method of moments framework. Finally, we present several examples to demonstrate these commands.

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“…This paper contributes to the literature on the …xed-smoothing asymptotics in general and the asymptotic F and t test theory in particular. The asymptotic F and t tests have been developed in Sun (2011) for linear trend regressions, in Sun (2013) for stationary moment processes, in Sun (2014c) for highly persistent moment processes, in Hansen (2007) for stationary panel time series, and in Hwang and Sun (2017) for stationary data in an overidenti…ed GMM framework. Lazarus, Lewis, Stock, and Watson (2016) provide some practical guidance on the F and t tests for time series regressions.…”

Section: Introductionmentioning

confidence: 99%

A simple and trustworthy asymptotic t test in difference-in-differences regressions

Liu

Sun

2019

Journal of Econometrics

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We propose an asymptotically valid t test that uses Student's t distribution as the reference distribution in a di¤erence-in-di¤erences regression. For the asymptotic variance estimation, we adopt the clustering-by-time approach to accommodate cross-sectional dependence. This approach often assumes the clusters to be independent across time, but we allow them to be temporally dependent. The proposed t test is based on a special heteroscedasticity and autocorrelation robust (HAR) variance estimator. We target the type I and type II errors and develop a testing-oriented method to select the underlying smoothing parameter. By capturing the estimation uncertainty of the HAR variance estimator, the t test has more accurate size than the corresponding normal test and is just as powerful as the latter. Compared to the nonstandard test developed in the literature, the standard t test is just as accurate but much more convenient to use. Model-based and empirical-data-based Monte Carlo simulations show that the t test works quite well in …nite samples.

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AsymptoticFandttests in an efficient GMM setting

Cited by 18 publications

References 26 publications

Simple and trustworthy cluster-robust GMM inference

Simple and trustworthy cluster-robust GMM inference

Heteroskedasticity- and Autocorrelation-robust F and t Tests in Stata

A simple and trustworthy asymptotic t test in difference-in-differences regressions

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