Several large volatility matrix inference procedures have been developed, based on the latent factor model. They often assumed that there are a few of common factors, which can account for volatility dynamics. However, several studies have demonstrated the presence of local factors. In particular, when analyzing the global stock market, we often observe that nation-specific factors explain their own country’s volatility dynamics. To account for this, we propose the Double Principal Orthogonal complEment Thresholding (Double-POET) method, based on multi-level factor models, and also establish its asymptotic properties. Furthermore, we demonstrate the drawback of using the regular principal orthogonal component thresholding (POET) when the local factor structure exists. We also describe the blessing of dimensionality using Double-POET for local covariance matrix estimation. Finally, we investigate the performance of the Double-POET estimator in an out-of-sample portfolio allocation study using international stocks from 20 financial markets.
The paper proposes a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. The formula additionally corrects for the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005) which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. An important feature of the proposed double correction is that it automatically provides robustness to misspecification of the moment condition. In contrast, the conventional variance estimator and the Windmeijer correction are inconsistent under misspecification. That is, the proposed double correction formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.
This article, authored with with Seojeong Lee (UNSW) and Byunghoon Kang (Lancaster Univ), is one of two that Professor Hwang has recently had accepted for publication. Details of the other article may be found at:
This paper develops a new asymptotic theory for GMM estimation and inference in the presence of clustered dependence. The key feature of the alternative asymptotic is that the number of clusters is regarded as “fixed” as the sample size increases. The paper shows that the Wald and t-tests in two-step GMM are asymptotically pivotal only if one recenters the estimated moment process in the clustered covariance estimator (CCE). Also, the J statistic, the trinity of two-step GMM statistics (QLR, LM, and Wald), and the t statistic can be modified to have an asymptotic standard F distribution or t distribution.
The paper also first suggests a finite-sample variance correction in the literature of cluster-robust methods and further improves the F and t approximations’ accuracy. The proposed tests in this paper are very appealing to practitioners because the test statistics are simple modifications of conventional GMM test statistics, and critical values are readily available from F and t tables without any extra simulations or resampling steps.
This sole authored article is one of two that Professor Hwang has recently had accepted for publication. Details of the other article may be found at:
Professor Jungbin Hwang’s paper “Should We Go One Step Further? An Accurate Comparison of One-step and Two-step Procedures in a Generalized Method of Moments Framework”, co-authored with Yixiao Sun, has been accepted for publication in the Journal of Econometrics, one of the top scholarly journals in theoretical econometrics. The paper started as a third-year paper project when Professor Hwang was a graduate student in the University of California, San Diego.
Professor Hwang’s paper provides an assessment of the merits of the first step GMM estimator and test relative to the two-step GMM estimator and test. The article shows the two-step procedure outperforms the one-step method only when the benefit of using the optimal weighting matrix outweighs the cost of estimating it. The qualitative message applies to both the asymptotic variance comparison and power comparison of the associated tests.
According to the conventional asymptotic theory, the two-step Generalized Method of Moments (GMM) estimator and test perform as least as well as the one-step estimator and test in large samples. The conventional asymptotic theory, as elegant and convenient as it is, completely ignores the estimation uncertainty in the weighting matrix, and as a result it may not reflect finite sample situations well. In this paper, we employ the fixed-smoothing asymptotic theory that accounts for the estimation uncertainty, and compare the performance of the one-step and two-step procedures in this more accurate asymptotic framework. We show that the two-step procedure outperforms the one-step procedure only when the benefit of using the optimal weighting matrix outweighs the cost of estimating it. This qualitative message applies to both the asymptotic variance comparison and power comparison of the associated tests. A Monte Carlo study lends support to our asymptotic results.
Professor Jungbin Hwang has published the paper “Asymptotic F and t tests in an efficient GMM setting” with his co-author Yixiao Sun in the Journal of Econometrics Volume 198, Issue 2, June 2017, Pages 277-295.
In this paper, they propose a simple and easy-to-implement modification to the trinity of test statistics in the two-step efficient GMM setting and show that the modified test statistics are all asymptotically F distributed under the so-called fixed-smoothing asymptotics. The main contributions of this paper are developing convenient asymptotic F tests whose critical values, i.e., the standard F critical values, are readily available from standard statistical tables and programming environments. For testing a single restriction with a one-sided alternative, the paper also develops an asymptotic test theory using the standard t distribution as the reference distribution.