Statistical Inferences Using Large Estimated Covariances for Panel Data and Factor Models

37 Pages Posted: 14 Nov 2013

See all articles by Jushan Bai

Jushan Bai

New York University (NYU) - Department of Economics

Yuan Liao

Rutgers, The State University of New Jersey - New Brunswick/Piscataway

Date Written: November 12, 2013

Abstract

While most of the convergence results in the literature on high dimensional covariance matrix are concerned about the accuracy of estimating the covariance matrix (and precision matrix), relatively less is known about the effect of estimating large covariances on statistical inferences. We study two important models: factor analysis and panel data model with interactive effects, and focus on the statistical inference and estimation efficiency of structural parameters based on large covariance estimators. For efficient estimation, both models call for a weighted principle components (WPC), which relies on a high dimensional weight matrix. This paper derives an efficient and feasible WPC using the covariance matrix estimator of Fan et al. (2013). However, we demonstrate that existing results on large covariance estimation based on absolute convergence are not suitable for statistical inferences of the structural parameters. What is needed is some weighted consistency and the associated rate of convergence, which are obtained in this paper. Finally, the proposed method is applied to the US divorce rate data. We find that the efficient WPC identifies the significant effects of divorce-law reforms on the divorce rate, and it provides more accurate estimation and tighter confidence intervals than existing methods.

Keywords: High dimensionality, unknown factors, conditional sparsity, thresholding, cross-sectional correlation, heteroskedasticity, optimal weight matrix, interactive effect

Suggested Citation

Bai, Jushan and Liao, Yuan, Statistical Inferences Using Large Estimated Covariances for Panel Data and Factor Models (November 12, 2013). Available at SSRN: https://ssrn.com/abstract=2353396 or http://dx.doi.org/10.2139/ssrn.2353396

Jushan Bai

New York University (NYU) - Department of Economics ( email )

269 Mercer Street, 7th Floor
New York, NY 10003
United States

Yuan Liao (Contact Author)

Rutgers, The State University of New Jersey - New Brunswick/Piscataway ( email )

94 Rockafeller Road
New Brunswick, NJ 08901
United States

HOME PAGE: http://rci.rutgers.edu/~yl1114

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