Robust Estimation and Inference in Panels with Interactive Fixed Effects

We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We show that previously developed estimators and confidence intervals (CIs) might be heavily biased and size-distorted when some of the factors are weak. We propose estimators with improved rates of convergence and bias-aware CIs that are uniformly valid regardless of whether the factors are strong or not. Our approach applies the theory of minimax linear estimation to form a debiased estimate using a nuclear norm bound on the error of an initial estimate of the interactive fixed effects. We use the obtained estimate to construct a bias-aware CI taking into account the remaining bias due to weak factors. In Monte Carlo experiments, we find a substantial improvement over conventional approaches when factors are weak, with little cost to estimation error when factors are strong.

[1]  Kohei Yata.  Optimal Decision Rules Under Partial Identification , 2021, 2111.04926.

[2]  Ayden Higgins.  Fixed $T$ Estimation of Linear Panel Data Models with Interactive Fixed Effects , 2021, 2110.05579.

[3]  M. Weidner,et al.  Linear panel regressions with two-way unobserved heterogeneity , 2021, Journal of Econometrics.

[4]  Takuya Ishihara,et al.  Evidence Aggregation for Treatment Choice , 2021, 2108.06473.

[5]  Timothy B. Armstrong,et al.  Bias-Aware Inference in Regularized Regression Models , 2020, 2012.14823.

[6]  M. Weidner,et al.  Low-rank approximations of nonseparable panel models , 2020, The Econometrics Journal.

[7]  Vasilis Sarafidis,et al.  A Linear Estimator for Factor-Augmented Fixed-T Panels With Endogenous Regressors , 2020, Journal of Business & Economic Statistics.

[8]  J. Westerlund,et al.  CCE in fixed‐ T panels , 2019, Journal of Applied Econometrics.

[9]  C. Rothe,et al.  Bias-Aware Inference in Fuzzy Regression Discontinuity Designs , 2019, 1906.04631.

[10]  Victor Chernozhukov,et al.  Inference for heterogeneous effects using low-rank estimations , 2018, 1812.08089.

[11]  Martin Weidner,et al.  Nuclear norm regularized estimation of panel regression models , 2018, 1810.10987.

[12]  Stefan Wager,et al.  Augmented minimax linear estimation , 2017, The Annals of Statistics.

[13]  G. Imbens,et al.  Matrix Completion Methods for Causal Panel Data Models , 2017, Journal of the American Statistical Association.

[14]  Serena Ng,et al.  Principal Components and Regularized Estimation of Factor Models , 2017, 1708.08137.

[15]  Peng Wang,et al.  Econometric Analysis of Large Factor Models , 2016 .

[16]  Timothy B. Armstrong,et al.  Optimal Inference in a Class of Regression Models , 2015, 1511.06028.

[17]  Trevor Hastie,et al.  Statistical Learning with Sparsity: The Lasso and Generalizations , 2015 .

[18]  Elena Manresa,et al.  Grouped Patterns of Heterogeneity in Panel Data , 2015 .

[19]  M. Weidner,et al.  Linear Regression for Panel with Unknown Number of Factors as Interactive Fixed Effects , 2014 .

[20]  Vasilis Sarafidis,et al.  Fixed T dynamic panel data estimators with multifactor errors , 2014 .

[21]  Adel Javanmard,et al.  Confidence intervals and hypothesis testing for high-dimensional regression , 2013 .

[22]  Seung C. Ahn,et al.  Panel Data Models with Multiple Time-Varying Individual Effects , 2013 .

[23]  Alexei Onatski,et al.  Asymptotics of the principal components estimator of large factor models with weakly influential factors , 2012 .

[24]  A. Onatski.  Determining the Number of Factors from Empirical Distribution of Eigenvalues , 2010, The Review of Economics and Statistics.

[25]  Donald Robertson,et al.  IV Estimation of Panels with Factor Residuals , 2010 .

[26]  A. Tsybakov,et al.  Estimation of high-dimensional low-rank matrices , 2009, 0912.5338.

[27]  J. Bai,et al.  Panel Data Models With Interactive Fixed Effects , 2009 .

[28]  Pablo A. Parrilo,et al.  Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , 2007, SIAM Rev..

[29]  M. Pesaran.  Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure , 2004, SSRN Electronic Journal.

[30]  Peter Schmidt,et al.  GMM estimation of linear panel data models with time-varying individual effects , 2001 .

[31]  D. Donoho.  Statistical Estimation and Optimal Recovery , 1994 .

[32]  W. Newey,et al.  Estimating vector autoregressions with panel data , 1988 .

[33]  P. Robinson.  ROOT-N-CONSISTENT SEMIPARAMETRIC REGRESSION , 1988 .

[34]  S. Geman.  A Limit Theorem for the Norm of Random Matrices , 1980 .

[35]  Andrei.  Identification and Estimation of Network Models with Nonparametric Unobserved Heterogeneity , 2019 .

[36]  Marcelo J. Moreira,et al.  DECISION THEORY APPLIED TO A LINEAR PANEL DATA MODEL , 2009 .

[37]  I. Ibragimov,et al.  On Nonparametric Estimation of the Value of a Linear Functional in Gaussian White Noise , 1985 .

[38]  John Wiley,et al.  A wiley-interscience publication , 1972 .