Robust Nearly-Efficient Estimation of Large Panels With Factor Structures

Abstract

This paper studies estimation of linear panel regression models with heterogeneous coefficients, when both the regressors and the residual contain a possibly common, latent, factor structure. Our theory is (nearly) efficient, because based on the GLS principle, and also robust to the specification of such factor structure, because it does not require any information on the number of factors nor estimation of the factor structure itself. We first show how the unfeasible GLS estimator not only affords an efficiency improvement but, more importantly, provides a bias-adjusted estimator with the conventional limiting distribution, for situations where the OLS is affected by a first-order bias. The technical challenge resolved in the paper is to show how these properties are preserved for a class of feasible GLS estimators in a double-asymptotics setting. Our theory is illustrated by means of Monte Carlo exercises and, then, with an empirical application using individual asset returns and firms' characteristics data.

Dynamic Heterogeneous Panel Data Models with Cross-Section Dependence

“…The only other estimation method, to our knowledge, that is explicitly designed to estimate cross-section specific coefficients with lagged dependent variables and a multifactor error structure, with regressors that can exhibit cross-section dependence unrelated to the factor shocks, as well as residual cross-section dependence, is the GLS method of Avarucci and Zaffaroni (2019). The main asymptotic result of Avarucci and Zaffaroni (2019) relies on a rate of convergence T 3 N 2 → 0, which can be a stronger condition than √ T N → 0. 2 We consider one experiment without a lagged dependent variable and eight with a lagged dependent variable.…”

“…We consider one experiment without a lagged dependent variable and eight with a lagged dependent variable. For the experiment without a lagged dependent variable, we compare the RBC-IFE method, the Song (2013) IFE method, the CCE method of Pesaran (2006), the GLS method of Avarucci and Zaffaroni (2019), and the SCAD estimated IFE method of Ando and Bai (2015). The CCE method of Pesaran (2006) and the SCAD estimated IFE method of Ando and Bai (2015) do not accommodate lagged dependent variables, so these methods are not included in the other experiments.…”

“…The GLS estimator of Avarucci and Zaffaroni (2019) has an associated asymptotic theory that shows it provides consistent cross-section heterogeneous coefficient estimates in the presence of a common factor structure with weakly cross-section dependent idiosyncratic errors. The authors claim their method can also accommodate lagged dependent variables as regressors.…”

“…However, we found this procedure was unstable so we take (2.5) as our GLS estimate. 13 The main result of Avarucci and Zaffaroni (2019) shown above is derived assuming that the factor loadings λ 0 i are uncorrelated to the regressors s it . 14 Their main result also requires that the regression coefficients β 0,i be non-stochastic.…”

“…Following Ando and Bai (2015), we use sparse vector (2.7) so that their assumptions on the true value of the coefficients are satisfied. The coefficient vector (2.7) is non-stochastic, which means the regression coefficient assumptions of Avarucci and Zaffaroni (2019) are satisfied. The vector also satisfies the assumptions of Pesaran (2006), Song (2013), and the asymptotic theory presented in Chapter 1.…”