Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

Hyungsik Roger Moon · Martin Weidner

299 citations0/0 files storedEconometrica

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Spatial and Panel Data Analysis Statistical Methods and Inference Advanced Statistical Methods and Models

Abstract

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross-sectional units jointly go to infinity. The main result of the paper is that under certain assumptions the limiting distribution of the LS estimator is independent of the number of factors used in the estimation, as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed effects consistently.

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References

1981Biases in Dynamic Models with Fixed Effects 2006Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure 1988Estimating Vector Autoregressions with Panel Data 2002Determining the Number of Factors in Approximate Factor Models 2002Forecasting Using Principal Components From a Large Number of Predictors 2009Panel Data Models With Interactive Fixed Effects 2006Did Unilateral Divorce Laws Raise Divorce Rates? A Reconciliation and New Results 2011Weak and strong cross‐section dependence and estimation of large panels

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2015DYNAMIC LINEAR PANEL REGRESSION MODELS WITH INTERACTIVE FIXED EFFECTS 2021A Bias-Corrected CD Test for Error Cross-Sectional Dependence in Panel Data Models with Latent Factors 2020Misallocation in the Market for Inputs: Enforcement and the Organization of Production*2017Spatial dynamic panel data models with interactive fixed effects 2013TESTING HOMOGENEITY IN PANEL DATA MODELS WITH INTERACTIVE FIXED EFFECTS

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