Robust SE Fixed Effects

Robust SE Fixed Effects - Robust Standard Error Estimation...

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Robust Standard Error Estimation In Fixed-E f ects Panel Models G´abor K´ ezdi Budapest University of Economics, IE/HAS ,andCEU October 13, 2003 Abstract This paper focuses on standard error estimation in FE models if there is serial correlation in the error process. Applied researchers have often ignored the problem, probably because major statistical packages do not estimate robust standard errors in FE models. Not surprisingly, this can lead to severe bias in the standard error estimates, both in hypothetical and real-life situations. The paper gives a systematic overview of the di f ernt standard error estimators and the assumptions under which they are consistent (in the usual large N ,sma l l T asymptotics). One of the possible reasons why the robust estimators are not used often is a fear of their bad f nite sample properties. The most important results of the paper, based on an extensive Monte Carlo study, show that those fears are in general unwarranted. I also present evidence that it is the abolute size of the cross-sectional sample that primarily a f ects the f nite-sample behavior, not the relaitve size compared to the time-series dimension. That indicates good small-sample behavior even when N T . I introduce a simple direct test analogous to that of White ( 1 980) for the restrictive assumptions behind the estimators. Its f nite sample properties are f ne except for low power in very small samples. This paper focuses on Fixed-E f ects panel models (FE) with exogenous regressors on pooled cross sectional and time series data with relatively few within-individual observations. Empirical studies that estimate this kind of FE models are abundant, and they routinely estimate standard errors under the assumption of no serial error correlation within individual units. In the past three years, the top three economics journals with a focus on applied empirical research published 42 papers that estimated linear FE models with time series My f rst thanks go to John Bound and Gary Solon for their suggestions and support. Jinyong Hahn, Steven Levitt, Shinichi Sakata, and Douglas Staiger provided many helpful comments. All remaining errors are mine. Correspondance: [email protected] Institute of Economics, Hungarian Academy of Sciences Central European University, Budapest 1
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within individual units. 1 Out of the 42, only 6 took serial correlation into account when estimated the standard errors. 2 Serial correlation in the error process a f ects standard errors in FE models with more than two observations per individual unit, unless all right-hand side variables are serially uncorre- lated. The e f ect is larger the stronger the correlation and the longer the time horizon. Serial correlation consistent standard error estimators for panel models without f xed e f ects are covered by most econometrics textbooks. Same is not true, however for FE. Similar estima- tors were developed explicitly for FE models by Kiefer (1980), Bhargava et al. (1982), and Arellano (1987), but they have been overlooked by practitioners. It seems that worries about
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Robust SE Fixed Effects - Robust Standard Error Estimation...

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