Abstract
We derive the asymptotic distribution of the standard F-test statistic for fixed effects, in static linear panel data models, under both non-normality and heteroskedasticity of the error terms, when the cross-section dimension is large but the time series dimension is fixed. It is shown that a simple linear transformation of the F-test statistic yields asymptotically valid inferences and under local fixed (or correlated) individual effects, this heteroskedasticity-robust F-test enjoys higher asymptotic power than a suitably robustified Random Effects test. Wild bootstrap versions of these tests are considered which, in a Monte Carlo study, provide more reliable inference in finite samples.
Highlights
In an earlier paper, Orme and Yamagata (2006) added to the already large literature on the analysis of variance testing, by establishing that, in a static linear panel data model, the standard F-test for individual e¤ects remains asymptotically valid under non-normality of the error term
11 We considered a pure random e¤ects speci...cation, i = v ; R2 = 0, and the results show that the power properties of the modi...ed ...xed e¤ects test and the modi...ed random e¤ects test are very similar. 12The estimator !~N, based on the unrestricted estimator (i.e., ...xed e¤ects estimator), is considered, but the ...nite sample performance of the tests considered is monotonically inferior to that based on the estimator of !^N : 2. One sided Random E¤ects test (RE-test) statistics
This paper has provided an asymptotic analysis of the sampling behaviour of the standard F-test statistic for ...xed e¤ects, in a static linear panel data model, under both non-normality and heteroskedasticity of the error terms, when the number of cross-sections, N; is large and T; the number of time periods, is ...xed
Summary
Orme and Yamagata (2006) added to the already large literature on the analysis of variance testing, by establishing that, in a static linear panel data model, the standard F-test for individual e¤ects remains asymptotically valid (large N; ...xed T ) under non-normality of the error term. Given the result of Proposition 1, below, Wooldridge’s (2010, p.299) heteroskedasticrobust RE-test suggests the appropriate transformation required of the standard F-test statistic in order to recover its asymptotically validity under general heteroskedasticity of unknown form. This transformation, or correction, involves simple functions of the pooled model’s residuals (i.e., the restricted residuals), of which there are a number of asymptotically valid choices. Following the literature on heteroskedasticity robust inference, restricted residuals are employed as advocated, for example, by Davidson and MacKinnon (1985) and Godfrey and Orme (2004), who report reliable sampling performance of tests of linear restrictions in the linear model when employing restricted residuals in the construction of heteroskedasticity robust standard errors.[2]
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