Leave-out estimation of variance components
Raffaele Saggio () and
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We propose a framework for unbiased estimation of quadratic forms in the parameters of linear models with many regressors and unrestricted heteroscedasticity. Applications include variance component estimation and tests of linear restrictions in hierarchical and panel models. We study the large sample properties of our estimator allowing the number of regressors to grow in proportion to the number of observations. Consistency is established in a variety of settings where jackknife bias corrections exhibit first-order biases. The estimator's limiting distribution can be represented by a linear combination of normal and non-central $\chi^2$ random variables. Consistent variance estimators are proposed along with a procedure for constructing uniformly valid confidence intervals. Applying a two-way fixed effects model of wage determination to Italian social security records, we find that ignoring heteroscedasticity substantially biases conclusions regarding the relative contribution of workers, firms, and worker-firm sorting to wage inequality. Monte Carlo exercises corroborate the accuracy of our asymptotic approximations, with clear evidence of non-normality emerging when worker mobility between groups of firms is limited.
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