A new Stata command for estimating confidence intervals for the variance component of random-effects linear models

The Stata command xtreg estimates the random-effects linear regression model, for which the random effects are assumed to be normally distributed with zero mean and non-negative variance, s^2_{i,t}. Testing homogeneity across units is equivalent to testing the null hypothesis H_0: s^2_{i,t} = 0, which is a value on the boundary of the parameter space. The command xtreg provides the upper-tail probability of the appropriate asymptotic distribution of the likelihood ratio test statistic. However, such a method cannot be used to construct confidence intervals for the parameter s^2_{i,t}. Besides, confidence intervals for the random-effect variance that are based on a Wald-type test, too often used, can be shown to be asymptotically wrong. Based on the asymptotic theory for singular information problems, a method is developed and implemented in the Stata command xtci, which provides asymptotically-correct confidence intervals. Also, when testing the hypothesis of homogeneity across units, the proposed method is shown to have better small-sample properties than one based on the likelihood ratio test statistic.