We present the postestimation command xtvc to provide confidence intervals for the variance components of random-effects linear regression models. This command must be used after xtreg with option mle. Confidence intervals are based on the inversion of a score-based test (Bottai 2003).
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Bottai, M., & Orsini, N. (2004). Confidence Intervals for the Variance Component of Random-effects Linear Models. The Stata Journal: Promoting Communications on Statistics and Stata, 4(4), 429–435. https://doi.org/10.1177/1536867x0400400405