Leave‐Out Estimation of Variance Components

By Patrick M. Kline, R. Saggio, Mikkel Sølvsten. Econometrica, 2018

173 citations recorded by the source corpus.

We propose leave‐out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An approximation algorithm is provided that enables accurate computation of the estimator in very large data sets. 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 plug‐in methods and estimators predicated on homoscedasticity exhibit first‐order biases. For quadratic forms of increasing rank, the limiting distribution can be represented by a linear combination of normal and non‐central χ 2 random variables, with normality ensuing under strong identification. Standard error estimators are proposed that enable tests of linear restrictions and the construction of uniformly valid confidence intervals for quadratic forms of interest. We find in Italian social security records that leave‐out estimates of a variance decomposition in a two‐way fixed effects model of wage determination yield substantially different conclusions regarding the relative contribution of workers, firms, and worker‐firm sorting to wage inequality than conventional methods. Monte Carlo exercises corroborate the accuracy of our asymptotic approximations, with clear evidence of non‐normality emerging when worker mobility between blocks of firms is limited.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/14f2c1cc6ed1ef5692315d894f807b3b5360d7ac

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Citations in the corpus

A Distributional Framework for Matched Employer Employee Data (2019, unknown): “We verify in simulations that our estimator performs well in data sets 3See Abowd et al. (2004), Andrews et al. (2008, 2012), and recently Kline et al. (2018) for methods to address incidental parameter bias in fixed-effects regressions.”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, methodology): “…(1994), van der Vaart (1998), Robinson (1988), Ai and Chen (2003), Robins and Rotnitzky (1995), Belloni et al. (2015), Chen and Christensen (2018), Kline et al. (2018), Cattaneo et al. (2019)), dependent (Chen and Christensen (2015), Li and Liao (2020)) and panel data settings (Henderson et al.…”
Revisiting event study designs: robust and efficient estimation (2021, unknown): “Our leave-out strategy differs from leave-out variance estimation procedures of Mackinnon and White (1985) and Kline et al. (2020). Those papers assume that the OLS parameter vector is still identified when dropping individual units. In fact, Lemma 1 in Kline et al. (2020) shows that unbiased varian”