Leave out estimation of variance components
Seminar | November 1 | 4-5 p.m. | 1011 Evans Hall
Patrick Kline, University of California, Berkeley
We propose a general framework for unbiased estimation of quadratic forms of regression coefficients in linear models with unrestricted heteroscedasticity. Economic applications include variance component estimation in multi-way fixed effects and random coefficient models. The large sample distribution of our estimator is studied in an asymptotic framework where the number of regressors grows in proportion to the number of observations. We show that the limiting distribution is non-standard and can be represented by a linear combination of independent normal and non-central chi-squared random variables. Consistent variance estimators are proposed along with a conservative inference procedure. In an application to Italian worker-firm data, we demonstrate that ignoring heteroscedasticity can substantially bias conclusions about the relative contribution of workers, firms, and worker-firm sorting to wage inequality.