Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from their true values, in line with our theoretical formulas. The formulas provide a benchmark for judging the observed highly variable cross country estimates of the expectations coefficient in yield curve regressions.

Heavy tails, OLS estimator distribution, Small sample inference,
Journal of Econometrics
Erasmus MC: University Medical Center Rotterdam

Mikosch, T, & de Vries, C.G. (2013). Heavy tails of OLS. In Journal of Econometrics (Vol. 172, pp. 205–221). doi:10.1016/j.jeconom.2012.08.015