On skewness and kurtosis of econometric estimators

Summary We derive the approximate results for two standardized measures of deviation from normality, namely, the skewness and excess kurtosis coefficients, for a class of econometric estimators. The results are built on a stochastic expansion of the moment condition used to identify the econometric estimator. The approximate results can be used not only to study the finite sample behaviour of a particular estimator, but also to compare the finite sample properties of two asymptotically equivalent estimators. We apply the approximate results to the spatial autoregressive model and find that our results approximate the non‐normal behaviours of the maximum likelihood estimator reasonably well. However, when the weights matrix becomes denser, the finite sample distribution of the maximum likelihood estimator departs more severely from normality and our results provide less accurate approximation.