A Unified Approach to Robust, Regression-Based Specification Tests

Abstract

This paper develops a general approach to robust, regression-based specification tests for (possibly) dynamic econometric models. A useful feature of the proposed tests is that, in addition to estimation under the null hypothesis, computation requires only a matrix linear least-squares regression and then an ordinary least-squares regression similar to those employed in popular nonrobust tests. For the leading cases of conditional mean and/or conditional variance tests, the proposed statistics are robust to departures from distributional assumptions that are not being tested, while maintaining asymptotic efficiency under ideal conditions. Moreover, the statistics can be computed using any √T-consistent estimator, resulting in significant simplifications in some otherwise difficult contexts. Among the examples covered are conditional mean tests for models estimated by weighted nonlinear least squares under misspecification of the conditional variance, tests of jointly parameterized conditional means and variances estimated by quasi-maximum likelihood under nonnormality, and some robust specification tests for a dynamic linear model estimated by two-stage least squares.