A New Semiparametric Approach for Nonstandard Econometric Problems

Abstract

This paper generalizes the approach of Zhou, van den Akker, Werker (2019), which was designed to derive semiparametric power envelope and construct efficient rank-based tests for the univariate unit root testing problem. The generalization is threefold. First, it becomes a unified method applicable to all LAN, LAMN, and LABF type limit experiments. Such a class covers a wide range of econometric problems including ones of nonstandard limits. Second, in addition to the innovation density shape parameter (the nonparametric part), it also deals with the density location parameter. Third, this approach extends to the multivariate case. This is straightforward for the step of deriving semiparametric power envelopes, but nontrivial for the step of constructing rank-based tests. For the latter purpose, we propose a novel structure based on componentwise rank statistics. We apply this approach to two multivariate econometric problems having nonstandard limits: (i) cointegration rank testing and (ii) regression with weak instruments. For each application, we address the semiparametric efficiency issue by deriving the power envelope and proposing rank-based tests having power close to it. Simulation results show that these rank-based tests have correct sizes and outperform their widely-used competitors in power.