Bootstrap tests for time varying cointegration

Abstract

This article proposes wild and the independent and identically distibuted (i.i.d.) parametric bootstrap implementations of the time-varying cointegration test of Bierens and Martins (2010). The bootstrap statistics and the original likelihood ratio test share the same first-order asymptotic null distribution. Monte Carlo results suggest that the bootstrap approximation to the finite-sample distribution is very accurate, in particular for the wild bootstrap case. The tests are applied to study the purchasing power parity hypothesis for twelve Organisation for Economic Cooperation and Development (OECD) countries and we only find evidence of a constant long-term equilibrium for the U.S.-U.K. relationship.