Testing for structural change in conditional models

In the past decade, we have seen the development of a new set of tests for structural change of unknown timing in regression models, most notably the SupF statistic of Andrews (1993, Econometrica 61, 825-856), the ExpF and Av eF statistics of Andrews-Ploberger (1994, Econometrica 62, 1383-1414), and the L statistic of Nyblom (1989, Journal of American Statistical Associatio n 84, 223-230). The distribution theory used for these tests is primarily a symptotic, and has been derived under the maintained assumption that the re gressors are stationary. This excludes structural change in the marginal di stribution of the regressors. As a result, these tests technically cannot d iscriminate between structural change in the conditional and marginal distr ibutions. This paper attempts to remedy this deficiency by deriving the lar ge sample distributions of the test statistics allowing for structural chan ge in the marginal distribution of the regressors. We find that the asympto tic distributions of the SupF, ExpF, AveF and L statistics are not invarian t to structural change in the regressors. To solve the size problem, we int roduce a 'fixed regressor bootstrap' which achieves the first-order asympto tic distribution, and appears to possess reasonable size properties in smal l samples. Our bootstrap theory allows for arbitrary structural change in t he regressors, including structural shifts, polynomial trends, and exogenou s stochastic trends. It allows for lagged dependent variables and heteroske dastic error processes. (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification: C22.