Testing for structural change and parameter instability has a long history in econometrics and statistics. Parameters are frequently reduced forms of unobservables, such as taste, technology and institutions. Although it may be reasonable to believe that these unobservables have been roughly constant over the sample period, it is rarely a priori obvious and should therefore be subject to a specification test. Despite the long history of study of this problem, most researchers apply simple sample split tests or forecast error tests, neither of which are optimal. The purpose of this project is to develop a powerful test for parameter instability calculated under the null hypothesis of constant parameters which is easy to calculate, even in non-linear contexts. The approach taken is to use an approximate Lagrange Multiplier test against the alternative that the parameter is martingale. This includes simple structural breaks as well as random walks. The asymptotic distribution is non-standard, but invariant to nuisance parameters if the regressors are non-trended. Appropriate asymptotic theory is developed, which makes use of some recent developments in stochastic process theory.
