Tests for Parameter Instability in Regressions with I(1) Processes

This paper derives the large sample distributions of Lagrange multiplier tests for parameter instability against several alternatives of interest in the context of cointegrated regression models. The test statistics considered include the SupF test of Quandt (1960), as well as the LM test of Nyblom (1989). It is found that the asymptotic distributions depend upon the nature of the regressor processes, i.e., if the regressors are stochastic or deterministic trends. The distributions are noticeably different from the distributions when the data are weakly dependent. The tests are applied to three data sets: an aggregate consumption function, a present value model of stock prices and dividends, and the term structure of interest rates.