Bootstrap tests for structural breaks when the regressors and the serially correlated error term are unstable

Structural break problems in linear regression coefficients are often accompanied by the instabilities of the regressors and/or the serially correlated error term such as structural changes in their marginal distributions. In these circumstances, we find that existing tests as well as Hansen (2000)'s fixed regressor bootstrap have serious size distortions, although the latter is designed to overcome the unstable regressors. To tackle this problem, we propose a method that combines the fixed regressor bootstrap and the sieve wild bootstrap. We show that the sieve wild bootstrap asymptotically replicates a broad set of serially correlated unstable error processes. Using that the fixed regressor bootstrap is designed to capture the instability of the regressors, the mixture of the two is then shown to provide correct asymptotic critical values of the existing tests in various feasible nonstandard cases. Monte Carlo experiments show significant improvements in size and power.