External bootstrap tests for parameter stability

This article considers tests for parameter stability over time in general econometric models, possibly nonlinear-in-variables. Existing test statistics are commonly not asymptotically pivotal under nonstandard conditions. In such cases, the external bootstrap tests proposed in this paper are appealing from a practical viewpoint. We propose to use bootstrap versions of the asymptotic critical values based on a first-order asymptotic expansion of the test statistics under the null hypothesis, which consists of a linear transformation of the unobserved “innovations” partial sum process. The nature of these transformations under nonstandard conditions is discussed for the main testing principles. Also, we investigate the small sample performance of the proposed bootstrap tests by means of a small Monte Carlo experiment.