  This paper analyses the use of bootstrap methods to test for parameter change
in linear models estimated via Two Stage Least Squares (2SLS). Two types of
test are considered: one where the null hypothesis is of no change and the
alternative hypothesis involves discrete change at k unknown break-points in
the sample; and a second test where the null hypothesis is that there is
discrete parameter change at l break-points in the sample against an
alternative in which the parameters change at l + 1 break-points. In both
cases, we consider inferences based on a sup-Wald-type statistic using either
the wild recursive bootstrap or the wild fixed bootstrap. We establish the
asymptotic validity of these bootstrap tests under a set of general conditions
that allow the errors to exhibit conditional and/or unconditional
heteroskedasticity, and report results from a simulation study that indicate
the tests yield reliable inferences in the sample sizes often encountered in
macroeconomics. The analysis covers the cases where the first-stage estimation
of 2SLS involves a model whose parameters are either constant or themselves
subject to discrete parameter change. If the errors exhibit unconditional
heteroskedasticity and/or the reduced form is unstable then the bootstrap
methods are particularly attractive because the limiting distributions of the
test statistics are not pivotal.
