### Abstract

Original language | English |
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Journal | Journal of Econometrics |

Publication status | Accepted/In press - Jun 2019 |

### Fingerprint

### Keywords

- multiple break points
- instrumental variables estimation
- two-stage least squares
- wild bootstrap
- recursive bootstrap
- fixed-regressor bootstrap
- heteroskedasticity

### Cite this

*Journal of Econometrics*.

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*Journal of Econometrics*.

**Bootstrapping structural change tests.** / Boldea, Otilia; Cornea-Madeira, Adriana; Hall, Alastair R.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Bootstrapping structural change tests

AU - Boldea, Otilia

AU - Cornea-Madeira, Adriana

AU - Hall, Alastair R.

PY - 2019/6

Y1 - 2019/6

N2 - 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.

AB - 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.

KW - multiple break points

KW - instrumental variables estimation

KW - two-stage least squares

KW - wild bootstrap

KW - recursive bootstrap

KW - fixed-regressor bootstrap

KW - heteroskedasticity

M3 - Article

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

ER -