A Note on Estimating and Testing for Multiple Structural Changes in Models With Endogenous Regressors via 2sls

Abstract

This note provides a simple proof for the problem of estimating and testing for multiple breaks in a single equation framework with regressors that are endogenous. We show based on standard assumptions about the regressors, instruments and errors that the second stage regression of the instrumental variable (IV) procedure involves regressors and errors that satisfy all the assumptions in Perron and Qu (2006) so that the results about consistency, rate of convergence and limit distributions of the estimates of the break dates, as well as the limit distributions of the tests, are obtained as simple consequences. The results are obtained within a uni…ed framework for various cases about the nature of the reduced form: stable, no structural changes but time variations in the parameters, structural changes at dates that are common to those of the structural form, and structural changes occurring at arbitrary dates. JEL Classi…cation Number: C22.

A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models

“…Important early contributions about the limit distribution of the estimate of the break date, from which con…dence intervals can be obtained, include Bai (1994) for a change in mean in a linear process and Bai (1997) for a one time change in some coe¢ cients in a linear regression model. These results have been extended to multiple structural changes by Perron (1998, 2003) for the linear regression model, Perron and Qu (2006) for the case with restrictions on the parameters (and relaxations of the conditions on the regressors and errors), Perron and Yamamoto (2013) for linear models estimated via band spectral regression and Perron and Yamamoto (2014) for the case of linear models with endogenous regressors estimated by two-stage least squares. In all cases, the limit distributions of the estimates of the break dates have a common structure and are obtained using an asymptotic framework whereby the magnitude of the change shrinks as the sample size increases.…”

Threshold regression with endogeneity

“…Kapetanios (2010) tests exogeneity of the instruments used in threshold regression by bootstrapping a Hausman-type test statistic within the Hansen (2000) framework. The common solution to the endogeneity problem in all this work is to employ instruments and to apply two-stage-least squares (2SLS) estimation, just as in linear regression (For related work on 2SLS estimation of structural change regression without thresholding, see Boldea et al (2012), Hall et al (2012) and Perron and Yamamoto (2012a)). However, Yu (2013a) shows that three typical 2SLS estimators of are generally inconsistent.…”

Editors’ introduction

“…The instability of the reduced form affects the asymptotic distribution of the Wald test for testing parameter instability which, in this case, differs from that obtained for OLS by Bai and Perron (1998). This paper complements the work by Perron and Yamamoto (2009) who show that tests for breaks based on OLS estimation have power even when the regressors are endogenous. The 2SLS approach of Hall, Han, and Boldea has the advantage to deliver consistent estimates of coefficients while OLS does not.…”