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Abstract
ABSTRACTModels with multiple discrete breaks in parameters are usually estimated via least squares. This paper, first, derives the asymptotic expectation of the residual sum of squares and shows that the number of estimated break points and the number of regression parameters affect the expectation differently. Second, we propose a statistic for testing the joint hypothesis that the breaks occur at specified points in the sample. Our analytical results cover models estimated by the ordinary, nonlinear, and two-stage least squares. An application to U.S. monetary policy rejects the assumption that breaks are associated with changes in the chair of the Fed.
Highlights
There has been a considerable literature in econometrics on least square-based estimation and testing in models with discrete breaks in the parameters
The seminal paper by Bai and Perron (1998) developed a framework for estimation and inference in linear regression models estimated via ordinary least squares (OLS) that has served as the template for similar frameworks in more general models, including systems of linear regression models (Perron and Qu, 2006), linear models with endogenous regressors estimated via two stage least squares (2SLS, Hall et al, 2012), and nonlinear regression models estimated by Nonlinear Least Squares (NLS, Boldea and Hall, 2013)
Our analysis of the asymptotic expectation of the residual sum of squares cover both linear and nonlinear regression models estimated by least squares
Summary
There has been a considerable literature in econometrics on least square-based estimation and testing in models with discrete breaks in the parameters. The seminal paper by Bai and Perron (1998) developed a framework for estimation and inference in linear regression models estimated via ordinary least squares (OLS) that has served as the template for similar frameworks in more general models, including systems of linear regression models (Perron and Qu, 2006), linear models with endogenous regressors estimated via two stage least squares (2SLS, Hall et al, 2012), and nonlinear regression models estimated by Nonlinear Least Squares (NLS, Boldea and Hall, 2013) Within these models, the key parameters of interest are those indexing the breaks—the break fractions—and the regime speci c coe cients.
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