The Asymptotic Behaviour of the Residual Sum of Squares in Models with Multiple Break Points

Models with multiple discrete breaks in parameters are usually estimated via least squares. This paper, firstly, derives the asymptotic expectation of the residual sum of squares, the form of which indicates that the number of estimated break points and the number of regression parameters affect the expectation in different ways. Secondly, we propose a statistic for testing the joint hypothesis that the breaks occur at specified points in the sample and show that the statistic hasa limiting null distribution that is non-standard but simulatable. In an important special case, the statistic can be normalized to make it pivotal and we provide percentiles for the associated limiting distribution. Our analytical results cover linear and nonlinear regression models with exogenous regressors estimated via Ordinary (or Nonlinear) Least Squares and a linear model in which some regressors are endogenous and the model is estimated via Two Stage Least Squares. An application to US monetary policy rejects the common assumption that identified breaks are associated with changes in the chair of the Fed.