## 1 INTRODUCTION

Both the statistics and econometrics literature contain a vast amount of work on issues related to structural change, most of it specifically designed for the case of a single change. The problem of multiple structural changes has received considerably less but an increasing attention. Related literature includes Andrews, Lee and Ploberger, (1996), Garcia and Perron (1996), Liu, Wu and Zidek (1997), Pesaran and Timmermann (‘Model instability and choice of observation window’, unpublished manuscript, 1999), Lumsdaine and Papell (1997), and Morimune and Nakagawa (1997). Most of these studies are concerned with issues related to hypothesis testing in the context of multiple changes. Recently, Bai and Perron (1998) considered estimating multiple structural changes in a linear model estimated by least-squares. They derived the rate of convergence and the limiting distributions of the estimated break points. The results are obtained under a general framework of partial structural changes which allows a subset of the parameters not to change (and, of course, includes a pure structural change model as a special case). They also addressed the important problem of testing for multiple structural changes: a sup Wald type tests for the null hypothesis of no change versus an alternative containing an arbitrary number of changes and a procedure that allows one to test the null hypothesis of, say, ℓ changes, versus the alternative hypothesis of ℓ + 1 changes. The latter is particularly useful in that it allows a specific to general modelling strategy to consistently determine the appropriate number of changes in the data.

The present study focuses on the empirical implementation of the theoretical results of Bai and Perron (1998), henceforth referred to as BP. We first address the problem of the estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals based on the principle of dynamic programming which requires at most least-squares operations of order *O*(*T*^{2}) for any number of breaks. Our method can be applied to both pure and partial structural change models. We also consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and errors across segments. In particular, we may allow the data and errors to have different distributions across segments or impose a common structure. The issue of testing for structural changes is also considered under very general conditions on the data and the errors. We discuss how the tests can be constructed allowing different serial correlation in the errors, different distribution for the data and the errors across segments or imposing a common structure. We also address the issue of estimating the number of breaks. To that effect, we discuss methods based on information criteria and a method based on a sequential testing procedure. Empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program.

The rest of this paper is structured as follows. Section 2 presents the model and the estimator. Section 3 discusses in detail an algorithm, based on the principle of dynamic programming, that allows us to efficiently estimate models with multiple structural changes. Section 4 discusses the construction of confidence intervals for the various parameters, in particular the break dates. Section 5 discusses tests for multiple structural changes, methods to estimate the number of breaks and summarizes practical recommendations based on a simulation study presented in Bai and Perron (‘Multiple structural change models: a simulation analysis’, unpublished manuscript, 2000). Empirical applications are presented in Section 6. Some conclusions are contained in Section 7.