Testing for structural breaks in discrete choice models

Abstract

A structural break refers to a shift in the parameters of the model of interest. When the conditional relationship between the dependent and explanatory variables contains a structural break, estimates of model coefficients will be inaccurate across different regimes. As such, estimations that do not account for structural breaks will be biased and inconsistent. Ever since the seminal work of Chow [1960], there have been numerous other tests proposed for detecting various forms of structural breaks in different contexts. Chow [1960] proposed an F-statistic to detect a single structural break with known location in the context of a linear model. One of the most commonly used tests is the Andrews [1993], which generalised Chow [1960] to the Sup Wald, LR, and LM tests for linear models when the position of the breakpoint is unknown. Other important contributions to the literature include Bai and Perron [1998] and Bai [1999], both of which constructed tests that detect multiple structural breaks in linear models. Studying the properties of such tests is particularly important because the theoretical distribution of most of the test statistics have only been identified asymptotically, but the same critical values are also used for smaller sample sizes in practice. Furthermore, the theoretical properties of the test statistics are usually established only under certain restrictions such asi:i:d: assumptions that may not hold in practice for various reasons. While present literature does include studies of structural break tests where the changepoint is unknown, such as Diebold and Chen [1996], and Bai and Perron [2004], these have mostly been restricted to linear regression models. To our knowledge, no study has been carried out thus far to evaluate the properties of any structural break test in the context of binary choice models, such as probit models, which will be the main contribution of this paper. This paper considers the size and power of the three Andrews [1993] Sup-type tests when applied to probit models with different levels of autocorrelation and varying sample sizes using a simulation-based approach similar to Diebold and Chen [1996], which tested the sizes of the tests in the linear regression model . We carry out the same procedure with a different data generating process, but also further the study by comparing the results in the linear model with that of a probit model. In addition, we also consider the power of the tests in both models, as well as a few different levels of data trimming. The main findings of this paper are that the shortcomings of the Andrews [1993] Sup-type tests in linear models are magnified in probit models. In particular, the tests exhibit greater size distortion, lower power, and become more imprecise in identifying the position of the structural break when the samples are small or when the errors are autocorrelated.