The impact of serial correlation on testing for structural change in binary choice model: Monte Carlo evidence

This paper examines the finite sample properties of structural change tests with an unknown breakpoint for the probit model in the presence of serial correlation. The combination of structural change and serial correlation renders model estimation challenging, affecting the consistency of coefficient estimates. Although there is vast literature concerning structural change tests for linear time series models, the literature for such tests in the context of binary choice models is somewhat sparse. More importantly, the empirical literature has applied the standard tests of structural change on the discrete choice model, despite the fact that most of these tests were developed specifically for the linear regression model. Subsequently, the theoretical properties of these tests in the context of non-linear models are unknown. This includes the class of discrete choice models, such as probit and logit. The issue becomes even more complicated in the presence of serial correlation, since typical tests for structural change often require the assumption of independence in the error terms. Even when the tests allow for a weakly dependent structure in the data, their finite sample performance remains unknown. This paper conducts simulation analysis on the size of ‘supremum’ Wald, LR and LM tests for structural change in the context of the probit model with varying levels of serial correlation. It is found that the shortcomings of the tests in linear models are magnified in probit models. In particular, the tests exhibit greater size distortion for the probit model than the linear model with the same level of serial correlation. Bootstrapping is also considered as an alternative approach to obtaining critical values, and though it reduces the size distortion in finite samples, it is unable to accommodate the distortion associated with a high level of serial correlation.