On the Distribution of the Break-Date Estimator Implied by the Perron-Type Statistics When the Form of Break is Misspecified

Montañés, Olloqui, and Calvo (2005, Journal of Econometrics) argue that use of the Perron-type minimum t-statistics will lead the practitioner to incorrectly assess the time series properties of the variable under investigation when the form of break is misspecified. However, their simulations do not provide insight into the distribution of the estimated break-date implied by the unknown break-date Perron-type statistics when the form of break is misspecified. Using finite sample simulations, we show that the break-date implied by the Mixed model will tend to estimate the break-date consistently even when the form of break is misspecified. The practitioner should, therefore, use the Mixed model as the appropriate trend-break stationary alternative when testing for a unit root with an endogenous break-date.