Linear regression under two separate regimes: An empirical distribution for Quandt's log likelihood ratio

In the empirical analysis of structural changes, Quandt's test for detecting a single change in a regression relationship at an unknown point of time is frequently applied. A limitation regarding the applicability of the method is that the distribution of the Quandt's log likelihood ratio is unknown. The purpose of this work is to derive an empirical distribution for Quandt's statistic which enables the researcher to approximate the level of significance when testing the stability of regression relationships over time.