A bent line Tobit regression model with application to household financial assets

In this article, we consider a bent line Tobit regression model with an unknown change point due to a covariate threshold. The regression function is constrained to be everywhere continuous with a kink at an unknown change point. We propose a grid search method to simultaneously estimate the change point and other regression parameters for the bent line Tobit regression model. The limiting distribution of the proposed estimator is established via empirical processes theory. We also propose a test procedure for testing the existence of the change point. Simulation studies illustrate that the proposed estimator and test procedure have good finite sample performance. The proposed method is applied to analyze a set of data for household financial assets.