Random change point model with an application to the China Household Finance Survey

We consider a linear model with a change point according to the unknown random threshold of a covariate. We give the expectation-maximization (EM) estimation of the regression and change point parameters. The existence of the random change point is detected by the supremum (SUP) test of score statistics. Theoretically, we establish the convergence and asymptotic distribution of the estimation and show that the EM estimates converge in distribution to a normal distribution. In addition, the numerical performance of the proposed approach is demonstrated through simulation studies. Finally, applying our methodology to household financial decisions, we see that the average debt tolerance of Chinese households is estimated to be 1.1364 times the sum of total household income and financial assets. The effect of assets and income on consumption shows a rapid decline if the household exceeds the average debt tolerance.