Random change point model with an application to the potato’s contribution to population

In this paper, we investigate a linear regression model with a change point that depends on an unknown random threshold of a covariate. We account for the heterogeneity of change points, propose an EM estimation method for both the regression and change point parameters, and employ the supremum test of score statistics to detect the random change point. We establish the consistency and asymptotic normality of our estimation method in theory, and verify these properties through simulation studies. Furthermore, we apply our methodology to the case of Nunn and Qian (2011) on the introduction of potatoes to the Old World. Our analysis reveals that the introduction of potatoes played a significant role in the population growth observed during the eighteenth and nineteenth centuries. Importantly, we demonstrate that there exists a threshold effect of the amount of suitable land, with heterogeneity across countries, on stimulating population growth, as estimated by our random change point model.