Dealing with endogeneity in threshold models using copulas : an illustration to the foreign trade multiplier

We suggest a new method dealing with the problem of endogeneity of the threshold variable in single regression threshold models and seemingly unrelated systems of them based on copula theory. This theory enables us to relax the assumption that the threshold variable is normally distributed and to capture the dependence between the error term and the threshold variable in each regime of the model independently of the marginal distribution of the threshold variable. This distribution can be estimated non-parametrically conditionally on the value of threshold parameter. To estimate the slope and threshold parameters of the model adjusted for the endogeneity of the threshold variable, we suggest a two-step concentrated least squares estimation method where the threshold parameter is estimated based on a search procedure, in the first step. A Monte Carlo study indicates that the suggested method deals with the endogeneity problem of the threshold variable satisfactorily. As an empirical illustration, we estimate a threshold model of the foreign-trade multiplier conditional on the real exchange rate volatility regime. We suggest a bootstrap procedure to examine if there are significant differences in the foreign-trade multiplier effects across the two regimes of the model, under potential endogeneity of the threshold variable.