Variable selection in threshold model with a covariate-dependent threshold

This paper studies the variable selection problem in threshold model with a covariatedependent threshold, in which the threshold is modeled by a function of candidate variables that affect the separation of regimes. To simultaneously select explanatory variables and the variables that affect the threshold, we develop a variable selection procedure via mixed integer optimization in the l(0)-penalization framework. Monte Carlo simulations are conducted to assess the performance of the suggested variable selection procedure, and the simulation results indicate that the variable selection procedure works well in finite samples. The empirical usefulness of the proposed approach is illustrated with an application to the famous growth-debt nexus.