Using 2SLS estimation, we propose two tests for a threshold in models with endogenous regressors: a sup LR test and a sup Wald test. Here, the 2SLS estimation is not conventional because it uses additional information about the first-stage being linear or not. Because of this additional...

We propose two new parametric tests for an unknown threshold in models with endogenous regressors. They are both based on unconventional 2SLS estimators that use additional information about the linearity of the first stage. This information leads to more accurate residuals and therefore tests...