Nonlinear Threshold Tests

Implements a Wald-like test for a nonlinear threshold model.

Implements a Wald-type test for the threshold model
y=x*b+1(x>delta)*x*b+u

when the nuisance parameter (delta) is not identified under the nil. It can even be unknown in value. For a technical discussion compare Hansen (1996) "Inference when a nuisance parameter is not identified under the null hypothesis". Dentler, Rojas and Olmo (2014) "Endogeneity in threshold nonlinearity tests" discuss that under mild conditions the Wald test is valid even when x and u are correlated (x is endogenous).

The routine effectively reports the p-values for a conventional test of significance using a mean, sup and exponential average a la Andrews and Ploberger (1994) "Optimal Tests when a Nuisance Paramtere is Present Only under the Alternative".

The routine also encompasses a model of the form

y=x*beta1+1(x>delta)*x*beta2+w*gamma1+1(x>delta)*x*gamma2+u

For an example see help