Trivariate probit with double sample selection: theory and application

We develop the trivariate probit model in which the sample incidentally truncates twice (i.e. in the first and in the second equations), which is not solved in the literature. The model is analogue to the so called Bivariate Probit with Sample Selection (also referred as Bivariate Probit with Partial Partial Observabilty, Censored Probit or Heckman Probit) but in this case there are three equations and two truncations. We also present an application that shows the estimation biases when the incidental truncations are ignored.