- , and α∗ i ⊥ ⊥ δ∗ i , for i = 1, . . . , n. This parametrization is similar to that adopted by Semykina and Wooldridge (2018) for binary panel data models with a binary endogenous explanatory variable in a static framework. The assumption of a bivariate normal distribution for the unobserved heterogeneity allows us to write the model as a function of two independent normally distributed random variables and the marginalization with respect to the randomeffects is then performed by two independent consecutive integrations (Raymond et al., 2010). Let Õ be the vector collecting the model parameters Õ = (γ, Æ, β0 , ζ, θ, λ, À0, ξ, κ, ÃÂ, Ãα, Ãη)0. Then the likelihood function for individual i is Li(Õ) = Z < Z < Pi dΦ α∗ i Ãα dΦ δ∗ i
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