6. Following Kozumi (2002), simulate data under an endogenous switching model with yi ∼ Po(xi + Ti + ui1), T ∗

i

= 1 + 2zi + ui2, xi ∼ N(0, 1); zi ∼ N(0, 1); ui,1:2 ∼ N(0,u), with (see Equation 15.9) σ2 = 0.3, and ρ = 0.75. Using the simulated data, estimate the treatment effect (with true value unity) via a standard Poisson regression (without the endogenous treatment feature, that is with ρ = 0) and via the full model allowing correlated errors.