rameter and ˆ D$_{2}$ denotes negative inverse Hessian, obtained by maximizing the log-likelihood with respect to δ . Given the current value δ$_{c}$ , the proposed value δ ′ is accepted with MH probability, α$_{MH}$ ( δ$_{c}$, δ $^{′}$) = min { 0 , ln [ f ( y | β, σ, γ, δ $^{′}$) π ( β, σ, γ, δ $^{′}$) f ( y β, σ, γ, δ$_{c}$ ) π ( β, σ, γ, δ$_{c}$ ) ]} , otherwise, the current value δ$_{c}$ is repeated. The variance of u may be tuned as required for an appropriate step-size and acceptance rate. (6) The full conditional density of the latent variable z is a truncated normal distribution where the cut-point vector ξ is obtained based on one-to-one mapping with δ . Hence, z is sampled as z$_{i}$ | β, ν, h, σ, γ, δ, y ∼ T N$_{(}$$_{ξ}$$_{j}$$_{−}$$_{1}$$_{, ξ}$$_{j}$$_{)}$ ( x ′ $_{i}$β + Aν$_{i}$ + C | γ | h$_{i}$, σBν$_{i}$ ) for i = 1 , · · · , n and j = 1 , · · · , J . We thank professor Ivan Jeliazkov (University of California Irvine) and participants at the Asian Meeting of the Econometric Society (2017, Hong Kong) for some extremely valuable comments. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Acknowledgement 40