Question: 4. (a) Derive the conditional posterior distributions necessary to set up a Gibbs sampler with data augmentation for the random coefficients panel probit model introduced

(a) Derive the conditional posterior distributions necessary to set up a Gibbs sampler with data augmentation for the random coefficients panel probit model introduced (9.26).

(b) Program up the Gibbs sampler described in part

(a) and test your program using artificial data.

(c) How would your answer to part

(a) and program in part

(b) change for the random coefficients panel multinomial probit model?

(d) Using artificial data or the full cracker data set (available on the website associated with this book or at the Journal of Applied Econometrics data archive, http://qed.econ.queensu.ca/jae/, listed under Paap and Franses, 2000) carry out Bayesian inference in the random coefficients panel probit model.

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