Based on the paper Hierarchical Bayesian Analysis of the Seemingly Unrelated Regression and Simultaneous Equations Models Using a Combination of Direct Monte Carlo and Importance Sampling Techniques, we reproduce some of its results.
The paper considers the SUR (seemingly unrelated regression) problem and its transformed version. It proposes a DMC-IS method (direct monte carlo with importance sampling) to simulate the parameters in SUR.
Here, we implement and compare three methods:
- MCMC on original SUR
- DMC on transformed SUR
- DMC-IS on transformed SUR