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An Introduction to Bayesian Econometrics with Applications in Non-market Valuation
Dec. 7 – Dec 11, 2009

Instructors: Jorge E. Araña, Klaus Moeltner

Course Outline

Day 1 (Dec. 7, 2009)

Session S1: Introduction to Bayesian Statistics (Araña)
Session S2: Recap: Least squares and Maximum Likelihood Estimation, Asymptotics (Moeltner)
- S2_data (Matlab script to simulate data for the normal regression model)
- S2_ols (Matlab script to estimate the normal regression model via OLS)
- S2_sampling (Matlab script to illustrate sampling distributions conditional and unconditional on X)
- S2_mle1 (Matlab script for estimation of the normal regression model via MLE, with numerical gradient & Hessian)
- S2_mle2 (Matlab script for estimation of the normal regression model via MLE, with analytical gradient & Hessian)
- S2_asymptotics1 (script illustrating convergence in probability)
- S2_asymptotics2 (script illustrating convergence in distribution)
- S2_asymptotics3 (script illustrating convergence under stabilizing transformation)
- normal_mle (function with MLE optimization code based on numerical gradient and Hessian - courtesy of Prof. Shonkwiler)
- normal_mle_analytical (function with MLE optimization code based on analytical gradient and Hessian)
- normal_L (function producing log-likelihood vector for the normal regression model, called by "normal_mle")
- normal_analytical llf (function producing sample log-likelihood, gradient, and Hessian for the normal regression model, called by "normal_mle_analytical")
- epanech_klaus (function to compute nonparametric density estimates using the Epanechnikov kernel - place it in your "functions" folder)
- wage data (for MLE examples)
Session S3: Priors and Analytical Bayes
Session S4: Normal Linear Regression Model with Conjugate Priors
- S4_priors (Script for prior plots)
- S4_main (Main estimation script)
- S4_plots (Script to plot priors vs. posteriors)
- S4_constrained (estimation script for constrained model)
- S4_compare (script for model comparison)
- mvtrnd_klaus (function to generate random draws from the multivariate t-distribution)

Day 2 (Dec. 8, 2009)

Session S5: Bayes with Simulation
Session S6: Normal Linear Regression Model with Independent Priors
- inverse_gamma_plots (Script to create plots for the ig density under different settings for shape and scale)
- S6_main (main estimation script, using simulated data from Session 2)
- S6_plots (script generating prior vs posterior plots for application with simulated data)
- S6_convergence_plots (script generating convergence plots for a variety of sample sizes and starting draws)
- S6_convergence_plots2 (same as above, but for simulated data with high correlation amongst regressors)
- S6_application (estimation script for wage data)
- S6_application_plots (posterior plots for wage data application)
- gs_normal_independent (Gibbs Sampler, implemented as a function called by S6_main)
- gs_normal_independent_keepall (same as above, but preserves burn-in draws; use with convergence plots)
- labor supply data (Mroz, 1987; tab-delimited txt format)
Session 7: MCMC Methods II
Session 8: Normal Linear Regression Model via Gibbs Sampling: Diagnostics
- S8_blocking (script for an alternative Gibbs Sampler with an excessive number of blocks)
- S8_ac_plots (comparison of efficient and inefficient Gibbs Sampler based on AC plots)
- S8_convergence_plots (comparison of efficient and inefficient Gibbs Sampler based on convergence plots)
- S8_wetlands (main script for wetland valuation data, vague priors)
- S8_wetlands2 (same script with refined (more informed) priors))
- S8_wetlands_plots (prior/posterior plots comparing uninformed and informed results)
- gs_normal_blocked (Gibbs Sampler for the inefficient model)
- gs_normal_blocked_keepall (same as above, but preserves burn-in draws; use with convergence plots)