Bayesian Methods in Econometrics
This module introduces Bayesian statistics and its application to econometrics, contrasting the Bayesian approach with the classical/frequentist approach. Students learn how to construct and interpret posterior distributions, apply Markov chain Monte Carlo methods such as Gibbs sampling and the Metropolis-Hastings algorithm, and use Bayesian techniques including Bayesian Model Averaging and hierarchical priors to address problems in econometrics.
Delivery
Two-hour lectures per day over five days, plus a one-hour tutorial each day. Sessions are live online and recorded.
Study Hours
Approximately 100 hours of study, of which 15 are contact hours and 85 are private study.
Software Used
Python, R
Credits
10 CATS credits
Module Lead
Programme Faculty
Key Outcomes
- —The basis and motivation for Bayesian Econometrics
- —The distinction between inference and estimation in Bayesian versus classical methods
- —How to construct posterior distributions of unknown parameters
- —The application of Bayesian methods to problems in microeconometrics
Desired Skills
- —Communicate and present complex arguments in oral and written form with clarity
- —Appreciate instances where the application of Bayesian methods is appropriate
- —Work with R and/or Python to operationalize Bayesian methods
Lecture Programme
- WK 01
Lecture 1: Introduction to Bayesian statistics and its differences versus the classical/frequentist approach
- ·Advantages of the Bayesian approach over the frequentist approach: general theory and simple examples
- ·Bayes' rule: prior density, likelihood, posterior density and posterior density kernel
- ·Informative versus non-informative priors
- ·Bayesian analysis of model with Bernoulli/binomial distribution under uniform prior
- WK 02
Lecture 2: Prior specification in simple econometric models, Gibbs sampling
- ·Conjugate priors
- ·Bayesian analysis of model with Bernoulli/binomial distribution under conjugate (beta) prior distribution
- ·Bayesian analysis of model with Geometric distribution
- ·Proper versus improper priors
- ·Bayesian analysis of model with normal distribution with known and unknown variance (under normal and flat prior distributions)
- ·Markov chain Monte Carlo (MCMC) methods: burn-in, Gibbs sampling method
- WK 03
Lecture 3: Metropolis-Hastings algorithms (methods and applications in econometric models)
- ·Markov chain Monte Carlo (MCMC) methods: random walk Metropolis(-Hastings) method, candidate distribution, diagnostic checks, acceptance percentage
- ·Bayesian estimation of (G)ARCH models
- ·Bayesian estimation of Poisson regression model
- ·Markov chain Monte Carlo (MCMC) methods: independence chain Metropolis-Hastings method, candidate distribution, diagnostic checks, acceptance percentage
- WK 04
Lecture 4: Posterior model probabilities, normal linear regression model, Bayesian Model Averaging for forecast combination of autoregressive models
- ·Posterior model probabilities: posterior odds ratio, prior odds ratio, Bayes factor, marginal likelihood
- ·Monte Carlo methods: importance sampling method, acceptance-rejection method
- ·Bayesian analysis of model with normal distribution with unknown variance under flat prior: Student-t marginal posterior of the mean
- ·Bayesian analysis of normal linear regression model under flat prior: Student-t marginal posterior of the coefficients, symmetry and differences between Bayesian and classical/frequentist results
- ·Savage-Dickey density ratio for computing the Bayes factor of nested models
- ·Posterior predictive density in autoregressive (AR) models
- ·Bayesian Model Averaging (BMA) for forecast combination
- ·Jeffreys-Lindley-Bartlett paradox and the need for proper priors in BMA
- WK 05
Lecture 5: Gibbs sampling with data augmentation (method and applications in econometric models), hierarchical prior, Jeffreys prior, numerical standard errors
- ·Markov chain Monte Carlo (MCMC) methods: Gibbs sampling with data augmentation
- ·Bayesian estimation of a mixture model with known/fixed number of components
- ·Bayesian estimation of a mixture model with unknown/flexible number of components: hierarchical priors, sparse finite mixture
- ·Bayesian estimation of probit, tobit models
- ·Jeffreys prior
- ·Numerical precision of simulation results: numerical standard errors, relative numerical efficiency
Assessment
Online coursework submission with the support of your module lecturer and tutor. All sessions are conducted live online at a scheduled time and recorded for review.
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