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## Bayesian econometrics

### Highlights

• Estimation
• Built-in models with over 60 likelihoods and over 30 priors
• Custom likelihoods and priors
• Univariate, multivariate, and multiple-equation models
• Linear, generalized linear, and nonlinear models
• Random effects and latent factors
• Flexible control of MCMC sampling
• Multiple chains
• Bayesian model averaging (BMA)
• Postestimation
• Convergence diagnostics
• Posterior means, medians, and standard deviations
• Equal-tailed and HPD credible intervals
• Interval hypothesis testing
• Model comparison using DIC and Bayes factors
• Predictions

Stata does econometrics. Stata does Bayesian statistics. Stata combines both to do Bayesian econometrics.

Bayesian econometrics uses Bayesian principles to study economic relationships. How likely is it that an extra year of schooling will increase wages? Are those who participate in a job-training program more likely to stay employed for the next five years? What is the probability of default for a low default portfolio? Such questions can be answered naturally within the Bayesian paradigm, which can estimate the probability of any hypothesis of interest. See What is Bayesian analysis? to learn more.

One of the appeals for using Bayesian methods in econometric modeling is to incorporate the external information about model parameters often available in practice. This information may come from historical data, or it may come naturally from the knowledge of an economic process. For instance, income elasticity may be known to be less than 1 for some countries, or autocorrelation is known to be between -1 and 1. Either way, a Bayesian approach allows us to combine that external information with what we observe in the current data to form a more realistic view of the economic process of interest.

You may ask: What if I do not have any external information? No problem. Without any informative prior knowledge, the results will be similar to those you would have obtained using classical econometrics methods. But their interpretation may be more intuitive. For instance, a 95% credible interval—a Bayesian counterpart of a confidence interval—can be interpreted as a range in which a parameter lies with a 0.95 probability.

There is another reason Bayesian econometrics may be appealing in the absence of strong external knowledge. Econometrics models often describe complex economic theories and thus tend to have many parameters—often so many that it becomes infeasible to fit the models without incorporating some information about model parameters. In such situations, Bayesian econometrics modeling can provide a balance between what's observed in the data and what's reasonable to assume about model parameters to obtain reliable inference.

For instance, vector autoregressive (VAR) models are known to have many parameters relative to the data size. Bayesian analysis of these models introduces specialized priors that allow you to obtain more stable parameter estimates.

Also, dynamic stochastic general equilibrium (DSGE) models are known to have parameters that have direct economic interpretations and often have logical bounds that can be easily incorporated by a variety of prior distributions.

Bayesian model averaging (BMA) is a popular tool to account for model uncertainty in your analysis. It uses fundamental Bayesian principles to provide easily interpretable estimates of model and predictor probabilities. Its estimation approach can be applied universally to all data analyses. BMA's ability to specify model and parameter prior distributions provides a natural framework for sensitivity analyses to various assumptions about the importance of different models and predictors.

You can find Bayesian VAR models, Bayesian linear and nonlinear DSGE models, and BMA among the Bayesian econometrics features of Stata, and much more:

You may also be interested in other existing features, including

and more.

Extensive Bayesian inference is available after estimation, including Markov chain Monte Carlo (MCMC) diagnostics, posterior summaries of linear and nonlinear functions of parameters, interval hypothesis testing, and model comparison using Bayes factors; see [BAYES] Bayesian postestimation for a full list of features.