Background
The concept of ‘posterior’ in Bayesian econometrics stems from the broader field of Bayesian statistics. It’s an integral part of Bayesian inference, which combines prior knowledge or beliefs with new evidence to update the probability estimate for a hypothesis.
Historical Context
The foundation for posterior stems from the 18th-century work of Thomas Bayes, who formulated Bayes’ Theorem. This theorem became a cornerstone of Bayesian economics and econometrics in the 20th and 21st centuries, thanks to advancements in computing power that allowed for more complex calculations and models.
Definitions and Concepts
Posterior: In Bayesian econometrics, the posterior is the revised belief or distribution of a parameter after considering new sample data. It is obtained by updating the prior (the previously assumed distribution) using Bayes’ Theorem.
Major Analytical Frameworks
Classical Economics
Classical economics, with its focus on equilibrium and deterministic models, generally does not incorporate the concept of subjective probability updates, making the use of posteriors outside its framework.
Neoclassical Economics
While neoclassical economics employs deterministic models, the incorporation of Bayesian methods, particularly posterior distributions, has penetrated in microeconomic modeling and forecasting as a way to incorporate evolving information.
Keynesian Economics
Though originally outside the Bayesian framework, modern Keynesian models can integrate Bayesian posteriors, especially in the adaptive expectations and the updating of macroeconomic parameters and forecasts.
Marxian Economics
Marxian economics typically does not use Bayesian methods directly. However, the probabilistic approach in data analysis related to economic classes and dynamics could utilize posterior distributions theoretically.
Institutional Economics
Institutional economics might use Bayesian statistics and posterior distributions to revise theories or parameters when new institutional data or evidence becomes available, allowing for a cyclic update of models.
Behavioral Economics
Behavioral economists can use posterior distributions to understand how individuals update their beliefs and make decisions based on new information, fitting seamlessly with cognitive biases studies.
Post-Keynesian Economics
Similar to Keynesian economics, Post-Keynesian streams have the potential to incorporate Bayesian updating to refine models based on evolving economic data and structural shifts.
Austrian Economics
Austrian economics values subjective interpretations of economic phenomena and could theoretically employ posterior distributions to describe updates in subjective beliefs.
Development Economics
In studying the dynamics of developing economies, posterior distributions can help incorporate new data to update models on growth, inequality, and other developmental parameters.
Monetarism
Monetarists can use Bayesian updating, particularly in the realm of expectations and policies to understand how new data about money supply and velocity influences revised beliefs about macroeconomic outcomes.
Comparative Analysis
Posterior distributions provide Bayesian econometrics a distinctive strength in dynamically updating models based on new data. Unlike traditional frequentist approaches which rely on fixed parameter estimates, posteriors offer a continuous and flexible updating mechanism.
Case Studies
Case studies in which posterior distributions have been crucial include financial market predictions, healthcare economics for updating disease control parameters, and policy studies where new economic indicators necessitate model updates.
Suggested Books for Further Studies
- “Bayesian Theory” by José M. Bernardo and Adrian F. M. Smith
- “Bayesian Data Analysis” by Andrew Gelman et al.
- “Bayesian Econometric Methods” by Gary Koop, Dale J. Poirier, and Justin L. Tobias
Related Terms with Definitions
- Prior: The initial distribution of a parameter before any new data is considered in Bayesian analysis.
- Bayesian Inference: A method of statistical inference in which Bayes’ Theorem is used to update the probability estimate for a hypothesis as more evidence or information becomes available.
