RATS 10.1
RATS 10.1

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RATS Bayesian Econometrics e-course

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This workbook is based upon the content of the RATS e-course on Bayesian Econometrics, offered in spring 2009 and updated to a 2nd edition in 2013. It covers most of the most important methods now used in Bayesian analysis in econometrics, including Gibbs sampling, Metropolis-Hastings and importance sampling. The applications are to a broad range of topics, including time series, cross-section and panel data. It assumes that the user is comfortable with such basic instructions as COMPUTE, DISPLAY, GRAPH, SCATTER and LINREG, and can use simple programming techniques such as DO loops. In each chapter, there is a "Tips and Tricks" section which covers in greater detail any functions or instructions that might be unfamiliar.

 

The presentation is based largely on Gary Koop's Bayesian Econometrics(2003). We've added to that in several areas, with a chapter on vector autoregressions, and examples from the literature for panel, cross-sectional data and state-space models. In most cases, we've included much of the statistical derivations from the book, presented in a way to highlight the calculations as they are done with RATS, so even those without the book can benefit.

 

The advanced simulation-based techniques are also used in the contents of many of the other e-courses.

 

This includes the book in PDF form, with the running examples and required data. The contents are:

Preface

1 Introduction

 1.1 Bayesian Statistics: An Overview
 1.2 Single Parameter--Brute Force
 1.3 RATS Tips and Tricks
 Example 1.1 Brute Force: Analyzing on a Grid

2 Linear Regression Model with Conjugate Prior

 2.1 LRM with a Single Variable
 2.2 Normal Linear Model: Theory
 2.3 Using Cross Product Matrices
 2.4 Calculations
 2.5 Simulations
 2.6 RATS Tips and Tricks
 Example 2.1 Linear Model: Single Variable
 Example 2.2 Multiple Regression: Conjugate Prior
 Example 2.3 Multiple Regression with Conjugate Prior: Simulations

3 Normal Linear Model with Independent Prior

 3.1 Theory
 3.2 Calculations
 3.3 Diagnostics
 3.4 The Bayesian Approach to Hypothesis Testing
 3.5 Hypothesis Testing with the Linear Model
 3.6 RATS Tips and Tricks
 Example 3.1 Linear Model with Independent Prior
 Example 3.2 Linear Regression: Conjugate Prior with Restrictions

4 Nonlinear Regression: Introduction to Metropolis-Hastings

 4.1 Theory
 4.2 Calculations
 4.3 RATS Tips and Tricks
 Example 4.1 Non-linear Regression: Random Walk MH
 Example 4.2 Non-linear Regression: Independence MH
 

5 Linear Regression with Non-Spherical Errors

 5.1 Heteroscedasticity of Known Form
 5.2 Heteroscedasticity of Unknown Form
 5.3 Serially Correlated Errors
 5.4 Seemingly Unrelated Regressions
 5.5 RATS Tips and Tricks
 Example 5.1 Heteroscedastic errors with a known form
 Example 5.2 Heteroscedastic errors with a unknown functional form
 Example 5.3 Linear regression with AR(1) errors
 Example 5.4 Seemingly unrelated regression

6 Vector Autoregressions

 6.1 Flat Prior
 6.2 Antithetic Acceleration
 6.3 An Application: Blanchard-Quah Model
 6.4 Structural VAR's
 6.5 Informative Prior for Univariate Autoregressions
 6.6 VAR with Informative Prior (BVAR)
 6.7 RATS Tips and Tricks
 Example 6.1 Antithetic Acceleration
 Example 6.2 VAR with flat prior
 Example 6.3 Structural VAR: Importance sampling
 Example 6.4 Structural VAR: Random Walk MH
 Example 6.5 Structural VAR: Independence Chain MH
 Example 6.6 Univariate autoregression with prior
 Example 6.7 Univariate Autoregression: Out-of-sample forecast performance
 Example 6.8 Bayesian VAR: Gibbs sampling

7 Cross Section and Panel Data

 7.1 Panel Data
 7.2 Probit and Tobit Models
 7.3 RATS Tips and Tricks
 Example 7.1 Panel data: LSDV
 Example 7.2 Panel data: Fixed Effects
 Example 7.3 Panel data: Random Effects (hierarchical prior)
 Example 7.4 Panel data: Random coefficients model
 Example 7.5 Tobit model
 Example 7.6 Probit model

8 State Space Models

 Example 8.1 State-space model: Independence MH
 Example 8.2 State Space Model: Gibbs sampling
 Example 8.3 State space model: Time-varying coefficients
 


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