Bayesian Methods in Econometrics

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Bayesian Methods in Econometrics

• James D. Hamilton
• University of California, San Diego

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Bayesian Econometrics

• A. Introduction

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• Classical statistician says
• No, no, no! ? is the true value. It either
  equals 5 or it doesnt. There is no probability
  statement about ?.
• What is true is that if we use this
  procedure to construct an interval in thousands
  of different samples, in 95 of those samples,
  our interval will contain the true ?.

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• Suppose we ask the classical statistician
• Do you know the true ??
• No.
• Choose between these options. Option A I
  give you 5 now. Option B I give you 10 if the
  true ? is in the interval between 2.0 and 3.5.
• Ill take the 5, thank you.

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• How about these? Option A I give you 5 now.
  Option B I give you 10 if the true ? is
  between -5.0 and 10.7.
• OK, Ill take option B.

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• Option A I generate a uniform number between
  0 and 1. If the number is less than ?, I give
  you 5. Option B I give you 5 if the true ? is
  in the interval (2.0,4.0). The value of ? is
  0.2
• Option B.
• How about if ? 0.8?
• Option A.

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• One way to find this posterior distribution is
  by brute force (integrating and dividing).
• An easier way to come up with the identical
  answer is to factor the joint density into a
  component that depends on ? and a component that
  does not depend on ?

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I. Bayesian econometrics

• Introduction
• Bayesian inference in the univariate regression
  model

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• So what priors would we believe?
• Fama stock prices are random walk
• Hall consumption is random walk
• Mankiw marginal tax rates are random walk

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I. Bayesian econometrics

• Introduction
• Bayesian inference in the univariate regression
  model
• Numerical Bayesian methods
• 1. Importance sampling

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I. Bayesian econometrics

• Introduction
• Bayesian inference in the univariate regression
  model
• Some general issues in Bayesian inference
• Numerical Bayesian methods
• 1. Importance sampling
• 2. The Gibbs sampler

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I. Bayesian econometrics

• Introduction
• Bayesian inference in the univariate regression
  model
• Numerical Bayesian methods
• 1. Importance sampling
• 2. The Gibbs sampler
• 3. Metropolis-Hastings algorithm

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