Bayesian Model Averaging in the Instrumental Variable Regression Model

Gary Koop, Roberto Leon-Gonzalez, Rodney Strachan

Research output: Working paper › Discussion paper

Abstract

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very flexible and can be easily adapted to analyze any of the different priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.
LanguageEnglish
Place of PublicationGlasgow
PublisherUniversity of Strathclyde
Pages1-48
Number of pages49
Volume11
Publication statusPublished - Jan 2011

Fingerprint

Instrumental variables regression
Regression model
Bayesian model averaging
Uncertainty
Markov chain Monte Carlo
Instrumental variables
Exogeneity
Posterior distribution
Discrepancy
Jump
Model selection
Returns to schooling
Diagnostics
Posterior probability

Keywords

  • bayesian
  • endogeneity
  • simultaneous equations
  • reversible jump Markov chain Monte Carlo

Cite this

Koop, G., Leon-Gonzalez, R., & Strachan, R. (2011). Bayesian Model Averaging in the Instrumental Variable Regression Model. (12 ed.) (pp. 1-48). Glasgow: University of Strathclyde.
Koop, Gary ; Leon-Gonzalez, Roberto ; Strachan, Rodney. / Bayesian Model Averaging in the Instrumental Variable Regression Model. 12. ed. Glasgow : University of Strathclyde, 2011. pp. 1-48
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Koop, G, Leon-Gonzalez, R & Strachan, R 2011 'Bayesian Model Averaging in the Instrumental Variable Regression Model' 12 edn, University of Strathclyde, Glasgow, pp. 1-48.

Bayesian Model Averaging in the Instrumental Variable Regression Model. / Koop, Gary; Leon-Gonzalez, Roberto; Strachan, Rodney.

12. ed. Glasgow : University of Strathclyde, 2011. p. 1-48.

Research output: Working paper › Discussion paper

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T1 - Bayesian Model Averaging in the Instrumental Variable Regression Model

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AU - Leon-Gonzalez, Roberto

AU - Strachan, Rodney

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N2 - This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very flexible and can be easily adapted to analyze any of the different priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

AB - This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very flexible and can be easily adapted to analyze any of the different priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

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Koop G, Leon-Gonzalez R, Strachan R. Bayesian Model Averaging in the Instrumental Variable Regression Model. 12 ed. Glasgow: University of Strathclyde. 2011 Jan, p. 1-48.

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