Bayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo

Arnold Zellner, Tomohiro Ando, Nalan Baştürk, Lennart Hoogerheide, Herman K. van Dijk

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We discuss Bayesian inferential procedures within the family of instrumental variables regression models and focus on two issues: existence conditions for posterior moments of the parameters of interest under a flat prior and the potential of Direct Monte Carlo (DMC) approaches for efficient evaluation of such possibly highly non-elliptical posteriors. We show that, for the general case of m endogenous variables under a flat prior, posterior moments of order r exist for the coefficients reflecting the endogenous regressors' effect on the dependent variable, if the number of instruments is greater than m +r, even though there is an issue of local non-identification that causes non-elliptical shapes of the posterior. This stresses the need for efficient Monte Carlo integration methods. We introduce an extension of DMC that incorporates an acceptance-rejection sampling step within DMC. This Acceptance-Rejection within Direct Monte Carlo (ARDMC) method has the attractive property that the generated random drawings are independent, which greatly helps the fast convergence of simulation results, and which facilitates the evaluation of the numerical accuracy. The speed of ARDMC can be easily further improved by making use of parallelized computation using multiple core machines or computer clusters. We note that ARDMC is an analogue to the well-known "Metropolis-Hastings within Gibbs" sampling in the sense that one 'more difficult' step is used within an 'easier' simulation method. We compare the ARDMC approach with the Gibbs sampler using simulated data and two empirical data sets, involving the settler mortality instrument of Acemoglu et al. (2001) and father's education's instrument used by Hoogerheide et al. (2012a). Even without making use of parallelized computation, an efficiency gain is observed both under strong and weak instruments, where the gain can be enormous in the latter case.

Original languageEnglish
Pages (from-to)3-35
Number of pages33
JournalEconometric Reviews
Volume33
Issue number1-4
DOIs
Publication statusPublished - 2014 Feb

Fingerprint

Bayesian analysis
Acceptance
Instrumental variables
Evaluation
Instrumental variables regression
Efficiency gains
Endogenous regressors
Monte Carlo method
Gibbs sampler
Monte Carlo integration
Acceptance sampling
Simulation methods
Weak instruments
Gibbs sampling
Endogenous variables
Mortality
Coefficients
Education
Empirical data
Regression model

Keywords

  • Acceptance-Rejection
  • Bayesian inference
  • Direct Monte Carlo
  • Instrumental variables
  • Numerical standard errors

ASJC Scopus subject areas

  • Economics and Econometrics

Cite this

Bayesian Analysis of Instrumental Variable Models : Acceptance-Rejection within Direct Monte Carlo. / Zellner, Arnold; Ando, Tomohiro; Baştürk, Nalan; Hoogerheide, Lennart; van Dijk, Herman K.

In: Econometric Reviews, Vol. 33, No. 1-4, 02.2014, p. 3-35.

Research output: Contribution to journalArticle

Zellner, Arnold ; Ando, Tomohiro ; Baştürk, Nalan ; Hoogerheide, Lennart ; van Dijk, Herman K. / Bayesian Analysis of Instrumental Variable Models : Acceptance-Rejection within Direct Monte Carlo. In: Econometric Reviews. 2014 ; Vol. 33, No. 1-4. pp. 3-35.
@article{156e58d016e744a696bd8feb0a7e4672,
title = "Bayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo",
abstract = "We discuss Bayesian inferential procedures within the family of instrumental variables regression models and focus on two issues: existence conditions for posterior moments of the parameters of interest under a flat prior and the potential of Direct Monte Carlo (DMC) approaches for efficient evaluation of such possibly highly non-elliptical posteriors. We show that, for the general case of m endogenous variables under a flat prior, posterior moments of order r exist for the coefficients reflecting the endogenous regressors' effect on the dependent variable, if the number of instruments is greater than m +r, even though there is an issue of local non-identification that causes non-elliptical shapes of the posterior. This stresses the need for efficient Monte Carlo integration methods. We introduce an extension of DMC that incorporates an acceptance-rejection sampling step within DMC. This Acceptance-Rejection within Direct Monte Carlo (ARDMC) method has the attractive property that the generated random drawings are independent, which greatly helps the fast convergence of simulation results, and which facilitates the evaluation of the numerical accuracy. The speed of ARDMC can be easily further improved by making use of parallelized computation using multiple core machines or computer clusters. We note that ARDMC is an analogue to the well-known {"}Metropolis-Hastings within Gibbs{"} sampling in the sense that one 'more difficult' step is used within an 'easier' simulation method. We compare the ARDMC approach with the Gibbs sampler using simulated data and two empirical data sets, involving the settler mortality instrument of Acemoglu et al. (2001) and father's education's instrument used by Hoogerheide et al. (2012a). Even without making use of parallelized computation, an efficiency gain is observed both under strong and weak instruments, where the gain can be enormous in the latter case.",
keywords = "Acceptance-Rejection, Bayesian inference, Direct Monte Carlo, Instrumental variables, Numerical standard errors",
author = "Arnold Zellner and Tomohiro Ando and Nalan Başt{\"u}rk and Lennart Hoogerheide and {van Dijk}, {Herman K.}",
year = "2014",
month = "2",
doi = "10.1080/07474938.2013.807094",
language = "English",
volume = "33",
pages = "3--35",
journal = "Econometric Reviews",
issn = "0747-4938",
publisher = "Taylor and Francis Ltd.",
number = "1-4",

}

TY - JOUR

T1 - Bayesian Analysis of Instrumental Variable Models

T2 - Acceptance-Rejection within Direct Monte Carlo

AU - Zellner, Arnold

AU - Ando, Tomohiro

AU - Baştürk, Nalan

AU - Hoogerheide, Lennart

AU - van Dijk, Herman K.

PY - 2014/2

Y1 - 2014/2

N2 - We discuss Bayesian inferential procedures within the family of instrumental variables regression models and focus on two issues: existence conditions for posterior moments of the parameters of interest under a flat prior and the potential of Direct Monte Carlo (DMC) approaches for efficient evaluation of such possibly highly non-elliptical posteriors. We show that, for the general case of m endogenous variables under a flat prior, posterior moments of order r exist for the coefficients reflecting the endogenous regressors' effect on the dependent variable, if the number of instruments is greater than m +r, even though there is an issue of local non-identification that causes non-elliptical shapes of the posterior. This stresses the need for efficient Monte Carlo integration methods. We introduce an extension of DMC that incorporates an acceptance-rejection sampling step within DMC. This Acceptance-Rejection within Direct Monte Carlo (ARDMC) method has the attractive property that the generated random drawings are independent, which greatly helps the fast convergence of simulation results, and which facilitates the evaluation of the numerical accuracy. The speed of ARDMC can be easily further improved by making use of parallelized computation using multiple core machines or computer clusters. We note that ARDMC is an analogue to the well-known "Metropolis-Hastings within Gibbs" sampling in the sense that one 'more difficult' step is used within an 'easier' simulation method. We compare the ARDMC approach with the Gibbs sampler using simulated data and two empirical data sets, involving the settler mortality instrument of Acemoglu et al. (2001) and father's education's instrument used by Hoogerheide et al. (2012a). Even without making use of parallelized computation, an efficiency gain is observed both under strong and weak instruments, where the gain can be enormous in the latter case.

AB - We discuss Bayesian inferential procedures within the family of instrumental variables regression models and focus on two issues: existence conditions for posterior moments of the parameters of interest under a flat prior and the potential of Direct Monte Carlo (DMC) approaches for efficient evaluation of such possibly highly non-elliptical posteriors. We show that, for the general case of m endogenous variables under a flat prior, posterior moments of order r exist for the coefficients reflecting the endogenous regressors' effect on the dependent variable, if the number of instruments is greater than m +r, even though there is an issue of local non-identification that causes non-elliptical shapes of the posterior. This stresses the need for efficient Monte Carlo integration methods. We introduce an extension of DMC that incorporates an acceptance-rejection sampling step within DMC. This Acceptance-Rejection within Direct Monte Carlo (ARDMC) method has the attractive property that the generated random drawings are independent, which greatly helps the fast convergence of simulation results, and which facilitates the evaluation of the numerical accuracy. The speed of ARDMC can be easily further improved by making use of parallelized computation using multiple core machines or computer clusters. We note that ARDMC is an analogue to the well-known "Metropolis-Hastings within Gibbs" sampling in the sense that one 'more difficult' step is used within an 'easier' simulation method. We compare the ARDMC approach with the Gibbs sampler using simulated data and two empirical data sets, involving the settler mortality instrument of Acemoglu et al. (2001) and father's education's instrument used by Hoogerheide et al. (2012a). Even without making use of parallelized computation, an efficiency gain is observed both under strong and weak instruments, where the gain can be enormous in the latter case.

KW - Acceptance-Rejection

KW - Bayesian inference

KW - Direct Monte Carlo

KW - Instrumental variables

KW - Numerical standard errors

UR - http://www.scopus.com/inward/record.url?scp=84885357285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885357285&partnerID=8YFLogxK

U2 - 10.1080/07474938.2013.807094

DO - 10.1080/07474938.2013.807094

M3 - Article

AN - SCOPUS:84885357285

VL - 33

SP - 3

EP - 35

JO - Econometric Reviews

JF - Econometric Reviews

SN - 0747-4938

IS - 1-4

ER -