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

Tinbergen Institute Discussion Paper 12-098/III

35 Pages Posted: 27 Sep 2012

See all articles by Arnold Zellner

Arnold Zellner

University of Chicago, Booth School of Business (Deceased)

Tomohiro Ando

University of Melbourne - Melbourne Business School

Nalan Basturk

Maastricht University - Department of Quantitative Economics

Lennart F. Hoogerheide

VU University Amsterdam

H. K. van Dijk

Tinbergen Institute; Econometric Institute

Date Written: September 21, 2012

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 onelliptical 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: Instrumental variables, Bayesian inference, Direct Monte Carlo, Acceptance-Rejection, numerical standard errors

JEL Classification: C11, C15, C26, C36

Suggested Citation

Zellner, Arnold and Ando, Tomohiro and Basturk, Nalan and Hoogerheide, Lennart F. and van Dijk, Herman K., Bayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo (September 21, 2012). Tinbergen Institute Discussion Paper 12-098/III, Available at SSRN: https://ssrn.com/abstract=2152847 or http://dx.doi.org/10.2139/ssrn.2152847

Arnold Zellner (Contact Author)

University of Chicago, Booth School of Business (Deceased) ( email )

United States

Tomohiro Ando

University of Melbourne - Melbourne Business School ( email )

200 Leicester Street
Carlton, Victoria 3053 3186
Australia

Nalan Basturk

Maastricht University - Department of Quantitative Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

Lennart F. Hoogerheide

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Herman K. Van Dijk

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Burg. Oudlaan 50
Amsterdam/Rotterdam, 1082 MS
Netherlands
+31104088955 (Phone)
+31104089031 (Fax)

HOME PAGE: http://people.few.eur.nl/hkvandijk/

Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 4088955 (Phone)
+31 10 4527746 (Fax)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
70
Abstract Views
653
rank
419,729
PlumX Metrics