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

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

doi:10.1080/07474938.2013.807094

Cited by 26 publications

(32 citation statements)

References 21 publications

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“…We illustrate this issue in Figure 1. More details are given in the Supplementary material, in Hoogerheide et al (2007b) and Zellner et al (2014).…”

Section: Posteriors Of An Instrumental Variables (Iv) Modelmentioning

confidence: 99%

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

2017

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Abstract:Weak empirical evidence near and at the boundary of the parameter region is a predominant feature in econometric models. Examples are macroeconometric models with weak information on the number of stable relations, microeconometric models measuring connectivity between variables with weak instruments, financial econometric models like the random walk with weak evidence on the efficient market hypothesis and factor models for investment policies with weak information on the number of unobserved factors. A Bayesian analysis is presented of the common issue in these models, which refers to the topic of a reduced rank. Reduced rank is a boundary issue and its effect on the shape of the posteriors of the equation system parameters with a reduced rank is explored systematically. These shapes refer to ridges due to weak identification, fat tails and multimodality. Discussing several alternative routes to construct regularization priors, we show that flat posterior surfaces are integrable even though the marginal posterior tends to infinity if the parameters tend to the values corresponding to local non-identification. We introduce a lasso type shrinkage prior combined with * This paper should not be reported as representing the views of Norges Bank. The views expressed are those of the authors and do not necessarily reflect those of Norges Bank. The authors are indebted to Lukasz Gatarek and Richard Kleijn for expert research assistance. We also thank the editor, two anonymous referees and Mattias Villani for their comments on an earlier version of this paper.† Corresponding author: hkvandijk@ese.eur.nl.1 Baştürk, Hoogerheide, Van Dijk/Bayesian Analysis of Boundary and Near-Boundary Evidence 2 orthogonal normalization which restricts the range of the parameters in a plausible way. This can be combined with other shrinkage, smoothness and data based priors using training samples or dummy observations. Using such classes of priors, it is shown how conditional probabilities of evidence near and at the boundary can be evaluated effectively. These results allow for Bayesian inference using mixtures of posteriors under the boundary state and the near-boundary state. The approach is applied to the estimation of education-income effect in all states of the US economy. The empirical results indicate that there exist substantial differences of this effect between almost all states. This may affect important national and state-wise policies on required length of education. The use of the proposed approach may, in general, lead to more accurate forecasting and decision analysis in other problems in economics, finance and marketing.

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“…We illustrate this issue in Figure 1. More details are given in the Supplementary material, in Hoogerheide et al (2007b) and Zellner et al (2014).…”

Section: Posteriors Of An Instrumental Variables (Iv) Modelmentioning

confidence: 99%

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

2017

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“…This irregularity can be mitigated by the use of a Jeffrey's prior see Hoogerheide et al (2007a). In this case, the posterior is a proper density, but sampling methods such as the Gibbs sampler are not applicable, see Zellner et al (2014). The applicability of the MitISEM algorithm to the IV model and the speed gains compared with the griddy-Gibbs sampler (Ritter and Tanner, 1992) are shown in Baştürk et al (2016).…”

Section: Bayesian Inference Of the Instrumental Variables Modelmentioning

confidence: 99%

“…In such cases it is not trivial to perform inference on the joint posterior distribution of parameters using basic Markov Chain Monte Carlo (MCMC) methods, which may be inefficient and inaccurate due to the non-standard conditional densities. The difficulty of selecting an appropriate candidate density for algorithms where such a candidate needs to be defined is discussed in De Pooter et al (2008), Ardia et al (2012) and Zellner et al (2014) among several others. Efficient and accurate inference is, however, important in the context of measuring economic forecast uncertainty and economic policy effects.…”

Section: Introductionmentioning

confidence: 99%

Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

et al. 2016

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. (2012), provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. We present and discuss four canonical econometric models using a Graphics Processing Unit and a multi-core Central Processing Unit version of the MitISEM algorithm. The results show that the parallelization of the MitISEM algorithm on Graphics Processing Units and multi-core Central Processing Units is straightforward and fast to program using MATLAB. Moreover the speed performance of the Graphics Processing Unit version is much higher than the Central Processing Unit one. Terms of use: Documents in

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“…the standard deviation of the IS weights divided by their mean, as in , who use the candidate from MitISEM for importance sampling or the independence chain MH method. Zellner, Ando, Baştürk, Hoogerheide, and Van Dijk (2014), who use the MitISEM candidate for rejection sampling, propose an alternative criterion for the convergence of the MitISEM algorithm. They use the unconditional acceptance probability, which is a more natural and intuitive convergence criterion in this case of rejection sampling.…”

Section: Mitisem: the Basic Algorithmmentioning

confidence: 99%

“…For an exactly identified model with a single instrument, the posterior density resulting from this model is improper. For more details on the derivation we refer to Zellner et al (2014). We specify a Jeffreys prior which leads to a proper posterior density, see e.g.…”

Section: Approximating Posterior Densities: An IV Modelmentioning

confidence: 99%

The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference

et al. 2015

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This paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization) which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel -typically a posterior density kernel -using an adaptive mixture of Student-t densities as approximating density. In the first stage a mixture of Student-t densities is fitted to the target using an expectation maximization (EM) algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings (MH) method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bioinformatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of education's effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, 'sequential MitISEM', which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler candidate, as well as the Gibbs sampler. The MitISEM approach is also used for Bayesian model comparison using predictive likelihoods.

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

Cited by 26 publications

References 21 publications

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

Bayesian Analysis of Boundary and Near-Boundary Evidence in Econometric Models with Reduced Rank

Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference

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