T. Ando (Tomohiro)
http://repub.eur.nl/ppl/36432/
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RePub, Erasmus University RepositoryBayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo
http://repub.eur.nl/pub/37314/
Fri, 21 Sep 2012 00:00:01 GMT<div>A. Zellner</div><div>T. Ando</div><div>N. Basturk</div><div>H.K. van Dijk</div>
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 regressorsâ€™ 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.Instrumental Variables, Errors in Variables, and Simultaneous Equations Models: Applicability and Limitations of Direct Monte Carlo
http://repub.eur.nl/pub/26507/
Tue, 27 Sep 2011 00:00:01 GMT<div>A. Zellner</div><div>T. Ando</div><div>N. Basturk</div><div>L.F. Hoogerheide</div><div>H.K. van Dijk</div>
A Direct Monte Carlo (DMC) approach is introduced for posterior simulation in the Instrumental Variables (IV) model with one possibly endogenous regressor, multiple instruments and Gaussian errors under a flat prior. This DMC method can also be applied in an IV model (with one or multiple instruments) under an informative prior for the endogenous regressor's effect. This DMC approach can not be applied to more complex IV models or Simultaneous Equations Models with multiple endogenous regressors. An Approximate DMC (ADMC) approach is introduced that makes use of the proposed Hybrid Mixture Sampling (HMS) method, which facilitates Metropolis-Hastings (MH) or Importance Sampling from a proper marginal posterior density with highly non-elliptical shapes that tend to infinity for a point of singularity. After one has simulated from the irregularly shaped marginal distri- bution using the HMS method, one easily samples the other parameters from their conditional Student-t and Inverse-Wishart posteriors. An example illustrates the close approximation and high MH acceptance rate. While using a simple candidate distribution such as the Student-t may lead to an infinite variance of Importance Sampling weights. The choice between the IV model and a simple linear model un- der the restriction of exogeneity may be based on predictive likelihoods, for which the efficient simulation of all model parameters may be quite useful. In future work the ADMC approach may be extended to more extensive IV models such as IV with non-Gaussian errors, panel IV, or probit/logit IV.