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Priors, Posteriors and Bayes Factors for a Bayesian Analysis of Cointegration
 Journal of Econometrics
, 1999
"... Cointegration occurs when the long run multiplier of a vector autoregressive model exhibits rank reduction. Priors and posteriors of the parameters of the cointegration model are therefore proportional to priors and posteriors of the long run multiplier given that it has reduced rank. Rank reduction ..."
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Cointegration occurs when the long run multiplier of a vector autoregressive model exhibits rank reduction. Priors and posteriors of the parameters of the cointegration model are therefore proportional to priors and posteriors of the long run multiplier given that it has reduced rank. Rank reduction of the long run multiplier is modelled using a decomposition resulting from its singular value decomposition. It specifies the long run multiplier matrix as the sum of a matrix that equals the product of the adjustment parameters and the cointegrating vectors, i.e. the cointegration specification, and a matrix that models the deviation from cointegration. Priors and posteriors for the parameters of the cointegration model are obtained by restricting the latter matrix to zero in the prior and posterior of the unrestricted long run multiplier. The special decomposition of the long run multiplier results in unique posterior densities. This theory leads to a complete Bayesian framework for cointegration analysis. It includes prior specification, simulation schemes for obtaining posterior distributions and determination of the cointegration rank via Bayes factors. We illustrate the analysis with several simulated series, the UK data
DeTerMinanTS oF eConoMiC groWTH WiLL DaTa TeLL? 1
, 2008
"... In 2008 all ECB publications feature a motif taken from the €10 banknote. ..."
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Cited by 18 (2 self)
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In 2008 all ECB publications feature a motif taken from the €10 banknote.
Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys Prior
 Journal of Econometrics
, 1998
"... Posterior distributions in limited information analysis of the simultaneous equations model using the ..."
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Cited by 12 (2 self)
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Posterior distributions in limited information analysis of the simultaneous equations model using the
Priors, posterior odds and Lagrange multiplier statistics in Bayesian analyses of cointegration
, 1997
"... Using the standard linear model as a base, a unified theory of Bayesian Analyses of Cointegration Models is constructed. This is achieved by defining (natural conjugate) priors in the linear model and using the implied priors for the cointegration model. Using these priors, posterior results for the ..."
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Cited by 4 (1 self)
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Using the standard linear model as a base, a unified theory of Bayesian Analyses of Cointegration Models is constructed. This is achieved by defining (natural conjugate) priors in the linear model and using the implied priors for the cointegration model. Using these priors, posterior results for the cointegration model are obtained using a MetropolisHasting sampler. To compare the cointegration models mutually and with the vector autoregressive model under stationarity, we use two strategies. The first strategy uses the Bayesian interpretation of a Lagrange Multiplier statistic. The second strategy compares the models using prior and posterior odds ratios. The latter enables us to compute prior and posterior distributions over the cointegration rank and shows close resemblance with the posterior information criterium from Phillips and Ploberger (1996). To show the applicability of the derived theory, the constructed procedures are applied to data from Johansen and Juselius (1990) and a few simulated data sets.
Adaptive Polar Sampling with an application to a Bayes measure of ValueatRisk
, 1999
"... AdaptivePolar Sampling #APS# is proposed as a Markovchain Monte Carlo method for Bayesian analysis of models with illbehaved posterior distributions. In order to sample e#ciently from such a distribution, a locationscale transformation and a transformation to polar coordinates are used. After t ..."
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Cited by 4 (2 self)
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AdaptivePolar Sampling #APS# is proposed as a Markovchain Monte Carlo method for Bayesian analysis of models with illbehaved posterior distributions. In order to sample e#ciently from such a distribution, a locationscale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a MetropolisHastings algorithm is applied to sample directions and, conditionally on these, distances are generated byinverting the CDF. A sequential procedure is applied to update the location and scale.
A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments
, 2000
"... We compare the finite sample performance of a number of Bayesian and classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider recent Bayesian approaches developed by Chao and Phillips (1998, CP), Geweke (1996), Kleibergen a ..."
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We compare the finite sample performance of a number of Bayesian and classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider recent Bayesian approaches developed by Chao and Phillips (1998, CP), Geweke (1996), Kleibergen and van Dijk (1998, KVD), and Zellner (1998). Amongst the sampling theory methods, OLS, 2SLS, LIML, Fuller's modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist, Imbens and Krueger (1999) and Blomquist and Dahlberg (1999) are also considered. Since the posterior densities and their conditionals in CP and KVD are nonstandard, we propose a "Gibbs within MetropolisHastings" algorithm, which only requires the availability of the conditional densities from the candidate generating density. Our results show that in cases with very weak instruments, there is no single estimator that is superior to others in all cases. When endogeneity is weak, Zellner's MELO does the best. When the
On Bayesian Structural Inference in a Simultaneous Equation Model
 in Econometrics and the philosophy of economics, ed. by B.P. Stigum
, 2002
"... Econometric issues that are considered fundamental in the development of Bayesian structural inference within a Simultaneous Equation Model are surveyed. ..."
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Cited by 3 (2 self)
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Econometric issues that are considered fundamental in the development of Bayesian structural inference within a Simultaneous Equation Model are surveyed.
NORMALIZATION IN ECONOMETRICS
"... □ The issue of normalization arises whenever two different values for a vector of unknown parameters imply the identical economic model. A normalization implies not just a rule for selecting which among equivalent points to call the maximum likelihood estimate (MLE), but also governs the topography ..."
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□ The issue of normalization arises whenever two different values for a vector of unknown parameters imply the identical economic model. A normalization implies not just a rule for selecting which among equivalent points to call the maximum likelihood estimate (MLE), but also governs the topography of the set of points that go into a smallsample confidence interval associated with that MLE. A poor normalization can lead to multimodal distributions, disjoint confidence intervals, and very misleading characterizations of the true statistical uncertainty. This paper introduces an identification principle as a framework upon which a normalization should be imposed, according to which the boundaries of the allowable parameter space should correspond to loci along which the model is locally unidentified. We illustrate these issues with examples taken from mixture models, structural vector autoregressions, and cointegration models.
ECONOMETRICS FOR POLICY ANALYSIS: PROGRESS AND REGRESS ECONOMETRICS FOR POLICY ANALYSIS: PROGRESS AND REGRESS
"... I don’t want to rehash that. (II) Time I spent last year visiting central banks and interviewing people there about what econometric models they use and how they use them. (III) Recent technical developments that have converted theoretical advantages of Bayesian over classical approaches to inferenc ..."
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Cited by 1 (1 self)
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I don’t want to rehash that. (II) Time I spent last year visiting central banks and interviewing people there about what econometric models they use and how they use them. (III) Recent technical developments that have converted theoretical advantages of Bayesian over classical approaches to inference into practical reality in some applied areas. Associated applied work and methodological commentary emerging in the literature. (IV) Haavelmo’s 1944 paper/monograph “The Probability Approach in Econometrics”, and some related previous literature. We are going to begin by discussing (IV), using it as a kind of table of contents for aspects of (II) and (III).