R.W. Strachan (Rodney)
http://repub.eur.nl/ppl/1183/
List of Publicationsenhttp://repub.eur.nl/logo.jpg
http://repub.eur.nl/
RePub, Erasmus University RepositoryEvidence on features of a dsge business cycle model from bayesian model averaging
http://repub.eur.nl/pub/38911/
Fri, 01 Feb 2013 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
The empirical support for features of a Dynamic Stochastic General Equilibrium model with two technology shocks is evaluated using Bayesian model averaging over vector autoregressions. The model features include equilibria, restrictions on long-run responses, a structural break of unknown date, and a range of lags and deterministic processes. We find support for a number of features implied by the economic model, and the evidence suggests a break in the entire model structure around 1984, after which technology shocks appear to account for all stochastic trends. Business cycle volatility seems more due to investment-specific technology shocks than neutral technology shocks. Evidence on Features of a DSGE Business Cycle Model from Bayesian Model Averaging
http://repub.eur.nl/pub/32101/
Tue, 20 Mar 2012 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
The empirical support for features of a Dynamic Stochastic General Equilibrium model with two technology shocks is valuated using Bayesian model averaging over vector autoregressions. The model features include equilibria, restrictions on long-run responses, a structural break of unknown date and a range of lags and deterministic processes. We find support for a number of features implied by the economic model and the evidence suggests a break in the entire model structure around 1984 after which technology shocks appear to account for all stochastic trends. Business cycle volatility seems more due to investment specific technology shocks than neutral technology shocks.
Divergent Priors and well Behaved Bayes Factors
http://repub.eur.nl/pub/22334/
Sat, 01 Jan 2011 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
Divergent priors are improper when defined on unbounded supports. Bartlett's paradox has been taken to imply that using improper priors results in ill-defined Bayes factors, preventing model comparison by posterior probabilities. However many improper priors have attractive properties that econometricians may wish to access and at the same time conduct model comparison. We present a method of computing well defined Bayes factors with divergent priors by setting rules on the rate of diffusion of prior certainty. The method is exact; no approximations are used. As a further result, we demonstrate that exceptions to Bartlett's paradox exist. That is, we show it is possible to construct improper priors that result in well defined Bayes factors. One important improper prior, the Shrinkage prior due to Stein (1956), is one such example. This example highlights pathologies with the resulting Bayes factors in such cases, and a simple solution is presented to this problem. A simple Monte Carlo experiment demonstrates the applicability of the approach developed in this paper.Evidence on a Real Business Cycle Model with Neutral and Investment-Specific Technology Shocks using Bayesian Model Averaging
http://repub.eur.nl/pub/19511/
Mon, 17 May 2010 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
The empirical support for a real business cycle model with two technology shocks is evaluated using a Bayesian model averaging procedure. This procedure makes use of a finite mixture of many models within the class of vector autoregressive (VAR) processes. The linear VAR model is extended to permit cointegration, a range of deterministic processes, equilibrium restrictions and restrictions on long-run responses to technology shocks. We find support for a number of the features implied by the real business cycle model. For example, restricting long run responses to identify technology shocks has reasonable support and important implications for the short run responses to these shocks. Further, there is evidence that savings and investment ratios form stable relationships, but technology shocks do not account for all stochastic trends in our system. There is uncertainty as to the most appropriate model for our data, with thirteen models receiving similar support, and the model or model set used has signficant implications for the results obtained.Bayesian Averaging over Many Dynamic Model Structures with Evidence on the Great Ratios and Liquidity Trap Risk
http://repub.eur.nl/pub/14049/
Thu, 02 Oct 2008 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
A Bayesian model averaging procedure is presented that makes use of a finite mixture of many model structures within the class of vector autoregressive (VAR) processes. It is applied to two empirical issues. First, stability of the Great Ratios in U.S. macro-economic time series is investigated, together with the effect of permanent shocks on business cycles. Second, the linear VAR model is extended to include a smooth transition function in a (monetary) equation and stochastic volatility in the disturbances. The risk of a liquidity trap in the U.S.A. and Japan is evaluated. Although this risk found to be reasonably high, we find only mild evidence that the monetary policy transmission mechanism is different and that central banks consider the expected cost of a liquidity trap in policy setting. Posterior probabilities of different models are evaluated using Markov chain Monte Carlo techniques.Bayesian model averaging in vector autoregressive processes with an investigation of stability of the US great ratios and risk of a liquidity trap in the USA, UK and Japan
http://repub.eur.nl/pub/9303/
Sun, 25 Mar 2007 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
A Bayesian model averaging procedure is presented within the class of
vector autoregressive (VAR) processes and applied to two empirical issues.
First, stability of the "Great Ratios" in U.S. macro-economic time series is
investigated, together with the presence and e¤ects of permanent shocks.
Measures on manifolds are employed in order to elicit uniform priors on
subspaces defned by particular structural features of linear VARs. Second,
the VAR model is extended to include a smooth transition function in a
(monetary) equation and stochastic volatility in the disturbances. The risk
of a liquidity trap in the USA, UK and Japan is evaluated, together with the
expected cost of a policy adjustment of central banks. Posterior probabilities
of different models are evaluated using Markov chain Monte Carlo techniques.Model uncertainty and Bayesian model averaging in vector autoregressive processes
http://repub.eur.nl/pub/7446/
Fri, 03 Feb 2006 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
Economic forecasts and policy decisions are often informed by empirical analysis based on econometric models. However, inference based upon a single model, when several viable models exist, limits its usefulness. Taking account of model uncertainty, a Bayesian model averaging procedure is presented which allows for unconditional inference within the class of vector autoregressive (VAR) processes. Several features of VAR process are investigated. Measures on manifolds are employed in order to elicit uniform priors on subspaces defined by particular structural features of VARs. The features considered are the number and form of the equilibrium economic relations and deterministic processes. Posterior probabilities of these features are used in a model averaging approach for forecasting and impulse response analysis. The methods are applied to investigate stability of the “Great Ratios” in U.S. consumption, investment and income, and the presence and effects of permanent shocks in these series. The results obtained indicate the feasibility of the proposed method.Weakly informative priors and well behaved Bayes factors
http://repub.eur.nl/pub/7027/
Mon, 07 Nov 2005 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
Bartlett's paradox has been taken to imply that using improper priors results in Bayes factors that are not well defined, preventing model comparison in this case. We use well understood principles underlying what is already common practice, to demonstrate that this implication is not true for some improper priors, such as the Shrinkage prior due to Stein (1956). While this result would appear to expand the class of priors that may be used for computing posterior odds, we warn against the straightforward use of these priors. Highlighting the role of the prior measure in the behaviour of Bayes factors, we demonstrate pathologies in the prior measures for these improper priors. Using this discussion, we then propose a method of employing such priors by setting rules on the rate of diffusion of prior certainty.Bayesian approaches to cointegratrion
http://repub.eur.nl/pub/1915/
Fri, 11 Mar 2005 00:00:01 GMT<div>G. Koop</div><div>R.W. Strachan</div><div>H.K. van Dijk</div><div>M. Villani</div>
The purpose of this paper is to survey and critically assess the Bayesian cointegration literature. In one sense, Bayesian analysis of cointegration is straightforward. The researcher can combine the likelihood function with a prior and do Bayesian inference with the resulting posterior. However, interesting and empirically important issues of global and local identification (and, as a result, prior elicitation) arise from the fact that the matrix of long run parameters is potentially of reduced rank. As we shall see, these identification problems can cause serious problems for Bayesian inference. For instance, a common noninformative prior can lead to a posterior distribution which is improper (i.e. is not a valid p.d.f. since it does not integrate to one) thus precluding valid statistical inference. This issue was brought forward by Kleibergen and Van Dijk (1994, 1998). The development of the Bayesian cointegration literature reflects an increasing awareness of these issues and this paper is organized to reflect this development. In particular, we begin by discussing early work, based on VAR or Vector Moving Average (VMA) representations which ignored these issues. We then proceed to a discussion of work based on the ECM representation, beginning with a simple specification using the linear normalization and normal priors before moving onto the recent literature which develops methods for sensible treatment of the identification issues.Valuing structure, model uncertainty and model averaging in vector autoregressive processes
http://repub.eur.nl/pub/1288/
Fri, 21 May 2004 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
Economic policy decisions are often informed by empirical analysis based on accurate econometric modeling. However, a decision-maker is usually only interested in good estimates of outcomes, while an analyst must also be interested in estimating the model. Accurate inference on structural features of a model improves policy analysis as it improves estimation, inference and forecast efficiency. In this paper a Bayesian inferential procedure is presented which allows for unconditional inference on structural features of vector autoregressive (VAR) processes. We employ measures on manifolds in order to elicit uniform priors on subspaces defined by particular structural features of VARs. The features considered are cointegration, exogeneity, deterministic processes and overidentification. Posterior probabilities of these features are used in a model averaging approach for forecasting and impulse response analysis. The methods are applied to three empirical economic issues: stability of Australian money demand; relative weights of permanent and transitory shocks in a US real business cycle model; and possible evidence on an inflationary oil price shock and a liquidity trap in a UK macroeconomic model. The results obtained illustrate the feasibility of the proposed methods.Improper priors with well defined Bayes Factors
http://repub.eur.nl/pub/1277/
Wed, 19 May 2004 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
A sensible Bayesian model selection or comparison strategy implies selecting the model with the highest posterior probability. While some improper priors have attractive properties such as, e.g., low frequentist risk, it is generally claimed that Bartlett's paradox implies that using improper priors for the parameters in alternative models results in Bayes factors that are not well defined, thus preventing model comparison in this case. In this paper we demonstrate this latter result is not generally true and expand the class of priors that may be used for computing posterior odds to include some improper priors. Our approach is to give a new representation of the issue of undefined Bayes factors and, from this representation, develop classes of improper priors from which well defined Bayes factors may be derived. This approach involves either augmenting or normalising the prior measure for the parameters. One of these classes of priors includes the well known and commonly employed shrinkage prior. Estimation of Bayes factors is demonstrated for a reduced rank model.The value of structural information in the VAR model
http://repub.eur.nl/pub/1717/
Tue, 17 Jun 2003 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
Economic policy decisions are often informed by empirical economic analysis. While the decision-maker is usually only interested in good estimates of outcomes, the analyst is interested in estimating the model. Accurate inference on the structural features of a model, such as cointegration, can improve policy analysis as it can improve estimation, inference and forecast efficiency from using that model. However, using a model does not guarantee good estimates of the object of interest and, as it assigns a probability of one to a model and zero to near-by models, takes extreme zero-one account of the "weight of evidence" in the data and the resarcher's uncertainty. By using the uncertainty associated with the structural features in a model set, one obtains policy analysis that is not conditional on the structure of the model and can improve efficiency if the features are appropriately weighted. In this paper tools are presented to allow for unconditional inference on the vector autoregressive (VAR) model. In particular, we employ measures on manifolds to elicit priors on subspaces defined by particular features of the VAR model. The features considered are cointegration, exogeneity, deterministic processes and overidentification. Two applications -- money demand in Australia, and a macroeconomic model of the UK proposed by Garratt, Lee, Persaran, and Shin (2002) are used to illustrate the feasibility of the proposed methods.Bayesian model selection for a sharp null and a diffuse alternative with econometric applications
http://repub.eur.nl/pub/1707/
Wed, 26 Mar 2003 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
In this paper a potential solution is given to the conflict in Bayesian inference between the desire to employ diffuse priors to represent ignorance and the desire to report proper posterior probabilities for alternative models. Using the concept of Stiefel manifolds, diffuse priors are specified on dimension and direction of subspaces of parameter spaces within the context of a linear regression model and a cointegration model. The approach is illustrated using a CAPM and a term structure of interest rates model.Bayesian model selection with an uninformative prior
http://repub.eur.nl/pub/11201/
Wed, 01 Jan 2003 00:00:01 GMT<div>R.W. Strachan</div><div>H.K. van Dijk</div>
Bayesian model selection with posterior probabilities and no subjective prior information is generally not possible because of the Bayes factors being ill-defined. Using careful consideration of the parameter of interest in cointegration analysis and a re-specification of the triangular model of Phillips (Econometrica, Vol. 59, pp. 283-306, 1991), this paper presents an approach that allows for Bayesian comparison of models of cointegration with 'ignorance' priors. Using the concept of Stiefel and Grassman manifolds, diffuse priors are specified on the dimension and direction of the cointegrating space. The approach is illustrated using a simple term structure of the interest rates model.