Bayesian Inference in Cointegrated I (2) Systems: a Generalisation of the Triangular Model

This paper generalises the cointegrating model of Phillips (1991) to allow for I (0) , I (1) and I (2) processes. The model has a simple form that permits a wider range of I (2) processes than are usually considered, including a more flexible form of polynomial cointegration. Further, the specification relaxes restrictions identified by Phillips (1991) on the I (1) and I (2) cointegrating vectors and restrictions on how the stochastic trends enter the system. To date there has been little work on Bayesian I (2) analysis and so this paper attempts to address this gap in the literature. A method of Bayesian inference in potentially I (2) processes is presented with application to Australian money demand using a Jeffreys prior and a shrinkage prior.

Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks

This paper builds a model which has two extensions over a standard VAR. The …rst of these is stochastic search variable selection, which is an automatic model selection device which allows for coefficients in a possibly over-parameterized VAR to be set to zero. The second allows for an unknown number of structual breaks in the VAR parameters. We investigate the in-sample and forecasting performance of our model in an application involving a commonly-used US macro-economic data set. We …nd that, in-sample, these extensions clearly are warranted. In a recursive forecasting exercise, we …nd moderate improvements over a standard VAR, although most of these improvements are due to the use of stochastic search variable selection rather than the inclusion of breaks

Efficient posterior simulation in cointegration models with priors on the cointegration space

A message coming out of the recent Bayesian literature on cointegration is that it is important to elicit a prior on the space spanned by the cointegrating vectors (as opposed to a particular identi…ed choice for these vectors). In this note, we discuss a sensible way of eliciting such a prior. Furthermore, we develop a collapsed Gibbs sampling algorithm to carry out e¢ cient posterior simulation in cointegration models. The computational advantages of our algorithm are most pronounced with our model, since the form of our prior precludes simple posterior simulation using conventional methods (e.g. a Gibbs sampler involves non-standard posterior conditionals). However, the theory we draw upon implies our algorithm will be more e¢ cient even than the posterior simulation methods which are used with identi…ed versions of cointegration models

Bayesian inference in the time varying cointegration model

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved Vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper we develop time varying parameter models which permit coin- tegration. Time-varying parameter VARs (TVP-VARs) typically use state space representations to model the evolution of parameters. In this paper, we show that it is not sensible to use straightforward extensions of TVP-VARs when allowing for cointegration. Instead we develop a speci…cation which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP-VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving a permanent/transitory variance decomposition for inflation

On the evolution of monetary policy

This paper investigates the evolution of monetary policy in the U.S. using a standard set of macroeconomic variables. Many recent papers have addressed the issue of whether the monetary transmission mechanism has changed (e.g. due to the Fed taking a more aggressive stance against in‡ation) or whether apparent changes are simply due to changes in the volatility of exogenous shocks. A subsidiary question is whether any such changes have been gradual or abrupt. In this paper, we shed light on these issues using a mixture innovation model which extends the class of time varying Vector Autoregressive models with stochastic volatility which have been used in the past. The advantage of our extension is that it allows us to estimate whether, where, when and how parameter change is occurring (as opposed to assuming a particular form of parameter change). Our empirical results strongly indicate that the transmission mechanism, the volatility of exogenous shocks and the correlations between exogenous shocks are all changing (albeit at different times and to di¤erent extents) Furthermore, evolution of parameters is gradual

It goes with the territory: Ownership across spatial boundaries.

Previous studies have shown that people are faster to process objects that they own as compared with objects that other people own. Yet object ownership is embedded within a social environment that has distinct and sometimes competing rules for interaction. Here we ask whether ownership of space can act as a filter through which we process what belongs to us. Can a sense of territory modulate the well-established benefits in information processing that owned objects enjoy? In 4 experiments participants categorized their own or another person’s objects that appeared in territories assigned either to themselves or to another. We consistently found that faster processing of self-owned than other-owned objects only emerged for objects appearing in the self-territory, with no such advantage in other territories. We propose that knowing whom spaces belong to may serve to define the space in which affordances resulting from ownership lead to facilitated processing

Bayesian inference in a cointegrating panel data model

This paper develops methods of Bayesian inference in a cointegrating panel data model. This model involves each cross-sectional unit having a vector error correction representation. It is flexible in the sense that different cross-sectional units can have different cointegration ranks and cointegration spaces. Furthermore, the parameters which characterize short-run dynamics and deterministic components are allowed to vary over cross-sectional units. In addition to a noninformative prior, we introduce an informative prior which allows for information about the likely location of the cointegration space and about the degree of similarity in coefficients in different cross-sectional units. A collapsed Gibbs sampling algorithm is developed which allows for efficient posterior inference. Our methods are illustrated using real and artificial data

Evidence on a DSGE Business Cycle model subject to Neutral and Investment-Specific Technology Shocks using Bayesian Model Averaging

The empirical support for a DSGE type of real business cycle model with two technology shocks is evaluated using a Bayesian model averaging procedure that 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 equilibrium restrictions and restrictions on long-run responses to technology shocks apart from having a range of lag structures and deterministic processes. These model features are weighted as posterior probabilites and computed using MCMC and analytical methods. Uncertainty exists as to the most appropriate model for our data, with five models receiving significant support. The model set used has substantial implications for the results obtained. We do find support for a number of features implied by the real business cycle model. Business cycle volatility seems more due to investment specific technology shocks than neutral technology shocks and this result is robust to model specification. These techonolgy schocks appear to account for all stochastic trends in our system after 1984. we provide evidence on the uncertainty bands associated with these results.

Bayesian Forecasting using Stochastic Search Variable Selection in a VAR Subject to Breaks

This paper builds a model which has two extensions over a standard VAR. The first of these is stochastic search variable selection, which is an automatic model selection device which allows for coefficients in a possibly over-parameterized VAR to be set to zero. The second allows for an unknown number of structual breaks in the VAR parameters. We investigate the in-sample and forecasting performance of our model in an application involving a commonly-used US macro-economic data set. We find that, in-sample, these extensions clearly are warranted. In a recursive forecasting exercise, we find moderate improvements over a standard VAR, although most of these improvements are due to the use of stochastic search variable selection rather than the inclusion of breaks. Classification-JEL:

Model Uncertainty and Bayesian Model Averaging in Vector Autoregressive Processes

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.Posterior probability; Grassman manifold; Orthogonal group; Cointegration; Model averaging; Stochastic trend; Impulse response; Vector autoregressive model.