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 identified choice for these vectors). In previous work, such priors have been found to greatly complicate computation. In this paper, we develop algorithms to carry out efficient posterior simulation in cointegration models. In particular, we develop a collapsed Gibbs sampling algorithm which can be used with just-identifed models and demonstrate that it has very large computational advantages relative to existing approaches. For over-identifed models, we develop a parameter-augmented Gibbs sampling algorithm and demonstrate that it also has attractive computational properties.
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.
This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very ‡exible and can be easily adapted to analyze any of the di¤erent priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.
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AbstractThe existing weight of evidence suggests that financial structure (the classification of a financial system as bank-based versus market-based) is irrelevant for economic growth. This contradicts the common belief that the institutional structure of a financial system matters. We re-examine this issue using a novel dataset covering 69 countries over 1989-2011 in a Bayesian framework. Our results are conformable to the belief -a market-based system is relevant -with sizable economic effects for the high-income but not for the middle-and-low-income countries. Our findings provide a counterexample to the weight of evidence. We also identify a regime shift in 2008.
Factor models are used in a wide range of areas. Two issues with Bayesian versions of these models are a lack of invariance to ordering of the variables and computational inefficiency. This paper develops invariant and efficient Bayesian methods for estimating static factor models. This approach leads to inference on the number of factors that does not depend upon the ordering of the variables, and we provide arguments to explain this invariance. Beginning from identified parameters which have nonstandard forms, we use parameter expansions to obtain a specification with standard conditional posteriors. We show significant gains in computational efficiency. Identifying restrictions that are commonly employed result in interpretable factors or loadings and, using our approach, these can be imposed ex-post. This allows us to investigate several alternative identifying schemes without the need to respecify and resample the model. We apply our methods to a simple example using a macroeconomic dataset.
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 cointegration. 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 in ‡ation.
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