4Non-technical summary 5 1. Introduction 7 2. The model 10
Inference 14
Model selection 185. Dynamic analysis 19
Recursive unconditional forecasts 195.2 Impulse responses 20
Conditional forecasts 236. The transmission of shocks in G-7 countries 24
Conclusions 29 References 31European Central Bank Working Paper Series 34
AbstractThis paper describes a methodology to estimate the coefficients, to test specification hypotheses and to conduct policy exercises in multi-country VAR models with cross unit interdependencies, unit specific dynamics and time variations in the coefficients. The framework of analysis is Bayesian: a prior flexibly reduces the dimensionality of the model and puts structure on the time variations; MCMC methods are used to obtain posterior distributions; and marginal likelihoods to check the fit of various specifications. Impulse responses and conditional forecasts are obtained with the output of MCMC routine. The transmission of certain shocks across G7 countries is analyzed.
Non-technical SummaryWhen dealing with multi-country data, the empirical literature has taken a number of short cuts.For example, it is typical to assume that in the dynamic specification slope coefficients are common across (subsets of the) units; that there are no interdependencies across units or that they can be summarized with a simple time and unit invariant index; that the structural relationships are stable over time; that asymptotics in the time series dimension apply; or a combination of all of these.None of these restrictions is appealing: short time series are the result, in part, of new definitions and the adaptation of international standards to data collection in developing countries; unit specific relationships may reflect difference in national regulations or policies; interdependencies results from world markets integration and time instabilities from evolving macroeconomic structures. This paper shows how to conduct inference in multi-country VAR models featuring short time series and, potentially, unit specific dynamics, lagged interdependences and structural time variations. Since these last three features make the number of coefficients of the model large, no classical estimation method is feasible. We take a flexible Bayesian viewpoint and weakly restrict the coefficient vector to depend on a low dimensional vector of time varying factors. These factors capture, for example, variations in the coefficients which are common across units and variables (a "common" effect); variations which are specific to the unit (a "fixed" effect) , variations which are specific to a variable (a "variable" effect), etc. Factors relating to lags and time periods, or capturing the extent of lagged interdependencies across units, can also be included. We complete the specifications using a hierarchical structure which allows for exchangeability in the fixed effects, and time variations in the law of motion of the factors and in the variance of their innovations.The factor structure we employ effectively transfo...