Suppose one were interested in forecasting output growth and inflation across a number of different countries; how would one go about it? What additional variables might help in such forecasting (the oil price comes to mind), and should one also consider adding financial variables such as equity returns and the long term interest rate? Should they be treated separately (two isolated equations) or together, say in a VAR? Should one consider only domestic or also foreign variables? If foreign variables are included, should they be endogenised as well? How important are cointegrating relationships, either across variables within a country or even across countries (PPP relationships come to mind)? And how should one address the ever present problem of structural breaks which may happen multiple times in any one or several of the relations in the forecasting model under consideration?
In this paper we employ the Global Vector Autoregressive (GVAR) model, originally introduced in Pesaran, Schuermann and Weiner, PSW, (2004), and further developed in Dees, de Mauro, Pesaran and Smith, DdPS, (2007), for answering some of these questions. We do so with the recognition that macroeconomic policy analysis and risk management require taking account of the increasing interdependencies that exist across markets and countries. Indeed there are major differences in cross country correlation of output growths, inflation, and interest rates. For instance, equity returns and long term interest rates are much more closely correlated across countries as compared to output growth and inflation. This invariably means that many different channels of transmissions must be taken into account. The GVAR approach directly models the interlinkages using trade weighted observable macroeconomic aggregates and financial variables. It allows for interdependence at a variety of levels in a transparent manner that can be empirically evaluated, including long run relationships consistent with the theory and short run relationships consistent with the data.
Nonetheless, with a modeling task of this size, it would be surprising if a single model would be universally preferred over any other. Recognising that a broader set of models might be needed to tackle the problem, we turn to the model averaging literature to arrive at better overall forecasts; Bayesian model averaging is a prominent example; see Timmermann (2006) for a recent survey on forecast combination. But simply averaging across models does not address the structural break problem. Indeed as we show, the standard Bayesian model averaging approach implicitly assumes that the underlying data generating process and the models remain stable.
We solve this problem by using recent developments in the forecast pooling literature that propose to estimate the model over different sample windows (Pesaran and Timmermann, 2007). In this way parameter estimates are automatically allowed to vary over time. This strategy is especially useful when not only the nature but also the number of breaks is unknown. Finally we combine the two averaging approaches wacross models and across sampling windows wto arrive at an average average (AveAve) forecast which turns out to outperform forecasts from any single model or estimation window.
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Forecasting Economic and Financial Variables with Global VARs
