Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections

Abstract

In 2014 all ECB publications feature a motif taken from the €20 banknote.NOTE: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily refl ect those of the ECB. AbstractThis paper describes an algorithm to compute the distribution of conditional forecasts, i.e. projections of a set of variables of interest on future paths of some other variables, in dynamic systems. The algorithm is based on Kalman filtering methods and is computationally viable for large models that can be cast in a linear state space representation. We build large vector autoregressions (VARs) and a large dynamic factor model (DFM) for a quarterly data set of 26 euro area macroeconomic and financial indicators. Both approaches deliver similar forecasts and scenario assessments. In addition, conditional forecasts shed light on the stability of the dynamic relationships in the euro area during the recent episodes of financial turmoil and indicate that only a small number of sources drive the bulk of the fluctuations in the euro area economy. JEL Classification: C11, C13, C33, C53Keywords: Vector Autoregression, Bayesian Shrinkage, Dynamic Factor Model, Conditional Forecast, Large Cross-Sections.ECB Working Paper 1733, September 2014 1 Non-technical summaryVector autoregressions (VARs) are very flexible and general models and provide a reliable empirical benchmark for alternative econometric representations such as dynamic stochastic general equilibrium (DSGE) models, which are more grounded in theory but, at the same time, impose more structure on the data.Recent literature has shown that VARs are viable tools also for large sets of data. In this paper we construct a large VAR for the euro area and we apply it to unconditional forecasting as well as for conditional forecasts and scenarios. These, along with structural analysis (assessing the effects of structural shocks), have been the main applications of VARs. Whereas large VARs have been used for unconditional forecasting and structural analysis, limited attention has been devoted as yet to conditional forecasting. This is because popular algorithms for deriving conditional forecasts have been computationally challenging for large data sets. We overcome this problem by computing the conditional forecasts recursively using Kalman filtering techniques.Conditional forecasts and, in particular, scenarios are projections of a set of variables of interest on future paths of some other variables. This is in contrast to unconditional forecasts, where no knowledge of the future path of any variables is assumed. The prior knowledge, albeit imperfect, of the future evolution of some economic variables may carry information for the outlook of other variables. For example, future fiscal packages would affect the future evolution of economic activity and, thus, might provide important off-model information. Moreover, it may be of interest to assess the impact of specific future events on a ...

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