Multivariate Forecasting with BVARs and DSGE Models

• Date: 01 December 2016
• Author: Tim Oliver Berg
• Published date: 01 December 2016
• DOI: http://doi.org/10.1002/for.2406

Journal of Forecasting,J. Forecast. 35, 718–740 (2016)

Published online 10 August 2016 in Wiley Online Library (wileyonlinelibrary.com)DOI: 10.1002/for.2406

Multivariate Forecasting with BVARs and DSGE Models

Tim Oliver Berg

Ifo Inst itut e, Munich, Germany

ABSTRACT

In this paper I assess the ability of Bayesian vector autoregressions (BVARs) and dynamic stochastic general equilib-

rium (DSGE) models of different size to forecast comovements of major macroeconomic series in the euro area. Both

approaches are compared to unrestricted VARsin terms of multivariate point and density forecast accuracy measures

as well as event probabilities. The evidence suggests that BVARs and DSGE models produce accurate multivariate

forecasts even for larger datasets. I also detect that BVARs are well calibrated for most events, while DSGE models

are poorly calibrated for some. In sum, I conclude that both are useful tools to achieve parameter dimension reduction.

Copyright © 2016 John Wiley & Sons, Ltd.

KEY WORDS BVARs; DSGE models; multivariate forecasting; large dataset; simulation methods; euro area

INTRODUCTION

Vector autoregressions (VARs) are useful and thus frequently used tools to forecast macroeconomic time series, in

particular when the interest is not only in the outcome of a single variable but also the comovement of several major

series. However, unrestricted VARs that are estimated by ordinary least squares (OLS) often suffer from their dense

parametrization, leading to unstable parameter estimates and hence inaccurate multivariate forecasts. The literature

proposes alternative ways to achieve parameter dimension reduction and improve multivariate forecast accuracy. For

instance, Ba´

nbura et al. (2010) suggest that VARs combined with Bayesian shrinkage (BVARs) can handle large

datasets and produce relatively accurate forecasts. The empirical restrictions they impose on the VAR parameters are

motivated by the integrating order of the underlying time series, shrinking the overparametrized VAR either towards

a parsimonious random walk (for non-stationary data) or a white noise process (for stationary data), while the degree

of shrinkage could be selected as in Carriero et al. (2015) by maximizing the marginal likelihood or estimated in a

hierarchical fashion as suggested by Giannone et al. (2015).

An alternative way to reduce the parameters to be estimated is to set up a dynamic stochastic general equilibrium

(DSGE) model which builds on explicit micro foundations and optimizing economic agents. Under certain condi-

tions1the state-space representation of a linearized DSGE model can be rewritten as a VAR and estimating such

models hence amounts to shrinking a high-dimensional vector of VAR parameters towards a lower-dimensional vec-

tor of structural parameters that can be motivated by economic theory. While DSGE models are particularly useful

for structural analyses and policy simulations, they are also widely used for forecasting (see, for example, Edge and

Gürkaynak, 2010; Christoffel et al., 2011; Del Negro and Schorfheide, 2013; Smets et al., 2014; Wolters, 2015).

So far, the literature on BVARs and DSGE models has predominantly focused on point and density forecasts for

individual series but neglected that, in particular, policymakers are often more interested in the comovement of major

variables such as GDP growth and inflation.2The contribution of this paper is to extend the scope of the evalua-

tion of BVARs and DSGE models to multivariate forecasts. In particular, I assess the ability of BVARs and DSGE

models of different size to forecast comovements of major macroeconomic series in the euro area. Both approaches

are compared to unrestricted VARs in terms of multivariate forecast accuracy measures. The forecast experiment

allows me to explore to what extent multivariate forecast accuracy is affected by the way restrictions are imposed

on model parameters (empirical, theoretical or no restrictions) and the number of series included in estimation

(from three up to 38).

One would expect that BVARs and DSGE models outperform unrestricted VARs in terms of multivariate forecast

accuracy, in particular when the size of the systems is relatively large. Yet it is not clear whether DSGE models

benefit from an explicit theoretical foundation of their restrictions compared to the purely empirical restrictions of

the BVARs. On the one hand, the large number of cross-equation restrictions that emerge from micro foundations

could help to produce a more realistic covariance structure between variables and hence improvemultivariate forecast

accuracy. On the other hand, if these restrictions are too rigid, forecasts could be biased in some direction, inflating

Correspondence to: Tim Oliver Berg, Ifo Institute, Munich, Germany. E-mail: berg@ifo.de

1If these conditions are not met, the state-space representation has a VARMAform, where the moving average term is not invertible, and a VAR

may be a poor approximation (see Franchi and Vidotto, 2013).

2Exceptions are Herbst and Schorfheide (2012) for the USA and Adolfson et al. (2007b) as well as Christoffel et al. (2011) for the euro area.

Copyright © 2016 John Wiley & Sons, Ltd

Multivariate Forecasting with BVARs and DSGE Models 719

forecast errors. For instance, DSGE models impose a common trend on real variables, an assumption that may not be

supported in certain samples.

I compare the multivariate forecast accuracy of BVARs to that of three DSGE models, which include progres-

sively larger sets of variables and hence increase in complexity; first, the small-scale closed economy model of An

and Schorfheide (2007) that is estimated on three variables: GDP, the GDP deflator and a short-term interest rate;

second, the medium-scale closed economy model of Smets and Wouters (2007) including, in addition, consumption,

investment, employment and wages (sevenvariables); and third, the medium-scale open-economy model of Adolfson

et al. (2007a), which is fitted also on exports, imports, the consumption deflator, the investment deflator, an exchange

rate, world GDP, the world GDP deflator and a world interest rate (15 variables). These models are frequently used

at central banks and policy institutions to conduct simulations and produce forecasts for major macroeconomic series

and are thus a natural competitor for BVARs.

Moreover, I add large and extra-large BVARs with, respectively, 23 and 38 variables, including series that could

be helpful in forecasting major macroeconomic variables, but are often not included as observables in DSGE mod-

els, such as commodity prices, survey data, a long-term interest rate or share prices. Several authors found that

such BVARs are useful for forecasting (see, for example, Ba´

nbura et al., 2010; Koop, 2013; Giannone et al., 2015;

Berg and Henzel, 2015; Pirschel and Wolters, 2014; Carriero et al., 2015).

The forecast models are compared in terms of multivariate point and density forecast accuracy measures as well

as event probabilities for different selections of euro area variables during the evaluation period from 1999:Q1 to

2011:Q4. Excluding the Great Recession (and the euro crisis) and shortening the evaluation period to 1999:Q1 to

2007:Q4 does not affect the model ranking.

Point forecasts are evaluated according to the trace and log determinant statistic of the scaled mean squared error

(MSE) matrix. It turns out that the multivariate point forecast accuracy of the unrestricted OLS-VARs declines with

the number of series included in estimation, whereas the accuracy of the BVARs does not. In fact, the large and extra-

large BVARs deliver the smallest forecast errors of all models for most variable selections. Therefore, I conclude

that BVARs can deal with the dimensionality problem and exploit the information in high-dimensional datasets. The

results are less clear cut for the DSGE models. While the small and medium-scale closed economy models show a

mixed performance, the open-economy model of Adolfson et al. (2007a) dominates the OLS-VARs and performs

similarly to the BVAR of same size. Thus I conclude that the underperformance of this model compared to the

large and extra-large BVAR is not related to its structure but the fact that the largest BVARs include series that are

particularly helpful in forecasting macroeconomic variables but are non-modeled in the open-economy DSGE model.

Density forecasts are evaluated in terms of log predictivescores, which also reflect the uncertainty that is associated

with forecasting macroeconomic outcomes. As policymakers nowadays closely monitor forecast uncertainty, the

MSE might not be the relevant loss function. While the satisfactory performance of the large and extra-large BVAR

is confirmed when the focus shifts from point to density forecasts, I also obtain that the predictive scores for all three

DSGE models are higher than their relative multivariatepoint forecast accuracy suggests. I suspect that the theoretical

restrictions embedded in these models are helpful in producing a plausible covariance structure between the forecasts.

In fact, the open-economy DSGE model of Adolfson et al. (2007a) outperforms all competitors in terms of predictive

scores for most variable selections.

Finally, I provide additional evidence on the ability of BVARs and DSGE models to forecast comovements of

major macroeconomic variables in the euro area by conducting an event study. Following Herbst and Schorfheide

(2012) I compare model-implied event probabilities to actual frequencies of events. If model probabilities and average

frequencies coincide, density forecasts are called well calibrated. In particular, I consider events that are highly rel-

evant for policymakers, as, for instance, GDP growth, inflation and the short-term interest rate, being above (below)

their respective long-run targets. The event study allows me to assess whether the models are able to forecast the

directional comovements of these variables, which provides some insights that may not be reflected in MSE or pre-

dictive scores. It turns out that the large and extra-large BVARs perform well in terms of multivariate event forecast

accuracy for most events. The DSGE models, on the other hand, are poorly calibrated for some events. One possible

reason for this deficiency is that the common trend assumption of the DSGE models is too restrictive.

DATASET

The dataset contains 38 quarterly euro area macroeconomic series for the period 1984:Q1 to 2011:Q4 and covers

seven categories labeled, respectively, national accounts, price index, international, employment, survey, monetary

aggregate and financial data. In most cases the series are from the 12th update of the Area-Wide Model (AWM)

database, which is maintained by the European Central Bank (ECB) and made available by the Euro Area Business

Cycle Network.3The AWM database is the preferred source for researchers and policymakers alike, interested in

3See also Fagan et al. (2005). The vintage I use is as of September 2012.

Copyright © 2016 John Wiley & Sons, Ltd J. Forecast. 35, 718–740 (2016)