ABSTRACT: This paper compares within-sample and out-of-sample fit of a DSGE model with rational expectations to a model with adaptive learning. The Galí, Smets and Wouters model is the chosen laboratory using quarterly real-time euro area data vintages, covering 2001Q1-2019Q4. The adaptive learning model obtains better within-sample fit for all vintages used for estimation in the forecast exercise and for the full sample. However, the rational expectations model typically predicts real GDP growth better as well as jointly with inflation. For the marginal inflation forecasts, the same holds for the inner quarters of the forecast horizon, while the adaptive learning model predicts better for the outer quarters.

KEYWORDS: Bayesian inference, CRPS, euro area, forecast comparison/evaluation, log score, real-time data.

JEL CLASSIFICATION NUMBERS: C11, C32, C52, C53, E37.

ABSTRACT: Euro area real-time density forecasts from three DSGE and three BVAR models are compared with six combination methods over the sample 2001Q1-2019Q4. The terms information and observation lag are introduced to distinguish time shifts between data vintages and actuals used to compute model weights and compare the forecast, respectively. Bounds for finite mixture combinations are presented, allowing for benchmarking them given the models. Empirically, combinations with limited weight variation often improve upon the individual models for the output and the joint forecasts with inflation. This reflects over-confident BVAR forecasts before the Great Recession. For inflation, a BVAR model typically performs best.

KEYWORDS: Bayesian inference, euro area, forecast comparisons, model averaging, prediction pools, predictive likelihood.

JEL CLASSIFICATION NUMBERS: C11, C32, C52, C53, E37.

ABSTRACT: This paper provides a detailed description of an extended version of the ECB’s New Area-Wide Model (NAWM) of the euro area (cf. Christoffel, Coenen, and Warne 2008). The extended model — called NAWM II — incorporates a rich financial sector with the threefold aim of (i) accounting for a genuine role of financial frictions in the propagation of economic shocks and policies and for the presence of shocks originating in the financial sector itself, (ii) capturing the prominent role of bank lending rates and the gradual interest-rate pass-through in the transmission of monetary policy in the euro area, and (iii) providing a structural framework useable for assessing the macroeconomic impact of the ECB’s large-scale asset purchases conducted in recent years. In addition, NAWM II includes a number of other extensions of the original model reflecting its practical uses in the policy process over the past ten years.

KEYWORDS: DSGE modelling, Bayesian inference, financial frictions, forecasting, policy analysis, euro area.

JEL CLASSIFICATION NUMBERS: C11, C52, E30, E37, E58.

ABSTRACT: We compare real-time density forecasts for the euro area using three DSGE models. The benchmark is the Smets and Wouters model and its forecasts of real GDP growth and inflation are compared with those from two extensions. The first adds financial frictions and expands the observables to include a measure of the external finance premium. The second allows for the extensive labor-market margin and adds the unemployment rate to the observables. The main question we address is if these extensions improve the density forecasts of real GDP and inflation and their joint forecasts up to an eight-quarter horizon. We find that adding financial frictions leads to a deterioration in the forecasts, with the exception of longer-term inflation forecasts and the period around the Great Recession. The labor market extension improves the medium to longer-term real GDP growth and shorter to medium-term inflation forecasts weakly compared with the benchmark model.

KEYWORDS: Bayesian inference, DSGE models, forecast comparison, inflation, output, predictive likelihood.

JEL CLASSIFICATION NUMBERS: C11, C32, C52, C53, E37.

ABSTRACT: We derive restrictions for Granger noncausality in Markov-switching vector autoregressive models and also show under which conditions a variable does not affect the forecast of the hidden Markov process. Based on Bayesian approach to evaluating the hypotheses, the computational tools for posterior inference include a novel block Metropolis-Hastings sampling algorithm for the estimation of the restricted models. We analyze a system of monthly US data on money and income. The test results in MS-VARs contradict those in linear VARs: the money aggregate M1 is useful for forecasting income and for predicting the next period's state.

KEYWORDS: Bayesian hypothesis testing, Markov-switching models, mixture models, posterior odds ratio, block Metropolis-Hastings sampling.

JEL CLASSIFICATION NUMBERS: C11, C12, C32, C53, E32.

ABSTRACT: In a Bayesian setting, the predictive likelihood is of particular relevance when the objective is to rank models in a forecast comparison exercise. We discuss how the predictive likelihood can be estimated, by means of marginalization, for any subset of the observable variables in linear Gaussian state-space models and propose to utilize a missing observations consistent Kalman filter for that purpose. Based on this convenient and simple approach, we analyze euro area data and compare the density forecast performance of a DSGE model to a DSGE-VAR, a large BVAR, and a multivariate random walk model over the forecast sample 1999Q1-2011Q4. While the BVAR generally provides superior density forecasts, its performance deteriorates substantially with the onset of the Great Recession. This is particularly notable for longer-horizon real GDP forecasts, where the DSGE and DSGE-VAR models with stronger economic foundations perform better. In fact, for longer horizons the ranking of models changes over the forecast sample when the focus is on a subset of variables comprising real GDP growth, GDP deflator inflation, and the nominal interest rate.

KEYWORDS: Bayesian inference, density forecasting, Kalman filter, missing data, Monte Carlo integration, predictive likelihood.

JEL CLASSIFICATION NUMBERS: C11, C32, C52, C53, E37.

ABSTRACT: This paper employs stochastic simulations of the New Area-Wide Model—a micro-founded open-economy model developed at the ECB—to investigate the consequences of the zero lower bound on nominal interest rates for the evolution of risks to price stability in the euro area during the recent financial crisis. Using a formal measure of the balance of risks, which is derived from policy-makers’ preferences about inflation outcomes, we first show that downside risks to price stability were considerably greater than upside risks during the first half of 2009, followed by a gradual rebalancing of these risks until mid-2011 and a renewed deterioration thereafter. We find that the lower bound has induced a noticeable downward bias in the risk balance throughout our evaluation period because of the implied amplification of deflation risks. We then illustrate that, with nominal interest rates close to zero, forward guidance in the form of a time-based conditional commitment to keep interest rates low for longer can be successful in mitigating downside risks to price stability. However, we find that the provision of time-based forward guidance may give rise to upside risks over the medium term if extended too far into the future. By contrast, time-based forward guidance complemented with a threshold condition concerning tolerable future inflation can provide insurance against the materialisation of such upside risks.

KEYWORDS: Monetary policy, deflation, zero lower bound, forward guidance, DSGE modelling, euro area.

JEL CLASSIFICATION NUMBERS: E31, E37, E52, E58.

ABSTRACT: This paper analyses the real-time forecasting performance of the New Keynesian DSGE model of Galí, Smets and Wouters estimated on euro area data. It investigates to what extent forecasts of inflation, GDP growth and unemployment by professional forecasters improve the forecasting performance. We consider two approaches for conditioning on such information. Under the "noise" approach, the mean professional forecasts are assumed to be noisy indicators of the rational expectations forecasts implied by the DSGE model. Under the "news" approach, it is assumed that the forecasts reveal the presence of expected future structural shocks in line with those estimated over the past. The forecasts of the DSGE model are compared with those from a Bayesian VAR model and a random walk.

KEYWORDS: Bayesian methods, DSGE model, real-time database, Survey of Professional Forecasters, macroeconomic forecasting, estimated New Keynesian model, euro are.

JEL CLASSIFICATION NUMBERS: E24, E31, E32.

ABSTRACT: This paper shows how to compute the h-step-ahead predictive likelihood for any subset of the observed variables in parametric discrete time series models estimated with Bayesian methods. The subset of variables may vary across forecast horizons and the problem thereby covers marginal and joint predictive likelihoods for a fixed subset as special cases. The basic idea is to utilize well-known techniques for handling missing data when computing the likelihood function, such as a missing observations consistent Kalman filter for linear Gaussian models, but it also extends to nonlinear, nonnormal state-space models. The predictive likelihood can thereafter be calculated via Monte Carlo integration using draws from the posterior distribution. As an empirical illustration, we use euro area data and compare the forecasting performance of the New Area-Wide Model, a small-open-economy DSGE model, to DSGE-VARs, and to reduced-form linear Gaussian models.

KEYWORDS: Bayesian inference, forecasting, Kalman filter, missing data, Monte Carlo integration.

JEL CLASSIFICATION NUMBERS: C11, C32, C52, C53, E37.

ABSTRACT: In this paper we review the methodology of forecasting with log-linearised DSGE models using Bayesian methods. We focus on the estimation of their predictive distributions, with special attention being paid to the mean and the covariance matrix of h-step ahead forecasts. In the empirical analysis, we examine the forecasting performance of the New Area-Wide Model (NAWM) that has been designed for use in the macroeconomic projections at the European Central Bank. The forecast sample covers the period following the introduction of the euro and the out-of-sample performance of the NAWM is compared to nonstructural benchmarks, such as Bayesian vector autoregressions (BVARs). Overall, the empirical evidence indicates that the NAWM compares quite well with the reduced-form models and the results are therefore in line with previous studies. Yet there is scope for improving the NAWM's forecasting performance. For example, the model is not able to explain the moderation in wage growth over the forecast evaluation period and, therefore, it tends to overestimate nominal wages. As a consequence, both the multivariate point and density forecasts using the log determinant and the log predictive score, respectively, suggest that a large BVAR can outperform the NAWM.

KEYWORDS: Bayesian Inference, DSGE Models, Euro Area, Forecasting, Open-Economy Macroeconomics, Vector Autorgression.

JEL CLASSIFICATION NUMBERS: C11, C32, E32, E37.

ABSTRACT: In this paper, we outline a version of the New Area-Wide Model (NAWM) of the euro area designed for use in the (Broad) Macroeconomic Projection Exercises regularly undertaken by ECB/Eurosystem staff. We present estimation results for the NAWM that are obtained by employing Bayesian inference methods and document the properties of the estimated model by reporting impluse-response functions and forecast-error-variance decompositions, by inspecting the model-based sample moments, and by examining the model's forecasting performance relative to a number of benchmarks, inlcuing a Bayesian VAR. We finally consider several applications to illustrate the potential contributions the NAWM can make to forecasting and policy analysis.

KEYWORDS: DSGE Modelling, Open-Economy Macroeconomics, Bayesian Inference, Forecasting, Policy Analysis, Euro Area.

JEL CLASSIFICATION NUMBERS: C11, C32, E32, E37.

ABSTRACT: The paper considers a Bayesian approach to the cointegrated VAR model with a uniform prior on the cointegration space. Building on earlier work by Villani (2005), where the posterior probability of the cointegration rank can be calculated conditional on the lag order, the current paper also makes it possible to compute the joint posterior probability of these two parameters as well as the marginal posterior probabilities under the assumption of a known upper bound for the lag order. When the marginal likelihood identity is used for calculating these probabilities, a point estimator of the cointegration space and the weights is required. Analytical expressions are therefore derived of the mode of the joint posterior of these parameter matrices. The procedure is applied to a money demand system for the euro area and the results are compared to those obtained from a maximum likelihood analysis.

KEYWORDS: Bayesian inference, cointegration, lag order, money demand, vector autoregression.

JEL CLASSIFICATION NUMBERS: C11, C15, C32, E41.

ABSTRACT: Structural VARs have been extensively used in empirical macroeconomics during the last two decades, particularly in analyses of monetary policy. Existing Bayesian procedures for structural VARs are at best confined to a severely limited handling of cointegration restrictions. This paper extends the Bayesian analysis of structural VARs to cover cointegrated processes with an arbitrary number of cointegrating relations and general linear restrictions on the cointegration space. A reference prior distribution with an optional small open economy effect is proposed and a Gibbs sampler is derived for a straightforward evaluation of the posterior distribution. The methods are used to analyze the effects of monetary policy in Sweden.

KEYWORDS: Structural, Vector Autoregression, Monetary Policy, Impulse Responses, Counterfactual Experiments.

JEL CLASSIFICATION NUMBERS: C11, C32, E52.

ABSTRACT: This paper re-examines two data issues concerning euro area money demand: aggregation of national data and measurement of the own rate. The main purpose is to study if euro area money demand is subject to parameter non-constancies using formal tests rather than informal diagnostics. As a complement to inference based on asymptotics we perform small-scale bootstraps. The empirical evidence supports the existence of a stable long-run relationship between money and output and that the cointegration space is constant over time. However, the interest rate semi-elasticities are imprecisely estimated. Conditional on the cointegration relations the remaining parameters of the system appear to be constant. We also examine the relevance of stock prices for money demand and find that our measure does not not matter for the long-run relations, but may be useful in forecasting exercises. Finally, the conclusions are robust for the aggregation method and the choice of sample.

KEYWORDS: Aggregation, Bootstrap, Money Demand, Own Rate of Money, Parameter Constancy.

JEL CLASSIFICATION NUMBERS: C22, C32, E41.

ABSTRACT: This paper presents estimates of the effects of monetary policy shocks on the Swedish economy. A theoretical model of an open economy is used to identify a structural VAR model. The empirical results from the identified VAR model are compared with two less structural approaches for identification of monetary policy shocks. The first assumes that shocks can be measured as deviations from a forward looking interest rate rule, estimated using Sveriges Riksbank's (Swedish central bank) own forecasts. The second approach focuses on the effects of "narrative" monetary policy shocks as given by devaluations of the Swedish currency. We find that plausible theoretical restrictions often result in price puzzles. Although conventional results obtain with certain theoretical restrictions imposed on the VAR, another way to achieve this is by using external information about large policy shocks. Thus, we find that the effects of some devaluations are consistent with the conventional wisdom about the effects of monetary policy shock.

KEYWORDS: Common trends, devaluations, identification, inflation, monetary policy shocks, open economy, structural vector autoregression.

JEL CLASSIFICATION NUMBERS: C32, E31, E52.

ABSTRACT: This paper analyses three Granger noncausality hypotheses within a conditionally Gaussian MS-VAR model. Noncausality in mean is based on Granger's original concept for linear predictors by defining noncausality from the 1-step ahead forecast error variance for the conditional expectation. Noncausality in mean-variance concerns the conditional forecast error variance, while noncausality in distribution refers to the conditional distribution of the forecast errors. Necessary and sufficient parametric conditions for noncausality are presented for all hypotheses. As an illustration, the hypotheses are tested using monthly postwar U.S. data on money and income. We find that money is not Granger causal in mean for income, but Granger causal in mean-variance, i.e. there is unique information in money for predicting the next period regime and the regime affects the uncertainty about the income forecast.

KEYWORDS: Granger causality, Markov process, regime switching, vector autoregression.

JEL CLASSIFICATION NUMBERS: C32.

ABSTRACT: In this paper we study 2-state Markov switching VAR models of monthly unemployment and inflation for three countries: Sweden, United Kingdom, and the United States. The primary purpose is to examine if periods of low inflation are associated with high or low unemployment volatility. We find that MS-VAR models seem to provide a better description of the data than single regime VARs and need fewer lags to account for serial correlation. To interpret the regimes the empirical results are compared with the predictions from a version of Rogoff's (1985) model of monetary policy. We find that both the theoretical and the empirical results suggest that an increase in central bank "conservativeness" can be associated with either a higher or a lower variance in unemployment. In the U.S. case we find that the variance of unemployment is lower in the low inflation regime than in the high inflation regime, while the Swedish and the U.K. cases suggest that unemployment variability is higher in the low inflation regime.

KEYWORDS: Cointegration, monetary policy, Phillips curve, regime switching.

JEL CLASSIFICATION NUMBERS: C32, E31, E52.

ABSTRACT: We report evidence that the relation between the financial sector share, private savings and growth in the United States 1948-1996 is characterized by several regime shifts. The finding is based on vector autoregressions on quarterly data that allow for Markov switching regimes. The evidence may be interpreted as support for a hypothesis that the relation between financial development and growth evolves in a stepwise fashion. Theoretical models where financial market extensions entail fixed costs imply such stepwise patterns. The estimated variable relations are roughly consistent with the patterns to be expected from such models, although our data do not admit definite conclusions. The timing of the shifts coincide with changes in regulation and in the financial market structure.

KEYWORDS: Financial markets extensions, growth, Markov switching, saving, vector autoregression.

JEL CLASSIFICATION NUMBERS: C32, E44, O16, O51.

ABSTRACT: Common trends models provide a useful tool for studying growth and business cycle phenomena in a joint framework. In this paper we study the problem of how to estimate and analyse a common stochastic trends model for an n dimensional time series which is cointegrated of order (1,1) with r<n cointegration vectors. Identification of k=n-r permanent (trend) and r transitory innovations is discussed in terms of impulse responses and variance decompositions. Finally, we derive analytical expressions of the asymptotic distributions for estimates of these functions, thereby making formal hypothesis testing and inference possible within this framework.

KEYWORDS: Cointegration, common trends, impulse response function, permanent and transitory shocks, variance decomposition.

JEL CLASSIFICATION NUMBERS: C32, C51.