Evaluating Point and Density Forecasts of DSGE Models

This paper investigates the accuracy of forecasts from four dynamic stochastic general equilibrium (DSGE) models for inflation, output growth and the federal funds rate using a real‐time dataset synchronized with the Fed's Greenbook projections. Conditioning the model forecasts on the Greenbook nowcasts leads to forecasts that are as accurate as the Greenbook projections for output growth and the federal funds rate. Only for inflation are the model forecasts dominated by the Greenbook projections. A comparison with forecasts from Bayesian vector autoregressions shows that the economic structure of the DSGE models which is useful for the interpretation of forecasts does not lower the accuracy of forecasts. Combining forecasts of several DSGE models increases precision in comparison to individual model forecasts. Comparing density forecasts with the actual distribution of observations shows that DSGE models overestimate uncertainty around point forecasts. Copyright © 2013 John Wiley & Sons, Ltd.     

Does Forecast Combination Improve Norges Bank Inflation Forecasts?*

We develop a system that provides model‐based forecasts for inflation in Norway. We recursively evaluate quasi out‐of‐sample forecasts from a large suite of models from 1999 to 2009. The performance of the models are then used to derive quasi real time weights that are used to combine the forecasts. Our results indicate that a combination forecast improves upon the point forecasts from individual models. Furthermore, a combination forecast outperforms Norges Bank's own point forecast for inflation. The beneficial results are obtained using a trimmed weighted average. Some degree of trimming is required for the combination forecasts to outperform the judgmental forecasts from the policymaker.     

EVALUATING MACROECONOMIC FORECASTS: A CONCISE REVIEW OF SOME RECENT DEVELOPMENTS

Macroeconomic forecasts are frequently produced, widely published, intensively discussed, and comprehensively used. The formal evaluation of such forecasts has a long research history. Recently, a new angle to the evaluation of forecasts has been addressed, and in this review we analyze some recent developments from that perspective. The literature on forecast evaluation predominantly assumes that macroeconomic forecasts are generated from econometric models. In practice, however, most macroeconomic forecasts, such as those from the IMF, World Bank, OECD, Federal Reserve Board, Federal Open Market Committee (FOMC), and the ECB, are typically based on econometric model forecasts jointly with human intuition. This seemingly inevitable combination renders most of these forecasts biased and, as such, their evaluation becomes nonstandard. In this review, we consider the evaluation of two forecasts in which: (i) the two forecasts are generated from two distinct econometric models; (ii) one forecast is generated from an econometric model and the other is obtained as a combination of a model and intuition; and (iii) the two forecasts are generated from two distinct (but unknown) combinations of different models and intuition. It is shown that alternative tools are needed to compare and evaluate the forecasts in each of these three situations. These alternative techniques are illustrated by comparing the forecasts from the (econometric) Staff of the Federal Reserve Board and the FOMC on inflation, unemployment, and real GDP growth. It is shown that the FOMC does not forecast significantly better than the Staff, and that the intuition of the FOMC does not add significantly in forecasting the actual values of the economic fundamentals. This would seem to belie the purported expertise of the FOMC.     

Predicting economic contractions and expansions with the aid of professional forecasts

Traditional econometric models of economic contractions typically perform poorly in forecasting exercises. This criticism is also frequently levelled at professional forecast probabilities of contractions. This paper addresses the problem of incorporating the entire distribution of professional forecasts into an econometric model for forecasting contractions and expansions. A new augmented probit approach is proposed, involving the transformation of the distribution of professional forecasts into a ‘professional forecast’ prior for the economic data underlying the probit model. Since the object of interest is the relationship between the distribution of professional forecasts and the probit model’s economic-data dependent parameters, the solution avoids criticisms levelled at the accuracy of professional forecast based point estimates of contractions. An application to US real GDP data shows that the model yields significant forecast improvements relative to alternative approaches.     

Forecast Encompassing and Parameter Estimation*

A desirable property of a forecast is that it encompasses competing predictions, in the sense that the accuracy of the preferred forecast cannot be improved through linear combination with a rival prediction. In this paper, we investigate the impact of the uncertainty associated with estimating model parameters in‐sample on the encompassing properties of out‐of‐sample forecasts. Specifically, using examples of non‐nested econometric models, we show that forecasts from the true (but estimated) data generating process (DGP) do not encompass forecasts from competing mis‐specified models in general, particularly when the number of in‐sample observations is small. Following this result, we also examine the scope for achieving gains in accuracy by combining the forecasts from the DGP and mis‐specified models.     

Forecasting with Global Vector Autoregressive Models: a Bayesian Approach

This paper develops a Bayesian variant of global vector autoregressive (B‐GVAR) models to forecast an international set of macroeconomic and financial variables. We propose a set of hierarchical priors and compare the predictive performance of B‐GVAR models in terms of point and density forecasts for one‐quarter‐ahead and four‐quarter‐ahead forecast horizons. We find that forecasts can be improved by employing a global framework and hierarchical priors which induce country‐specific degrees of shrinkage on the coefficients of the GVAR model. Forecasts from various B‐GVAR specifications tend to outperform forecasts from a naive univariate model, a global model without shrinkage on the parameters and country‐specific vector autoregressions. Copyright © 2016 John Wiley & Sons, Ltd.     

Marginalized Predictive Likelihood Comparisons of Linear Gaussian State‐Space Models with Applications to DSGE,DSGE‐VAR,and VAR Models

The predictive likelihood is useful for ranking models in forecast comparison exercises using Bayesian inference. We discuss how it can be estimated, by means of marzginalization, for any subset of the observables in linear Gaussian state‐space models. We compare macroeconomic density forecasts for the euro area of a DSGE model to those of a DSGE‐VAR, a BVAR and a multivariate random walk over 1999:Q1–2011:Q4. While the BVAR generally provides superior 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 perform better. Copyright © 2016 John Wiley & Sons, Ltd.     

Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility

This paper compares alternative models of time‐varying volatility on the basis of the accuracy of real‐time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time‐varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of innovation models. The results show that the AR and VAR specifications with conventional stochastic volatility dominate other volatility specifications, in terms of point forecasting to some degree and density forecasting to a greater degree. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting realized volatility: a Bayesian model‐averaging approach

How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.     

The Incremental Predictive Information Associated with Using Theoretical New Keynesian DSGE Models vs. Simple Linear Econometric Models*

In this paper we construct output gap and inflation predictions using a variety of dynamic stochastic general equilibrium (DSGE) sticky price models. Predictive density accuracy tests related to the test discussed in Corradi and Swanson [Journal of Econometrics (2005a), forthcoming] as well as predictive accuracy tests due to Diebold and Mariano [Journal of Business and Economic Statistics (1995) , Vol. 13, pp. 253–263]; and West [Econometrica (1996) , Vol. 64, pp. 1067–1084] are used to compare the alternative models. A number of simple time‐series prediction models (such as autoregressive and vector autoregressive (VAR) models) are additionally used as strawman models. Given that DSGE model restrictions are routinely nested within VAR models, the addition of our strawman models allows us to indirectly assess the usefulness of imposing theoretical restrictions implied by DSGE models on unrestricted econometric models. With respect to predictive density evaluation, our results suggest that the standard sticky price model discussed in Calvo [Journal of Monetary Economics (1983), Vol. XII, pp. 383–398] is not outperformed by the same model augmented either with information or indexation, when used to predict the output gap. On the other hand, there are clear gains to using the more recent models when predicting inflation. Results based on mean square forecast error analysis are less clear‐cut, although the standard sticky price model fares best at our longest forecast horizon of 3 years, it performs relatively poorly at shorter horizons. When the strawman time‐series models are added to the picture, we find that the DSGE models still fare very well, often outperforming our forecast competitions, suggesting that theoretical macroeconomic restrictions yield useful additional information for forming macroeconomic forecasts.     

The tourism forecasting competition

We evaluate the performances of various methods for forecasting tourism data. The data used include 366 monthly series, 427 quarterly series and 518 annual series, all supplied to us by either tourism bodies or academics who had used them in previous tourism forecasting studies. The forecasting methods implemented in the competition are univariate and multivariate time series approaches, and econometric models. This forecasting competition differs from previous competitions in several ways: (i) we concentrate on tourism data only; (ii) we include approaches with explanatory variables; (iii) we evaluate the forecast interval coverage as well as the point forecast accuracy; (iv) we observe the effect of temporal aggregation on the forecasting accuracy; and (v) we consider the mean absolute scaled error as an alternative forecasting accuracy measure. We find that pure time series approaches provide more accurate forecasts for tourism data than models with explanatory variables. For seasonal data we implement three fully automated pure time series algorithms that generate accurate point forecasts, and two of these also produce forecast coverage probabilities which are satisfactorily close to the nominal rates. For annual data we find that Naïve forecasts are hard to beat.     

Real‐time forecast combinations for the oil price

Baumeister and Kilian (Journal of Business and Economic Statistics, 2015, 33(3), 338–351) combine forecasts from six empirical models to predict real oil prices. In this paper, we broadly reproduce their main economic findings, employing their preferred measures of the real oil price and other real‐time variables. Mindful of the importance of Brent crude oil as a global price benchmark, we extend consideration to the North Sea‐based measure and update the evaluation sample to 2017:12. We model the oil price futures curve using a factor‐based Nelson–Siegel specification estimated in real time to fill in missing values for oil price futures in the raw data. We find that the combined forecasts for Brent are as effective as for other oil price measures. The extended sample using the oil price measures adopted by Baumeister and Kilian yields similar results to those reported in their paper. Also, the futures‐based model improves forecast accuracy at longer horizons.     

Forecasting inflation using time‐varying Bayesian model averaging

This paper presents a Bayesian model averaging regression framework for forecasting US inflation, in which the set of predictors included in the model is automatically selected from a large pool of potential predictors and the set of regressors is allowed to change over time. Using real‐time data on the 1960–2011 period, this model is applied to forecast personal consumption expenditures and gross domestic product deflator inflation. The results of this forecasting exercise show that, although it is not able to beat a simple random‐walk model in terms of point forecasts, it does produce superior density forecasts compared with a range of alternative forecasting models. Moreover, a sensitivity analysis shows that the forecasting results are relatively insensitive to prior choices and the forecasting performance is not affected by the inclusion of a very large set of potential predictors.     

Forecasting with an econometric model: Some recent results using the national institute model

It is widely believed that the large econometric models cannot be used for forecasting without considerable intervention on the part of the forecaster. In this paper we challenge this view by reproducing a number of recent forecasts published by the National Institute but without the ad hoc interventions used at the time. We show that in no case would the forecast, produced by the model used mechanically, have been radically different from that actually published. Further, in an ex-post comparison against actual out-turns, the mechanical model forecast is not obviously dominated by the published version.     

Inside the Crystal Ball: New Approaches to Predicting the Gasoline Price at the Pump

Appropriate real‐time forecasting models for the US retail price of gasoline yield substantial reductions in the mean‐squared prediction error (MSPE) at horizons up to 2 years as well as substantial increases in directional accuracy. Even greater MSPE reductions are possible by constructing a pooled forecast that assigns equal weight to five of the most successful forecasting models. Pooled forecasts have lower MSPE than the US Energy Information Administration gasoline price forecasts and the gasoline price expectations in the Michigan Survey of Consumers. We also show that as much as 39% of the decline in gas prices between June and December 2014 was predictable. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

How accurate are government forecasts of economic fundamentals? The case of Taiwan

A government’s ability to forecast key economic fundamentals accurately can affect business confidence, consumer sentiment, and foreign direct investment, among others. A government forecast based on an econometric model is replicable, whereas one that is not fully based on an econometric model is non-replicable. Governments typically provide non-replicable forecasts (or expert forecasts) of economic fundamentals, such as the inflation rate and real GDP growth rate.In this paper, we develop a methodology for evaluating non-replicable forecasts. We argue that in order to do so, one needs to retrieve from the non-replicable forecast its replicable component, and that it is the difference in accuracy between these two that matters. An empirical example to forecast economic fundamentals for Taiwan shows the relevance of the proposed methodological approach. Our main finding is that the undocumented knowledge of the Taiwanese government reduces forecast errors substantially.     

Modelling and Forecasting Fiscal Variables for the Euro Area*

In this paper, we assess the possibility of producing unbiased forecasts for fiscal variables in the Euro area by comparing a set of procedures that rely on different information sets and econometric techniques. In particular, we consider autoregressive moving average models, Vector autoregressions, small‐scale semistructural models at the national and Euro area level, institutional forecasts (Organization for Economic Co‐operation and Development), and pooling. Our small‐scale models are characterized by the joint modelling of fiscal and monetary policy using simple rules, combined with equations for the evolution of all the relevant fundamentals for the Maastricht Treaty and the Stability and Growth Pact. We rank models on the basis of their forecasting performance using the mean square and mean absolute error criteria at different horizons. Overall, simple time‐series methods and pooling work well and are able to deliver unbiased forecasts, or slightly upward‐biased forecast for the debt–GDP dynamics. This result is mostly due to the short sample available, the robustness of simple methods to structural breaks, and to the difficulty of modelling the joint behaviour of several variables in a period of substantial institutional and economic changes. A bootstrap experiment highlights that, even when the data are generated using the estimated small‐scale multi‐country model, simple time‐series models can produce more accurate forecasts, because of their parsimonious specification.     

The Measurement and Behavior of Uncertainty: Evidence from the ECB Survey of Professional Forecasters

We examine matched point and density forecasts of output growth, inflation and unemployment from the ECB Survey of Professional Forecasters. We construct measures of uncertainty from individual histograms, and find that the measures display countercyclical behavior and have increased across all forecast horizons since 2007. We also derive measures of forecast dispersion and forecast accuracy, and find that they are not reliable proxies for uncertainty. There is, however, evidence of a meaningful co‐movement between uncertainty and aggregate point predictions for output growth and unemployment. These results are robust to changes in the composition of the survey respondents over time. Copyright © 2015 John Wiley & Sons, Ltd.     

Subjective evaluation of composite econometric policy inputs

Studies have suggested that a composite forecast may be preferred to a single forecast. In addition, forecasting objectives are often conflicting. For example, one forecast may have the smallest sum of absolute forecast errors, while another has the smallest maximum absolute error. This paper examines the appropriateness of using multiple objective linear programming to determine weighted linear combinations of forecasts to be used as inputs for policy analysis. An example is presented where the methodology is used to combine the forecasts for several policy variables. The forecasts are selected from large econometric, consensus, and univariate time series models.