Estimating GVAR weight matrices

The objective of this paper is to illustrate how the weights that are needed to construct foreign variable vectors in global vector autoregressive (GVAR) models can be estimated jointly with the GVAR’s parameters. An application to real gross domestic product (GDP) growth and inflation as well as a controlled Monte Carlo simulation serve to highlight that (1) in the application at hand, the estimated weights differ for some countries significantly from trade-based ones; (2) misspecified weights can bias the GVAR and, hence, distort the impulse responses; and (3) using estimated weights instead of trade-based ones can enhance the out-of-sample forecast performance of the GVAR. Devising a method for estimating GVAR weights is particularly useful for contexts in which it is not obvious how weights could otherwise be constructed from data.     

Probabilistic forecasting of output growth,inflation and the balance of trade in a GVAR framework

We apply a global vector autoregressive (GVAR) model to the analysis of inflation, output growth and global imbalances among a group of 33 countries (26 regions). We account for structural instability by use of country‐specific intercept shifts, the timings of which are identified taking into account both statistical evidence and our knowledge of historic economic conditions and events. Using this model, we compute both central forecasts and scenario‐based probabilistic forecasts for a range of events of interest, including the sign and trajectory of the balance of trade, the achievement of a short‐term inflation target, and the incidence of recession and slow growth. The forecasting performance of the GVAR model in relation to the ongoing financial crisis is quite remarkable. It correctly identifies a pronounced and widespread economic contraction accompanied by a marked shift in the net trade balance of the Eurozone and Japan. Moreover, this promising out‐of‐sample forecasting performance is substantiated by a raft of statistical tests which indicate that the predictive accuracy of the GVAR model is broadly comparable to that of standard benchmark models over short horizons and superior over longer horizons. Hence we conclude that GVAR models may be a useful forecasting tool for institutions operating at both the national and supra‐national levels. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Asymmetric loss in the Greenbook and the Survey of Professional Forecasters

This paper examines the forecast rationality of the Greenbook and the Survey of Professional Forecasters (SPF) under asymmetric loss functions, using the method proposed by Elliott, Komunjer, and Timmermann (2005) with a rolling window strategy. Over rolling periods, the degree and direction of the asymmetry in forecast loss functions are time-varying. While rationality under symmetric loss is often rejected, forecast rationality under asymmetric loss fails to be rejected over nearly all rolling periods. Besides, real output growth is consistently under-predicted in the 1990s, and the inflation rate is consistently over-predicted in the 1980s and 1990s. In general, inflation forecasts, especially for long horizons, exhibit greater levels of loss asymmetry in magnitude and frequency. The loss asymmetry of real output growth forecasts is more pronounced when the last revised vintage data are used than when the real-time vintage is used. All of these results hold for both the Greenbook and SPF forecasts. The results are also similar with the use of different sets of instrumental variables for estimating the asymmetric loss and testing for forecast rationality.     

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.     

Combining survey long-run forecasts and nowcasts with BVAR forecasts using relative entropy

This paper constructs hybrid forecasts that combine forecasts from vector autoregressive (VAR) model(s) with both short- and long-term expectations from surveys. Specifically, we use the relative entropy to tilt one-step-ahead and long-horizon VAR forecasts to match the nowcasts and long-horizon forecasts from the Survey of Professional Forecasters. We consider a variety of VAR models, ranging from simple fixed-parameter to time-varying parameters. The results across models indicate meaningful gains in multi-horizon forecast accuracy relative to model forecasts that do not incorporate long-term survey conditions. Accuracy improvements are achieved for a range of variables, including those that are not tilted directly but are affected through spillover effects from tilted variables. The accuracy gains for hybrid inflation forecasts from simple VARs are substantial, statistically significant, and competitive to time-varying VARs, univariate benchmarks, and survey forecasts. We view our proposal as an indirect approach to accommodating structural change and moving end points.     

Inflation forecasts and core inflation measures: Where is the information on future inflation?

This paper uses the forecast from a random walk model of inflation as a benchmark to test and compare the forecast performance of several alternatives of future inflation, including the Greenbook forecast by the Fed staff, the Survey of Professional Forecasters median forecast, CPI inflation minus food and energy, CPI weighted median inflation, and CPI trimmed mean inflation. The Greenbook forecast was found in previous literature to be a better forecast than other private sector forecasts. Our results indicate that both the Greenbook and the Survey of Professional Forecasters median forecasts of inflation and core inflation measures may contain better information than forecasts from a random walk model. The Greenbook's superiority appears to have declined against other forecasts and core inflation measures.     

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.     

Combining forecasts: Performance and coherence

There is general agreement in many forecasting contexts that combining individual predictions leads to better final forecasts. However, the relative error reduction in a combined forecast depends upon the extent to which the component forecasts contain unique/independent information. Unfortunately, obtaining independent predictions is difficult in many situations, as these forecasts may be based on similar statistical models and/or overlapping information. The current study addresses this problem by incorporating a measure of coherence into an analytic evaluation framework so that the degree of independence between sets of forecasts can be identified easily. The framework also decomposes the performance and coherence measures in order to illustrate the underlying aspects that are responsible for error reduction. The framework is demonstrated using UK retail prices index inflation forecasts for the period 1998–2014, and implications for forecast users are discussed.     

Do survey joiners and leavers differ from regular participants? The US SPF GDP growth and inflation forecasts

If ‘learning by doing’ is important for macro-forecasting, newcomers might be different from regular, established participants. Stayers may also differ from the soon-to-leave. We test these conjectures for macro-forecasters’ point predictions of output growth and inflation, and for their histogram forecasts. Histogram forecasts of inflation by both joiners and leavers are found to be less accurate, especially if we suppose that joiners take time to learn. For GDP growth, there is no evidence of differences between the groups in terms of histogram forecast accuracy, although GDP point forecasts by leavers are less accurate. These findings are predicated on forecasters being homogeneous within groups. Allowing for individual fixed effects suggests fewer differences, including leavers’ inflation histogram forecasts being no less accurate.     

Forecasting United States–Asia international message telephone service

This study compares forecasts of US international message telephone service (IMTS) traffic using several relative mean squared error statistics. The forecasts are obtained from time-series extrapolation, univariate autoregressive integrated moving average (ARIMA), error correction and vector autoregressive models. The models are estimated on annual US IMTS outgoing traffic data for six US–Asia bilateral markets for the period 1964 to 1993. No single approach provides best forecasts. However, forecast evaluation statistics indicate that econometric models generally outperform the alternatives.     

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.     

Measuring output gap nowcast uncertainty

We propose a methodology for gauging the uncertainty in output gap nowcasts across a large number of commonly-deployed vector autoregressive (VAR) specifications for inflation and the output gap. Our approach utilises many output gap measures to construct ensemble nowcasts for inflation using a linear opinion pool. The predictive densities for the latent output gap utilise weights based on the ability of each specification to provide accurate probabilistic forecasts of inflation. In an application based on US real-time data, nowcasting over the out-of-sample evaluation period from 1991q2 to 2010q1, we demonstrate that a system of bivariate VARs produces well-calibrated ensemble densities for inflation, in contrast to univariate autoregressive benchmarks. The implied nowcast densities for the output gap are multimodal and indicate a considerable degree of uncertainty. For example, we assess the probability of a negative output gap at around 45% between 2004 and 2007. Despite the Greenspan policy regime, there still remained a substantial risk that the nowcast for output was below potential in real time. We extend our methodology to include distinct output gap measures, based on alternative filters, and show that, in our application, the nowcast density for the output gap is sensitive to the detrending method.     

Oil exports and the Iranian economy

This paper presents an error-correcting macroeconometric model for the Iranian economy estimated using a new quarterly data set over the period 1979Q1–2006Q4. It builds on a recent paper by the authors, Esfahani, Mohaddes, and Pesaran (in press), which develops a theoretical long-run growth model for major oil exporting economies. The core variables included in this paper are real output, real money balances, inflation, exchange rate, oil exports, and foreign real output, although the role of investment and consumption are also analysed in a sub-model. The paper finds clear evidence for the existence of two long-run relations: an output equation as predicted by the theory and a standard real money demand equation with inflation acting as a proxy for the (missing) market interest rate. The results show that real output in the long run is influenced by oil exports and foreign output. However, it is also found that inflation has a significant negative long-run effect on real GDP, which is suggestive of economic inefficiencies and is matched by a negative association between inflation and the investment–output ratio. Finally, the results of impulse responses show that the Iranian economy adjusts quite quickly to the shocks in foreign output and oil exports, which could be partly due to the relatively underdeveloped nature of Iran's financial markets.     

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.     

Raiders of the lost high-frequency forecasts: New data and evidence on the efficiency of the Fed's forecasting

We introduce a new dataset of real gross domestic product (GDP) growth and core personal consumption expenditures (PCE) inflation forecasts produced by the staff of the Board of Governors of the Federal Reserve System. In contrast to the eight Greenbook forecasts a year the staff produce for Federal Open Market Committee (FOMC) meetings, our dataset has roughly weekly forecasts. We use these data to study whether the staff forecasts efficiently. Prespecified regressions of forecast errors on forecast revisions show the staff's GDP forecasts exhibit time-varying inefficiency between FOMC meetings, and also show some evidence for inefficient inflation forecasts.     

Evaluating a three-dimensional panel of point forecasts: The Bank of England Survey of External Forecasters

This article provides a first analysis of the forecasts of inflation and GDP growth obtained from the Bank of England's Survey of External Forecasters, considering both the survey average forecasts published in the quarterly Inflation Report, and the individual survey responses, recently made available by the Bank. These comprise a conventional incomplete panel dataset, with an additional dimension arising from the collection of forecasts at several horizons; both point forecasts and density forecasts are collected. The inflation forecasts show good performance in tests of unbiasedness and efficiency, albeit over a relatively calm period for the UK economy, and there is considerable individual heterogeneity. For GDP growth, inaccurate real-time data and their subsequent revisions are seen to cause serious difficulties for forecast construction and evaluation, although the forecasts are again unbiased. There is evidence that some forecasters have asymmetric loss functions.     

CONSTRUCTING OPTIMAL DENSITY FORECASTS FROM POINT FORECAST COMBINATIONS

Decision makers often observe point forecasts of the same variable computed, for instance, by commercial banks, IMF and the World Bank, but the econometric models used by such institutions are frequently unknown. This paper shows how to use the information available on point forecasts to compute optimal density forecasts. Our idea builds upon the combination of point forecasts under general loss functions and unknown forecast error distributions. We use real‐time data to forecast the density of US inflation. The results indicate that the proposed method materially improves the real‐time accuracy of density forecasts vis‐à‐vis those from the (unknown) individual econometric models. Copyright © 2013 John Wiley & Sons, Ltd.     

REAL‐TIME FORECASTING OF INFLATION AND OUTPUT GROWTH WITH AUTOREGRESSIVE MODELS IN THE PRESENCE OF DATA REVISIONS

We examine how the accuracy of real‐time forecasts from models that include autoregressive terms can be improved by estimating the models on ‘lightly revised’ data instead of using data from the latest‐available vintage. The benefits of estimating autoregressive models on lightly revised data are related to the nature of the data revision process and the underlying process for the true values. Empirically, we find improvements in root mean square forecasting error of 2–4% when forecasting output growth and inflation with univariate models, and of 8% with multivariate models. We show that multiple‐vintage models, which explicitly model data revisions, require large estimation samples to deliver competitive forecasts. Copyright © 2012 John Wiley & Sons, Ltd.     

Are macroeconomic density forecasts informative?

We consider whether survey density forecasts (such as the inflation and output growth histograms of the US Survey of Professional Forecasters) are superior to unconditional density forecasts. The unconditional forecasts assume that the average level of uncertainty that has been experienced in the past will continue to prevail in the future, whereas the SPF projections ought to be adapted to the current conditions and the outlook at each forecast origin. The SPF forecasts might be expected to outperform the unconditional densities at the shortest horizons, but it transpires that such is not the case for the aggregate forecasts of either variable, or for the majority of the individual respondents for forecasting inflation.