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.     

Forecasting with vector autoregressive (VAR) models subject to business cycle restrictions

In the last decade VAR models have become a widely-used tool for forecasting macroeconomic time series. To improve the out-of-sample forecasting accuracy of these models, Bayesian random-walk prior restrictions are often imposed on VAR model parameters. This paper focuses on whether placing an alternative type of restriction on the parameters of unrestricted VAR models improves the out-of-sample forecasting performance of these models. The type of restriction analyzed here is based on the business cycle characteristics of U.S. macroeconomic data, and in particular, requires that the dynamic behavior of the restricted VAR model mimic the business cycle characteristics of historical data. The question posed in this paper is: would a VAR model, estimated subject to the restriction that the cyclical characteristics of simulated data from the model “match up” with the business cycle characteristics of U.S. data, generate more accurate out-of-sample forecasts than unrestricted or Bayesian VAR models?     

Forecasting with Medium and Large Bayesian VARS

This paper is motivated by the recent interest in the use of Bayesian VARs for forecasting, even in cases where the number of dependent variables is large. In such cases factor methods have been traditionally used, but recent work using a particular prior suggests that Bayesian VAR methods can forecast better. In this paper, we consider a range of alternative priors which have been used with small VARs, discuss the issues which arise when they are used with medium and large VARs and examine their forecast performance using a US macroeconomic dataset containing 168 variables. We find that Bayesian VARs do tend to forecast better than factor methods and provide an extensive comparison of the strengths and weaknesses of various approaches. Typically, we find that the simple Minnesota prior forecasts well in medium and large VARs, which makes this prior attractive relative to computationally more demanding alternatives. Our empirical results show the importance of using forecast metrics based on the entire predictive density, instead of relying solely on those based on point forecasts. Copyright © 2011 John Wiley & Sons, Ltd.     

Professional forecasters and real-time forecasting with a DSGE model

This paper analyses the real-time forecasting performance of the New Keynesian DSGE model of Galí, Smets and Wouters (2012), estimated on euro area data. It investigates the extent to which the inclusion of 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 in the past. The forecasts of the DSGE model are compared with those from a Bayesian VAR model, an AR(1) model, a sample mean and a random walk.     

Bayesian VAR forecasts,survey information,and structural change in the euro area

We incorporate external information extracted from the European Central Bank’s Survey of Professional Forecasters into the predictions of a Bayesian VAR using entropic tilting and soft conditioning. The resulting conditional forecasts significantly improve the plain BVAR point and density forecasts. Importantly, we do not restrict the forecasts at a specific quarterly horizon but their possible paths over several horizons jointly since the survey information comes in the form of one- and two-year-ahead expectations. As well as improving the accuracy of the variable that we target, the spillover effects on “other-than-targeted” variables are relevant in size and are statistically significant. We document that the baseline BVAR exhibits an upward bias for GDP growth after the financial crisis, and our results provide evidence that survey forecasts can help mitigate the effects of structural breaks on the forecasting performance of a popular macroeconometric model.     

Forecasts of market shares from VAR and BVAR models: a comparison of their accuracy

This paper develops a Bayesian vector autoregressive model (BVAR) for the leader of the Portuguese car market to forecast the market share. The model includes five marketing decision variables. The Bayesian prior is selected on the basis of the accuracy of the out-of-sample forecasts. We find that BVAR models generally produce more accurate forecasts. The out-of-sample accuracy of the BVAR forecasts is also compared with that of forecasts from an unrestricted VAR model and of benchmark forecasts produced from three univariate models. Additionally, competitive dynamics are revealed through variance decompositions and impulse response analyses.     

Forecasting with High‐Dimensional Panel VARs

This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressions of large dimensions with time‐varying parameters and stochastic volatility. We exploit a hierarchical prior that takes into account possible pooling restrictions involving both VAR coefficients and the error covariance matrix, and propose a Bayesian dynamic learning procedure that controls for various sources of model uncertainty. We tackle computational concerns by means of a simulation‐free algorithm that relies on analytical approximations to the posterior. We use our methods to forecast inflation rates in the eurozone and show that these forecasts are superior to alternative methods for large vector autoregressions.     

NUMERICAL METHODS FOR ESTIMATION AND INFERENCE IN BAYESIAN VAR-MODELS

In Bayesian analysis of vector autoregressive models, and especially in forecasting applications, the Minnesota prior of Litterman is frequently used. In many cases other prior distributions provide better forecasts and are preferable from a theoretical standpoint. Several of these priors require numerical methods in order to evaluate the posterior distribution. Different ways of implementing Monte Carlo integration are considered. It is found that Gibbs sampling performs as well as, or better, then importance sampling and that the Gibbs sampling algorithms are less adversely affected by model size. We also report on the forecasting performance of the different prior distributions. © 1997 by John Wiley & Sons, Ltd.     

Nowcasting GDP using machine-learning algorithms: A real-time assessment

Can machine-learning algorithms help central banks understand the current state of the economy? Our results say yes! We contribute to the emerging literature on forecasting macroeconomic variables using machine-learning algorithms by testing the nowcast performance of common algorithms in a full ‘real-time’ setting—that is, with real-time vintages of New Zealand GDP growth (our target variable) and real-time vintages of around 600 predictors. Our results show that machine-learning algorithms are able to significantly improve over a simple autoregressive benchmark and a dynamic factor model. We also show that machine-learning algorithms have the potential to add value to, and in one case improve on, the official forecasts of the Reserve Bank of New Zealand.     

Forward guidance and expectation formation: A narrative approach

How forward guidance influences expectations is not fully understood. To study this, I construct central bank data that includes forward guidance and its attributes, central bank projections, and quantitative easing, which I combine with survey data. I describe how, when, and where forward guidance has worked. I estimate that forecasters revised their interest rate forecasts in the intended direction by five basis points on average following a forward guidance change. I provide estimates for The Federal Reserve, European Central Bank, Bank of England, Bank of Canada, Reserve Bank of Australia, Reserve Bank of New Zealand, Sveriges Riksbank, and Norges Bank.     

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.     

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.     

A large factor model for forecasting macroeconomic variables in South Africa

This paper uses large Factor Models (FMs), which accommodate a large cross-section of macroeconomic time series for forecasting the per capita growth rate, inflation, and the nominal short-term interest rate for the South African economy. The FMs used in this study contain 267 quarterly series observed over the period 1980Q1-2006Q4. The results, based on the RMSEs of one- to four-quarter-ahead out-of-sample forecasts from 2001Q1 to 2006Q4, indicate that the FMs tend to outperform alternative models such as an unrestricted VAR, Bayesian VARs (BVARs) and a typical New Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model in forecasting the three variables under consideration, hence indicating the blessings of dimensionality.     

Scoring rules and survey density forecasts

This article provides a practical evaluation of some leading density forecast scoring rules in the context of forecast surveys. We analyse the density forecasts of UK inflation obtained from the Bank of England’s Survey of External Forecasters, considering both the survey average forecasts published in the Bank’s quarterly Inflation Report, and the individual survey responses recently made available to researchers by the Bank. The density forecasts are collected in histogram format, and the ranked probability score (RPS) is shown to have clear advantages over other scoring rules. Missing observations are a feature of forecast surveys, and we introduce an adjustment to the RPS, based on the Yates decomposition, to improve its comparative measurement of forecaster performance in the face of differential non-response. The new measure, denoted RPS*, is recommended to analysts of forecast surveys.     

Do precious metal prices help in forecasting South African inflation?

In this paper we test whether the key metals prices of gold and platinum significantly improve inflation forecasts for the South African economy. We also test whether controlling for conditional correlations in a dynamic setup, using bivariate Bayesian-Dynamic Conditional Correlation (B-DCC) models, improves inflation forecasts. To achieve this we compare out-of-sample forecast estimates of the B-DCC model to Random Walk, Autoregressive and Bayesian VAR models. We find that for both the BVAR and BDCC models, improving point forecasts of the Autoregressive model of inflation remains an elusive exercise. This, we argue, is of less importance relative to the more informative density forecasts. For this we find improved forecasts of inflation for the B-DCC models at all forecasting horizons tested. We thus conclude that including metals price series as inputs to inflation models leads to improved density forecasts, while controlling for the dynamic relationship between the included price series and inflation similarly leads to significantly improved density forecasts.     

Forecasting with Bayesian Vector Autoregressions Estimated Using Professional Forecasts

We propose a Bayesian shrinkage approach for vector autoregressions (VARs) that uses short‐term survey forecasts as an additional source of information about model parameters. In particular, we augment the vector of dependent variables by their survey nowcasts, and claim that each variable modelled in the VAR and its nowcast are likely to depend in a similar way on the lagged dependent variables. In an application to macroeconomic data, we find that the forecasts obtained from a VAR fitted by our new shrinkage approach typically yield smaller mean squared forecast errors than the forecasts obtained from a range of benchmark methods. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Steady‐state priors for vector autoregressions

Bayesian priors are often used to restrain the otherwise highly over‐parametrized vector autoregressive (VAR) models. The currently available Bayesian VAR methodology does not allow the user to specify prior beliefs about the unconditional mean, or steady state, of the system. This is unfortunate as the steady state is something that economists usually claim to know relatively well. This paper develops easily implemented methods for analyzing both stationary and cointegrated VARs, in reduced or structural form, with an informative prior on the steady state. We document that prior information on the steady state leads to substantial gains in forecasting accuracy on Swedish macro data. A second example illustrates the use of informative steady‐state priors in a cointegration model of the consumption‐wealth relationship in the USA. Copyright © 2009 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.