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.     

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.     

Evaluating the conditionality of judgmental forecasts

We propose a framework for evaluating the conditionality of forecasts. The crux of our framework is the observation that a forecast is conditional if revisions to the conditioning factor are incorporated faithfully into the remainder of the forecast. We consider whether the Greenbook, Blue Chip survey and Survey of Professional Forecasters exhibit systematic biases in the manner in which they incorporate interest rate projections into the forecasts of other macroeconomic variables. We do not find strong evidence of systematic biases in the three economic forecasts that we consider, as the interest rate projections in these forecasts appear to be incorporated efficiently into the forecasts of other economic variables.     

Density forecasting with Bayesian Vector Autoregressive models under macroeconomic data uncertainty

Macroeconomic data are subject to data revisions. Yet, the usual way of generating real-time density forecasts from Bayesian Vector Autoregressive (BVAR) models makes no allowance for data uncertainty from future data revisions. We develop methods of allowing for data uncertainty when forecasting with BVAR models with stochastic volatility. First, the BVAR forecasting model is estimated on real-time vintages. Second, the BVAR model is jointly estimated with a model of data revisions such that forecasts are conditioned on estimates of the ‘true’ values. We find that this second method generally improves upon conventional practice for density forecasting, especially for the United States.     

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.     

Short-term inflation projections: A Bayesian vector autoregressive approach

In this paper we construct a large Bayesian Vector Autoregressive model (BVAR) for the Euro area that captures the complex dynamic inter-relationships between the main components of the Harmonized Index of Consumer Prices (HICP) and their determinants. The model generates accurate conditional and unconditional forecasts in real-time. We find a significant pass-through effect of oil-price shocks on core inflation and a strong Phillips curve during the Great Recession.     

A new marked point process model for the federal funds rate target: Methodology and forecast evaluation

Forecasts of key interest rates set by central banks are of paramount concern for investors and policy makers. Recently it has been shown that forecasts of the federal funds rate target, the most anticipated indicator of the Federal Reserve Bank's monetary policy stance, can be improved considerably when its evolution is modeled as a marked point process (MPP). This is due to the fact that target changes occur in discrete time with discrete increments, have an autoregressive nature and are usually in the same direction. We propose a model which is able to account for these dynamic features of the data. In particular, we combine Hamilton and Jordà's [2002. A model for the federal funds rate target. Journal of Political Economy 110(5), 1135–1167] autoregressive conditional hazard (ACH) and Russell and Engle's [2005. A discrete-state continuous-time model of financial transactions prices and times: the autoregressive conditional multinomial-autoregressive conditional duration model. Journal of Business and Economic Statistics 23(2), 166 – 180] autoregressive conditional multinomial (ACM) model. The paper also puts forth a methodology to evaluate probability function forecasts of MPP models. By improving goodness of fit and point forecasts of the target, the ACH–ACM qualifies as a sensible modeling framework. Furthermore, our results show that MPP models deliver useful probability function forecasts at short and medium term horizons.     

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.     

Efficient forecast tests for conditional policy forecasts

Central Banks regularly make forecasts, such as the Fed’s Greenbook forecast, that are conditioned on hypothetical paths for the policy interest rate. While there are good public policy reasons to evaluate the quality of such forecasts, up until now, the most common approach has been to ignore their conditional nature and apply standard forecast efficiency tests. In this paper we derive tests for the efficiency of conditional forecasts. Intuitively, these tests involve implicit estimates of the degree to which the conditioning path is counterfactual and the magnitude of the policy feedback over the forecast horizon. We apply the tests to the Greenbook forecast and the Bank of England’s inflation report forecast, finding some evidence of forecast inefficiency. Nonetheless, we argue that the conditional nature of the forecasts made by central banks represents a substantial impediment to the analysis of their quality—stronger assumptions are needed and forecast inefficiency may go undetected for longer than would be the case if central banks were instead to report unconditional forecasts.     

Tests of Predictive Ability for Vector Autoregressions Used for Conditional Forecasting

Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Even though conditional forecasting is common, there has been little work on methods for evaluating conditional forecasts. This paper provides analytical, Monte Carlo and empirical evidence on tests of predictive ability for conditional forecasts from estimated models. In the empirical analysis, we examine conditional forecasts obtained with a VAR in the variables included in the DSGE model of Smets and Wouters (American Economic Review 2007; 97 : 586–606). Throughout the analysis, we focus on tests of bias, efficiency and equal accuracy applied to conditional forecasts from VAR models. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting in GARCH models with polynomially modified innovations

Orthogonal polynomials can be used to modify the moments of the distribution of a random variable. In this paper, polynomially adjusted distributions are employed to model the skewness and kurtosis of the conditional distributions of GARCH models. To flexibly capture the skewness and kurtosis of data, the distributions of the innovations that are polynomially reshaped include, besides the Gaussian, also leptokurtic laws such as the logistic and the hyperbolic secant. Modeling GARCH innovations with polynomially adjusted distributions can effectively improve the precision of the forecasts. This strategy is analyzed in GARCH models with different specifications for the conditional variance, such as the APARCH, the EGARCH, the Realized GARCH, and APARCH with time-varying skewness and kurtosis. An empirical application on different types of asset returns shows the good performance of these models in providing accurate forecasts according to several criteria based on density forecasting, downside risk, and volatility prediction.     

Forecasting Australia’s economic performance during the Asian crisis

During the Asian economic crisis of 1997–98, published forecasts from a Bayesian vector autoregressive (BVAR) model consistently indicated that the crisis would have little or no effect on Australia’s economic performance, despite the deterioration in the trade balance. The worsening trade deficit led many other forecasters to predict a sharp fall in Australia’s GDP growth rate, as the countries most severely affected by the crisis represent over 60 percent of Australia’s export markets. This paper argues that the more pessimistic forecasts attached too much weight to the links between Australia’s external accounts and GDP growth. In particular, I show that forecasts for the period September 1997 to December 1998, conditional on the actual path of the merchandise trade balance, predict higher inflation and interest rates than unconditional forecasts from a model without the trade balance. There does, however, appear to be useful information in the individual components of the trade deficit. Conditioning on the actual paths of both exports and imports generally produces more accurate forecasts than conditioning on net exports. In particular, conditioning on the trade balance results in the least accurate forecasts for inflation and interest rates of any of the models considered here. On the other hand, conditioning on the individual trade flows produces the most accurate forecasts for inflation, and the second-most accurate for interest rates. Taken together, the results presented here lend support to the argument that Australia’s trade flows represent the outcomes of optimizing decisions, rather than defining constraints on economic growth.     

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.     

Demographic forecasts and fiscal policy rules

All quantitative evaluations of fiscal sustainability that include the effects of population ageing must utilize demographic forecasts. It is well known that such forecasts are uncertain, and some studies have taken that into account by using stochastic population projections jointly with economic models. We develop this approach further by introducing regular demographic forecast revisions that are embedded in stochastic population projections. This allows us to separate, for each demographic outcome and under different policy rules, the expected and realized effects of population ageing on public finances. In our Finnish application, demographic uncertainty produces a considerable sustainability risk. We consider policies that reduce the likelihood of getting highly indebted and demonstrate that, although demographic forecasts are uncertain, they contain enough information to be useful in forward-looking policy rules.     

The COVID-19 shock and challenges for inflation modelling

We document the impact of COVID-19 on inflation modelling within a vector autoregression (VAR) model and provide guidance for forecasting euro area inflation during the pandemic. We show that estimated parameters are strongly affected, leading to different and sometimes implausible projections. As a solution, we propose to augment the VAR by allowing the residuals to have a fat-tailed distribution instead of a Gaussian one. This also outperforms with respect to unconditional forecasts. Yet, what brings sizeable forecast gains during the pandemic is adding meaningful off-model information, such as that entailed in the Survey of Professional Forecasters. The fat-tailed VAR loses part, but not all of its relative advantage compared to the Gaussian version when producing conditional inflation forecasts in a real-time setup. It is the joint fat-tailed errors and multi-equation modelling that manage to robustify models against extreme observations; in a single-equation model the same solution is less effective.     

Toward a New Model for Probabilistic Household Forecasts

Household projections are key components of analyses of several issues of social concern, including the welfare of the elderly, housing, and environmentally significant consumption patterns. Researchers or policy makers that use such projections need appropriate representations of uncertainty in order to inform their analyses. However, the weaknesses of the traditional approach of providing alternative variants to single "best guess" projection are magnified in household projections, which have many output variables of interest, and many input variables beyond fertility, mortality, and migration. We review current methods of household projections and the potential for using them to produce probabilistic projections, which would address many of these weaknesses. We then propose a new framework for a household projection method of intermediate complexity that we believe is a good candidate for providing a basis for further development of probabilistic household projections. An extension of the traditional headship rate approach, this method is based on modelling changes in headship rates decomposed by household size as a function of variables describing demographic events such as parity specific fertility, union formation and dissolution, and leaving home. It has moderate data requirements, manageable complexity, allows for direct specification of demographic events, and produces output that includes the most important household characteristics for many applications. An illustration of how such a model might be constructed, using data on the U.S. and China over the past several decades, demonstrates the viability of the approach.     

Forecasting from others’ experience: Bayesian estimation of the generalized Bass model

We propose a Bayesian estimation procedure for the generalized Bass model that is used in product diffusion models. Our method forecasts product sales early based on previous similar markets; that is, we obtain pre-launch forecasts by analogy. We compare our forecasting proposal to traditional estimation approaches, and alternative new product diffusion specifications. We perform several simulation exercises, and use our method to forecast the sales of room air conditioners, BlackBerry handheld devices, and compressed natural gas. The results show that our Bayesian proposal provides better predictive performances than competing alternatives when little or no historical data are available, which is when sales projections are the most useful.     

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.     

On the value of free foreign-exchange forecasts

The objective of this paper is to assess the value of free foreign-exchange forecasts. Taking the exchange-rate projections published by Lloyds Bank as an example, it is shown that there is no reason to assume that these projections consistently outperform the most easily available benchmark, the current spot exchange rate. Moreover, the returns to speculative investment based on these projections seem to be, at best, insignificant. The value of such forecasts must, therefore, be regarded as negligible.     

Oil price shocks and economic growth: The volatility link

This paper shows that oil shocks impact economic growth primarily through the conditional variance of growth. Our comparison of models focuses on density forecasts. Over a range of dynamic models, oil shock measures and data, we find a robust link between oil shocks and the volatility of economic growth. We then develop a new measure of oil shocks and show that it is superior to existing measures; it indicates that the conditional variance of growth increases in response to an indicator of the local maximum oil price exceedance. The empirical results uncover a large pronounced asymmetric response of the growth volatility to oil price changes. The uncertainty about future growth is considerably lower than with a benchmark AR(1) model when no oil shocks are present.