Evaluating predictive densities of US output growth and inflation in a large macroeconomic data set

We evaluate conditional predictive densities for US output growth and inflation using a number of commonly-used forecasting models that rely on large numbers of macroeconomic predictors. More specifically, we evaluate how well conditional predictive densities based on the commonly-used normality assumption fit actual realizations out-of-sample. Our focus on predictive densities acknowledges the possibility that, although some predictors can cause point forecasts to either improve or deteriorate, they might have the opposite effect on higher moments. We find that normality is rejected for most models in some dimension according to at least one of the tests we use. Interestingly, however, combinations of predictive densities appear to be approximated correctly by a normal density: the simple, equal average when predicting output growth, and the Bayesian model average when predicting inflation.     

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.     

Forecasting the Covid-19 recession and recovery: Lessons from the financial crisis

We consider simple methods to improve the growth nowcasts and forecasts obtained by mixed-frequency MIDAS and UMIDAS models with a variety of indicators during the Covid-19 crisis and recovery period, such as combining forecasts across various specifications for the same model and/or across different models, extending the model specification by adding MA terms, enhancing the estimation method by taking a similarity approach, and adjusting the forecasts to put them back on track using a specific form of intercept correction. Among these methods, adjusting the original nowcasts and forecasts by an amount similar to the nowcast and forecast errors made during the financial crisis and subsequent recovery seems to produce the best results for the US, notwithstanding the different source and characteristics of the financial crisis. In particular, the adjusted growth nowcasts for 2020Q1 get closer to the actual value, and the adjusted forecasts based on alternative indicators become much more similar, all unfortunately indicating a much slower recovery than without adjustment, and very persistent negative effects on trend growth. Similar findings also emerge for forecasts by institutions, for survey forecasts, and for the other G7 countries.     

Forecasting US output growth using leading indicators: an appraisal using MIDAS models

We evaluate the predictive power of leading indicators for output growth at horizons up to 1 year. We use the MIDAS regression approach as this allows us to combine multiple individual leading indicators in a parsimonious way and to directly exploit the information content of the monthly series to predict quarterly output growth. When we use real‐time vintage data, the indicators are found to have significant predictive ability, and this is further enhanced by the use of monthly data on the quarter at the time the forecast is made. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

BAYESIAN MODEL SELECTION AND FORECASTING IN NONCAUSAL AUTOREGRESSIVE MODELS

In this paper, we propose a Bayesian estimation and forecasting procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, yielding predictive densities as a by‐product. We show that the posterior model probabilities provide a convenient model selection criterion in discriminating between alternative causal and noncausal specifications. As an empirical application, we consider US inflation. The posterior probability of noncausality is found to be high—over 98%. Furthermore, the purely noncausal specifications yield more accurate inflation forecasts than alternative causal and noncausal AR models. Copyright © 2010 John Wiley & Sons, Ltd.     

Estimating and accounting for the output gap with large Bayesian vector autoregressions

We consider how to estimate the trend and cycle of a time series, such as real gross domestic product, given a large information set. Our approach makes use of the Beveridge–Nelson decomposition based on a vector autoregression, but with two practical considerations. First, we show how to determine which conditioning variables span the relevant information by directly accounting for the Beveridge–Nelson trend and cycle in terms of contributions from different forecast errors. Second, we employ Bayesian shrinkage to avoid overfitting in finite samples when estimating models that are large enough to include many possible sources of information. An empirical application with up to 138 variables covering various aspects of the US economy reveals that the unemployment rate, inflation, and, to a lesser extent, housing starts, aggregate consumption, stock prices, real money balances, and the federal funds rate contain relevant information beyond that in output growth for estimating the output gap, with estimates largely robust to substituting some of these variables or incorporating additional variables.     

Forecasting and forecast narratives: The Bank of England Inflation Reports

We analyze the narratives that accompany the numerical forecasts in the Bank of England’s Quarterly Inflation Reports, 1997–2018. We focus on whether the narratives contain useful information about the future course of key macro variables over and above the point predictions, in terms of whether the narratives can be used to enhance the accuracy of the numerical forecasts. We also consider whether the narratives are able to predict future changes in the numerical forecasts. We find that a measure of sentiment derived from the narratives can predict the errors in the numerical forecasts of output growth, but not of inflation. We find no evidence that past changes in sentiment predict subsequent changes in the point forecasts of output growth or of inflation, but do find that the adjustments to the numerical output growth forecasts have a systematic element.     

This is what the leading indicators lead

We propose an optimal filter to transform the Conference Board Composite Leading Index (CLI) into recession probabilities in the US economy. We also analyse the CLI's accuracy at anticipating US output growth. We compare the predictive performance of linear, VAR extensions of smooth transition regression and switching regimes, probit, non‐parametric models and conclude that a combination of the switching regimes and non‐parametric forecasts is the best strategy at predicting both the NBER business cycle schedule and GDP growth. This confirms the usefulness of CLI, even in a real‐time analysis. Copyright © 2002 John Wiley & Sons, Ltd.     

Euromind‐ : A Density Estimate of Monthly Gross Domestic Product for the Euro Area

EuroMInd‐ is a density estimate of monthly gross domestic product (GDP) constructed according to a bottom‐up approach, pooling the density estimates of 11 GDP components, by output and expenditure type. The components' density estimates are obtained from a medium‐size dynamic factor model handling mixed frequencies of observation and ragged‐edged data structures. They reflect both parameter and filtering uncertainty and are obtained by implementing a bootstrap algorithm for simulating from the distribution of the maximum likelihood estimators of the model parameters, and conditional simulation filters for simulating from the predictive distribution of GDP. Both algorithms process the data sequentially as they become available in real time. The GDP density estimates for the output and expenditure approach are combined using alternative weighting schemes and evaluated with different tests based on the probability integral transform and by applying scoring rules. Copyright © 2016 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.     

Likelihood-based scoring rules for comparing density forecasts in tails

We propose new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region of interest, such as the left tail in financial risk management. These scoring rules can be interpreted in terms of Kullback-Leibler divergence between weighted versions of the density forecast and the true density. Existing scoring rules based on weighted likelihood favor density forecasts with more probability mass in the given region, rendering predictive accuracy tests biased toward such densities. Using our novel likelihood-based scoring rules avoids this problem.     

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.     

Higher order properties of the wild bootstrap under misspecification

We examine the higher order properties of the wild bootstrap (Wu, 1986) in a linear regression model with stochastic regressors. We find that the ability of the wild bootstrap to provide a higher order refinement is contingent upon whether the errors are mean independent of the regressors or merely uncorrelated with them. In the latter case, the wild bootstrap may fail to match some of the terms in an Edgeworth expansion of the full sample test statistic. Nonetheless, we show that the wild bootstrap still has a lower maximal asymptotic risk as an estimator of the true distribution than a normal approximation, in shrinking neighborhoods of properly specified models. To assess the practical implications of this result we conduct a Monte Carlo study contrasting the performance of the wild bootstrap with a normal approximation and the traditional nonparametric bootstrap.     

A Simple Approach for Diagnosing Instabilities in Predictive Regressions

We introduce a method for detecting the presence of structural breaks in the parameters of predictive regressions linking noisy variables such as stock returns to persistent predictors such as valuation ratios. Our approach relies on the least squares‐based squared residuals of the predictive regression and is straightforward to implement. The distributions of the two test statistics we introduce are shown to be free of nuisance parameters, valid under dependent errors, already tabulated in the literature and robust to the degree of persistence of the chosen predictor. Our proposed method is subsequently applied to the predictability of US stock returns.     

Statistical inference on seemingly unrelated non‐parametric regression models with serially correlated errors

This article is concerned with the inference on seemingly unrelated non‐parametric regression models with serially correlated errors. Based on an initial estimator of the mean functions, we first construct an efficient estimator of the autoregressive parameters of the errors. Then, by applying an undersmoothing technique, and taking both of the contemporaneous correlation among equations and serial correlation into account, we propose an efficient two‐stage local polynomial estimation for the unknown mean functions. It is shown that the resulting estimator has the same bias as those estimators which neglect the contemporaneous and/or serial correlation and smaller asymptotic variance. The asymptotic normality of the resulting estimator is also established. In addition, we develop a wild block bootstrap test for the goodness‐of‐fit of models. The finite sample performance of our procedures is investigated in a simulation study whose results come out very supportive, and a real data set is analysed to illustrate the usefulness of our procedures.     

Does judgment improve macroeconomic density forecasts?

This paper presents empirical evidence on how judgmental adjustments affect the accuracy of macroeconomic density forecasts. Judgment is defined as the difference between professional forecasters’ densities and the forecast densities from statistical models. Using entropic tilting, we evaluate whether judgments about the mean, variance and skew improve the accuracy of density forecasts for UK output growth and inflation. We find that not all judgmental adjustments help. Judgments about point forecasts tend to improve density forecast accuracy at short horizons and at times of heightened macroeconomic uncertainty. Judgments about the variance hinder at short horizons, but can improve tail risk forecasts at longer horizons. Judgments about skew in general take value away, with gains seen only for longer horizon output growth forecasts when statistical models took longer to learn that downside risks had reduced with the end of the Great Recession. Overall, density forecasts from statistical models prove hard to beat.     

Predictive regressions under asymmetric loss: Factor augmentation and model selection

This paper discusses the specifics of forecasting using factor-augmented predictive regressions under general loss functions. In line with the literature, we employ principal component analysis to extract factors from the set of predictors. In addition, we also extract information on the volatility of the series to be predicted, since the volatility is forecast-relevant under non-quadratic loss functions. We ensure asymptotic unbiasedness of the forecasts under the relevant loss by estimating the predictive regression through the minimization of the in-sample average loss. Finally, we select the most promising predictors for the series to be forecast by employing an information criterion that is tailored to the relevant loss. Using a large monthly data set for the US economy, we assess the proposed adjustments in a pseudo out-of-sample forecasting exercise for various variables. As expected, the use of estimation under the relevant loss is found to be effective. Using an additional volatility proxy as the predictor and conducting model selection that is tailored to the relevant loss function enhances the forecast performance significantly.     

Real-time macroeconomic projection using narrative central bank communication

Unlike the central banks of most developed economies, the People's Bank of China (PBC) does not release its macroeconomic forecasts to the public but instead carries out narrative communication. We apply a hurdle distributed multinomial regression to PBC communication texts in real time, addressing the ultrahigh dimensionality, sparsity, and look-ahead biases. In addition, we embed text-based indices into mixed-data sampling (MIDAS)-type models and conduct forecast combinations for prediction. Our results argue that the predictive information from communication texts improves the real-time out-of-sample prediction performance. We connect textual analysis and real-time macroeconomic projection, providing new insights into the value of central bank communication.     

Evaluating DSGE model forecasts of comovements

This paper develops and applies tools to assess multivariate aspects of Bayesian Dynamic Stochastic General Equilibrium (DSGE) model forecasts and their ability to predict comovements among key macroeconomic variables. We construct posterior predictive checks to evaluate conditional and unconditional density forecasts, in addition to checks for root-mean-squared errors and event probabilities associated with these forecasts. The checks are implemented on a three-equation DSGE model as well as the Smets and Wouters (2007) model using real-time data. We find that the additional features incorporated into the Smets–Wouters model do not lead to a uniform improvement in the quality of density forecasts and prediction of comovements of output, inflation, and interest rates.