Rudebusch and Williams (2009) predict recessions in the United States utilising a probit model with the lagged yield spread as a real-time predictor. Mindful of the importance of recent yield curve movements, we update their analysis and evaluate quarterly forecasts from their probit model up to the end of 2023. We also analyze lagged financial conditions as an alternative real-time predictor. We find that both the yield spread and financial conditions perform relatively well at the longer horizons considered by the experts in the Survey of Professional Forecasters.

Adrian, Boyarchenko and Giannone ((2019), ABG) adapt quantile regression (QR) methods to examine the relationship between US economic growth and financial conditions. We confirm their empirical findings, using their methodology and their pre-2016 sample. Mindful of the importance of the Covid-19 pandemic, we extend the sample to 2021Q3 and find attenuation of the key estimated coefficients using ABG's empirical methods. Given the pandemic observations, we provide robust QR analysis of dependence based on ranked data and explain the relationship with extant copula modelling methods.

The linear opinion pool (LOP) produces potentially non-Gaussian combination forecast densities. In this paper, we propose a computationally convenient transformation for the LOP to mirror the non-Gaussianity exhibited by the target variable. Our methodology involves a Smirnov transform to reshape the LOP combination forecasts using the empirical cumulative distribution function. We illustrate our empirically transformed opinion pool (EtLOP) approach with an application examining quarterly real-time forecasts for U.S. inflation evaluated on a sample from 1990:1 to 2020:2. EtLOP improves performance by approximately 10% to 30% in terms of the continuous ranked probability score across forecasting horizons.

We explore the historical relationship between financial conditions and real economic growth for quarterly U.S. data from 1875 to 2017 with a flexible empirical copula modelling methodology. We compare specifications with both linear and non-linear dependence, and with both Gaussian and non-Gaussian marginal distributions. Our results indicate strong statistical support for models that are both non-Gaussian and nonlinear for our historical data, with considerable heterogeneity across sub-samples. We demonstrate that ignoring the contribution of financial conditions typically understates the conditional downside risks to economic growth in crises. For example, accounting for financial conditions more than doubles the probability of negative growth in the year following the 1929 stock market crash.

Many studies have found that combining forecasts improves predictive accuracy. An often-used approach developed by Granger and Ramanathan (GR, 1984) utilises a linear-Gaussian regression model to combine point forecasts. This paper generalises their approach for an asymmetrically distributed target variable. Our copula point forecast combination methodology involves fitting marginal distributions for the target variable and the individual forecasts being combined; and then estimating the correlation parameters capturing linear dependence between the target and the experts’ predictions. If the target variable and experts’ predictions are individually Gaussian distributed, our copula point combination reproduces the GR combination. We illustrate our methodology with two applications examining quarterly forecasts for the Federal Funds rate and for US output growth, respectively. The copula point combinations outperform the forecasts from the individual experts in both applications, with gains in root mean squared forecast error in the region of 40% for the Federal Funds rate and 4% for output growth relative to the GR combination. The fitted marginal distribution for the interest rate exhibits strong asymmetry.

Baumeister and Kilian (2015) 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 similar 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 to fill in missing values of oil price futures in the source 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 (2015) yields similar results to those reported in their paper. And the futures-based model improves forecast accuracy at longer horizon forecasts. The real-time data set is available for download from shaunvahey.com.

SummaryBaumeister 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.

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.

We consider the fundamental issue of what makes a “good” probability forecast for a central bank operating within an inflation targeting framework. We provide two examples in which the candidate forecasts comfortably outperform those from benchmark specifications by conventional statistical metrics such as root mean squared prediction errors and average logarithmic scores. Our assessment of economic significance uses an explicit loss function that relates economic value to a forecast communication problem for an inflation targeting central bank. We analyse the Bank of England’s forecasts for inflation during the period in which the central bank operated within a strict inflation targeting framework in our first example. In our second example, we consider forecasts for inflation in New Zealand generated from vector autoregressions, when the central bank operated within a flexible inflation targeting framework. In both cases, the economic significance of the performance differential exhibits sensitivity to the parameters of the loss function and, for some values, the differentials are economically negligible.

We propose a methodology to gauge the uncertainty in output gap nowcasts across a large number of commonly deployed vector autoregressions in US inflation and various measures of the output gap. Our approach constructs ensemble nowcast densities using a linear opinion pool. This yields well-calibrated nowcasts for US inflation in real time from 1991q2 to 2010q1, in contrast to those from a univariate autoregressive benchmark. The ensemble nowcast densities for the output gap are considerably more complex than for a single VAR specification. They cannot be described adequately by the first two moments of the forecast densities. To illustrate the usefulness of our approach, we calculate the probability of a negative output gap at around 45 percent between 2004 and 2007. Despite the Greenspan policy regime, and some large point estimates of the output gap, there remained a substantial risk that output was below potential in real time. Our ensemble approach also facilitates probabilistic assessments of “alternative scenarios”. A “dove” scenario (based on distinct output gap measurements) typically raises substantially the probability of a negative output gap (including 2004 through 2007) but has little impact in slumps, in our illustrative example.

Some prominent economic experts have contended that (the early stages of) the Great Recession resembled the Great Depression. In this paper, we utilize an expert-based framework to produce probabilistic projections for output growth and ination during the recent slump. We divide our US data prior to the Great Recession into ve distinct historical eras. Each expert estimates a vector autoregressive model (VAR) on data from a unique era, with epoch dates reecting conventional timing assumptions adopted in the economic history literature. We

This paper proposes an international collaboration between researchers in academia and policymaking institutions to stimulate and coordinate research on probability forecasting in macroeconomics, developing a toolbox for short-term prediction. The toolbox should include time series models, methods for forecast combination, and techniques for probabilistic forecast evaluation in order to reduce the setup costs and risks to both individual researchers and policymaking organizations. A particular emphasis should be placed on replication studies with the toolbox so that central bankers can be sure that they are utilizing best practice techniques to produce probabilistic forecasts of events of interest. Full publication: Globalisation and Inflation Dynamics in Asia and the Pacific