C53 Forecasting and Other Model Applications

March 3, 2010

We propose a methodology for producing density forecasts for the output gap in real time using a large number of vector autoregessions in inflation and output gap measures. Density combination utilizes a linear mixture of experts framework to produce potentially non-Gaussian ensemble densities for the unobserved output gap. In our application, we show that data revisions alter substantially our probabilistic assessments of the output gap using a variety of output gap measures derived from univariate detrending filters. The resulting ensemble produces well-calibrated forecast densities for US inflation in real time, in contrast to those from simple univariate autoregressions which ignore the contribution of the output gap. Combining evidence from both linear trends and more flexible univariate detrending filters induces strong multi-modality in the predictive densities for the unobserved output gap. The peaks associated with these two detrending methodologies indicate output gaps of opposite sign for some observations, reflecting the pervasive nature of model uncertainty in our US data.

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October 1, 2009

We defend the forecasting performance of the FOMC from the recent criticism of Christina and David Romer. Our argument is that the FOMC forecasts a worst-case scenario that it uses to design decisions that will work well enough (are robust) despite possible misspecification of its model. Because these FOMC forecasts are not predictions of what the FOMC expects to occur under its model, it is inappropriate to compare their performance in a horse race against other forecasts. Our interpretation of the FOMC as a robust policymaker can explain all the findings of the Romers and rationalises differences between FOMC forecasts and forecasts published in the Greenbook by the staff of the Federal Reserve System.

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February 1, 2011

We use TVP models and real-time data to describe the evolution of the leading properties of the yield spread for output growth in five European economies and in the US over the last decades and until the third quarter of 2010. We evaluate the predictive performance of benchmark term-structure models and identify structural breaks in the marginal processes of term spreads and government bond yields to shed light on the dynamic characteristics of the yield curve. Econometric analysis shows that: (i) the predictive content of the term spread is not always significant over time and across countries; (ii) the spread significantly contributes to the forecast performance of simple growth regressions in Europe, but not in the US in recent years; (iii) the variance of the random shocks to the term spreads tends to fall in all countries. This decline is accompanied by vanishing leading properties from the mid-1990s. Such properties reappear after 2008.

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August 1, 2005

This paper formalizes the process of updating the nowcast and forecast on output and inflation as new releases of data become available. The marginal contribution of a particular release for the value of the signal and its precision is evaluated by computing 'news' on the basis of an evolving conditioning information set. The marginal contribution is then split into what is due to timeliness of information and what is due to economic content. We find that the Federal Reserve Bank of Philadelphia surveys have a large marginal impact on the nowcast of both inflation variables and real variables and this effect is larger than that of the Employment Report. When we control for timeliness of the releases, the effect of hard data becomes sizeable. Prices and quantities affect the precision of the estimates of GDP while inflation is only affected by nominal variables and asset prices.

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January 1, 2005

The Paper provides new tools for the evaluation of DSGE models, and applies it to a large-scale New Keynesian dynamic stochastic general equilibrium (DSGE) model with price and wage stickiness and capital accumulation. Specifically, we approximate the DSGE model by a vector autoregression (VAR), and then systematically relax the implied cross-equation restrictions. Let delta denote the extent to which the restrictions are being relaxed. We document how the in- and out-of-sample fit of the resulting specification (DSGE-VAR) changes as a function of delta. Furthermore, we learn about the precise nature of the misspecification by comparing the DSGE model’s impulse responses to structural shocks with those of the best-fitting DSGE-VAR. We find that the degree of misspecification in large-scale DSGE models is no longer so large to prevent their use in day-to-day policy analysis, yet it is not small enough that it cannot be ignored.

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February 1, 2006

We explore whether forecasting an aggregate variable using information on its disaggregate components can improve the prediction mean squared error over first forecasting the disaggregates and then aggregating those forecasts, or, alternatively, over using only lagged aggregate information in forecasting the aggregate. We show theoretically that the first method of forecasting the aggregate should outperform the alternative methods in population. We investigate whether this theoretical prediction can explain our empirical findings and analyse why forecasting the aggregate using information on its disaggregate components improves forecast accuracy of the aggregate forecast of euro area and US inflation in some situations, but not in others.

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January 1, 2007

This paper estimates and tests a new Keynesian small open economy model in the tradition of Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003) using Bayesian estimation techniques on Swedish data. To account for the switch to an inflation targeting regime in 1993 we allow for a discrete break in the central bank's instrument rule. A key equation in the model - the uncovered interest rate parity (UIP) condition - is well known to be rejected empirically. Therefore we explore the consequences of modifying the UIP condition to allow for a negative correlation between the risk premium and the expected change in the nominal exchange rate. The results show that the modification increases the persistence and volatility in the real exchange rate and that this model has an empirical advantage compared with the standard UIP specification.

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October 1, 2005

This paper explores the usefulness of bagging methods in forecasting economic time series from linear multiple regression models. We focus on the widely studied question of whether the inclusion of indicators of real economic activity lowers the prediction mean-squared error of forecast models of US consumer price inflation. We study bagging methods for linear regression models with correlated regressors and for factor models. We compare the accuracy of simulated out-of-sample forecasts of inflation based on these bagging methods to that of alternative forecast methods, including factor model forecasts, shrinkage estimator forecasts, combination forecasts and Bayesian model averaging. We find that bagging methods in this application are almost as accurate or more accurate than the best alternatives. Our empirical analysis demonstrates that large reductions in the prediction mean squared error are possible relative to existing methods, a result that is also suggested by the asymptotic analysis of some stylized linear multiple regression examples.

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October 1, 2005

We extend the standard approach to Bayesian forecast combination by forming the weights for the model averaged forecast from the predictive likelihood rather than the standard marginal likelihood. The use of predictive measures of fit offers greater protection against in-sample overfitting and improves forecast performance. For the predictive likelihood we show analytically that the forecast weights have good large and small sample properties. This is confirmed in a simulation study and an application to forecasts of the Swedish inflation rate where forecast combination using the predictive likelihood outperforms standard Bayesian model averaging using the marginal likelihood.

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October 1, 2005

We document the empirical properties of revisions to major macroeconomic variables in the United States. Our findings suggest that they do not satisfy simple desirable statistical properties. In particular, we find that these revisions do not have a zero mean, which indicates that the initial announcements by statistical agencies are biased. We also find that the revisions are quite large compared to the original variables and they are predictable using the information set at the time of the initial announcement, which means that the initial announcements of statistical agencies are not rational forecasts. We also provide evidence that professional forecasters ignore this predictability.

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