This paper is concerned with evaluating value at risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Maganelli (2004) are based on such variables. In this paper we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker & Xiao, 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series.

The departure from the traditional concern with the central tendency is in line with the increasing recognition that an assessment of the degree of uncertainty surrounding a point forecast is indispensable (Clements 2004). We propose an econometric model to estimate the conditional density without relying on assumptions about the parametric form of the conditional distribution of the target variable. The methodology is applied to the U.S. unemployment rate and the survey of professional forecasts. Specification tests based on Koenker and Xiao (2002) and Gaglianone et al. (2011) indicate that our approach correctly approximates the true conditional density.

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a b s t r a c tThis paper investigates macro stress testing of system-wide credit risk with special focus on the tails of the credit risk distributions conditional on adverse macroeconomic scenarios. These tails determine the ex-post solvency probabilities derived from the scenarios. This paper estimates the macro-credit risk link by the traditional Wilson (1997a,b) model as well as by an alternative proposed quantile regression (QR) method (Koenker and Xiao, 2002), in which the relative importance of the macro variables can vary along the credit risk distribution, conceptually incorporating uncertainty in default correlations. Stress-testing exercises on the Brazilian household sector at the one-quarter horizon indicate that unemployment rate distress produces the most harmful effect, whereas distressed inflation and distressed interest rate show higher impacts at longer periods. Determining which of the two stress-testing approaches perceives the scenarios more severely depends on the type of comparison employed. The QR approach is revealed more conservative based on a suggested comparison of vertical distances between the tails of the conditional and unconditional credit risk cumulative distributions.

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SUMMARY 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.

In this paper we investigate fiscal sustainability by using a quantile autoregression (QAR) model. We propose a novel methodology to separate periods of nonstationarity from stationary ones, allowing us to identify various trajectories of public debt that are compatible with fiscal sustainability. We use such trajectories to construct a debt ceiling, that is, the largest value of public debt that does not jeopardize long-run fiscal sustainability. We make an out-of-sample forecast of such a ceiling and show how it could be used by Policy makers interested in keeping the public debt on a sustainable path. We illustrate the applicability of our results using Brazilian data.

Rational inattention" is becoming increasingly prominent in economic modelling, but there is little empirical evidence for its central premise-that the choice of attention results from a cost-benefit optimization. Observational data typically do not allow researchers to infer attention choices from observables. We fill this gap in the literature by exploiting a unique dataset of professional forecasters who update their inflation forecasts at days of their choice. In the data we observe how many forecasters update (extensive margin of updating), the magnitude of the update (intensive margin), and the objective of optimization (forecast accuracy). There are also "shifters" in incentives: A contest that increases the benefit of accurate forecasting, and the release of official data that reduces the cost of information acquisition. These features allow us to link observables to attention and incentive parameters. We structurally estimate a model where the decision to update and the magnitude of the update are endogenous and the latter is the outcome of a rational inattention optimization. The model fits the data and gives realistic predictions. We find that shifts in incentives affect both extensive and intensive margins, but the shift in benefits from the contest has the largest aggregate effect. Counterfactuals reveal that accuracy is maximized if the contest coincides with the release of information, aligning higher benefits with lower costs of attention.