Minchul Shin

Bayesian Estimation and Comparison of Moment Condition Models

ABSTRACT In this article, we develop a Bayesian semiparametric analysis of moment condition models by casting the problem within the exponentially tilted empirical likelihood (ETEL) framework. We use this framework to develop a fully Bayesian analysis of correctly and misspecified moment condition models. We show that even under misspecification, the Bayesian ETEL posterior distribution satisfies the Bernstein–von Mises (BvM) theorem. We also develop a unified approach based on marginal likelihoods and Bayes factors for comparing different moment-restricted models and for discarding any misspecified moment restrictions. Computation of the marginal likelihoods is by the method of Chib (1995) as extended to Metropolis–Hastings samplers in Chib and Jeliazkov in 2001. We establish the model selection consistency of the marginal likelihood and show that the marginal likelihood favors the model with the minimum number of parameters and the maximum number of valid moment restrictions. When the models are misspecified, the marginal likelihood model selection procedure selects the model that is closer to the (unknown) true data-generating process in terms of the Kullback–Leibler divergence. The ideas and results in this article broaden the theoretical underpinning and value of the Bayesian ETEL framework with many practical applications. The discussion is illuminated through several examples. Supplementary materials for this article are available online.

A New Approach to Identifying the Real Effects of Uncertainty Shocks

ABSTRACT This article introduces the use of the sign restrictions methodology to identify uncertainty shocks. We apply our methodology to a class of vector autoregression models with stochastic volatility that allow volatility fluctuations to impact the conditional mean. We combine sign restrictions on the conditional mean and conditional second moment impulse responses to identify financial and macro uncertainty shocks. On U.S. data, we find stronger evidence that financial uncertainty shocks lead to a decline in real activity and an easing of the federal funds rate relative to macro uncertainty shocks. Supplementary materials for this article are available online.

On the Comparison of Interval Forecasts: ON THE COMPARISON OF INTERVAL FORECASTS

We explore interval forecast comparison when the nominal coni¬ dence level is specii¬ ed, but the quantiles on which intervals are based are not specii¬ ed. It turns out that the problem is dii¬ƒcult, and perhaps unsolvable. We i¬ rst consider a situation where intervals meet the Christoi¬€ersen conditions (in particular, where they are correctly calibrated), in which case the common prescription, which we rationalize and explore, is to prefer the interval of shortest length. We then allow for mis-calibrated intervals, in which case there is a calibration-length tradeoi¬€. We propose two natural conditions that interval forecast loss functions should meet in such environments, and we show that a variety of popular approaches to interval forecast comparison fail them. Our negative results strengthen the case for abandoning interval forecasts in favor of density forecasts: Density forecasts not only provide richer information, but also can be readily compared using known proper scoring rules like the log predictive score, whereas interval forecasts cannot.

Measuring International Uncertainty: the Case of Korea

We leverage a data rich environment to construct and study a measure of macroeconomic uncertainty for the Korean economy. We provide several stylized facts about uncertainty in Korea from 1991M10-2016M5. We compare and contrast this measure of uncertainty with two other popular uncertainty proxies, financial and policy uncertainty proxies, as well as the U.S. measure constructed by Jurado et. al. (2015).

Real-Time Forecast Evaluation of DSGE Models with Stochastic Volatility

Recent work has analyzed the forecasting performance of standard dynamic stochastic general equilibrium (DSGE) models, but little attention has been given to DSGE models that incorporate nonlinearities in exogenous driving processes. Against that background, we explore whether incorporating stochastic volatility improves DSGE forecasts (point, interval, and density). We examine real-time forecast accuracy for key macroeconomic variables including output growth, inflation, and the policy rate. We find that incorporating stochastic volatility in DSGE models of macroeconomic fundamentals markedly improves their density forecasts, just as incorporating stochastic volatility in models of financial asset returns improves their density forecasts.

Finance and Economics Discussion Series

A structural model with stochastic volatility and jumps implies specific relationships between observed equity returns and credit spreads. This paper explores such effects in the credit default swap (CDS) market. We use a novel approach to identify the realized jumps of individual equities from high frequency data. Our empirical results suggest that volatility risk alone predicts 50 percent of the variation in CDS spreads, while jump risk alone forecasts 19 percent. After controlling for credit ratings, macroeconomic conditions, and firms’ balance sheet information, we can explain 77 percent of the total variation. Moreover, the pricing effects of volatility and jump measures vary consistently across investment-grade and high-yield entities. The estimated nonlinear effects of volatility and jumps are in line with the model-implied relationships between equity returns and credit spreads. JEL Classification Numbers: G12, G13, C14.