Evaluating Asset-Pricing Models Using The Hansen-Jagannathan Bound: A Monte Carlo Investigation

We conduct Monte Carlo experiments to examine whether the bound proposed by Hansen and Jagannathan (1991) is a useful device for evaluating asset pricing models. Specifically, we use recently developed statistical tests, which are based on a 'distance' between the model and the Hansen-Jagannathan bound, to compute the rejection rates of true models. We provide finite-sample critical values for asset pricing models with time separable preferences, and show how they depend upon nuisance parameters—risk aversion and the rate of time preference. Further, we show that the finite-sample distribution of the test statistic associated with the risk-neutral case is extreme, in the sense that critical values based on this distribution will deliver type I errors no larger than intended—regardless of risk aversion or the rate of time preference. Extending the analysis to accommodate other preferences, we show that in the state non-separable case, the small-sample distributions of the test statistics are influenced significantly by the degree of intertemporal substitution, but not by attitudes toward risk. For habit formation preferences, the small-sample distributions are strongly influenced by the habit parameter. However, the maximal-size critical values for time-separable preferences are appropriate for habit formation as well as state non-separable preferences. We conclude that with these critical values the HJ bound is indeed a useful evaluation device. We then use the critical values to evaluate three asset pricing models using U.S. data. We find evidence against the time-separable model and mixed evidence on the remaining two models.

Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders

This paper develops a dynamic asset pricing model with persistent heterogeneous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia’s (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents’ information sets. When these conditions are satisfied, agents must ‘forecast the forecasts of others’. The paper provides an explicit analytical characterization of the resulting higher-order belief dynamics. These additional dynamics can explain apparent violations of variance bounds and rejections of cross-equation restrictions.Asymmetric Information, Blaschke Factors

Forecasting using relative entropy

The paper describes a relative entropy procedure for imposing moment restrictions on simulated forecast distributions from a variety of models. Starting from an empirical forecast distribution for some variables of interest, the technique generates a new empirical distribution that satisfies a set of moment restrictions. The new distribution is chosen to be as close as possible to the original in the sense of minimizing the associated Kullback-Leibler Information Criterion, or relative entropy. The authors illustrate the technique by using several examples that show how restrictions from other forecasts and from economic theory may be introduced into a model's forecasts.Forecasting

Worldwide Persistence, Business Cycles, and Economic Growth

We study the time series properties of aggregate data drawn from the Penn World Tables using numerical Bayesian procedures which facilitate inference with small samples. We find substantial persistence in world aggregates, and some evidence for a world business cycle. Across economies, there is great dispersion in our measure of persistence of shocks to real gross domestic product. That we also find no evidence of a relationship between growth and persistence sheds light on which of two competing models of endogenous growth is likely to be able to explain the PWT data

Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders

This paper develops a dynamic asset pricing model with persistent heterogeneous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia’s (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents’ information sets. When these conditions are satisfied, agents must ‘forecast the forecasts of others’. The paper provides an explicit analytical characterization of the resulting higher-order belief dynamics. These additional dynamics can explain apparent violations of variance bounds and rejections of cross-equation restrictions

Worldwide Persistence, Business Cycles, and Economic Growth

We study the time series properties of aggregate data drawn from the Penn World Tables using numerical Bayesian procedures which facilitate inference with small samples. We find substantial persistence in world aggregates, and some evidence for a world business cycle. Across economies, there is great dispersion in our measure of persistence of shocks to real gross domestic product. That we also find no evidence of a relationship between growth and persistence sheds light on which of two competing models of endogenous growth is likely to be able to explain the PWT data

Endogenous term premia and anomalies in the term structure of interest rates: explaining the predictability smile

Recent studies have documented the existence of a "predictability smile" in the term structure of interest rates: spreads between long maturity rates and short rates predict subsequent movements in interest rates provided the long horizon is three months or less or if the long horizon is two years or more, but not for intermediate maturities. Accounts for portions of the smile involve interest rate smoothing by the Fed, time-varying risk premia, "Peso problems," and measurement error. We take a more nearly general equilibrium approach to explaining this phenomenon and show that despite its highly restrictive nature, the Cox-Ingersoll-Ross (1985) model of the term structure can account for the predictability smile.Financial markets ; Interest rates

Interactions between downslope flows and a developing cold-air pool

A numerical model has been used to characterize the development of a region of enhanced cooling in an alpine valley with a width of order (Formula presented.) km, under decoupled stable conditions. The region of enhanced cooling develops largely as a region of relatively dry air which partitions the valley atmosphere dynamics into two volumes, with airflow partially trapped within the valley by a developing elevated inversion. Complex interactions between the region of enhanced cooling and the downslope flows are quantified. The cooling within the region of enhanced cooling and the elevated inversion is almost equally partitioned between radiative and dynamic effects. By the end of the simulation, the different valley atmospheric regions approach a state of thermal equilibrium with one another, though this cannot be said of the valley atmosphere and its external environment.Peer reviewe