We study how a concern for robustness modifies a policy maker's incentive to experiment. A policy maker has a prior over two submodels of inflation-unemployment dynamics. One submodel implies an exploitable trade-off, the other does not. Bayes' law gives the policy maker an incentive to experiment. The policy maker fears that both submodels and prior probability distribution over them are misspecified. We compute decision rules that are robust to misspecifications of the dynamics posited by each submodel as well as the prior distribution over submodels. We compare robust rules to ones that Cogley, Colacito, and Sargent (2007) computed assuming that the models and the prior distribution are correctly specified. We explain why the policy maker's desires to protect against misspecifications of the submodels, on the one hand, and misspecifications of the prior over them, on the other, have different effects on the decision rule. (With Tim W. Cogley, Lars Peter Hansen and Tom J. Sargent)

In this paper we document the presence of a time structure of risk and we propose how to measure it using alternative models to forecast volatility and the VaR at different horizons. We then quantify the benefits of an investor that is aware of the existence of a term structure of risk in the context of an asset allocation exercise. (With Robert Engle)

A policy maker knows two models of inflation-unemployment dynamics. One implies an exploitable trade-off. The other does not. The policy maker's prior probability over the two models is part of his state vector. Bayes law converts the prior into a posterior at each date and gives the policy maker an incentive to experiment. For a model calibrated to U.S. data through the early 1960s, we isolate the component of government policy that is due to experimentation by comparing the outcomes from two Bellman equations, the first of which embodies a `experiment and learn' setup, the second of which embodies a `don't experiment, do learn' view. We interpret the second as an example of an `anticipated utility' model and study how well its outcomes approximate those from the `experiment and learn' Bellman equation. (With Tim Cogley and Tom Sargent)

We evaluate alternative models of variances and correlations with an economic loss function. We construct portfolios to minimize predicted variance subject to a required return. It is shown that the realized volatility is smallest for the correctly specified covariance matrix for any vector of expected returns. A test of relative performance of two covariance matrices is based on Diebold and Mariano (1995). The method is applied to stocks and bonds and then to highly correlated assets. On average dynamically correct correlations are worth around 60 basis points in annualized terms but on some days they may be worth hundreds. (With Robert F. Engle)