Papers

Reinterpreting most of the market price of risk as a price of model uncertainty eradicates a link between asset prices and measures of the welfare costs of aggregate fluctuations that was proposed by Hansen, Sargent, and Tallarini [17], Tallarini [30], Alvarez and Jermann [1]. Prices of model uncertainty contain information about the benefits of removing model uncertainty, not the consumption fluctuations that Lucas [22] and [23] studied. A max–min expected utility theory lets us reinterpret Tallarini’s risk-aversion parameter as measuring a representative consumer’s doubts about the model specification. We use model detection instead of risk-aversion experiments to calibrate that parameter. Plausible values of detection error probabilities give prices of model uncertainty that approach the Hansen and Jagannathan [11] bounds. Fixed detection error probabilities give rise to virtually identical asset prices as well as virtually identical costs of model uncertainty for Tallarini’s two models of consumption growth.

@article{bhs:2009,
  title={Doubts or Variability?},
  author={Barillas, Francisco and Hansen, Lars Peter and Sargent, Thomas J},
  journal={journal of economic theory},
  volume={144},
  number={6},
  pages={2388--2418},
  year={2009},
  publisher={Elsevier}
}

We study how a concern for robustness modifies a policymaker’s incentive to experiment. A policymaker 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 policymaker an incentive to experiment. The policymaker fears that both submodels and his prior probability distribution over them are misspecified. We compute decision rules that are robust to misspecifications of each submodel and of 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 how the policymaker’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.

@article{cchs:2008,
  title={Robustness and US Monetary Policy Experimentation},
  author={Cogley, Timothy and Colacito, Riccardo and Hansen, Lars Peter and Sargent, Thomas J},
  journal={Journal of Money, Credit and Banking},
  volume={40},
  number={8},
  pages={1599--1623},
  year={2008},
  publisher={Wiley Online Library}
}

In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes’ law under an approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby when measured by their expected log likelihood ratios (entropies). Martingales represent alternative models. A decision maker constructs a sequence of robust decision rules by pretending that a sequence of minimizing players choose increments to martingales and distortions to the prior over the hidden state. A risk sensitivity operator induces robustness to perturbations of the approximating model conditioned on the hidden state. Another risk sensitivity operator induces robustness to the prior distribution over the hidden state. We use these operators to extend the approach of Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40(5) (1995) 968–971] to problems that contain hidden states.