Working Papers

Estimating Robustness
[PDF, September 2017] [online_appendix] [code]I estimate and evaluate a model with a representative agent who is concerned that the persistence properties of her baseline model of consumption and inflation are misspecified. Coping with model uncertainty, she discovers a pessimistically biased worstcase model that dictates her behavior. I combine interest rates and aggregate macro series with crossequation restrictions implied by robust control theory to estimate this worstcase distribution and show that (1) the model’s predictions about key features of the yield curve are in line with the data, and (2) the degree of pessimism underlying these findings is plausible. Interpreting the worstcase as the agent’s subjective belief, I derive model implied interest rate forecasts and compare them with analogous survey expectations. I find that the model can replicate the dynamics and average level of bias found in the survey.

Twisted Probabilities, Uncertainty, and Prices
(with Lars Peter Hansen, Thomas J. Sargent, and Lloyd Han)
[PDF, May 2019]A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent alternatives that are statistically close to a decision maker’s baseline model. The set is twisted to include some specific models of interest. Maxmin expected utility over that set gives rise to equilibrium prices of model uncertainty expressed as worstcase distortions to drifts in a representative investor’s baseline model. Three quantitative illustrations start with baseline models having exogenous longrun risks in technology shocks. These put endogenous longrun risks into consumption dynamics that differ in details that depend on how shocks affect returns to capital stocks. We describe sets of alternatives to a baseline model that generate countercyclical prices of uncertainty.

Learning with Misspecified Models
(with Daniel Csaba)
[PDF, June 2019]
We consider Bayesian learning about a stable environment when the learner’s entertained set of probability distributions (likelihoods) is misspecified. We study how this entertained set affects the agent’s welfare through the limit point of learning and the associated bestresponding policy. To this end, we introduce a performance measure of likelihoods based on their induced policies’ longrun average payoff. Using this measure we define two asymptotic properties of sets of likelihoods that a utilitymaximizing agent would find desirable. We show that arbitrary sets of likelihoods coupled with Bayesian learning fail to satisfy both of our properties. However, we characterize a class of decision problems for which one can construct a misspecified set of likelihoods that achieves the highest attainable longrun average payoff irrespective of the data generating process. Our recommendation builds on the payoffrelevant moments—specific to the decision problem at hand—to provide the sufficient statistics of an exponential family of likelihoods. This set of likelihoods coupled with Bayesian learning ensures that the moments targeted by learning coincide with the moments that are relevant for implementing wellperforming policies.

Optimal Positive Capital Taxes at Interior Steady States
(with Jess Benhabib)
[PDF, May 2019]
We generalize recent results of Bassetto and Benhabib (2006) and Straub and Werning (2018) in a model with endogenous laborleisure choice where all agents are allowed to save and accumulate capital. In particular, using a neoclassical infinite horizon model with standard balanced growth preferences and agents heterogeneous in their initial wealth holdings, we provide a sufficient condition under which optimal redistributive capital taxes can remain at their allowed upper bound forever, even if the resulting equilibrium trajectory converges to a unique steady state with positive and finite consumption, capital, and labor. We first generate some simple parametric examples which satisfy our sufficient condition and for which closed form solutions exist. We then provide an interpretation of our sufficient condition for equilibria induced by general constant returns neoclassical production functions. Using recent evidence on wealth distribution in the United States,
we argue that our sufficient condition is empirically plausible.