Working papers
 Spectral Conditions for Existence and Uniqueness of Recursive Utilities (with John Stachurski)We study existence, uniqueness and computability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences—one that analyzes principal eigenvalues of valuation operators and another that exploits the theory of monotone concave operators—we obtain conditions that are both necessary and sufficient for existence and uniqueness of solutions. We also show that the natural iterative algorithm is convergent if and only if a solution exists. Consumption processes are allowed to be nonstationary.
 Identifying Ambiguity Shocks in Business Cycle Models Using Survey Data (with Anmol Bhandari and Paul Ho)We develop a framework to analyze economies with agents facing timevarying concerns for model misspecification. These concerns lead agents to interpret economic outcomes and make decisions through the lens of a pessimistically biased `worstcase' model. We combine survey data and implied theoretical restrictions on the relative magnitudes and comovement of forecast biases across macroeconomic variables to identify ambiguity shocks as exogenous fluctuations in the worstcase model. Our solution method delivers tractable linear approximations that preserve the effects of timevarying ambiguity concerns and permit estimation using standard Bayesian techniques. Applying our framework to an estimated NewKeynesian business cycle model with frictional labor markets, we find that ambiguity shocks explain a substantial portion of the variation in labor market quantities.

Revise and resubmit, Journal of Political Economy[PDF, 17 October 2016] [bibtex] Circulated under the title Heterogeneous Beliefs under Recursive Preferences.Online appendix with additional discussion and resultsI study the longrun behavior of an economy with two types of agents who differ in their beliefs and are endowed with homothetic recursive preferences of the DuffieEpsteinZin type. Contrary to models with separable preferences in which the wealth of agents with incorrect beliefs vanishes in the long run, recursive preference specifications lead to longrun outcomes where both agents survive, or more incorrect agents dominate. I derive analytical conditions for the existence of nondegenerate longrun equilibria in which agents with differently accurate beliefs coexist in the long run, and show that these equilibria exist for broad ranges of plausible parameterizations when risk aversion is larger than the inverse of the intertemporal elasticity of substitution. The results highlight a crucial interaction between risk sharing, speculative behavior and consumptionsaving choice of agents with heterogeneous beliefs, and the role of equilibrium prices in shaping longrun outcomes.
Work in progress
 Discount Rates and Employment Fluctuations (with Katarína Borovičková)
 Optimal Policies with Robust Concerns (with Anmol Bhandari and Paul Ho)
 Robust Preference Expansions (with Lars Peter Hansen, available on request)
 Pricing Rare Events (with Lars Peter Hansen and José Scheinkman)
Publications
 Misspecified Recovery (with Lars Peter Hansen and José Scheinkman)Journal of Finance (2016) 71 (6): 24932544.Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from riskadjusted discounting, we use PerronFrobenius Theory to isolate a positive martingale component of the stochastic discount factor process. This component recovers a probability measure that absorbs longterm risk adjustments. When the martingale is not degenerate, surmising that this recovered probability captures investors' beliefs distorts inference about riskreturn tradeoffs. Stochastic discount factors in many structural models of asset prices have empirically relevant martingale components.
 Term Structure of Uncertainty in the Macroeconomy (with Lars Peter Hansen)Handbook of Macroeconomics: Volume 2B (2016) Chapter 20, Elsevier B.V., 16411696.Dynamic economic models make predictions about impulse responses that characterize how macroeconomic processes respond to alternative shocks over different horizons. From the perspective of asset pricing, impulse responses quantify the exposure of macroeconomic processes and other cash flows to macroeconomic shocks. Financial markets provide compensations to investors who are exposed to these shocks. Adopting an asset pricing vantage point, we describe and apply methods for computing exposures to macroeconomic shocks and the implied compensations represented as elasticities over alternative payoff horizons. The outcome is a term structure of macroeconomic uncertainty.
 Shock Elasticities and Impulse Responses (with Lars Peter Hansen and José Scheinkman)Mathematics and Financial Economics (2014) 8 (4): 333354.We construct shock elasticities that are pricing counterparts to impulse response functions. Recall that impulse response functions measure the importance of nextperiod shocks for future values of a time series. Shock elasticities measure the contributions to the price and to the expected future cash flow from changes in the exposure to a shock in the next period. They are elasticities because their measurements compute proportionate changes. We show a particularly close link between these objects in environments with Brownian information structures.
 Examining Macroeconomic Models through the Lens of Asset Pricing (with Lars Peter Hansen)Journal of Econometrics (2014) 183 (1): 6790.Shock elasticity toolbox for the computation of shock elasticities in models solved by Dynare/Dynare++ can be downloaded from the software page.We develop new methods for representing the assetpricing implications of stochastic general equilibrium models. We provide assetpricing counterparts to impulse response functions and the resulting dynamic value decompositions (DVDs). These methods quantify the exposures of macroeconomic cash flows to shocks over alternative investment horizons and the corresponding prices or investors' compensations. We extend the continuoustime methods developed in Hansen and Scheinkman (2012) and Borovička, Hansen, Hendricks, and Scheinkman (2011) by constructing discretetime, statedependent, shockexposure and shockprice elasticities as functions of the investment horizon. Our methods are applicable to economic models that are nonlinear, including models with stochastic volatility.Dynare model code [ZIP file] for the example in Section 7, based on the paper by Ai, Croce and Li (2010). Use in conjunction with the shock elasticity toolbox to produce the shock elasticities.
 RiskPrice Dynamics (with Lars Peter Hansen, Mark Hendricks, and José Scheinkman)Journal of Financial Econometrics (2011) 9 (1): 365.We present a novel approach to depicting asset pricing dynamics by characterizing shock exposures and prices for alternative investment horizons. We quantify the shock exposures in terms of elasticities that measure the impact of a current shock on future cashflow growth. The elasticities are designed to accommodate nonlinearities in the stochastic evolution modeled as a Markov process. Stochastic growth in the underlying macroeconomy and stochastic discounting in the representation of asset values are central ingredients in our investigation. We provide elasticity calculations in a series of examples featuring consumption externalities, recursive utility, and jump risk.