# Working Papers

**Costs of Financing US Federal Debt: 1791-1933**

(*with George Hall, Jonathan Payne, and Thomas J. Sargent*)**[PDF, August 2021]**

We use computational Bayesian methods to estimate parameters of a statistical model of gold, greenback, and real yield curves for US federal debt from 1791 to 1933. Posterior probability coverage intervals indicate more uncertainty about yields during periods in which data are especially sparse. We detect substantial discrepancies between our approximate yield curves and standard historical series on yields on US federal debt, especially during War of 1812 and Civil War surges in government expenditures that were accompanied by units of account ambiguities. We use our approximate yield curves to describe how long it took to achieve Alexander Hamilton’s goal of reducing default risk premia in US yields by building a reputation for servicing debts as promised. We infer that during the Civil War suspension of convertibility of greenback dollars into gold dollars, US creditors anticipated a rapid post war return to convertibility at par, but that after the war they anticipated a slower return.

**Learning with Misspecified Models**(

*with Dániel Csaba*)

**[PDF, May 2020]**

We consider likelihood-based learning when the learner’s entertained set of likelihoods is misspecified. We focus on the welfare implications of misspecified sets through the limit point of learning and the associated best-responding policy. Building on their best-responding policy, we define consistency requirements for sets of likelihoods that a utility-maximizing agent would find desirable. We show that learning with arbitrary sets of likelihoods fails to satisfy our consistency requirements. However, we characterize a class of decision problems for which one can construct exponential families of likelihoods—using the payoff-relevant moments as sufficient statistics—that guarantee the implementation of optimal policies irrespective of the data generating process.

**Uncertainty Shocks in a Monetary Economy[PDF, November 2019]**

This paper studies a stochastic economy with flexible prices in which money has real effects. A representative household faces a portfolio choice between a nominally safe asset that provides transaction services and a risky productive capital with time-varying return volatility. Stochastic volatility and the behavior of the central bank determine an equilibrium asset allocation. When the objective of monetary policy is to stabilize inflation around a fixed target, the nominally safe asset becomes a relatively safe store of value in real terms as well. As a result, in response to higher uncertainty, the private sector shifts resources away from risky capital, causing output and investment to fall. To investigate the resulting non-linear dynamics, I solve the model globally and compute generalized impulse response functions across the support of the stationary distribution. Impulse response functions with respect to volatility shocks exhibit strong state dependence: large falls in investment are more likely in a high-risk (low interest rate) environment than in a low-risk (high interest rate) environment. I use the calibrated model to interpret recent events and find that the model predicts comovements observed among a set of key macro variables during and after the Great Recession.

# Published or Forthcoming Papers

**Estimating Robustness**

*Journal of Economic Theory*, forthcoming, doi: 10.1016/j.jet.2021.105225

[PDF, February 2021] [online_appendix] [code]

[PDF, February 2021] [online_appendix] [code]

featured in the inaugural David K. Backus Memorial Lecture by Tom Sargent [video]

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 worst-case model that dictates her behavior. I combine interest rates and aggregate macro series with cross-equation restrictions implied by robust control theory to estimate this worst-case 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 worst-case 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.

**Optimal Positive Capital Taxes at Interior Steady States**(

*with Jess Benhabib*)

*AEJ:Macroeconomics*(2021) 13 (1): 114-50, doi: 10.1257/mac.20180191

**[PDF, January 2020]**

**[**

*NBER working paper 25895*

**]**

We generalize recent results of Bassetto and Benhabib (2006) and Straub and Werning (2018) in a model with endogenous labor-leisure 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.

**Twisted Probabilities, Uncertainty, and Prices**(

*with Lars Peter Hansen, Thomas J. Sargent, and Lloyd Han*)

*Journal of Econometrics*(2020) 216 (1) : 151-174, doi: 10.1016/j.jeconom.2020.01.011

**[PDF, January 2020]**

**[online appendix] [code, binder]**

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 worst-case distortions to drifts in a representative investor’s baseline model. Three quantitative illustrations start with baseline models having exogenous long-run risks in technology shocks. These put endogenous long-run 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.