## Working Papers:

### Fiscal Policy and Debt Management with Incomplete Markets (with Anmol Bhandari, Mikhail Golosov, and Thomas Sargent), forthcoming *Quarterly Journal of Economics*

A Ramsey planner chooses a distorting tax on labor and manages a portfolio of securities in an environment with incomplete markets. We develop a method that uses second order approximations of the policy functions to the planner’s Bellman equation to obtain expressions for the unconditional and conditional moments of debt and taxes in closed form such as the mean and variance of the invariant distribution as well as the speed of mean reversion. Using this, we establish that asymptotically the planner’s portfolio minimizes an appropriately defined measure of fiscal risk. Our analytic expressions that approximate moments of the invariant distribution can be readily applied to data recording the primary government deficit, aggregate consumption, and returns on traded securities. Applying our theory to U.S. data, we find that an optimal target debt level is negative but close to zero, that the invariant distribution of debt is very dispersed, and that mean reversion is slow.

### Public Debt in Economies with Heterogeneous Agents (joint with Anmol Bhandari, Mikhail Golosov and Thomas Sargent), forthcoming JME

We study public debt in competitive equilibria in which a government chooses transfers and taxes optimally and in addition decides how thoroughly to enforce debt contracts. If the government enforces perfectly, asset inequality is determined in an optimum competitive equilibrium but the level of government debt is not. Welfare increases if private debt contracts are not enforced. Borrowing frictions let the government gather monopoly rents that come from issuing public debt without facing competing private borrowers. Regardless of whether the government chooses to enforce private debt contracts, the level of initial government debt does not affect an optimal allocation.

### Inequality, Business Cycles and Monetary-Fiscal- Policy (joint with Anmol Bhandari, Mikhail Golosov and Thomas Sargent)

We study fluctuations in macroeconomic aggregates and cross-section income and wealth distributions in a heterogeneous agent model with incomplete markets and sticky nominal prices. Optimal fiscal-monetary policy balances gains from “fiscal hedging” against benefits from “redistributional hedging” that responds to social concerns about inequality. A Ramsey planner uses inflation to offset inequality-increasing shocks to the cross-section distribution of labor earnings. A calibration that imitates how US recessions reshape that cross-section distribution in ways documented by Guvenen et al. (2014) indicates that substantial welfare benefits come from making inflation respond to aggregate shocks.

### The Optimal Maturity of Government Debt (joint with Anmol Bhandari, Mikhail Golosov and Thomas Sargent)

A Ramsey planner chooses a distorting tax on labor and manages a portfolio of bonds of different maturities in a representative agent economy with aggregate shocks. Covariances of bonds’ returns with the primary deficit are key determinants of Ramsey portfolios. We estimate these moments in U.S. data and calibrate a model with a representative agents who has Epstein-Zin preferences that matches these moments. The implied optimal portfolio does not short any bond and allocates approximately equal portfolio shares to bonds of different maturities, slightly tilt towards longer maturities when the outstanding debt is large, and requires little re-balancing in response to aggregate shocks. These portfolio prescriptions differ from those of models often used in the business cycle literature. The differences are driven by counterfactual asset pricing implications of the standard models.

### Optimal Taxation with Persistent Idiosyncratic Investment Risk

We study the role of capital taxation in a general equilibrium heterogeneous agent economy with uninsurable investment risk characterized by persistent productivity shocks to the firms privately owned by the entrepreneurs. In contrast to models with i.i.d. investment risk, the inclusion of persistent investment risk does not allow for easy aggregation. Instead, in solving this model we use a novel application of perturbation theory to economies with heterogeneous agents. This application exploits a symmetry that reduces the computational burden of approximating policy rules via a truncated Taylor expansion, allowing us to change the point of approximation to be the closest non-degenerate steady state to the current state of the planner’s problem as the economy evolves. The presence of idiosyncratic investment risk leads to an under-accumulation of capital, which leads the Ramsey planner to have two conflicting motives in setting the capital tax. On the one hand, the planner wishes to correct the under-accumulation of capital by subsidizing saving. On the other hand, the planner wants to use capital taxes to redistribute from agents whose investments paid off to those whose investments did not perform well. In the presence of i.i.d. productivity shocks the first motive dominates and the planner moves to correct the savings decisions of the agents, but we find that with persistent shocks the motive for redistribution dominates, leading the government to tax capital. This result is robust to the inclusion of financial frictions.

## Work In Progress

### Perturbation Theory with Heterogeneous Agents: A Multi-Country Application.

### Switching Costs and Returns in Factor Markets (with Keaton Miller)

### Endogenous neighborhood selection, the distribution of income, and identification of neighborhood effects (with Bryan Graham)