**Papers**

**Survey data and subjective beliefs in business cycle models**** ** (joint with Jaroslav Borovicka and Paul Ho) [**pdf**]

Survey data on household forecasts for unemployment and inflation rates reveal large upward biases that are positively correlated and counter-cyclical. We develop a framework to analyze general equilibrium settings where agents' subjective beliefs are endogenous and shaped by time-varying concerns for model misspecification. Applying our framework to a New-Keynesian model with frictional labor markets we find that an increase in concerns for model uncertainty generates large belief distortions which reduce aggregate demand and propagate through frictional goods and labor market to cause a contraction. As a part of our analysis we also develop solution techniques that preserve the effects of time-varying concerns for model misspecification with linear solutions.

**Sweat Equity in U.S. Private Business **(with Ellen McGrattan) [pdf]

This paper uses theory disciplined by U.S. national accounts and business census data to measure

private business sweat equity, which is the value of time to build customer bases, client lists,

and other intangible assets. We estimate an aggregate sweat equity value of 0.65 times GDP,

with little cross-sectional dispersion in valuations when compared to business net incomes and

large cross-sectional dispersion in rates of return. Our estimate of sweat equity is close to the

estimate of marketable fixed assets used in production by private businesses, implying a high ratio

of intangible to total assets. We use the model to evaluate impacts of greater tax compliance of

private businesses and lower tax rates on net income of both privately-held and publicly-traded

businesses.

**The Optimal Maturity of Government Debt **(joint with David Evans, Mikhail Golosov and Thomas Sargent)[pdf]

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.

**Inequality, Business Cycles and Monetary-****Fiscal- Policy**** **(joint with David Evans, Mikhail Golosov and Thomas Sargent)[pdf]

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.

**Asset Pricing with Endogenously Uninsurable Tail Risks **(joint with Hengjie Ai) **[paper],[technical appendix] ***R&R Econometrica*

This paper studies asset pricing in a setting where idiosyncratic risks in labor productivities are uninsurable due to limited commitment. Firms provide insurance to workers using long-term contracts but neither side can commit to these relationships. Under the optimal contract, sufficiently adverse shocks to worker productivity are uninsured. as firms cannot commit to negative net present value projects. In general equilibrium, exposure to down-side tail risks results in higher risk premia, more volatile returns and variation of returns across firms. The risk sharing patterns are also consistent with the observed cross-sectional variation in heterogeneity in earnings and wealth sensitivities to aggregate shocks.

**Public Debt in Economies with Heterogeneous Agents** (joint with David Evans, Mikhail Golosov and Thomas Sargent) [pdf] 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.

**Fiscal Policy and Debt Management with Incomplete Markets **(joint with David Evans, Mikhail Golosov and Thomas Sargent) [pdf] QJE

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 a planner's Bellman equation to obtain expressions for the mean, the variance, and the speed of convergence to the invariant distribution of debt, tax revenues and tax rates in closed form. 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.

**Doubts, Asymmetries, and Insurance **[pdf][slides]

This paper studies an insurance problem where agents doubt their forecasting models. Using Hansen-Sargent multiplier preferences, these doubts are represented as sets of probability distributions that are statistically hard to discriminate. Agents differ endogenously in two aspects - their forecasting models and the extent of doubts surrounding them. This heterogeneity gives rise to a new insurance channel that depends on sensitivity of marginal utilities to changes in consumption. We show how this interacts with other motives present when agents have exogenous heterogeneous beliefs or heterogeneous information about private insurance needs. The main results document the differences in limiting cross-sectional consumption patterns that arise from introducing a small amount of doubts. The transient wealth dynamics affects properties of asset prices and motives for trading on public signals.

**Practicing Dynare **(joint with Francisco Barillas, Saki Bigio, Riccardo Colacito, Sagiri Kitao, Christian Matthes, Thomas Sargent and Yongseok Shin) [pdf]

This paper teaches Dynare by applying it to approximate equilibria and estimate ten dynamic economic model. This is a revised version that includes a new section solving examples from the revised chapter `Fiscal Policies in a Growth Model' from the soon to be published third edition of Recursive Macroeconomic Theory by Ljungqvist and Sargent

**Working projects**

**Reverse Engineering Heterogeneous Beliefs [pdf]**

In a setting with heterogeneous agents and standard expected utility preferences, this paper reverse engineers a cross-section of beliefs that is consistent with an arbitrary stochastic discount factor process. A key feature of the construction is that no agent makes systematic errors and there is substantial trade across agents induced by belief differences. Applying our methods to the asset pricing model of Bansal and Yaron (2004), we find that the dispersion of reverse engineered beliefs tracks measures of cross-sectional forecast variance compugmted using panel data on professional forecasters. A lower bound on belief dispersion, which can be directly computed from data on returns and aggregate consumption, is also provided.

**Low Frequency Decomposition of Asset Prices** [pdf]

What determines low-frequency movements in aggregate asset returns ? This paper obtains a decomposition of asset returns into 3 components - Extent, Composition and Price Sensitivity of Risks. I estimate a multi-factor version of a standard asset pricing model with time-varying parameters to capture the changes in the three components mentioned before. The results highlight that there is a lot of heterogeneity in the time-variation of the 3 components and point to the importance of interaction effects in analyzing asset returns

**Risk sharing with model misspecification in economies without aggregate fluctuations** [pdf]

In a previous paper, Bhandari (2013a) studied a redistribution problem with heterogeneous beliefs, heterogeneous information and aggregate fluctuations. A Pareto planner assigned consumption to two uncertainty averse agents who differed in their initial priors over a common set of forecasting models of aggregate endowment and one of the agents received a privately observed taste shock. The analysis exploited two key features, presence of aggregate risk and the multiplicative nature of taste shocks. In this paper we study implications of model misspecification in environments with no aggregate risk and additive un-insurable idiosyncratic income risk. Absent other forms of heterogeneities, under complete markets, risk sharing scheme implies constant consumption for all the agents. In the paper we study the consequences of two forms of market incompleteness- 1) Firstly when insurance markets are exogenously incomplete and agents only trade a risk-free bond and 2) Secondly when insurance markets are endogenously incomplete due to unobservable individual incomes