
with Lars Peter Hansen
December 2016
A decision maker expresses ambiguity about statistical models in the following ways. He has a family of
structured parametric probability models but suspects that their parameters vary over time in unknown ways that he does not describe probabilistically. He expresses a further suspicion that all of these parametric models are misspecified by entertaining alternative unstructured probability distributions that he represents only as positive martingales and that he restricts to be statistically close to the structured parametric models. Because he is averse to ambiguity, he uses a maxmin criterion to evaluate alternative plans. We characterize equilibrium uncertainty prices by confronting a decision maker with a portfolio choice problem. We offer a quantitative illustration for structured parametric models that focus uncertainty on macroeconomic growth and its persistence. There emerge nonlinearities in marginal valuations that induce time variation in market prices uncertainty. Prices of uncertainty fluctuate because the investor especially fears high persistence in bad states and low persistence in good ones.

with Anmol Bhandari, David Evans, and Mikhail Golosov
December 2016
We study public debt in an economy in which taxes and transfers are chosen optimally subject to heterogeneous agents' diverse resources. We assume a government that commits to policies and can enforce tax and debt payments. 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 the government introduces borrowing frictions and commits not to enforce private debt contracts. That lets it reduce competition on debt markets and gather monopoly rents from providing liquidity. Regardless of whether the government chooses to enforce private debt contracts, the level of initial government debt does not affect an optimal allocation, but the distribution of net assets does.

December 2016
A government defines a dollar as a list of quantities of one or more precious metals. If issued in sufficiently limited amounts, token money is a perfect substitute for precious metal money. Atemporal equilibrium conditions determine how quantities of precious metals and token monies affect an equilibrium price level. Under some circumstances, a government can peg the relative price of two precious metals, confirming an analysis that Irving Fisher in 1911 used to answer a classic criticism of bimetallism.

with Lars Ljungqvist
June 2016
To generate big responses of unemployment to productivity changes, researchers have reconfigured matching models in various ways: by elevating the utility of leisure, by making wages sticky, by assuming alternatingoffer wage bargaining, by introducing costly acquisition of credit, by assuming fixed matching costs, or by positing government mandated unemployment compensation and layoff costs. All of these redesigned matching models increase responses of unemployment to movements in productivity by diminishing the fundamental surplus fraction, an upper bound on the fraction of a job’s output that the invisible hand can allocate to vacancy creation. Business cycles and welfare state dynamics of an entire class of reconfigured matching models all operate through this common channel.

with P. Battigalli, S. CerreiaVioglio, F. Maccheroni, M. Marinacci
March 2016
This paper provides a general framework for the analysis of selfconfirming policies. We first study selfconfirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. Next we illustrate the theory with a characterization of stationary monetary policies in a linearquadratic setting. Finally we provide a more general discussion of selfconfirming policies.

with Anmol Bhandari, David Evans, and Mikhail Golosov
July 2016
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.

with Sagiri Kitao and Lars Ljungqvist
December 2015
To understand transAtlantic employment experiences since World War II, we build an overlapping generations model with two types of workers whose different skill acquisition technologies affect their career decisions. Search frictions affect shortrun employment outcomes. The model focuses on labor supply responses near beginnings and ends of lives and on whether unemployment and early retirements are financed by personal savings or public benefit programs. Higher minimum wages in Europe explain why youth unemployment has risen more there than in the U.S. Higher risks of human capital depreciation after involuntary job destructions cause longterm unemployment in Europe, mostly among older workers, but leave U.S. unemployment unaffected. Increased probabilities of skill losses after involuntary job separation interact with workers' subsequent decisions to invest in human capital in ways that generate the agedependent increases in autocovariances of income shocks observed by Moffitt and Gottschalk (1995).

with George J. Hall
December 2015
Congress first imposed an aggregate debt limit in 1939 when it delegated decisions about designing US debt instruments to the Treasury. Before World War I, Congress designed each bond and specified a maximum amount of each bond that the Treasury could issue. It usually specified purposes for which proceeds could be spent. We construct and interpret a Federal debt limit before 1939.

with Lars Peter Hansen
December 2015
A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent parametric alternatives to a baseline model and also nonparametric models statistically close to both the baseline model and the parametric alternatives. 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. We offer quantitative illustrations for baseline models of consumption dynamics that display longrun risk. We describe a set of parametric alternatives that generates countercyclical prices of uncertainty.

with Lawrence E. Blume, Timothy Cogley, David A. Easley, and Viktor Tsyrennikov
June 2015
We propose a new welfare criterion that allows us to rank alternative financial market structures in the presence of belief heterogeneity. We analyze economies with complete and incomplete financial markets and/or restricted trading possibilities in the form of borrowing limits or transaction costs. We describe circumstances under which various restrictions on financial markets are desirable according to our welfare criterion.

February 2015
This is an essay about my role in the history of rational expectations econometrics, written for the Trinity University series ``Lives of the Laureates".

November 2014
This paper is a critical review of and a reader’s guide to a collection of papers by Robert E. Lucas, Jr. about fruitful ways of using general equilibrium theories to understand measured economic aggregates. These beautifully written and wisely argued papers integrated macroeconomics, microeconomics, finance, and econometrics in ways that restructured big parts of macroeconomic research.

with Timothy Cogley and Paolo Surico
November 2014
Was UK inflation was more stable and/or less uncertain before 1914 or after 1945? We address these questions by estimating a statistical model with changing volatilities in transient and persistent components of inflation. Three conclusions emerge. First, since periods of high and low volatility occur in both eras, neither features uniformly greater stability or lower uncertainty. When comparing peaks with peaks and troughs with troughs, however, we find clear evidence that the price level was more stable before World War I. We also find some evidence for lower uncertainty at pre1914 troughs, but its statistical significance is borderline.

with Lawrence E. Blume
August 2014
Harrod’s 1939 “Essay in Dynamic Theory” is celebrated as one of the foundational papers in the modern theory of economic growth. Linked eternally to Evsey Domar, he appears in the undergraduate and graduate macroeconomics curricula, and his “fundamental equation” appears as the central result of the AK model in modern textbooks. Reading his Essay today, however, the reasons for his centrality are less clear. Looking forward from 1939, we see that the main stream of economic growth theory is built on neoclassical distribution theory rather than on the Keynesian principles Harrod deployed. Looking back, we see that there were many antecedent developments in growth economics, some much closer than Harrod’s to contemporary developments. So what, then, did Harrod accomplish?

with Lars Ljungqvist
July 2014
You have disagreed in print about the size of the aggregate labor supply elasticity. Recent changes in the ``aggregation theory'' that Prescott uses brings you closer together at least in the sense that now you share a common theoretical structure.

with Martin Ellison
September 2014
The welfare cost of random consumption fluctuations is known from De Santis (2007) to be increasing in the level of individual consumption risk in the economy. It is also known from Barillas et al. (2009) to increase if agents in the economy care about robustness to model misspecification. In this paper, we combine these two effects and calculate the cost of business cycles in an economy with consumers who face individual consumption risk and who fear model misspecification. We find that individual risk has a greater impact on the cost of business cycles if agents already have a preference for robustness. Correspondingly, we find that endowing agents with concerns about a preference for robustness is more costly if there is already individual risk in the economy. The combined effect exceeds the sum of the individual effects.

with Timothy Cogley
August 2014
We measure pricelevel uncertainty and instability in the U.S. over the period 18502012. Major outbreaks of pricelevel uncertainty and instability occur both before and after World War II, alternating with three pricelevel moderations,one near the turn of 20th century, another under Bretton Woods, and a thirdin the 1990s. There is no evidence that the price level was systematically more stable or less uncertain before or after the Second World War. Moderations sometimes involved links to gold, but the experience of the 1990s proves that a wellmanaged fiat regime can achieve the same outcome.

with Lars Ljungqvist
May 2014
Rogerson and Wallenius (2013) draw an incorrect inference about a labor supply elasticity at an intensive margin from premises about an option to work part time that retiring workers decline. We explain how their false inference rests on overgeneralizing outcomes from a particular example and how Rogerson and Wallenius haven't identified an economic force beyond the two  indivisible labor and time separable preferences  that drive a high labor supply elasticity at an interior solution at an extensive margin.

with Lars Peter Hansen
May 2014
This paper studies alternative ways of representing uncertainty about a law of motion in a version of a classic macroeconomic targeting problem of Milton Friedman (1953). We study both "unstructured uncertainty"  ignorance of the conditional distribution of the target next period as a function of states and controls  and more "structured uncertainty"  ignorance of the probability distribution of a response coefficient in an otherwise fully trusted specification of the conditional distribution of next period's target. We study whether and how different uncertainties affect Friedman's advice to be cautious in using a quantitative model to fine tune macroeconomic outcomes.

with George J. Hall
June 2013
In 1790, a U.S. paper dollar was widely held in disrepute (something shoddy was not `worth a Continental'). By 1879, a U.S. paper dollar had become `as good as gold.' These outcomes emerged from how the U.S. federal government financed three wars: the American Revolution, the War of 1812, and the Civil War. In the beginning, the U.S. government discriminated greatly in the returns it paid to different classes of creditors; but that pattern of discrimination diminished over time in ways that eventually rehabilitated the reputation of federal paper money as a store of value.

with Timothy Cogley and Viktor Tsyrennikov
July 2012
In our heterogenousbeliefs incompletemarkets models, precautionary and speculative motives coexist. Missing markets for Arrow securities affect the size and avenues for precautionary savings. Survival dynamics suggested by Friedman (1953) and studied by Blume and Easley (2006) depend on whether agents can trade a disasterstate security. When the market for a disasterstate security is closed, precautionary savings flow into riskfree bonds, prompting lessinformed investors to accumulate wealth. Because speculation motives are strongest for the disasterstate Arrow security, opening this market brings outcomes close to those for a completemarkets benchmark where instead it is wellinformed investors who accumulate wealth. Speculation is more limited in other cases, and outcomes for wealth dynamics are closer to those in an economy in which only a riskfree bond can be traded.

with Lars Peter Hansen
July 2012
For each of three types of ambiguity, we compute a robust Ramsey plan and an associated worstcase probability model. Ex post, ambiguity of type I implies endogenously distorted homogeneous beliefs, while ambiguities of types II and III imply distorted heterogeneous beliefs. Martingales characterize alternative probability specifications and clarify distinctions among the three types of ambiguity. We use recursive formulations of Ramsey problems to impose local predictability of commitment multipliers directly. To reduce the dimension of the state in a recursive formulation, we transform the commitment multiplier to accommodate the heterogeneous beliefs that arise with ambiguity of types II and III. Our formulations facilitate comparisons of the consequences of these alternative types of ambiguity.

with George Evans, Seppo Honkapohja, and Noah Williams
January 2012
Agents have two forecasting models, one consistent with the unique rational expectations equilibrium, another that assumes a timevarying parameter structure. When agents use Bayesian updating to choose between models in a selfreferential system, we find that learning dynamics lead to selection of one of the two models. However, there are parameter regions for which the nonrational forecasting model is selected in the longrun. A key structural parameter governing outcomes measures the degree of expectations feedback in Muth’s model of price determination.

December 2011
Under the Articles of Confederation, the central government of the United States had limited power to tax. That made it difficult for it to service the debts that the government had incurred during our War of Independence, with the consequence that debt traded at deep discounts. That situation framed a U.S.\ fiscal crisis of the 1780s. A political revolution  for that was what our founders scuttling of the Articles of Confederation in favor of the Constitution of the United States of America was  solved the fiscal crisis by transferring authority to levy tariffs from the state governments to the federal government. The Constitution and Acts of the First Congress of the United States in August 1790 completed a grand bargain that made creditors of the government become advocates of a federal government with authority to raise revenues sufficient to service the government's debt. In 1790, the Congress carried out a comprehensive bailout of state government's debts, another part of the grand bargain that made creditors of the states become advocates of ample federal taxes. That bailout may have created unwarranted expectations about future federal bailouts that a costly episode in the early 1840s corrected. Aspects of these early U.S.\ circumstances and choices remind me of the European Union today.

with Timothy Cogley and Viktor Tsyrenniko
December 2011
This paper studies market prices of risk in an economy with two types of agents with diverse beliefs. The paper studies both a complete markets economy and a riskfree bonds only (Bewley) economy.

with Timothy Cogley and Viktor Tsyrennikov
December 2012
We study an economy in which two types of agents have diverse beliefs about the law of motion for an exogenous endowment. One type knows the true law of motion, and the other learns about it via Bayes’s theorem. Financial markets are incomplete, the only traded asset being a riskfree bond. Borrowing limits are imposed to ensure the existence of an equilibrium. We analyze how financialmarket structure affects the distribution of financial wealth and survival of the two agents. When markets are complete, the learning agent loses wealth during the learning transition and eventually exits the economy Blume and Easley 2006). In contrast, in a bondonly economy, the learning agent accumulates wealth, and both agents survive asymptotically, with the knowledgeable agent being driven to his debt limit. The absence of markets for certain Arrow securities is central to reversing the direction in which wealth is transferred.

with Lars Ljungqvist
November 2012
The same high labor supply elasticity that characterizes a representative family model with indivisible labor and employment lotteries can also emerge without lotteries when selfinsuring individuals choose career lengths. Off corners, the more elastic the earnings profile is to accumulated working time, the longer is a worker's career. Negative (positive) unanticipated earnings shocks reduce (increase) the career length of a worker holding positive assets at the time of the shock, while the effects are the opposite for a worker with negative assets. By inducing a worker to retire at an official retirement age, government provided social security can attenuate responses of career lengths to earnings profile slopes, earnings shocks, and taxes.

with Lars Ljungqvist
January 2011
Until recently, an insurmountable gulf separated a high labor supply elasticity macro camp from a low labor supply elasticity micro camp was fortified by a contentious aggregation theory formerly embraced by real business cycle theorists. The repudiation of that aggregation theory in favor of one more genial to microeconomic observations opens possibilities for an accord about the aggregate labor supply elasticity. The new aggregation theory drops features to which empirical microeconomists objected and replaces them with lifecycle choices that microeconomists have long emphasized. Whether the new aggregation theory ultimately indicates a small or large macro labor supply elasticity will depend on how shocks and government institutions interact to determine whether workers choose to be at interior solutions for career length.

with David Evans
January 2011
A planner is compelled to raise a prescribed present value of revenues by levying a distorting tax on the output of a representative firm that faces adjustment costs and resides within a rational expectations equilibrium. We describe recursive representations both for a Ramsey plan and for a set of credible plans. Continuations of Ramsey plans are not Ramsey plans. Continuations of credible plans are credible plans. As they are often constructed, continuations of optimal inflation target paths are not optimal inflation target paths.

September 2010
What kinds of assets should financial intermediaries be permitted to hold and what kinds of liabilities should they be allowed to issue? This paper reviews how tensions involving stability versus efficiency and regulation versus laissez faire have for centuries run through macroeconomic analysis of these questions. The paper also discusses how two leading models raise questions of whether deposit insurance is a good or bad arrangement. This paper is the text of the Phillips Lecture, given at the London School of Economics on February 12, 2010.

with Lars Peter Hansen
January 2011
We formulate two continuoustime hidden Markov models in which a decision maker distrusts both his model of state dynamics and a prior distribution of unobserved states. We use relative entropy's role in statistical model discrimination % using historical data, we use measures of statistical model detection to modify Bellman equations in light of model ambiguity and to calibrate parameters that measure ambiguity. We construct two continuous time models that are counterparts of two discretetime recursive models of \cite{hansensargent07}. In one, hidden states appear in continuation value functions, while in the other, they do not. The formulation in which continuation values do not depend on hidden states shares features of the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji. For this model, we use our statistical detection calculations to guide how to adjust contributions to entropy coming from hidden states as we take a continuous time limit.

with A. Bhandari, F. Barillas, R. Colacito, S. Kitao, C. Matthes, and Y. Shin
December 2010
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. This paper teaches Dynare by applying it to approximate equilibria and estimate nine dynamic economic models. Among the models estimated are a 1977 rational expectations model of hyperinflation by Sargent, Hansen, Sargent, and Tallarini’s risksensitive permanent income model, and one and twocountry stochastic growth models. The examples.zip file contains dynare *.mod and data files that implement the examples in the paper.
Source Code

with George Hall
February 2010
This paper uses the sequence of government budget constraints to motivate estimates of interest payments on the U.S. Federal government debt. We explain why our estimates differ conceptually and quantitatively from those reported by the U.S. government. We use our estimates to account for contributions to the evolution of the debt to GDP ratio made by inflation, growth, and nominal returns paid on debts of different maturities.

with Martin Ellison
July 2010
In this much revised version, we defend the forecasting performance of the FOMC from the recent criticism of Christina and David Romer. Our argument is that the FOMC forecasts a worstcase scenario that it uses to design decisions that will work well enough (are robust) despite possible misspecification of its model. Because these FOMC forecasts are not predictions of what the FOMC expects to occur under its model, it is inappropriate to compare their performance in a horse race against other forecasts. Our interpretation of the FOMC as a robust policymaker can explain all the findings of the Romers and rationalises differences between FOMC forecasts and forecasts published in the Greenbook by the staff of the Federal Reserve System.

with Lars Peter Hansen
May 2010
This is a survey paper about exponential twisting as a model of model distrust. We feature examples from macroeconomics and finance.

by Anastasios G. Karantounias (with Lars Peter Hansen and Thomas J. Sargent)
October 2009
This paper studies an optimal fiscal policy problem of Lucas and Stokey (1983) but in a situation in which the representative agent's distrust of the probability model for government expenditures puts model uncertainty premia into historycontingent prices. This gives rise to a motive for expectation management that is absent within rational expectations and a novel incentive for the planner to smooth the shadow value of the agent's subjective beliefs in order to manipulate the equilibrium price of government debt. Unlike the Lucas and Stokey (1983) model, the optimal allocation, tax rate, and debt all become history dependent despite complete markets and Markov government expenditures.

with Timothy Cogley and Giorgio E. Primiceri
December 2007
We use Bayesian Markov Chain Monte Carlo methods to estimate two models of post WWII U.S. inflation rates with drifting stochastic volatility and drifting coefficients. One model is univariate, the other a multivariate autoregression. We define the inflation gap as the deviation of inflation from a pure random walk component of inflation and use both of our models to study changes over time in the persistence of the inflation gap measured in terms of short to mediumterm predicability. We present evidence that our measure of the persistence of the inflation gap increased until Volcker brought mean inflation down in the early 1980s and that it then fell during the chairmanships of Volcker and Greenspan. Stronger evidence for movements in inflation gap persistence emerges from the VAR than from the univariate model. We interpret these changes in terms of a simple dynamic new Keynesian model that allows us to distinguish altered monetary policy rules and altered private sector parameters.

with Timothy Cogley
July 2008
We study prices and allocations in a completemarkets, pure endowment economy in which agents have heterogenous beliefs. Aggregate consumption growth evolves exogenously according to a twostate Markov process. The economy is populated by two types of agents, one that learns about transition probabilities and another that knows them. We examine how the presence of the betterinformed agent influences allocations, the market price of risk, and the rate at which asset prices converge to values that would be computed under the typical assumption that all agents know the transition probabilities.

with Lars Ljungqvist
January 2009
A finitely lived worker confronts a labor supply indivisibility, chooses when to work, and smooths consumption by trading an interest bearing security. The worker faces an exogenously given increasing schedule that maps accumulated time on the job into an earnings level. With a specification of the worker's preferences that macroeconomists commonly use to assure balanced growth paths, the more elastic are earnings to accumulated working time, the longer is a worker's career.