New Papers

Sets of Models and Prices of Uncertainty

with Lars Peter Hansen
March 2015
A representative consumer expresses distrust of a baseline probability model by using a convex set of martingales as likelihood ratios to represent other probability models. The consumer constructs the set to include martingales that represent particular parametric alternatives to the baseline model as well as others representing only vaguely specified models statistically close to the baseline model. The representative consumer’s max-min expected utility over that set gives rise to equilibrium prices of model uncertainty expressed as worst-case distortions to the drifts in his baseline model. We calibrate a quantitative example to aggregate US consumption data.

The Fundamental Surplus in Matching Models

with Lars Ljungqvist
February 2015
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 alternating-offer wage bargaining, by introducing costly acquisition of credit, or by positing government mandated unemployment com- pensation 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. This single common channel unites analyses of business cycle and welfare state dynamics.

Points of Departure

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".

Robert E. Lucas, Jr.’s Collected Papers on Monetary Theory

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.

Price-Level Uncertainty and Instability in the United Kingdom

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 pre-1914 troughs, but its statistical significance is borderline.

Harrod 1939

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?

An Open Letter to Professors Heckman and Prescott

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.

Welfare Cost of Business Cycles in Economies with Idiosyncratic Consumption Risk

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.

Measuring Price-Level Uncertainty and Instability in the U.S., 1850-2012

with Timothy Cogley
August 2014
We measure price-level uncertainty and instability in the U.S. over the period 1850-2012. Major outbreaks of price-level uncertainty and instability occur both before and after World War II, alternating with three price-level 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 well-managed fiat regime can achieve the same outcome.

What Nonconvexities Really Say about Labor Supply Elasticities

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.

Four Types of Ignorance

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 targetting 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 coeffcient in an otherwise fully trusted specication 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.

Optimal Taxation with Incomplete Markets

with Anmol Bhandari, David Evans, and Mikhail Golosov
November 2013
This paper characterizes tax and debt dynamics in Ramsey plans for incomplete markets economies that generalize an Aiyagari et al. (2002) economy by allowing a single asset traded by the government to be risky. Long run debt and tax dynamics can be attracted not only to the first-best continuation allocations discovered by Aiyagari et al. for quasi-linear preferences, but instead to a continuation allocation associated with a level of (marginal-utility-scaled) government debt that would prevail in a Lucas-Stokey economy that starts from a particular initial level of government debt. The paper formulates, analyzes, and numerically solves Bellman equations for two value functions for a Ramsey planner, one for t 1, the other for t = 0.

Taxes, debts, and redistributions with aggregate shocks

with Anmol Bhandari, David Evans, and Mikhail Golosov
September 2013
A planner sets a lump sum transfer and a linear tax on labor income in an economy with incomplete markets, heterogeneous agents, and aggregate shocks. The planner's concerns about redistribution impart a welfare cost to fluctuating transfers. The distribution of net asset holdings across agents affects optimal allocations, transfers, and tax rates, but the level of government debt does not. Two forces shape long-run outcomes: the planner's desire to minimize the welfare costs of fluctuating transfers, which calls for a negative correlation between the distribution of net assets and agents' skills; and the planner's desire to use fluctuations in the real interest rate to adjust for missing state-contingent securities. In a model parameterized to match stylized facts about US booms and recessions, distributional concerns mainly determine optimal policies over business cycle frequencies. These features of optimal policy differ markedly from ones that emerge from representative agent Ramsey models
like a 2002 JPE paper by Aiyagari et al.

Fiscal Discriminations in Three Wars

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.

Speculation And Wealth When Investors Have Diverse Beliefs And Financial Markets Are Incomplete

with Timothy Cogley and Viktor Tsyrennikov
July 2012
In our heterogenous-beliefs incomplete-markets 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 disaster-state security. When the market for a disaster-state security is closed, precautionary savings flow into risk-free bonds, prompting less-informed investors to accumulate wealth. Because speculation motives are strongest for the disaster-state Arrow security, opening this market brings outcomes close to those for a complete-markets benchmark where instead it is well-informed 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 risk-free bond can be traded.

Three Types of Ambiguity

with Lars Peter Hansen
July 2012
For each of three types of ambiguity, we compute a robust Ramsey plan and an associated worst-case 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.

Bayesian Model Averaging, Learning and Model Selection

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 time-varying parameter structure. When agents use Bayesian updating to choose between models in a self-referential system, we find that learning dynamics lead to selection of one of the two models. However, there are parameter regions for which the non-rational forecasting model is selected in the long-run. A key structural parameter governing outcomes measures the degree of expectations feedback in Muth’s model of price determination.

U.S. Then, Europe Now

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.

Market Prices of Risk with Diverse Beliefs, Learning, and Catastrophes

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 risk-free bonds only (Bewley) economy.

Wealth Dynamics in a Bond Economy with Heterogeneous Beliefs

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 risk-free bond. Borrowing limits are imposed to ensure the existence of an equilibrium. We analyze how financial-market 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 bond-only 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.

Career Length: Effects of Curvature of Earnings Profiles, Earnings Shocks, Taxes, and Social Security

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 self-insuring 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.

A Labor Supply Elasticity Accord?

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 life-cycle 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.

History dependent public policies

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.

Where to draw lines: stability versus efficiency

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.

Robustness and ambiguity in continuous time

with Lars Peter Hansen
January 2011
We formulate two continuous-time 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 discrete-time 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.

Practicing Dynare

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 risk-sensitive permanent income model, and one and two-country stochastic growth models. The file contains dynare *.mod and data files that implement the examples in the paper. Source Code

Interest rate risk and other determinants of post WWII U.S. government debt/GDP dynamics

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.

A defence of the FOMC

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 worst-case 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.

Wanting robustness in macroeconomics

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.

Managing expectations and fiscal policy

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 history-contingent 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.

Inflation-Gap Persistence in the U.S.

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 medium-term 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.

Diverse Beliefs, Survival, and the Market Price of Risk

with Timothy Cogley
July 2008
We study prices and allocations in a complete-markets, pure endowment economy in which agents have heterogenous beliefs. Aggregate consumption growth evolves exogenously according to a two-state 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 better-informed 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.

Curvature of Earnings Profile and Career Length

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.