Rational Expectations

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.

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.

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.

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.

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. Matlab files

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.

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 examples.zip 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.

Alternative Monetary Policies in a Turnpike Economy: Vintage Article

with Rodolfo Manuelli
June 2009
This paper modifies a Townsend turnpike model by letting agents stay at a location long enough to trade some consumption loans, but not long enough to support a Pareto optimal allocation. Monetary equilibria exist that are non-optimal in the absence of a scheme to pay interest on currency at a particular rate. Paying interest on currency at the optimal rate delivers a Pareto optimal allocation, but a different one than the allocation for an associated nonmonetary centralized economy. The price level remains determinate under an optimal policy. We study the response of the model to ``helicopter drops of currency, steady increases in the money supply, and restrictions on private intermediation.

The Timing of Tax Collections and the Structure of  "Irrelevance'' Theorems in a Cash-in-Advance Model: Vintage Article

with Bruce Smith
June 2009, Originally 1998
A standard timing protocol allows in a cash-in-advance model allows the government to elude the inflation tax. That matters. Altering the timing of tax collections to make the government hold cash overnight disables some classical propositions but enables others. The altered timing protocol loses a Ricardian proposition and also the proposition that open market operations, accompanied by tax adjustments needed to finance the change in interest on bonds due the public, are equivalent with pure units changes. The altered timing enables a Modigliani-Miller equivalence proposition that does not otherwise prevail.

Evolution and Intelligent Design

January 7, 2008
This paper is my AEA presidential address. It discusses the relationship between two sources of ideas that influence monetary policy makers today. The first is a set of analytical results that impose the rational expectations equilibrium concept and do `intelligent design' by solving Ramsey and mechanism design problems. The second is a long trial and error learning process that constrained government budgets and anchored the price level with a gold standard, then relaxed government budgets by replacing the gold standard with a fiat currency system wanting nominal anchors. Models of out-of-equilibrium learning tell us that such an evolutionary process will converge to a self-confirming equilibrium (SCE). In an SCE, a government's probability model is correct about events that occur under the prevailing government policy, but possibly wrong about the consequences of other policies. That leaves room for more mistakes and useful experiments than exist in a rational expectations equilibrium.

Israel 1983: A Bout of Unpleasant Monetarist Arithmetic

with Joseph Zeira
February 2008
This paper is about the consequences that using fiscal policy to bail out banks can have for inflation rates. It is a case study of a bail out of banks in Israel in 1983. That bailout might have been good news for banks’ shareholders, but it was not good news for people whose net wealth positions were harmed by inflation.

Some of Milton Friedman’s Scientific Contributions to Macroeconomics

An assessment of the enduring influences of Milton Friedman’s work in macroeconomics.

Two Questions about European Unemployment

with Lars Ljungqvist
June 2007
A general equilibrium search model makes layoff costs affect the aggregate unemployment rate in ways that depend on equilibrium proportions of frictional and structural unemployment that in turn depend on the generosity of government unemployment benefits and skill losses among newly displaced workers. The model explains how, before the 1970s, lower flows into unemployment gave Europe lower unemployment rates than the United States; and also how, after 1980, higher durations have kept unemployment rates in Europe persistently higher than in the U.S. These outcomes arise from the way Europe's higher firing costs and more generous unemployment compensation make its unemployment rate respond to bigger skill losses among newly displaced workers. Those bigger skill losses also explain why U.S. workers have experienced more earnings volatility after 1980 and why, especially among older workers, hazard rates of gaining employment in Europe now fall sharply with increases in the duration of unemployment.

Understanding European Unemployment with Matching and Search-Island Models

with Lars Ljungqvist
June 2007
To match broad macroeconomic observations about European and American unemployment during the last 60 years, we use a search-island model and some matching models with workers who have heterogeneous skills and entitlements to government benefits. There are labor market frictions in these models, but not in a closely related representative family model with employment lotteries(please see the following paper on this web page). High government mandated unemployment insurance (UI) and employment protection (EP) in Europe increase durations and levels of unemployment when there is higher `turbulence' in the sense of worse skill transition probabilities for workers who suffer involuntary layoffs. But when there is lower turbulence, high European EP suppresses unemployment rates despite high European UI. Different matching models assign unemployed workers to different waiting pools (i.e., matching functions). This affects how strongly unemployment responds to increases in turbulence. Unless the long-term unemployed share a matching function with other unemployed workers who are not discouraged, the economy almost closes down in turbulent times. This catastrophe does not occur in the search-island model where there are no labor market externalities and each worker bears the full consequences of his own decisions.

Understanding European Unemployment with a Representative Family Model

with Lars Ljungqvist
June 2007
A representative family model with indivisible labor and employment lotteries has no labor market frictions and complete markets .The high aggregate labor supply elasticity implies that when generous government-supplied unemployment insurance are included, we get the unrealistic result that economic activity collapses. Because there is no frictional unemployment, an increase in employment protection decreases aggregate work because the representative family substitutes into leisure. Therefore, the model does not provide the same successful accounting for a half century of European and American unemployment rates offered by the models in the previous paper on this web page or in our paper entitled Two Questions about European Unemployment.

Taxes, benefits, careers, and markets

with Lars Ljungqvist
May 2007
An incomplete markets life-cycle model with indivisible labor makes career lengths and human capital accumulation respond to labor tax rates and government supplied non-employment benefits. We compare aggregate and individual outcomes in this individualistic incomplete markets model with those in a comparable collectivist representative family with employment lotteries and complete insurance markets. The incomplete and complete market structures assign leisure to different types of individuals who are distinguished by their human capital and age. These microeconomic differences distinguish the two models in terms of how macroeconomic aggregates respond to some types of government supplied non-employment benefits, but remarkably, not to labor tax changes.

How Sweden's unemployment became more like Europe's

with Lars Ljungqvist
July 2007
Prepared for NBER-SNSS conference on reforming the Swedish welfare state
Until the mid 1990s, Sweden’s unemployment rate was different from the rest of Europe’s – it was systematically lower? This paper explains why and also why it has become more like Europe’s in the last decade.

Do Taxes Explain European Employment? Indivisible Labor, Human Capital, Lotteries, and Personal Savings

with Lars Ljungqvist
June 2006
Prepared for 2006 NBER Macroeconomics Annual conference
To appreciate the role of a `not-so-well-known aggregation theory' that underlies Prescott's (2002) conclusion that higher taxes on labor have depressed Europe relative to the U.S., this paper compares aggregate outcomes for economies with two alternative arrangements for coping with indivisible labor: (1) employment lotteries plus complete consumption insurance, and (2) individual consumption smoothing via borrowing and lending at a risk-free interest rate. We compare these two arrangements in both single-agent and general equilibrium models. Under idealized conditions, the two arrangements support equivalent outcomes when human capital is not present; when it is present, outcomes are naturally different. Households' reliance on personal savings in the incomplete markets model constrains the `career choices' that are implicit in their human capital acquisition plans relative to those that can be supported by lotteries and consumption insurance in the complete markets model. Lumpy career choices make the incomplete markets model better at coping with a generous system of government funded compensation to people who withdraw from work. Adding generous government supplied benefits to Prescott's model with employment lotteries and consumption insurance causes employment to implode and prevents the model from matching outcomes observed in Europe.

Jobs and Unemployment in Macroeconomic Theory: A Turbulence Laboratory

with Lars Ljungqvist
August 2005
This is the text of Sargent’s Presidential address to the World Congress of the Econometric Society in London on August 19,
We use three general equilibrium frameworks with jobs and unemployed workers to study the effects of government mandated unemployment insurance (UI) and employment protection (EP). To illuminate the forces in these models, we study how UI and EP affect outcomes when there is higher `turbulence' in the sense of worse skill transition probabilities for workers who suffer involuntary layoffs. Two of the frameworks have labor market frictions and incomplete markets – the matching and search-island models -- while the third one is a frictionless complete markets economy -- the representative family model with employment lotteries. Although they provide very different ways of thinking about the decisions faced by unemployed workers, the adverse welfare state dynamics that come from high UI indexed to past earnings, and that were isolated by Ljungqvist and Sargent in 1998, are so strong that they determine outcomes in all three frameworks. Another force stressed by Ljungqvist and Sargent in 2002, through which higher layoff taxes suppress frictional unemployment in less turbulent times, prevails in the models with labor market frictions, but not in the frictionless representative family model. In addition, the high aggregate labor supply elasticity that emerges from employment lotteries and complete insurance markets in the representative family model makes it impossible to incorporate European-style unemployment insurance in that model without getting the unrealistic result that economic activity virtually shuts down.

Obsolescence, Uncertainty, and Heterogeneity: The European Unemployment Experience

with Lars Ljungqvist
August 2005
A general equilibrium model of stochastically aging McCall workers whose human capital depreciates during spells of unemployment and appreciates during spells of employment. There are layoff taxes and government supplied unemployment compensation with a replacement ratio attached to past earnings, the product of human capital and a wage draw. The wage draw changes on the job via Markov chain, inspiring some quits. We use a common calibration of the model with “European” and “American” unemployment compensations to study the different unemployment experiences of Europe and the U.S. from the 1950s through 2000. The model succeeds in explaining why unemployment rates were lower in Europe in the 1950s and 1960s, but higher after the 1970s. The explanation is about how layoff taxes and unemployment compensation linked to past earnings interact with an increase in economic turbulence. The paper relates these macro outcomes to evidence from earnings distributions and displaced workers studies.

A, B, C, (and D)’s for Understanding VARs

with Juan Rubio, Jesus Villaverde, and Mark Watson
July 2006
An approximation to the equilibrium of a complete dynamic stochastic economic model can be expressed in terms of matrices (A,B,C,D) that define a state space system. An associated state space system (A,K,C,I) determines a vector autoregression for fixed observables available to an econometrician. We review a permanent income example that illustrates a simple special condition for checking whether the mapping from VAR shocks to economic shocks is invertible.

Ambiguity in American Monetary and Fiscal Policy

How a coherent monetary and fiscal policy somehow emerges out of the helter-skelter of U.S. politics, with some historical examples.

Business Cycle Modeling without Pretending to Have Too Much A Priori Economic Theory

with Christopher Sims
This paper is an out of print old timer. Several people asked me to put it on my webpage.

Is Keynesian Economics a Dead End?

October 1977
This paper is an old timer. It served as notes for my November 1977 talk to the Minnesota economics association. At those meetings, I saw my old undergraduate teacher Hyman Minsky for the first time since undergraduate days at Cal Berkeley.

Business Cycle Analysis with Unobservable Index Models and the Methods of the NBER

with Robert Litterman and Danny Quah
June, 1984
This is an unpublished paper about dynamic unobservable index models like the ones in the previous paper with Chris Sims.

Using Unobservable Index Models to Estimate Unobservables and Forecast Observables

with Robert Litterman and Danny Quah
April, 1984
This is another unpublished paper about dynamic unobservable index models..

Politics and Efficiency of Separating Capital and Ordinary Government Budgets

with Marco Bassetto with Thomas Sargent
December, 2004
We analyze the democratic politics of a rule that separates capital and ordinary account budgets and allows the government to issue debt to finance capital items only. Many national governments followed this rule in the 18th and 19th centuries and most U.S. states do today. This simple 1800s financing rule sometimes provides excellent incentives for majorities to choose an efficient mix of public goods in an economy with a growing population of overlapping generations of long-lived but mortal agents. In a special limiting case with demographics that make Ricardian equivalence prevail, the 1800s rule does nothing to promote efficiency. But when the demographics imply even a moderate departure from Ricardian equivalence, imposing the rule substantially improves the efficiency of democratically chosen allocations. We calibrate some examples to U.S.\ demographic data. We speculate why in the twentieth century most national governments abandoned the 1800s rule while U.S. state governments have retained it.

Lotteries for consumers versus lotteries for firms

with Lars Ljungqvist
October, 2003
A discussion of a paper by Edward Prescott for the Yale Cowles commission conference volume on general equilibrium theory. Prescott emphasizes the similarities in lotteries that can be used to aggregate over nonconvexities for firms, on the one hand, and households, on the other. We emphasize their differences.

Reactions to the Berkeley Story

October, 2002
This paper is my discussion of a paper at the 2002 Jackson Hole Conference by Christina and David Romer. The Romers’ paper uses narrative evidence to support and extend an interpretation of post war Fed policy that has also been explored by Brad DeLong and others. The basic story is that the Fed has a pretty good model in the 50s, forgot it under the influence of advocates of an exploitable Phillips curve in the late 60s, then came to its senses by accepting Friedman and Phelps’s version of the natural rate hypothesis in the 1970s. The Romers extend the story by picking up Orphanides’s idea that the Fed misestimated potential GDP or the natural unemployment rate in the 1970s. The Romers’ story is that the Fed needed to accept the natural rate hypothesis (which it did by 1970 according to them) and also to have good estimates of the natural rate (which according to them it didn’t until the late 70s or early 80s). The Romers story is about the Fed’s forgetting then relearning a good model. My comment features my own narration of a controversial paper by `Professors X and Y’.

European Unemployment and Turbulence Revisited in a Matching Model

with Lars Ljungqvist
September, 2003
This paper recalibrates a matching model of den Haan, Haefke, and Ramey and uses it to study how increased turbulence interacts with generous unemployment benefits to affect the equilibrium rate of unemployment. In contrast to den Haan, Haefke, and Ramey, we find that increased turbulence causes unemployment to rise. We trace the difference in outcomes to how we model the hazard of losing skills after a voluntary job change.

European Unemployment: From a Worker's Perspective

with Lars Ljungqvist
Sept 17, 2001
Prepared for an October 2001 conference in honor of Edmund Phelps. Within the environment of our JPE 1998 paper on European unemployment, this paper conducts artificial natural experiments that provoke ``conversations'' with two workers who experience identical shocks but make different decisions because they live on opposite sides of the Atlantic Ocean.

Optimal Taxation without State Contingent Debt

with Rao Aiyagari, Albert Marcet and Juha Seppala
Sept 29, 2001
An extensively revised version of a paper recasting Lucas and Stokey's analysis of optimal taxation in a market setting where the government can issue only risk free one-period government debt. This setting moves the optimal tax and debt policy substantially in the direction posited by Barro. The paper works out two examples by hand, another by the computer.

Comment on Christopher Sims's `Fiscal Consequences for Mexico of Adopting the Dollar'

June 13, 2000
A comment prepared for a conference on dollarization at the Federal Reserve Bank of Cleveland, June 1-3, 2000.

Optimal Taxation without State Contingent Debt

with Albert Marcet and Juha Seppala
Sept 29, 2001
An extensively revised version of a paper recasting Lucas and Stokey's analysis of optimal taxation in a market setting where the government can issue only risk free one-period government debt. This setting moves the optimal tax and debt policy substantially in the direction posited by Barro. The paper works out two examples by hand, another by the computer.

Optimal Fiscal Policy in a Linear Stochastic Economy

with Francois Velde
April 29, 1998

Mechanics of Forming and Estimating Dynamic Linear Economies

with Evan Anderson, Lars P. Hansen and Ellen McGrattan

The European Unemployment Dilemma

with Lars Ljungqvist
May 1997