-
with Sebastian Graves, Victoria Gregory, and Lars Ljungqvist
October 2025
The Heckman, Lochner, and Taber (1998) (HLT) model includes credit markets and within-period labor supply indivisibilities, two essential features of Ljungqvist and Sargent (2006) ``time-averaging'' models. But by assuming inelastic labor supplies until a mandatory retirement age, it shuts down time-averaging. We activate time-averaging by endogenizing retirement ages. Our addition of a baseline social security system puts all workers at corner solutions of their retirement decisions, letting our model reproduce most outcomes in HLT's model. By dislodging workers from those corners, social security and tax reforms raise the aggregate labor supply elasticity and can bring about a ``dual labor market.'' HLT's Ben-Porath human capital technologies generate steeper earnings profiles for college-educated workers that in our model make their labor supplies more resilient to tax and social security reforms than high school workers' labor supplies. % in their labor supply. But nonconvexities inherent in the Ben-Porath technologies can bring ``tipping points'' at which tax increases cause workers who at lower tax rates had chosen long careers and made substantial human capital investments to jump discretely to choosing much shorter careers and doing much less on-the-job human capital accumulation.
-
with Yatheesan J. Selvakumar
September 2025
This paper uses additive functionals and dynamic mode decompositions to represent and analyze the co-evolution of cross-sections of private earned income, post-tax-and-transfer income, and consumption in the Consumer Expenditure Survey (CEX) from 1990 to 2023. We quantify how cross-sectional inequality and redistribution interact with aggregate income. Although cross-section dynamics contribute only modestly to the innovation variance of aggregate income growth, an innovation to aggregate income affects cross-section dynamics more. We construct value functions for heterogeneous synthetic consumers who are exposed to both serially correlated and i.i.d risks in income and consumption growth rates. For the median household, the welfare costs associated with serially correlated risk are orders of magnitude larger than the welfare costs associated with i.i.d risk. For each quantile, we also compare, benefits of eliminating risks in consumption growth with benefits from participating in the US tax and transfer system. In absolute values, benefits from the latter, which are positive (negative) for low (high) quantile consumers, far exceed those from the former.
-
with George J. Hall
August 2025
Post War-on-COVID-19 inflation and interest rate hikes imposed capital losses on federal creditors and motivated the Fed to transfer interest rate risk from private banks to itself. We compare prospective budget-feasible paths of US federal taxes,expenditures, interest payments, and debt in the post-COVID period to paths observed after big surges in government expenditures during four 19th and 20th century US wars. Government expenditure/GDP surges in past US wars were accompanied by permanent rises in both expenditure/GDP and tax collection/GDP ratios. Part of the War on COVID expenditure/GDP surge has persisted, but so far tax collections have not risen relative to GDP. Those two ratios shape prospects for the debt/GDP ratio and US inflation. Since 2000, ratios of tax collection and government expenditures to GDP have departed from 19th and 20th century US patterns. If these post-2000 departures become permanent, the consolidated federal government budget constraint portends permanent hikes in US inflation and nominal interest rates on US government interest-bearing bonds.
-
with Wei Jiang, Neng Wang, and Jinqiang Yang
August 2025
We use continuous-time recursive contracts theory to extend a model of Barro(1979) to include explicit randomness, an impatient representative consumer, the option for a government debt manager to default, and access of the government debt manager to markets for trading risks along lines suggested by Shiller (1994). We show that a benevolent Department of Treasury's optimal financing plan is dual to a contracting problem of a selfish tax farmer, that the two problems imply the same taxation and debt management policies, and that the initial value of risk-free government debt is a function of the expected utility that the tax farmer initially promises the representative consumer.
-
with Wei Jiang, Neng Wang, and Jinqiang Yang
July 2025
Distortions induce a benevolent government that must finance an exogenous expenditure
process to smooth taxes. An optimal fiscal plan determines the marginal cost $-p'$ of
servicing government debt and makes government debt risk-free. A convenience yield tilts
debts forward and taxes backward. An option to default determines debt capacity. Debt-GDP
ratio dynamics are driven by 1) a primary deficit, 2) interest payments, 3) GDP growth, and
4) hedging costs. We provide quantitative comparative dynamic statements about debt
capacity, debt-GDP ratio transition dynamics, and time to exhaust debt capacity.
-
with Wei Jiang and Neng Wang
June 2025
Debertoli, Nunes, and Yarded (2021) showed that when initial government debt is too high, Lucas and Stokey's (1983) debt management policy fails to implement a Ramsey plan for flat-rate taxes on labor. We show that preventing continuation Ramsey planners from resetting current-period tax rates and using short-term debt to finance accumulated primary deficits implements all Ramsey plans, including those with the high debt levels that trouble Lucas and Stokey's implementation. Our implementation equalizes Lagrange multipliers on distinct implementability constraints that face the Ramsey planner and the continuation planners, an essential indication of a successful implementation. We provide examples of our implementation under different initial debt structures and government spending patterns
-
with Ziyue Yang
March 2025
A computer program calculates a pair of infinite sequences of money creation and price level inflation rates that maximizes a benevolent time 0 government's objective function. A monotonically declining sequence of continuation values is a worst continuation value associated with a ``timeless perspective''. The time-invariant inflation rate associated with the worst continuation Ramsey plan is not the inflation rate associated with a restricted Ramsey plan in which a time 0 government is constrained to choose a time-invariant money creation rate. We Bellmanize the continuation Ramsey problem.
-
with Ziyue Yang
March 2025
We use a Python program to calculate a pair of infinite sequences of money creation and price level inflation rates that maximizes a benevolent time $0$ government's quadratic objective function for a linear-quadratic version of Calvo (1978). The program computes an open-loop representation of the optimal plan and an associated monotonically declining, bounded from below, sequence of continuation values whose limit is a worst continuation value that is associated with a ``timeless perspective''. We run some least squares regressions on fake data to try to learn about the structure of the optimal plan but are stymied by not knowing what variables should be on the right and left sides of our regressions. We use literary arguments to decide that, but they are inconclusive.
-
with Ziyue Yang
December 2024
Bellman equations for a continuation Ramsey plan and an inflation target determine a pair of infinite sequences of money creation and price level inflation rates that maximizes a benevolent time 0 government's objective function for a model of Calvo (1978). Dynamic programming provides a recursive representation of the optimal plan in which a promised inflation rate is the state variable that summarizes a continuation of a money growth sequence.
-
with Hans A. Holter, Lars Ljungqvist, and Serhiy Stepanchuk
September 2024
We study consequences of tax reforms in an incomplete markets overlapping generations model in which
male and female workers with different ability levels self-insure by acquiring a risk-free bond, ``time-averaging'' their life-cycle work schedules and career lengths, and possibly by marrying and divorcing. We study incidences of a flat-rate tax,
stylized versions of a negative income tax (NIT),
an earned income tax credit (EITC), and combinations of them. Tax reforms have diverse effects that differ by workers' abilities, marital statuses, and ages. A new ``ex post-ex ante'' criterion helps us to sort through welfare incidences. The importance of labor supply responses at the extensive margin makes the EITC better for redistribution than the NIT.
-
with Wei Jiang and Neng Wang
August 2024
Lucas and Stokey (1983) motivated future governments to confirm an optimal tax plan by rescheduling government debt appropriately. Debortoli et al. (2021) showed that sometimes that does not work. We show how a Ramsey plan can always be implemented by adding instantaneous debt to
Lucas and Stokey's contractible subspace and requiring that each continuation government preserve that debt's purchasing power instantaneously. We formulate the Ramsey problem with a Bellman equation and use it to study settings with various initial term debt structures and government spending processes. We extract implications about tax smoothing and effects of fiscal policies on bond markets.
-
September 2024
This sequel to ``After Keynesian Macroeconomics'' (1978) tells how equilibrium Markov processes underlie macroeconomics and much of applied dynamic economics today. It recalls how Robert E. Lucas, Jr., regarded Keynesian and rational expectations revolutions as interconnected transformations of economic and econometric theories and quantitative practices. It describes rules that Lucas used to guide and constrain his research. Lucas restricted himself to equilibrium Markov processes. He respected and conserved quantitative successes achieved by previous researchers, including those attained by quantitative Keynesian macroeconometric modelers.
-
with Jonathan Payne, Balint Szoke, and George Hall
September 2024
From a new data set, we infer time series of term structures of yields on US federal bonds
during the gold standard era from 1791-1933 and use our estimates to reassess historical
narratives about how the US expanded its fiscal capacity. We show that US debt carried a
default risk premium until the end of the nineteenth century when it started being priced as
an alternative safe-asset to UK debt. During the Civil War, investors expected the US to
return to a gold standard so the federal government was able to borrow without facing
denomination risk. After the introduction of the National Banking System, the slope of the
yield curve switched from down to up and the premium on US debt with maturity less than one
year disappeared.
-
with Wei Jiang, Neng Wang, and Jinqiang Yang
January 2024
To construct a stochastic version of Barro's (1979) normative model of tax rates and debt/GDP dynamics, we add risks and markets for trading them along lines suggested by Arrow (1964) and Shiller (1994). These modifications preserve Barro's prescriptions that a government should
keep its debt-GDP ratio and tax rate constant over time and also prescribe that the government insure its primary surplus risk by selling or buying the same number of shares of a Shiller macro security each period.
-
with with Isaac Bayley and Lars Ljungqvist
June 2023
Cross-phenomenon restrictions
associated with returns to labor mobility can inform calibrations
of productivity processes in macro-labor models. We
exploit how returns to labor mobility influence effects
on equilibrium unemployment of changes in (a) layoff costs,
and (b) distributions of skill losses coincident with quits
(``quit turbulence''). Returns to labor mobility intermediate both effects. Ample labor
reallocations observed across market economies
that have different layoff costs imply that a turbulence explanation of trans-Atlantic
unemployment experiences is robust to adding plausible quit turbulence.
-
with Sebastian Graves, Victoria Gregory, and Lars Ljungqvist
May 2023
We incorporate time-averaging into the canonical model of Heckman, Lochner, and Taber (1998)
(HLT) to study retirement decisions, government policies, and their interaction with the
aggregate labor supply elasticity. The HLT model forced all agents to retire at age 65,
while our model allows them to choose career lengths. A benchmark social security system
puts all of our workers at corner solutions of their career-length choice problems and lets
our model reproduce HLT model outcomes. But alternative tax and social security arrangements
dislodge some agents from those corners, bringing associated changes in equilibrium prices
and human capital accumulation decisions. A reform that links social security benefits to
age but not to employment status eliminates the implicit tax on working beyond 65. High
taxes with revenues returned lump-sum keep agents off corner solutions, raising the
aggregate labor supply elasticity and threatening to bring about a ``dual labor market'' in
which many people decide not to supply labor.
-
May 2023
After describing the landscape in macroeconomics and econometrics in Spring 1973 when Robert
E. Lucas first presented his Critique at the inaugural Carnegie-Rochester conference, I add
a fourth example based on Calvo (1978) to those appearing in section 5 of Lucas's paper. To
portray some consequences of Lucas's Critique, I use that example as a vehicle to describe
the time inconsistency of optimal plans and their credibility. I describe how different
theories of government policy imply distinct apparent dynamic chains of influence between
money and inflation. Different theories of policy bring with them different specifications
of state vectors in recursive representations of inflation-money-supply outcomes.
-
with Anmol Bhandari, David Evans, and Mikhail Golosov
January 2023
We decompose welfare effects of switching from government policy A to policy B into three
components: gains in aggregate efficiency from changes in total resources; gains in
redistribution from altered consumption shares that ex-ante heterogeneous households can
expect to receive; and gains in insurance from changes in households' consumption risks. Our
decomposition applies to a broad class of multi-person, multi-good, multi-period economies
with diverse specifications of preferences, shocks, and sources of heterogeneity. It has
several desirable properties that other decompositions lack. We apply our decomposition to
two fiscal policy reforms in quantitative incomplete markets settings.
-
with Isaac Baley and Lars Ljungqvist
December 2022
Returns to labor mobility
have too often
escaped the attention they deserve as conduits of
important forces
in macro-labor models.
These returns are shaped by calibrations
of productivity processes that use
theoretical perspectives and
data sources from (i) labor economics and
(ii) industrial organization.
By studying how equilibrium unemployment responds to
(a) layoff costs, and (b) likelihoods of skill losses
following quits, we tighten calibrations of
macro-labor models.
-
with P. Battigalli, S. Cerreia-Vioglio, F. Maccheroni, and M. Marinacci
January 2022
This paper provides a general framework for analyzing self-confirming policies. We study
self-confirming equilibria in recurrent decision problems with incomplete information about
the true stochastic model. We characterize stationary monetary policies in a
linear-quadratic setting.
-
September 2021
This is my contribution to a volume in memory of Marvin Goodfriend and in honor of his work.
It revisits issues analyzed in a classic 2005 paper by Marvin Goodfriend and Robert King.
-
September 2021
This paper recollects meetings with Robert E. Lucas, Jr. over many years. It describes how,
through personal interactions and studying his work, Lucas taught me to think about
economics.
-
with Neng Wang and Jinqiang Yang
April 2021
We solve a Bewley-Aiyagari-Huggett model almost by hand. Forces that shape wealth inequality
are intermediated through an individual’s nonfinancial earnings growth rate g and an
equilibrium interest rate r. Individuals’ earnings growth rate and survival probability
interact with their preferences about consumption plans to determine aggregate savings and
the interest rate and make wealth more unequally distributed and have a fatter tail than
labor earnings, as in US data.
-
with Lars Ljungqvist
April 2021
The fundamental surplus isolates parameters that determine the sensitivity of unemployment
to productivity in the matching model of Christiano, Eichenbaum, and Trabandt (2016 and
2021)
under either Nash bargaining or alternating-offer bargaining. Those models thus join a
collection of models
in which diverse forces are intermediated through the fundamental surplus.
-
with Neng Wang and Jinqiang Yang
April 2021
The cross-section distribution of U.S. wealth is more skewed and fatter tailed than is the
distribution of labor earnings.
Stachurski and Toda (2018) explain how plain vanilla Bewley-Aiyagari-Huggett (BAH) models
with infinitely lived agents can't
generate that pattern because of how a central limit theorem applies to a stationary labor
earnings process. Two modifications
of a BAH model suffice to generate a more skewed fatter-tailed wealth distribution: (1)
overlapping generations of agents
who pass through $N \geq 1$ life-stage transitions of stochastic lengths, and (2)
labor-earnings processes that exhibit
stochastic growth. With few parameters, our model does a good job of approximating the
mapping from the Lorenz curve,
Gini coefficient, and upper fat tail for cross-sections of labor earnings to their
counterparts for cross sections of wealth.
Three forces amplify wealth inequality relative to labor earnings inequality: stochastic
life-stage transitions that arrest
the central limit theorem force at work in Stachurski and Toda (2018); a strong
precautionary savings motive for high labor
income earners who receive positive permanent earnings shocks; and a life-cycle saving
motive for the young born with low wealth.
The outcome that the equilibrium risk-free interest rate exceeds a typical agent's
subjective discount rate fosters a
fat-tailed wealth distribution.
-
with Anmol Bhandari, David Evans, and Mikhail Golosov
March 2021
We study optimal monetary and fiscal policy in a model with heterogeneous agents, incomplete
markets, and nominal rigidities.
We show that functional derivative techniques can be applied to approximate equilibria in
such economies quickly and
efficiently. Our solution method does not require approximating policy functions around some
fixed point in the state space
and is not limited to first-order approximations. We apply our method to study Ramsey
policies in a textbook New Keynesian
economy augmented with incomplete markets and heterogeneous agents. Responses differ
qualitatively from those in a
representative agent economy and are an order of magnitude larger. Conventional price
stabilization motives are swamped
by an across person insurance motive that arises from heterogeneity and incomplete markets.
-
with Marco Bassetto
April 2020
This paper describes interactions between monetary and fiscal policies that affect
equilibrium price levels
and interest rates by critically surveying theories about (a) optimal anticipated inflation,
(b) optimal unanticipated inflation, and (c) conditions that secure a “nominal anchor” in
the sense of a
unique price level path. We contrast incomplete theories whose inputs are budget-feasible
sequences of government
issued bonds and money with complete theories whose inputs are bond-money policies described
as sequences of
functions that map time t histories into time t government actions. We cite historical
episodes that confirm
the theoretical insight that lines of authority between a Treasury and a Central Bank can be
ambiguous,
obscure, and fragile.
-
with Anmol Bhandari, David Evans, and Mikhail Golosov
February 2020
We study optimal monetary and fiscal policy in a model with heterogeneous agents, incomplete
markets, and nominal rigidities.
We show that functional derivative techniques can be applied to approximate equilibria in
such economies quickly and
efficiently. Our solution method does not require approximating policy functions around some
fixed point in the state space
and is not limited to first-order approximations. We apply our method to study Ramsey
policies in a textbook New Keynesian
economy augmented with incomplete markets and heterogeneous agents. Responses differ
qualitatively from those in a
representative agent economy and are an order of magnitude larger. Con- ventional price
stabilization motives are swamped
by an across person insurance motive that arises from heterogeneity and incomplete markets.
-
with George J. Hall
June 2019
World War I complicated US monetary, debt management, and tax policies. To finance the war,
the US Treasury borrowed $23 billion from its US citizens and lent $12 billion to 20 foreign
nations. What began as foreign loans by the early 1930s had become gifts. For the first time
in US history, the Treasury managed a large, permanent peacetime debt.
-
November 2018
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. Within limits, 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 Anmol Bhandari, David Evans, and Mikhail Golosov
September 2017
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.
-
August 2017
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. Within limits, 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 P. Battigalli, S. Cerreia-Vioglio, F. Maccheroni, M. Marinacci
August 2017
This paper provides a general framework for the analysis of self-confirming policies. We
first study self-confirming 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 linear-quadratic setting. Finally we
provide a more general discussion of self-confirming policies.
-
with Lars Ljungqvist
February 2017
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, 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 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.
-
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 trans-Atlantic 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 short-run 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 long-term 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 age-dependent increases in autocovariances of income shocks observed by
Moffitt and Gottschalk (1995).
-
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 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 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 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.
-
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 risk-free 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 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.
-
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.
-
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.
-
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
-
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 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
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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.
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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.
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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.
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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.
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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.
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An assessment of the enduring influences of Milton Friedman’s work in macroeconomics.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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How a coherent monetary and fiscal policy somehow emerges out of the helter-skelter of U.S.
politics, with some historical examples.
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with Christopher Sims
1977
This paper is an out of print old timer. Several people asked me to put it on my webpage.
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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.
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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.
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with Robert Litterman and Danny Quah
April, 1984
This is another unpublished paper about dynamic unobservable index models..
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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.
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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.
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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’.
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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.
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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.
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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.
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June 13, 2000
A comment prepared for a conference on dollarization at the Federal Reserve Bank of
Cleveland, June 1-3, 2000.
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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.
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March 25, 1999
NBER Florida conference on social security.
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with Francois Velde
April 29, 1998
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with George Hall
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with In-Koo Cho
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with Evan Anderson, Lars P. Hansen and Ellen McGrattan
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with He Huang and Selo Imrohoroglu
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with Bruce Smith
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with Lars Ljungqvist
May 1997
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with Lars Peter Hansen
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