
July 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 Wei Jiang and Neng Wang
July 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.

with Wei Jiang, Neng Wang, and Jinqiang Yang
February 2024
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 riskfree. A convenience yield tilts debts forward and taxes backward. An option to default determines debt capacity. DebtGDP 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, debtGDP ratio transition dynamics, and time to exhaust debt capacity.

with Jonathan Payne, Balint Szoke, and George Hall
January 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 17911933 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 safeasset 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 debtGDP 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 Yatheesan J. Selvakumar
December 2023
We state sufficient conditions on matrices defining a linear statespace
model that allow us to infer those matrices from a reducedrank firstorder vector
autoregression (VAR) for the observables. We use a Dynamic Mode Decomposition (DMD) to
compute that VAR and show how dynamic modes relate to hidden Markov states in the
statespace representation. We compute a reducedrank first order VAR for quantiles for
income, post tax and transfer income, and consumption from the US Consumer Expenditure
Survey. We relate our findings to the neoclassical synthesis that was widely practiced by
leading twentiethcentury macroeconomists.

with George G. Hall
November 2023
Post War on COVID19 Interest rate rises and inflation imposed losses on
federal creditors and motivated the Fed to transfer interest rate risk from private banks to
itself. We describe budgetfeasible paths for market values of US Treasury debt associated
with projections of taxes and
expenditures. We compare prospective paths of US federal taxes, expenditures, interest
payments, and debt in the postCOVID period to paths observed after big surges in government
expenditures during two twentiethcentury US wars. Government expenditure/GDP surges in past
US Wars had permanent components that were accompanied by permanent rises in tax
collections/GDP ratios. Although part of the War on COVID expenditure/GDP surge has endured,
so far tax collections haven't risen relative to GDP. The evolution of those two ratios will
determine future debt/GDP ratios.

with Lars Peter Hansen
September 2023
What are ``deep uncertainties'' and how should their presence alter
prudent courses of action? To help answer these questions, we bring ideas from robust
control theory into statistical decision theory. Decision theory in economics has its
origins in axiomatic formulations by von Neumann and Morgenstern as well as the
statisticians Wald and Savage. Since Savage's fundamental work, economists have provided
alternative axioms that formalize a notion of ambiguity aversion. Meanwhile, control
theorists created another way to construct decision rules that are robust to potential model
misspecifications. We reinterpret axiomatic foundations of some modern decision theories to
include ambiguity about a prior to put on a family of models simultaneously with concerns
about misspecifications of the corresponding likelihood functions. By building on ideas from
dynamic programming, our representations have recursive structures that preserve dynamic
consistency.

September 2023
This paper describes artificial intelligence and machine learning and how they were
invented.

August 2023
with John Stachurski
We introduce a “completely abstract” dynamic programming frame work in which dynamic
programs are sets of policy operators acting on a partially ordered space. We provide an
optimality theory based on highlevel assumptions. We then study symmetric and asymmetric
relationships between dynamic programs, and show how these relationships transmit optimality
properties. Our formulation includes and extends applications of dynamic programming across
many fields.

July 2023
I compare Heterogeneous Agent Old Keynesian models with Heterogeneous New Keynesian Models.
I describe evidence and data reduction techniques that led leading 20th century
macroeconomists to embrace HAOK models. I then describe other evidence that persuaded some
able 21st century macroeconomists to want to displace HAOK models. The HANK project carries
vast macroeconomic policy consequences.

with Jonathan Payne, Balint Szoke, and George Hall
July 2023
Estimating 19th century US federal bond yield curves presents challenges because few bonds
were traded, bonds had peculiar features, government policies changed often, and there were
wars. This paper compares statistical approaches for confronting these difficulties and
shows that a dynamic NelsonSiegel model with stochastic volatility and bondspecific
pricing errors does a good job for historical US bond prices. This model is flexible enough
to interpolate data across periods in a timevarying way without over fitting. We exploit
new computational techniques to deploy our model and estimate yield curves for US federal
debt from 17901933.

with with Isaac Bayley and Lars Ljungqvist
June 2023
Crossphenomenon restrictions
associated with returns to labor mobility can inform calibrations
of productivity processes in macrolabor 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 transAtlantic
unemployment experiences is robust to adding plausible quit turbulence.

with Sebastian Graves, Victoria Gregory, and Lars Ljungqvist
May 2023
We incorporate timeaveraging 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 careerlength 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 lumpsum 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 CarnegieRochester 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 inflationmoneysupply 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 exante heterogeneous households can
expect to receive; and gains in insurance from changes in households' consumption risks. Our
decomposition applies to a broad class of multiperson, multigood, multiperiod 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 macrolabor 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
macrolabor models.

with George Hall
June 2022
Directed by a consolidated government budget constraint, we compare US monetaryfiscal
responses to World Wars I and II, and the War on COVID19 with responses to the War of
Independence, the War of 1812, and the Civil War.

with George Hall
April 2022
With a consolidated government budget constraint as our guide, we compare US monetaryfiscal
responses to World Wars I and II and the War on COVID19.

with P. Battigalli, S. CerreiaVioglio, F. Maccheroni, and M. Marinacci
January 2022
This paper provides a general framework for analyzing selfconfirming policies. We study
selfconfirming equilibria in recurrent decision problems with incomplete information about
the true stochastic model. We characterize stationary monetary policies in a
linearquadratic 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 BewleyAiyagariHuggett 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 alternatingoffer 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 crosssection 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 BewleyAiyagariHuggett (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 fattertailed wealth distribution: (1)
overlapping generations of agents
who pass through $N \geq 1$ lifestage transitions of stochastic lengths, and (2)
laborearnings 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 crosssections of labor earnings to their
counterparts for cross sections of wealth.
Three forces amplify wealth inequality relative to labor earnings inequality: stochastic
lifestage 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 lifecycle saving
motive for the young born with low wealth.
The outcome that the equilibrium riskfree interest rate exceeds a typical agent's
subjective discount rate fosters a
fattailed 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 firstorder 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 Lars Peter Hansen
November 2020
A decision maker is averse to not knowing a prior
over a set of restricted structured models (ambiguity) and suspects that each structured
model is misspecified. The decision maker evaluates intertemporal plans under all of the
structured models and, to recognize possible misspecifications, under unstructured
alternatives that are statistically close to them. Likelihood ratio processes are used to
represent
unstructured alternative models, while relative entropy restricts a set of unstructured
models.
A set of structured models might be finite or indexed by a finitedimensional vector of
unknown
parameters that could vary in unknown ways over time. We model such a decision maker with a
dynamic version of variational preferences and revisit topics including dynamic consistency
and
admissibility.

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 budgetfeasible
sequences of government
issued bonds and money with complete theories whose inputs are bondmoney 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 George J. Hall
March 2020
From decompositions of U.S. federal fiscal accounts from 1790 to 1988, we describe
differences and patterns
in how expenditure surges were financed during 8 wars between 1812 and 1975. We also study
two insurrections.
We use two benchmark theories of optimal taxation and borrowing to frame a narrative of how
government decision
makers reasoned and learned about how to manage a common set of forces that bedeviled them
during all of the
wars, forces that included interest rate risks, unknown durations of expenditure surges,
government creditors’
debt dilution fears, and temptations to use changes in units of account and inflation to
restructure debts.
Ex post real rates of return on government securities are a big part of our story.

with Lars Peter Hansen
March 2020
Investors face uncertainty over models when they do not know which member of a set of
welldefined “structured models” is
best. They face uncertainty about models when they suspect that all of the structured models
might be misspecified.
We refer to worries about the first type of ignorance as ambiguity concerns and worries
about the second type as
misspecification concerns. These two types of ignorance about probability distributions of
risks add what we call
uncertainty components to equilibrium prices of those risks. A quantitative example
highlights a representative investor’s
uncertainties about the size and persistence of macroeconomic growth rates. Our model of
preferences under concerns about
model ambiguity and misspec ification puts nonlinearities into marginal valuations that
induce time variations in
market prices of uncertainty. These reflect the representative investor’s fears of high
persistence of low growth rate
states and low persistence of high growth rate states.

with Lars Peter Hansen and Balint Szoke and Lloyd S. Han
February 2020
A decision maker constructs a convex set of nonnegative martingales to use as likelihood
ratios that represent alternatives that are
statistically close to a decision maker's baseline model. The set is twisted to include some
specific models of interest. Maxmin expected utility
over that set gives rise to equilibrium prices of model uncertainty expressed as worstcase
distortions to drifts in a representative
investor's baseline model. Three quantitative illustrations start with baseline models
having exogenous longrun risks in technology shocks.
These put endogenous longrun risks into consumption dynamics that differ in details that
depend on how shocks affect returns to capital stocks.
We describe sets of alternatives to a baseline model that generate countercyclical prices of
uncertainty.

with Martin Ellison and Andrew Scott
July 2019
An analytical description of British fiscal policy during and after the Great War 19141918

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 Lawrence E. Blume, Timothy Cogley, David A. Easley, and Viktor Tsyrennikov
July 2018
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.

with George Hall, Jonathan Payne, and Balint Szoke
August 2021
This document describes Pandas DataFrames and the spreadsheets underlying them that contain
prices, quantities, and descriptions of bonds and notes issued by the United States Federal
government from 1776 to 1960. It contains directions to a public github repository at which
DataFrames and other files can be downloaded.

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.

with P. Battigalli, S. CerreiaVioglio, F. Maccheroni, M. Marinacci
August 2017
This paper provides a general framework for the analysis of selfconfirming policies. We
first study selfconfirming equilibria in recurrent decision problems with incomplete
information about the true stochastic model. Next we illustrate the theory with a
characterization of stationary monetary policies in a linearquadratic setting. Finally we
provide a more general discussion of selfconfirming policies.

with 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 alternatingoffer wage bargaining, by introducing costly
acquisition of credit, by assuming fixed matching costs, or by positing government mandated
unemployment compensation and layoff costs. All of these redesigned matching models increase
responses of unemployment to movements in productivity by diminishing the fundamental
surplus fraction, an upper bound on the fraction of a job’s output that the invisible hand
can allocate to vacancy creation. Business cycles and welfare state dynamics of an entire
class of reconfigured matching models all operate through this common channel.

February 2017
An essay on interests and forces that affect whether or not public debts are honored.
Written for the BeckerFriedman Institute at the University of Chicago. I confess that the
absence of equations from this essay makes it difficult to determine whether arguments
contradict one another.

with Anmol Bhandari, David Evans, and Mikhail Golosov
July 2016
A Ramsey planner chooses a distorting tax on labor and manages a portfolio of securities in
an environment with incomplete markets. We develop a method that uses second order
approximations of the policy functions to the planner's Bellman equation to obtain
expressions for the unconditional and conditional moments of debt and taxes in closed form
such as the mean and variance of the invariant distribution as well as the speed of mean
reversion. Using this, we establish that asymptotically the planner's portfolio minimizes an
appropriately defined measure of fiscal risk. Our analytic expressions that approximate
moments of the invariant distribution can be readily applied to data recording the primary
government deficit, aggregate consumption, and returns on traded securities. Applying our
theory to U.S.\ data, we find that an optimal target debt level is negative but close to
zero, that the invariant distribution of debt is very dispersed, and that mean reversion is
slow.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

with A. Bhandari, F. Barillas, R. Colacito, S. Kitao, C. Matthes, and Y. Shin
December 2010
This is a revised version that includes a new section solving examples from the revised
chapter `Fiscal Policies in a Growth Model' from the soon to be published third edition of
Recursive Macroeconomic Theory by Ljungqvist and Sargent. This paper teaches Dynare by
applying it to approximate equilibria and estimate nine dynamic economic models. Among the
models estimated are a 1977 rational expectations model of hyperinflation by Sargent,
Hansen, Sargent, and Tallarini’s risksensitive permanent income model, and one and
twocountry stochastic growth models. The examples.zip file contains dynare *.mod and data
files that implement the examples in the paper.
Source
Code

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

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

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

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

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

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

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