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Robust Hidden Markov LQG
Problems
(with Lars Peter Hansen and
Ricardo Mayer) , August 27, 2008 .
For linear quadratic
Gaussian problems, this paper uses two
risk-sensitivity operators defined by Hansen and Sargent to construct
decision rules that are robust to misspecifications of (1) transition dynamics for possibly hidden
state variables, and (2) a probability density over hidden states induced by Bayes' law. Duality of risk-sensitivity to the
`multiplier preferences’ min-max expected utility theory of Hansen and
Sargent allows us to compute risk-sensitivity operators by
solving two-player zero-sum games. That the approximating model is a Gaussian joint probability
density over sequences of signals and
states gives important computational simplifications. We exploit a modified certainty equivalence principle
to solve four games that differ in continuation value functions and
discounting of time t increments to
entropy. In Games I, II, and III, the
minimizing players' worst-case densities over hidden states are time
inconsistent, while Game IV is an LQG version of a game of \citet{hs2005a} that builds in time consistency. We
describe how detection error probabilities can be used to calibrate the
risk-sensitivity parameters that govern fear of model misspecification in
hidden Markov models.
Robustness and U.S.
Monetary Policy Experimentation
(with Timothy Cogley, Riccardo Colacito, and Lars Peter Hansen) , January 11,
2008 .
We study how a
concern for robustness modifies a policy maker's incentive to experiment. A
policy maker has a prior over two submodels of
inflation-unemployment dynamics. One submodel
implies an exploitable trade-off, the other does not. Bayes'
law gives the policy maker an incentive to experiment. The policy maker fears
that both submodels and his prior probability
distribution over them are misspecified. We compute
decision rules that are robust to misspecifications of each submodel
and of a prior distribution over submodels. We
compare robust rules to ones that Cogley, Colacito, and Sargent (2007)
computed assuming that the models and the prior distribution are correctly
specified. We explain how the policy maker's desires to protect against
misspecifications of the submodels, on the one
hand, and misspecifications of the prior over them, on the other, have
different effects on the decision rule.
Time Inconsistency of
Robust Control?
(with Lars Peter Hansen) , November 22, 2006 .
Responding to criticisms of Larry Epstein and his
coauthors, this paper describes senses in which various representations of
preferences from robust control are or are not time consistent. We argue that the senses in which
preferences are not time consistent do not hinder applications.
Doubts or Variability? (Formerly titled Reinterpreting a graph of
Tallarini)
(with Francisco
Barillas and Lars Peter Hansen) (July 2008).
Reinterpreting
most of the
market price of risk as a market price of model uncertainty eradicates the
link between asset prices and measures
of the welfare costs of aggregate fluctuations that were proposed by
Hansen, Sargent, and Tallarini (1999), Tallarini (2000), and Alvarez and Jermann
(2004). Market prices of model uncertainty contain informationabout
compensation for removing model uncertainty, not the consumption fluctuations
that Lucas
(1987, 2003) studied. By using the preference specification of
Kreps and Porteus with intertemporal
elasticity of one put the mean and standard deviation of the stochastic
discount factor close to the bounds of Hansen and Jagannathan
(1991), but only for very high values
of a risk aversion parameter, and he needed a substantially higher risk
aversion parameter for a trend-stationary model of consumption than for a
random walk model. A max-min expected utility theory lets us reinterpret Tallarini's risk-aversion parameter as measuring a representative consumer's doubts about the model specification. We use model detection error probabilities
instead of risk-aversion experiments to calibrate that parameter. Values of detection error probabilities
that imply a somewhat but not overly cautious representative consumer give
market prices of model uncertainty that approach the Hansen-Jagannathan bounds.
Fixed detection error probabilities give rise to virtually identical
asset prices for Tallarini's two models of
consumption growth. We calculate the welfare costs of removing model
uncertainty and find that they are large.
Fragile beliefs and the
price of model uncertainty
(with Lars Peter
Hansen) (June 2007).
We
use two risk-sensitivity operators to construct the stochastic discount
factor for a representative consumer who evaluates consumption streams in
light of parameter estimation and model selection problems that
present long run risks. The arrival of signals induces the consumer to alter his posterior
distribution over models and parameters. The consumer expresses his doubts
about model specifications and priors by slanting them in directions that are
pessimistic in terms of value functions. His twistings
over model probabilities
give rise to time-varying model uncertainty premia
that contribute a volatile time-varying component to the marketprice
of model uncertainty.
Robust Estimation and
Control under Commitment
(with Lars Peter Hansen) (June 2005).
In a Markov decision problem with
hidden state variables, a decision maker expresses fears that his model
is misspecified by surrounding it with a set of
alternatives that are nearby as measured by their expected log likelihood
ratios (entropies).Sets of martingales represent alternative models.
Within a two-player zero-sum game under commitment, a
minimizing player chooses a martingale at time $0$.Probability
distributions that solve distorted filtering problems serve as state
variables, much like the posterior in problems without concerns about
misspecification. We state conditions under which an equilibrium of the
zero-sum game with commitment has a recursive representation that can be
cast in terms of two risk-sensitivity
operators. We apply our results to a linear quadratic example that makes
contact with the analysis of Basar and Bernhard
(1995) and Whittle (1990).
Recursive Robust Estimation
and Control Without Commitment
(with Lars Peter Hansen) (May 2006).
In a Markov decision problem with
hidden state variables, a posterior distribution serves as a state
variable and Bayes' law under the approximating
model gives its law of motion. A decision maker
expresses fear that his model is misspecified
by surrounding it with a set of alternatives that are nearby as measured by
their expected log likelihood ratios (entropies). Sets of martingales
represent alternative models. A decision maker constructs a sequence of
robust decision rules by pretending that there is a sequence of minimizing
players who choose increments to a martingale from within this set. One risk
sensitivity operator induces robustness to perturbations of the approximating
model conditioned on the hidden state. Another risk sensitivity operator
induces robustness with respect to a prior distribution over the hidden
state. We thereby extend the approach of Hansen
and Sargent (IEEE Transactions on Automatic Control, 1995) to problems that
contain hidden states. We study linear quadratic examples.
Robust Control and
Misspecification
(with Lars Peter Hansen, Gauhar Turmuhambetova, and Noah Williams ) (September
2005).
This paper integrates a variety of results in robust
control theory in the context of an approximating model that is a diffusion. The paper is partly a response to some
criticisms of Anderson, Hansen, and Sargent (see below) by Chen and Epstein.
It formulates two robust control problems -- a multiplier problem from the
literature on robust control and a constraint formulation that looks like Gilboa-Schmeidler's min-max expected utility theory. The
paper studies the connection between the two problems, states an
observational equivalence result for them, links both problems to `risk
sensitive' optimal control, and discusses time consistency of the preference
orderings associated with the two robust control problems.
`Certainty equivalence’ and
`model uncertainty’
(with Lars Hansen ) , 2004. Prepared
for a Fed conference in honor of Dale Henderson, Richard Porter, and Peter
Tinsley.
The paper reviews how the structure of the Simon-Theil certainty equivalence result extends to models that
incorporate a preference for robustness to model uncertainty. A model
of precautionary savings is used an example.
A Quartet of Semi-Groups for
Model Specification, Robustness, Prices of Risk, and Model Detection
(with Evan Anderson and Hansen) April
2003.
This paper supercedes
`Risk and Robustness in Equilibrium’, also on this web page. A representative
agent fears that his model, a continuous time Markov process with jump and
diffusion components,is misspecified and therefore uses robust control theory to
make decisions. Under the decision maker's
approximating model, that cautious behavior puts adjustments for model
misspecification into market prices for risk factors. We use a statistical
theory of detection to quantify how much model
misspecification the decision maker should fear, given his historical data
record. A semigroup is a collection of objects connected by something like the law of iterated
expectations. The law of iterated expectations defines the semigroup for a Markov process, while similar laws define
other semigroups. Related semigroups
describe (1) an approximating model; (2) a
model misspecification adjustment to the continuation value in the decision
maker's Bellman equation;(3) asset prices; and (4) the behavior of the
model detection statistics that we use to calibrate how much robustness the
decision maker prefers. Semigroups 2, 3, and 4
establish a tight link between the market price of uncertainty and a bound on
the error in statistically discriminating between an approximating and a worst case model.
Robust control and
filtering of forward-looking models
(with Lars Hansen ). ( November 19, 2002 )
This is a comprehensive revision of an earlier
paper with the same title. We describe an equilibrium concept for models with
multiple agents who, as under rational expectations share a common model, but
all of whom doubt their model, unlike rational expectations. Agents all
fear model misspecification and perform their own worst-case analyses to
construct robust decision rules. Although the agents share the
approximating models, their differing preferences cause their worst-case
models to diverge. We show how to compute Stackelberg
(or Ramsey) plans where both leaders and followers fear model
misspecification.
Robust Control and Model
Uncertainty
(with Lars Peter Hansen) ( January
22, 2001 ).
Paper prepared for presentation at the meetings of
the American EconomicAssociation in New Orleans , Jan
5, 2001 . This paper is a summary of results presented in more
detail in Hansen, Sargent, Turmuhambetova, and
Williams (2001) -- see below. That paper formulates two robust control problems
-- a multiplier problem from the literature on robust control and a
constraint formulation that looks like Gilboa-Schmeidler's
min-max expected utility theory.
Robust Pricing with
Uncertain Growth
(with Marco Cagetti, Lars Peter
Hansen, and Noah Williams ) (January 2001).
A continuous time asset pricing model with robust
nonlinear filtering of a hidden Markov state.
Acknowledging Misspecification
in Macroeconomic Theory
(with Lars Peter Hansen, December 2000)
The text of Sargent's
Frisch lecture at the 2000 World Congress of the Econometric Society; also
the basis for Sargent's plenary lecture at the Society
for Economic Dynamics in Costa Rica, June 2000.
Robust Permanent Income and
Pricing with Filtering
(with Lars Peter Hansen and Neng
Wang, August 25, 2000)
This paper reformulate Hansen, Sargent, and Tallarini's 1999 (RESTud) model
by concealing elements of the state from the planner and the agents, forcing
them to filter. The paper describes how jointly to do robust filtering and
control, then computes the appropriate `market
prices of Knightian uncertainty.' Detection error
probabilities are used to discipline the one free parameter that robust
decision making adds to the standard rational expectations paradigm.
Robustness, Detection, and
the Price of Risk
( March
27, 2000 ) (with Evan Anderson
and Lars Hansen ) (Formerly known as `Risk and Robustness in Equilibrium ';)
This paper describes a preference for robust
decision rules in discrete time and continuous time models. The paper extends
earlier work of Hansen, Sargent, and Tallarini in
several ways. It permits non-linear-quadratic Gaussian set ups. It develops
links between asset prices and preferences for robustness. It links premia in asset prices from Knightian
uncertainty to detection error statistics for descriminating
between models.
Wanting Robustness in
Macroeconomics
(with Lars Peter Hansen, June 10, 2000 )
This paper is a `nontechnical' (according to
Hansen) survey of an approach to building a preference for robust decision
rules into macroeconomics.
Policy Rules for Open
Economies
(Discussion of Laurence
Ball) (January
1998)
Robust Permanent Income and
Pricing
(with Lars Peter Hansen and Thomas Tallarini) (April 30, 1999)
Robust Permanent Income and
Pricing
(with Lars Peter Hansen and Thomas Tallarini)
, (April 1997)
Old version with preference shock specification of model.
Discounted Linear
Exponential Quadratic Gaussian Control
(with Lars Peter Hansen)
Back to Summary
Inflation-Gap
Persistence in the U.S.
(with Timothy Cogley and Giorgio
E. Primiceri) , December 2007.
We use Bayesian Markov Chain Monte Carlo
methods to estimate two models of post WWII U.S. inflation rates with
drifting stochastic volatility and drifting coefficients. One model is univariate, the other a multivariate autoregression.
We define the inflation gap as the deviation of inflation from a pure random
walk component of inflation and use both of our models to study changes over
time in the persistence of the inflation gap measured in terms of short- to
medium-term predicability. We present evidence that
our measure of the persistence of the inflation gap increased until Volcker
brought mean inflation down in the early 1980s and that it then fell during
the chairmanships of Volcker and Greenspan. Stronger evidence for movements
in inflation gap persistence emerges from the VAR than from the univariate model. We interpret these changes in terms of a simple
dynamic new Keynesian model that allows us to distinguish altered monetary
policy rules and altered private
sector parameters.
Diverse Beliefs, Survival,
and the Market Price of Risk
(with Timothy Cogley), July 2008.
We
study prices and allocations in a complete-markets,
pure endowment economy in which
agents have heterogenous beliefs. Aggregate
consumption growth evolves exogenously according to a two-state Markov
process. The economy is populated by
two types of agents, one that learns about transition probabilities and
another that knows them. We examine how the presence of the better-informed
agent influences allocations, the market price of risk, and the rate at which
asset prices converge to values that would be computed under the typical
assumption that all agents know the transition probabilities.
The Conquest of South
American Inflation
(with Noah Williams and Tao Zha)
, August 2008.
This is an extensively revised and shortened
version of our 2006 paper. We infer
determinants of Latin American hyperinflations and stabilizations in 5 countries
by using the method of maximum likelihood to estimate a hidden Markov model that assigns roles both
to fundamentals in the form of government deficits that are financed by money
creation and to destabilizing expectations dynamics that can occasionally
divorce inflation from fundamentals.
Levels and conditional volatilities of monetized deficits drove most hyperinflations
and stabilizations, with a notable exception in Peru where a cosmetic reform of
the type emphasized by Marcet and Nicolini in 2003
seems to have been at work.
Self-Confirming Equilibrium
(with In-Koo Cho) , December
2006. Prepared for the New Palgrave Dictionary of Economics.
A
self-confirming equilibrium is the answer to the following question: what are
the possible limiting outcomes of purposeful interactions among a collection
of adaptive agents, each of whom averages past data to approximate moments of
the conditional probability distributions of interest?.
The Benefits from U.S. Monetary Policy
Experimentation in the Days of Samuelson and Solow and Lucas
(with Timothy Cogley and Riccardo Colacito) (September, 2005).
A policy maker knows two models
of inflation-unemployment dynamics. One implies an exploitable trade-off, the
other does not. The policy maker's prior probability over the two
models is part of his state vector. Bayes' law converts the prior into a
posterior at each date and gives the policy maker an incentive to
experiment. For a model calibrated to U.S. data through the early
1960s, we isolate the component of government policy that is due to
experimentation by comparing the outcomes from two Bellman equations, the
first of which `experiments and learns', the second of
which `learns but doesn't experiment'. We interpret the second as an `anticipated utility' model
and study how well its outcomes approximate those from the `experiment and
learn' Bellman equation. The approximation is good. We use the model to
study rates at which false models would be disposed of starting from initial
conditions designed to emulate (a) a situation in which the Samuelson-Solow model is true, but some prior
probability is attached to Lucas’s model, and (b) a situation in which the
Lucas model is true but some prior probability attaches to the
Lucas model. The rates differ in interesting ways.
The Market Price of Risk
and the Equity Premium: A Legacy of the Great Depression?
(with Timothy Cogley) , August,
2007 .
.A representative consumer is endowed with a prior
that is pessimistic relative to a true data generating mechanism. True
consumption growth follows a two state Markov chain with probabilities
calibrated by Cechetti, Lam, and Mark. We
obtain a pessimistic prior by using a calculation from robust control.
Then we endow agents with Bayes’ Law and let time
and chance remove their pessimism. From the
view point of a rational expectations
econometrician, the stochastic discount factor has a multiplicative
adjustment, the Radon-Nikodym derivative of the
decision maker’s model relative to the true one. We use this framework
to study how market prices of risk behave as Bayes’
Law causes the `legacy of the Great Depression’ gradually to wear off.
We obtain a high equity premium that gradually
falls during the post WWII period.
Anticipated Utility and
Rational Expectations as Approximations of Bayesian Decision Making
(with Timothy Cogley) , March,
2005 .
We regard as an `anticipated utility’ model
like ones advocated by David Kreps as an approximation to a model with
a Bayesian agent and study the quality of approximation in several contexts
of interest to a macroeconomist. We display some examples in which the
approximation is quite good.
Shocks and Government
Beliefs: The Rise and Fall of American Inflation
(with Noah Williams and Tao Zha)
, Revised, April 2005.
We
use a Bayesian Markov Chain Monte Carlo
algorithm jointly to estimate the parameters of a `true' data generating
mechanism and those of a sequence of approximating models that a monetary
authority uses to guide its decisions. Gaps between a true expectational Phillips curve and the monetary authority's
approximating non-expectational Phillips curve
models unleash inflation that a monetary authority that knows the true model
would avoid. A sequence of dynamic programming problems implies that the
monetary authority's inflation target evolves as its estimated Phillips curve
moves. Our estimates attribute the rise and fall of post WWII inflation in
the US
to an intricate interaction between the monetary authority's beliefs and
economic shocks. Shocks in the 1970s made the monetary authority perceive a
tradeoff between inflation and unemployment that ignited big inflation. The
monetary authority's beliefs about the Phillips curve changed in ways that
account for Volcker's conquest of US inflation.
The Conquest of U.S.
Inflation: Learning, Model Uncertainty, and Robustness
(with Timothy Cogley) (November, 2003).
An adaptive Fed’s model is a mixture of three
models. The Fed uses Bayesian methods to update estimates of three models of
the Phillips curve: a Samuelson-Solow model, a Solow-Tobin model, and a Lucas
model. Each period, the central bank also updates the probability that
it assigns to each of these three models, then
determines its first-period decision by solving a `Bayesian linear regulator
problem’. Although by the mid 1970s the U.S. data induce the Fed to
assign very high probability to the Lucas model, the government refrains from
adopting its low-inflation policy recommendation because that policy has very
bad consequences under one of the other low (but not zero) probability
models. The statistical model is thus able to explain the puzzling
delay in the Fed’s decision to deflate after learning the natural rate
hypothesis.
Knowing the Forecasts of
Others
(with Joseph G. Pearlman) , April 10, 2004 .
This paper uses recursive methods to compute an equilibrium of the notorious model in section 8 of
Townsend’s 1983 JPE paper `Forecasting the Forecasts of Others’. The
equilibrium is of finite (and even low) dimension. Market prices fully
reveal traders’ private information, making the equilibrium equivalent with
one in which traders pool their information before trading. This means
that the problem of forecasting the forecasts of others disappears in
equilibrium. There is no need to keep track of higher order beliefs.
Impacts of Priors on
Convergence and Escape from Nash Inflation
(with Noah Williams) , July 2004
.
This paper generalizes the learning model that Cho,
Williams, and Sargent (2002) and Sargent (1999) attributed to the government,
then calculates rates of convergence to and escape from self-confirming equilibria.
Drifts and
Volatilities: Monetary Policies and Outcomes in the Post WWII U.S.
(with Tim Cogley) , August 26, 2002 .
This paper answers criticisms of our 2001 NBER
Macro Annual paper made by Sims and Stock. We enrich our specification of a
drifting coefficient VAR to allow stochastic volatility and study whether our
earlier evidence for drifting coefficients survives this generalization. It
does. We investigate the power of various tests that have been used to test
time invariance of the autoregressive coefficients of VARs against
alternatives like ours. All except one have low power. These results about
power help reconcile our results with those of Sims and Bernanke and Mihov. We also study evidence that monetary policy rules
have drifted.
Bayesian Fan Charts for U.K.
Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary
System
(with Timothy Cogley and Sergei
Morozov) (September,
2003).
We use Bayesian methods to estimate a VAR with
drifting coefficients and volatilities then construct fan charts that we
compare with those of the Bank of England’s MPC. Our fan
charts incorporate several sources of uncertainty, including a form of model
uncertainty that is represented by drifting coefficients and volatilities.
Evolving Post-World War II U.S.
Inflation Dynamics
(with Timothy Cogley
) (Final Version, June 2001)
This paper uses Bayesian methods and post World War
II data on inflation, unemployment, and an interest rate to estimate a
`drifting coefficients' model. The model is used to construct
characterizations of the data that make contact with various points in Lucas's
Critique and Sargent's The Conquest of American
Inflation published by Princeton University Press. The paper constructs
various measures of posterior means and variances of inflation and
unemployment and studies their relationships. This paper will appear in the
2001 Macroeconomic Annual.
Escaping Nash Inflation
(with In-Koo Cho and Noah Williams ) (Very Revised, May 31, 2001)
This paper analytically computes the `escape route'
for a special case of the model in my Marshall
lectures The Conquest of American Inflation published by Princeton University
Press. We show that theoretical computations of the mean dynamics and escape
dynamics do a good job of explaining simulations like those in The Conquest
of American Inflation. The paper uses the mysterious insight of Michael
Harrison: `If an unlikely event occurs, it is very likely to occur in the
most likely way' .
Laboratory Experiments with
an Expectational Phillips Curve
(with Jasmina
Arifovic ), August 22, 2001 .
Experiments with human subjects in a Kydland-Prescott
Phillips curve economy.
Learning to be Credible
(with In-Koo Cho)
Back to Summary
Monetary Policies and
Low-Frequency Manifestations of the Quantity Theory
(with Paolo Surico), September
2008.
As a device to detect
manifestations of the quantity theory of money, we follow Lucas (1980) by looking at scatter plots
of filtered time series of inflation and money growth rates and interest
rates and money growth rates. In the
spirit of Whiteman (1984), we relate
those scatter plots to sums of
two-sided distributed lag coefficients estimated from fixed-coefficient and time-varying VARs for
U.S. data from 1900-2005. Then we interpret outcomes in terms of the
population values of those sums of coefficients implied by two DSGE models. The DSGE models make the sums of weights
depend on the
monetary policy rule, yet another example of the cross-equation
restrictions that Lucas (1972) and Sargent (1971) emphasized in the context
of testing the natural unemployment rate hypothesis. When the U.S. data are extended beyond
Lucas's 1955-1975, the patterns revealed by Lucas's scatter plots mutate in
ways that we want to attribute to alterations in prevailing monetary policy
rules.
The Timing of Tax Collections and the Structure of
``Irrelevance'' Theorems in a Cash-in-Advance Model
(with
Bruce Smith), May 2008 (originally, 1988).
A
standard timing protocol allows in a cash-in-advance model allows the
government to elude the inflation tax. That matters. Altering the timing of
tax collections to make the government hold cash overnight disables some
classical propositions
but enables others. The
altered timing protocol loses a Ricardian
proposition and also
the proposition that
open market operations, accompanied by tax adjustments needed to finance the
change in interest on bonds due the public, are equivalent with pure units
changes. The altered timing enables a
Modigliani-Miller equivalence proposition that does not otherwise prevail.
Evolution and Intelligent Design, January 7,
2008.
This paper is my AEA
presidential address. It discusses the
relationship between two sources of ideas that influence monetary policy
makers today. The first is a set of analytical results that impose the
rational expectations equilibrium concept and do `intelligent design' by solving Ramsey
and mechanism design problems. The second is a long trial and error
learning process that constrained government budgets and anchored the price level with a gold
standard, then relaxed government budgets by replacing the gold standard with a fiat currency system wanting nominal anchors. Models of out-of-equilibrium learning tell
us that such an evolutionary process will converge to a self-confirming
equilibrium (SCE). In an SCE, a
government's probability model is correct about events that occur under the
prevailing government policy, but possibly wrong about the consequences of
other policies. That leaves room for more mistakes and useful experiments
than exist in a rational expectations equilibrium.
Israel 1983: A Bout of Unpleasant Monetarist Arithmetic, (with
Joseph Zeira) February 2008.
This paper is about
the consequences that using fiscal policy to bail out banks can have for inflation
rates. It is a case study of a bail out of banks in Israel in 1983. That bailout
might have been good news for banks’ shareholders, but it was not good news
for people whose net wealth positions were harmed by inflation.
Some of Milton Friedman’s Scientific Contributions
to Macroeconomics.
An assessment of the
enduring influences of Milton Friedman’s work in macroeconomics.
Practicing Dynare (with F. Barillas, R. Colacito, S. Kitao,
C. Matthes, and Y. Shin), July 2007.
Click
here to download the examples.zip file
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.
Two Questions about European Unemployment (with Lars
Ljungqvist), June 2007.
A general equilibrium
search model makes layoff costs affect
the aggregate unemployment rate in ways that depend on equilibrium
proportions of frictional and structural unemployment that in turn depend on
the generosity of government
unemployment benefits and skill losses among newly displaced workers.
The model explains how, before the 1970s, lower flows into unemployment gave
Europe lower unemployment rates than the United
States; and also how,
after 1980, higher durations
have kept unemployment rates in Europe persistently higher than in the U.S.
These outcomes arise from the way Europe's
higher firing costs and more generous unemployment compensation make its
unemployment rate respond to bigger skill losses among newly displaced
workers. Those bigger skill losses also explain why U.S.\ workers have
experienced more earnings volatility after 1980 and why, especially among
older workers, hazard rates of gaining employment in Europe
now fall sharply with increases in the duration of unemployment.
Understanding European Unemployment with Matching
and Search-Island Models, (joint Lars Ljungqvist), July 2007.
To match broad
macroeconomic observations about European and American unemployment during
the last 60 years,we use a
search-island model and some matching models with workers who have
heterogeneous skills and entitlements
to government benefits. There are labor market frictions in these models, but
not in a closely related representative family model with employment lotteries(please see the following paper on this web
page). High government mandated unemployment insurance (UI) and employment
protection (EP) in Europe increase durations
and levels of unemployment when there is higher `turbulence' in the sense of worse skill transition probabilities for workers who suffer involuntary layoffs.
But when there is lower turbulence, high European EP suppresses unemployment
rates despite high European UI. Different matching models assign unemployed workers to
different waiting pools (i.e., matching functions). This affects how strongly unemployment
responds to increases in turbulence.
Unless the long-term unemployed share a matching function with other unemployed workers who
are not discouraged, the economy almost closes down in turbulent times. This
catastrophe does not occur in the search-island model where there are no
labor market externalities and each worker bears the full consequences of his
own decisions.
Understanding European Unemployment with a
Representative Family Model, (joint Lars
Ljungqvist), July 2007.
A representative
family model with indivisible labor and employment lotteries has no labor
market frictions and complete markets .The high aggregate labor supply
elasticity implies that when generous
government-supplied unemployment insurance are included, we get the unrealistic
result that economic activity collapses. Because there is no frictional
unemployment, an increase in employment protection decreases aggregate work
because the representative family substitutes into leisure. Therefore, the
model does not provide the same successful accounting for a half century of European and American
unemployment rates offered by the models in the previous paper on this web
page or in our paper entitled Two Questions
about European Unemployment.
Taxes, benefits, careers, and markets, (joint
Lars Ljungqvist), May 2007.
An incomplete markets
life-cycle model with indivisible labor makes career lengths and human
capital accumulation respond to labor tax rates and government supplied
non-employment benefits. We compare
aggregate and individual outcomes in this individualistic incomplete markets
model with those in a comparable collectivist representative family with employment lotteries and
complete insurance markets. The incomplete and complete market structures
assign leisure to different types of individuals who are distinguished by
their human capital and age. These microeconomic differences distinguish the
two models in terms of how macroeconomic aggregates respond to
some types of government supplied non-employment benefits, but remarkably,
not to labor tax changes.
How Sweden's
unemployment became more like Europe's, (joint
Lars Ljungqvist), Prepared for
NBER-SNSS conference on reforming the Swedish welfare state, July 2007.
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.
Indivisible Labor, Human Capital, Lotteries, and
Personal Savings: Do Taxes Explain European Employment? (joint Lars
Ljungqvist), Prepared for 2006 NBER
Macroeconomics Annual conference, June 2006.
To appreciate the
role of a `not-so-well-known aggregation theory' that underlies Prescott's
(2002) conclusion that higher taxes on labor have depressed Europe relative
to the U.S., this paper compares aggregate outcomes for economies with two
alternative arrangements for coping with indivisible labor: (1) employment
lotteries plus complete consumption insurance, and (2) individual consumption
smoothing via borrowing and lending at a risk-free interest rate. We compare these two arrangements in both
single-agent and
general equilibrium models.
Under idealized conditions, the two arrangements support equivalent
outcomes when human capital is not present; when it is present, outcomes are
naturally different. Households' reliance on personal savings in the
incomplete markets model constrains the `career choices' that are implicit in
their human capital acquisition plans relative to those that can be supported
by lotteries and consumption insurance in the complete markets model. Lumpy
career choices make
the incomplete markets model better at coping with a generous system of
government funded compensation to people who withdraw from work. Adding
generous government supplied benefits to Prescott's
model with employment lotteries and consumption insurance causes employment
to implode and prevents the model from matching outcomes observed in Europe.
Jobs and Unemployment in Macroeconomic Theory: A
Turbulence Laboratory, (joint 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, 2005
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.
The
European Unemployment Experience: Uncertainty and Heterogeneity
(with Lars Ljungqvist
, August 2005 ).
A general equilibrium model of
stochastically aging McCall workers whose human capital depreciates during
spells of unemployment and appreciates during spells of employment. There are
layoff taxes and government supplied unemployment compensation with a
replacement ratio attached to past earnings, the product of human capital and
a wage draw. The wage draw changes on the job via
Markov chain, inspiring some quits. We use a common calibration
of the model with “European” and “American” unemployment compensations to
study the different unemployment experiences of Europe and the U.S.
from the 1950s through 2000. The model succeeds in explaining why
unemployment rates were lower in Europe in
the 1950s and 1960s, but higher after the 1970s. The explanation is about how layoff taxes
and unemployment compensation linked to past earnings interact with an
increase in economic turbulence. The
paper relates these macro outcomes to evidence from earnings distributions
and displaced workers studies.
A, B, C, (and
D)’s for Understanding VARs (joint with Juan Rubio, Jesus Villaverde, and Mark Watson), July 2006.
An approximation to the equilibrium of a
complete dynamic stochastic economic model can be expressed in terms of
matrices (A,B,C,D)
that define a state space system. An associated state space system (A,K,C,I) determines a vector autoregression
for fixed observables available to an econometrician. We review a permanent
income example that illustrates a simple special condition for checking
whether the mapping from VAR shocks to economic shocks is invertible.
Ambiguity in American Monetary and Fiscal
Policy
(a lunch talk)
How a coherent monetary and
fiscal policy somehow emerges out of the helter-skelter of U.S. politics, with some
historical examples.
Business
Cycle Modeling without Pretending to Have Too Much A Priori Economic Theory
(with Christopher Sims) (1977).
This paper is an out of print old timer.
Several people asked me to put it on my webpage.
Business Cycle Analysis with Unobservable Index
Models and the Methods of the NBER
(with Robert Litterman
and Danny Quah) (June, 1984).
This is an unpublished paper about dynamic
unobservable index models like the ones in the previous paper with Chris
Sims.
Using Unobservable Index Models to Estimate Unobservables and Forecast Observables
(with Robert Litterman
and Danny Quah) (April, 1984).
This is another unpublished paper about
dynamic unobservable index models..
Politics and Efficiency of Separating Capital and
Ordinary Government Budgets
(Marco Bassetto with Thomas
Sargent) (December, 2004).
We analyze the democratic politics of a rule
that separates capital and ordinary account budgets and allows the government
to issue debt to finance capital items only.
Many national governments followed this rule in the 18th and 19th centuries
and most U.S.
states do today. This simple 1800s financing
rule sometimes provides excellent incentives for majorities to choose an
efficient mix of public goods in an economy with a growing population of
overlapping generations of long-lived but mortal agents. In a special
limiting case with demographics that make Ricardian
equivalence prevail, the 1800s rule does nothing to promote efficiency.
But when the demographics imply even a moderate
departure from Ricardian equivalence,
imposing the rule substantially improves the efficiency of democratically
chosen allocations. We calibrate some examples to U.S.\ demographic data. We
speculate why in the twentieth century most
national governments abandoned the 1800s rule while U.S. state governments have
retained it.
Lotteries for
consumers versus lotteries for firms
(with Lars Ljungqvist)
(October, 2003).
A discussion of a paper by Edward Prescott
for the Yale Cowles commission conference volume on general equilibrium
theory. Prescott emphasizes the similarities in lotteries that can be used to
aggregate over nonconvexities for firms, on the one
hand, and households, on the other. We emphasize their differences.
Reactions
to the Berkeley
Story
(October, 2002).
This paper is my discussion of a paper at the 2002 Jackson Hole Conference by Christina and David Romer. The Romers’
paper uses narrative evidence to support and extend an interpretation of post
war Fed policy that has also been explored by Brad DeLong
and others. The basic story is that the Fed has a pretty good model in
the 50s, forgot it under the influence of advocates of an exploitable
Phillips curve in the late 60s, then came to its senses by accepting Friedman
and Phelps’s version of the natural rate hypothesis in the 1970s. The Romers extend the story by picking up Orphanides’s
idea that the Fed misestimated potential GDP or the natural unemployment rate
in the 1970s. The Romers’ story is that the Fed
needed to accept the natural rate hypothesis (which it did by 1970 according
to them) and also to have good estimates of the natural rate (which according
to them it didn’t until the late 70s or early 80s). The Romers story is about the Fed’s forgetting then relearning
a good model. My comment features my own narration of a controversial
paper by `Professors X and Y’.
European Unemployment and Turbulence Revisited in a
Matching Model
(with Lars Ljungqvist ).
(September, 2003).
This paper recalibrates a matching model of den Haan, Haefke, and Ramey and
uses it to study how increased turbulence interacts with generous
unemployment benefits to affect the equilibrium rate of unemployment.
In contrast to den Haan, Haefke,
and Ramey, we find that increased turbulence causes unemployment to
rise. We trace the difference in outcomes to how we model the hazard of losing skills after a voluntary job change.
European Unemployment: From
a Worker's Perspective
(with Lars Ljungqvist ) , Sept 17, 2001.
Prepared for an October 2001 conference in honor of
Edmund Phelps. Within the environment of our JPE 1998 paper on European
unemployment, this paper conducts artificial natural experiments that provoke
``conversations'' with two workers who experience identical shocks but make
different decisions because they live on opposite sides of the Atlantic
Ocean.
Optimal Taxation without State Contingent Debt
(with Rao Aiyagari,
Albert Marcet and Juha Seppala) , Sept 29, 2001 .
An extensively revised version of a paper recasting
Lucas and Stokey's analysis of optimal taxation in
a market setting where the government can issue only risk free one-period
government debt. This |