Abstracts of Selected Earlier Publications
- Convergence in Monetary Inflation Models with
Heterogeneous Learning Rules (with Seppo Honkapohja and Ramon
Marimon), Macroeconomics Dynamics, Vol. 5,
2001, pp. 1-31.
Abstract: Inflation and the monetary financing of deficits are analyzed in an OLG model where the deficit is constrained to the less than a given fraction of GDP. Depending on parameter values, the model can have multiple steady states. Under adaptive learning with heterogeneous learning rules there is convergence to a subset of these steady states. In some cases the high inflation constrained steady state will emerge. However, with a sufficiently tight fiscal constraint the low inflation steady state is globally stable. We provide experimental evidence in support of our theoretical results.
- Convergence for Difference Equations with
Vanishing Time-Dependence, with Applications to
Adaptive Learning (with Seppo Honkapohja), Economic Theory,
Vol. 15, 2000, 717-725.
Abstract: We provide conditions for local stability and instability of an equilibrium point in certain systems of nonautonomous nonstochastic difference equations. In the systems under study the influence of time is present through a positive scalar "gain" parameter which converges in the limit to zero. These systems have recently been used to study the dynamics of adaptive learning in economic models, and we provide two economic illustrations of the formal results.
- Learning Dynamics (with Seppo Honkapohja), Chapter 7 of the Handbook of Macroeconomics, Vol.1, eds. J. Taylor and M.
Woodford,1999, North-Holland, pp.449-542.
Shortened Abstract: This paper provides a survey of the recent work on learning in the context of macroeconomics. The emphasis is on adaptive learning schemes in which agents use statistical or econometric techniques in self-referential stochastic systems. Both linear and nonlinear economic models are considered, and careful attention is given to learning in models with multiple
equilibria. This survey also discusses alternative approaches, including eductive approaches, artificial intelligence and other very recent topics.
- Growth Cycles (with Seppo Honkapohja and Paul
Romer), American Economic Review, Vol. 88,
Abstract: We construct a rational expectations model in which the economy switches stochastically between periods of low and high growth. When agents expect growth to be slow, the returns on investment are low and little investment take place. But if agents expect fast growth, investment is high, returns are high, and growth is rapid. This expectational indeterminacy is induced by monopolistic competition and complementarity between different types of capital goods. Neither externalities nor increasing returns to scale are required.
The equilibrium with growth cycles is stable under the dynamics implied by a simple learning rule.
- Calculation, Adaptation and Rational Expectations (with Garey Ramey), Macroeconomic Dynamics,
Vol. 2, 1998, 156-182.
Abstract: We propose an active cognition approach to bounded rationality, in which agents use a calculation algorithm to improve on the forecasts provided by a purely adaptive learning rule such as least squares learning. Agents' choices of calculation intensity depend on their estimates of the benefits of improved forecasts relative to calculation costs. Using an asset-pricing model, we show how more rapid adjustment to rational expectations and
forward-looking behavior arise naturally when there are large anticipated structural changes such as policy shifts. We also give illustrative applications in which the severity of asset price bubbles and the intensity of hyperinflationary episodes are related to the cognitive ability of the agents.
- Economic Dynamics with Learning: New Stability Results (with Seppo
Honkapohja), Review of Economic Studies,
Vol. 65, 1998, 23-44.
Abstract: Drawing upon recent contributions in the statistical literature , we present new results on the convergence of recursive, stochastic algorithms which can be applied to economic models with learning and which generalize previous results. The formal results provide probability bounds for convergence which can be used to describe the local stability under learning of rational expectations equilibria in stochastic models. Economic examples include local stability in a multivariate linear model with multiple equilibria and global convergence in a model with a unique equilibrium.
- Local Convergence of Recursive Learning to Steady states and Cycles in
Stochastic Nonlinear Models (with Seppo
Honkapohja), Econometrica, 1995, Vol. 63,
Unpublished Abstract: We analyze recursive adaptive learning in
nonlinear models with intrinsic uncertainty. We
provide generically necessary and sufficient
conditions for local convergence to rational
expectations stochastic steady states and cycles.
These are shown to be equivalent to easily
computable expectational stability (E-stability)
conditions. Due to nonlinearity the conditions
depend on the distribution of the random shocks. For
the case of small noise we link the results to the
stability of the equilibria in the corresponding
deterministic model. An economic example is used to
illustrate the importance of taking into account the
distribution of stochastic shocks when assessing
local stability in the general case.
- On the Stability of Sunspot Equilibria under Adaptive Learning Rules
Honkapohja), Journal of Economic Theory,
1994, Vol. 64, 142-161.
Abstract: We examine stability under learning
of stationary Markov sunspot equilibria (SSEs) in a
simple dynamic nonlinear model. Necessary and
sufficient conditions for local convergence of a
recursive learning algorithm to SSEs are shown to be
given (generically) by expectational stability
(E-stability) conditions. We distinguish between
weak and strong E-stability, where the latter
requires stability also with respect to
overparameterizations of the sunspot solutions.
Economic applications are given based on the
overlapping generations model.
- Information, Forecasts and Measurement of the Business Cycle (with
Lucrezia Reichlin), Journal of Monetary Economics,
1994, Vol. 33, 233-254.
Abstract: The Beveridge-Nelson (BN) technique
provides a forecast-based method of decomposing a
variable, such as output, into trend and cycle when
the variable is integrated of order one, I(1). This
paper considers the multivariate generalization of
the BN decomposition when the information set
includes other I(1) and/or stationary variables. We
show how the relative importance of the cyclical
component depends on the size of the information
set, and is necessarily higher with multivariate
decompositions. The results are illustrated using
post-WWII United States data. An explanation is also
provided for the empirical finding of a positive
association of the multivariate BN cycle with output
- Rationalizability, Strong Rationality and Expectational Stability
(with Roger Guesnerie), Games and Economic
Behavior, 1993, Vol. 5, 632-646.
Abstract: We examine the connection between
two stability concepts of rational expectations
equilibria: expectational stability, based on the
convergence of iterations of expectations, and
strong rationality, based on the uniqueness of the
rationalizable solutions of an associated game with
restrictions on beliefs. To compare concepts we
embed the standard expectations model in a
game-theoretic framework. It is shown that the two
stability concepts coincide when agents are
homogeneous. For the general case of heterogeneous
agents we show that expectational stability is a
necessary condition for strong rationality and we
provide a sufficient condition for the latter.
- On the Preservation of Deterministic Cycles when some Agents Perceive
Them to be Random Fluctuations (with Seppo
Honkapohja and Thomas J. Sargent), Journal of
Economic Dynamics and Control, 1993, Vol. 17,
Abstract: Some recent equilibrium models give
rise to complex but deterministic fluctuations. We
modify the hypothesis of universal perfect foresight
by injecting into the economy a nonnegligible
fraction of less informed agents who optimize their
expected utility with respect to the statistical
distribution of prices in the deterministic
dynamics. For the standard overlapping generations
model with money (the 'Samuelson' case) it is proved
that if the fraction of consumers with limited
knowledge is sufficiently high, then all equilibrium
cycles of period k≥2
disappear. The global properties of the case of
2-cycles are studied in detail. A brief analysis of
the 'classical' case is also given.
- Expectation Calculation and
Macroeconomic Dynamics (with Garey Ramey),
American Economic Review, 1992, Vol. 82,
Abstract: We establish a framework wherein
agents make expectation-revision decisions subject
to a specified calculation technology and
preferences over forecast errors. The technology
endows agents with correctly specified economic
models, but the cost of expectation calculation
using these models leads to gradual and incomplete
adjustment to long-run rational expectations
equilibrium. The rational expectations hypothesis
emerges as a special case of the equilibrium paths
obtained in our framework. In a natural-rate model
of monetary policy, calculation technology gives
rise to long-run nonneutrality and hysteresis
effects, and incomplete adjustment of forecast rules
causes output fluctuations to be amplified.
- On the Robustness of Bubbles in Linear RE Models (with Seppo
Honkapohja), International Economic Review,
1992, Vol. 33, 1-14.
Abstract: We analyze the expectational
stability (E-stability) of the different solutions
of a linear rational expectations model in which the
endogenous variable depends on expectations of its
current and future values, formed in the past, and
on its own lagged value. It is shown that the
continuum of bubble solutions cannot be strongly
E-stable. In contrast, for certain parameter values,
a particular solution which would normally be
identified as a bubble solution can be strongly
E-stable. The results are applied to a macroeconomic
model with real balance effects.
- Pitfalls in Testing for Explosive Bubbles in Asset Prices, American
Economic Review, 1991, Vol. 81, 922-930.
Unpublished Abstract: Rational bubbles in asset prices
are explosive in the sense that the conditional
expectation of their future values has a root larger
than one, and unit root and cointegration tests have
consequently been used to test for the presence of
bubbles. This paper shows that periodically
collapsing rational bubbles can appear to be
stationary when examined using standard unit root
tests, even though by construction they are
explosive in conditional mean. Cointegration tests
also will tend to falsely indicate that prices and
dividends are cointegrated when periodically
collapsing bubbles are present. Periodically
collapsing bubbles are thus not detectable using
standard tests to determine whether stock prices are
"more explosive" than dividends.
- Output and Unemployment Dynamics in the United States: 1950-1985,
Journal of Applied Econometrics, 1989, Vol. 4,
Abstract: For US data over 1950-1985 the
stochastic components of GNP growth and the
unemployment rate appear to be stationary, and there
is substantial feedback between these variables. The
unconditional mean rate of unemployment in a joint
model thus provides a natural benchmark in
discussions of the 'business cycle.' A bivariate VAR
model is used to describe output-unemployment
dynamics, to estimate the degree of persistence of
output innovations and to decompose output into
trend and cycle. The bivariate results are
interpreted using a restricted VAR and it is shown
that a closely related cyclical measure can be
obtained directly from the Okun's Law equation.
- The Fragility of Sunspots and Bubbles, Journal of Monetary
Economics, 1989, Vol. 23, 297-317.
Abstract: Expectational stability
(E-stability) is used to examine the multiplicity of
solutions in a range of models of interest,
including Muth's inventory model and an overlapping
generations model. In these models it is found that
sunspot and other 'rational bubble' solutions are
either E-unstable or weakly but not strongly
- A Complete Characterization of ARMA solutions to Linear Rational
Expectations Models (with Seppo
Honkapohja), Review of Economic Studies,
1986, Vol. 53, 227-239.
Abstract: Linear rational expectations models
with expectations of future endogenous variables
have multiple equilibria. For a scalar model with
k forward leads and l backward lags, this
paper characterizes the complete set of ARMA
solutions. It is shown that the maximum degree
solutions are ARMA(k+l,k), that the
solutions of maximum degree are obtained directly
from the characteristic polynomial but have
arbitrary MA parameters, and that all lower degree
ARMA solutions are obtained by deleting common
factors in the AR and MA lag polynomials. The
results are applied to several macroeconomic
- A Test for Speculative Bubbles in the Sterling-Dollar Exchange Rate:
1981-84, American Economic Review, 1986, Vol.
Abstract: The US dollar price of the UK pound
sterling is tested for a speculative bubble, defined
as a period with a nonzero median in excess returns.
A nonparametric procedure is developed which
controls for data mining over the period of flexible
exchange rates and finds a negative bubble in the
excess return to holding sterling rather than dollar
assets over 1981-84. Possible interpretations are
bootstrap equilibria (rational bubbles), asymmetric
fundamentals, and nonrational expectations.
- Selection Criteria for Models with Non-Uniqueness, Journal of
Monetary Economics, 1986, Vol. 18, 147-157.
Abstract: Three objections are considered to
the use of McCallum's rules for picking the minimal
state set solution in rational expectations models
with multiple equilibria. It is shown that these
difficulties can be resolved using the concept of
expectational stability as a selection device.
- Expectational Stability and the Multiple Equilibria Problem in Linear
Rational Expectations Models, Quarterly Journal
of Economics, 1985, Vol. 100, 1217-1234.
Abstract: Linear models involving
expectations of future endogenous variables
generally have multiple rational expectations
equilibria. This paper investigates the stability of
solutions in the disequilibrium sense of whether,
given a small deviation of expectations functions
from some rational expectations equilibrium, the
system returns to that solution under a natural
revision rule. Weak and strong local stability are
distinguished. Stability conditions are calculated
for a simple general linear model and applied to two
macroeconomic examples. In some cases there is a
unique stable equilibrium. In other cases a
continuum of equilibria forms a weakly but not
strongly stable class.
- Bottlenecks and the Phillips Curve: a Disaggregated Keynesian Model of
Inflation, Output and Unemployment, Economic
Journal, 1985, Vol. 95, 345-357.
Unpublished Abstract: A dynamic general equilibrium model
is developed, allowing for stochastic sectoral
shocks to demand, wages and labour supply, as well
as equilibrating movements of sectoral wage floors
and labour flows. The resulting model stresses the
importance of bottlenecks and structural imbalances
in determining the short-run aggregate supply curve,
the long-run natural rate of unemployment and the
dynamics of output and inflation.