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, 1998, 495-515.
  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, 195-206.
  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 (with Seppo 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 growth.
   
• 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, 705-721.
  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, 207-224.
  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, 213-237.
  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 E-stable.
   
• 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 examples.
   
• A Test for Speculative Bubbles in the Sterling-Dollar Exchange Rate: 1981-84, American Economic Review, 1986, Vol. 76, 621-636.  
  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.