The stationary sunspot equilibria of a simple overlapping generations economy with heterogeneous agents are considered. These equilibria are known to be suboptimal. The focus of the paper is on the efficacy, based on welfare economic considerations and informational requirements, of government policy in such an environment. The main result is that knowledge of the sunspot equilibrium net trades, weak interval-type information on two parameters, and weak set-type information on the location of some optimal stationary allocation is sufficient to induce a competitive equilibrium that is a Pareto optimal Pareto improvement over the sunspot allocation, which has the further property of reaching a Pareto optimal stationary allocation in finite time. The results are interpreted as demonstrating that, in a simple model with a sunspot environment, policy is very effective and welfare economic considerations lead to stabilization.

Are firms and households constrained in the use of a productive input? Theoretical approaches to this question range from exogenously imposed credit allocation rules to endogenous market failures stemming from some sort of limited-commitment or moral-hazard problem. However, when testing for constraints, researchers often simply ask firms or households if they would wish to borrow more at the current interest rate and/or test for suboptimal use of inputs in production functions relative to a full-information, full-commitment benchmark. We demonstrate that if credit is part of a much larger information-constrained (or limited-commitment) incentive scheme, then input use may very well be distorted away from the first-best. Further, households and firms, in certain well-defined circumstances, may, at the true interest rate or opportunity cost of credit, desire to borrow more (or less) than the assigned level of credit. In other, more constrained, contractual regimes, firms and households would say that they do not want to borrow more (or less), but these regimes are decidedly suboptimal, although the magnitude of the loss does depend on parameter values. We conclude with empirical methods that, in principle, could allow researchers armed with enough data to estimate parameters and distinguish regimes. Researchers then could see if firms and households are truly constrained and, if so, what the welfare loss might be.

The paper examines a stochastic analogue of the Polterovich model of economic dynamics. The study focuses on the asymptotic properties of equilibrium paths. The main results are stochastic turnpike theorems with exponential estimates of the convergence rate.

The objective of the paper is to develop a model of optimal endogenous technological progress that will exhibit two properties sought in growth models: (1) The bias will depend on the parameters of the model—particularly those affecting the cost of inputs—instead of being constrained to be Harrod neutral; (2) factor shares will be constant in steady state. Using previously derived sufficient conditions, we show the conditions under which such a model can be constructed.

The paper studies the nature of expectations formation rules for deterministic economic laws with an expectations feedback within the framework of dynamical systems theory. In such systems, the expectations formation rules, called predictors, have a dominant influence. The concept of a perfect predictor, which generates perfect-foresight orbits, is proposed and analyzed. Necessary and sufficient conditions are given for which local as well as global perfect foresight is possible. The concept is illustrated for the general linear model as well as for models of the cobweb type. For the standard overlapping generations model of economic growth, the existence of perfect predictions depends strongly on the savings behavior of the agents and on the technology.

A seasonal commodity is one that either (1) is not available during certain seasons or (2) is always available but its prices or quantities fluctuate with the season or time of year. The existence of type-1 seasonal commodities in consumer preference functions means that the usual economic approach to index number theory cannot be applied to construct a short-term month-to-month or quarter-to-quarter consumer price index. We postulate various separability assumptions on intertemporal preferences that can be used to justify various seasonal index number formulas. One of our approaches leads to an index number solution to the problem of seasonal adjustment.

We study the impact of a minimum consumption requirement on the rate of economic growth and the evolution of wealth distribution. The requirement introduces a positive dependence between the intertemporal elasticity of substitution and household wealth. This dependence implies a transition phase during which the growth rate of per-capita quantities rise toward their steady-state values and the distributions of wealth, consumption, and permanent income become more unequal. We calibrate the minimum consumption requirement to match estimates available for a sample of Indian villagers and find that these transitional effects are quantitatively significant and depend importantly on the economy's steady-state growth rate.

The interest in business-cycle asymmetry has been steadily increasing over the past 15 years. Most research has focused on the different behavior of macroeconomic variables during expansions and contractions, which by now is well documented. Recent evidence suggests that such a two-phase characterization of the business cycle might be too restrictive. In particular, it might be worthwhile to decompose the recovery phase in a high-growth phase (immediately following the trough of a cycle) and a subsequent moderate-growth phase. The issue of multiple regimes in the business cycle is addressed using smooth-transition autoregressive (STAR) models. A possible limitation of STAR models as they currently are used is that essentially they deal with only two regimes. We propose a generalization of the STAR model such that more than two regimes can be accommodated. It is demonstrated that the class of multiple-regime STAR (MRSTAR) models can be obtained from the two-regime model in a simple way. The main properties of the MRSTAR model and several issues that are relevant for empirical specification are discussed in detail. In particular, a Lagrange multiplier-type test is derived that can be used to determine the appropriate number of regimes. A limited simulation study indicates its practical usefulness. Application of the new model class to U.S. real GNP provides evidence in favor of the existence of multiple business-cycle phases.

The behavior of postwar real U.S. GNP, the inputs to an aggregate production function, and several formulations of the associated Solow residuals for the presence of nonlinearities in their generating mechanisms are examined. Three different statistical tests for nonlinearity are implemented: the McLeod-Li test, the BDS test, and the Hinich bicovariance test. We find substantial evidence for nonlinearity in the generating mechanism of real GNP growth but no evidence for nonlinearity in the Solow residuals. We further find that the generating mechanism of the labor input series is nonlinear, whereas that of the capital services input appears to be linear. We therefore conclude that the observed nonlinearity in real output arises from nonlinearities in the labor markets, not from nonlinearities in the technical shocks driving the system. Finally, we investigate the source of the nonlinearities in the labor markets by examining simulated data from a model of the Dutch economy with asymmetric adjustment costs.

This paper investigates the effects of introducing imperfect competition in an international business-cycle model. We provide some international evidence on markups and analyze the implications of increasing returns to scale and monopolistic competition for the effects and the international transmission of technology and government spending shocks. We also consider exogenous markup fluctuations as a source of shocks and of transmission of business cycles. We show that imperfect competition improves the behavior of a standard model driven by technology shocks, although the behavior of foreign trade variables remains unexplained. We also show that an imperfectly competitive model driven by government shocks can explain the international business cycle at least as well as a model driven by technology shocks.

In a seminal paper, Robert E. Lucas, Jr. provided the theoretical relationship between aggregate demand and real output based on relative price confusion at the individual market level. Subsequently, an alternative New Keynesian aggregate supply relationship was derived and it was demonstrated that the two theories can be distinguished on the basis of how both the rate of inflation and the volatility of relative prices affect its slope. By emphasizing the first implication of New Keynesian theory, strong evidence was obtained supporting this model using international data. We also concentrate on the second difference between the two theories. We derive the individual market-level equilibrium relationship for the Lucas model, i.e., the disaggregate supply curve. We estimate the crucial parameters of the relationship between aggregate nominal demand shocks and real output using U.S. intranational state and industry data. We find that the Lucas model omits important New Keynesian features of the data.

A simple technique for directly testing the parameters of a time-series regression model for instability across frequencies is presented. The method can be implemented easily in the time domain, so that parameter instability across frequency bands can be conveniently detected and modeled in conjunction with other econometric features of the problem at hand, such as simultaneity, cointegration, missing observations, and cross-equation restrictions. The usefulness of the new technique is illustrated with an application to a cointegrated consumption-income regression model, yielding a straightforward test of the permanent income hypothesis.

This paper studies the dynamic propagation of a liquidity shock through two real propagation channels: dynamic complementarities and time-varying capital utilization. The findings for an economy with intertemporal externalities are: (1) An otherwise transient liquidity shock will have real effects on output for several years; (2) time-varying capital utilization strongly augments this propagation; (3) the real effects of monetary shocks last longer when external productivity depreciates faster; and (4) nominal prices respond more sluggishly to a change in the money supply when there is a strong real propagation channel.

This is the second part of a two-part survey of the modern theory of nonlinear dynamical systems. We focus on the study of statistical properties of orbits generated by maps, a field of research known as ergodic theory. After introducing some basic concepts of measure theory, we discuss the notions of invariant and ergodic measures and provide examples of economic applications. The question of attractiveness and observability, already considered in Part I, is revisited and the concept of natural, or physical, measure is explained. This theoretical apparatus then is applied to the question of predictability of dynamical systems, and the notion of metric entropy is discussed. Finally, we consider the class of Bernoulli dynamical systems and discuss the possibility of distinguishing orbits of deterministic chaotic systems and realizations of stochastic processes.

This paper diagnoses the symptoms of the Dutch disease in a two-sector stochastic endogenous growth model. A productive, low-skill-intensive primary sector causes the currency to appreciate in real terms, thus hampering the development of a high-skill-intensive secondary sector and thereby reducing growth. Moreover, the volatility of the primary sector generates real-exchange-rate uncertainty and may thus reduce investment and learning in the secondary sector and hence also growth. Cross-sectional and panel regressions based on data for 125 countries in the period 1960–1992 confirm a statistically significant inverse relationship between the size of the primary sector and economic growth, but not between the volatility of the real exchange rate and growth.

We present a method for using rational expectations in a linear-quadratic optimization framework. Following the approach put forward by Sims, we solve the model through a QZ decomposition, which is generally easier to implement than the more widely used Blanchard-Kahn method.

This dialogue is the first to appear in Macroeconomic Dynamics. Other dialogues on topics of importance to macroeconomics will appear occasionally in this journal. Unlike interviews appearing in the MD Interview series, conversations appearing in the MD Dialogue series will not be focused on the life and work of a participant but rather on a particular research topic. Another distinction between the two series is the general format and structure. Each interview in the MD Interview series will include only one interviewee, although there may be multiple interviewers who jointly conduct an interview with a single interviewee (e.g., the interview of David Cass by Stephen Spear and Randall Wright in the preceding issue). In contrast, each dialogue will include at least two direct dialogue participants, and may or not be conducted by a third party to the conversation.

Foliations provide a general, convenient, geometric way to catalogue information from topics as varied as sufficient statistics, solutions of differential equations, indifference curves for utility functions, distributed computing, and so forth. An introduction to aspects of this area is provided.

This paper analyzes productive government expenditure in a stochastic AK growth model. First, a centrally planned economy is characterized, emphasizing the trade-off between the effects of both deterministic and stochastic government expenditures on the equilibrium growth rate and its variance. Both the growth-maximizing and the welfare-maximizing shares of government expenditure are derived and shown to depend (differentially) upon the degree of risk in the economy. Whereas production risk reduces the welfare-maximizing share of government expenditure, it may either increase or decrease the growth-maximizing share, depending upon the degree of risk aversion. Next, the stochastic equilibrium in a decentralized economy is derived. The first-best optimal tax structure is characterized and its dependence on risk is determined. The formal analysis is supplemented by some numerical simulations to assess the quantitative significance of risk and the divergence that this generates between the welfare-maximizing and growth-maximizing size of government.

Weekly live cattle prices in various markets would be expected to share common trends, i.e., they cannot be driven by separate nonstationarities because at some point the prices will diverge sufficiently for it to be economic to cross-ship the cattle, or at least the beef. This paper extends previous bivariate work to a multivariate analysis that is capable of modeling the multiple market linkages in prices for many geographical regions. The empirical estimation represents the application of an innovation on Aoki's Linear Systems State Space model that allows determination of long- and short-run dynamics common to multiple series. The common dynamics permit characterization of the multiple markets with a limited number of states (sufficient statistics for the past), resulting in dynamic arbitrage relations between the series. A nonparametric test is used to evaluate the value of expected arbitrage forecasts implied by the structure of the model. The arbitrage relationship also is employed to generate efficient discounts/premiums for either physical delivery or cash settlement of futures contracts. The proposed settlement mechanism accounts for spatial arbitrage opportunities and therefore better represents the true geographical discounts faced by traders in individual markets.