Real purchasing power in the neoclassical monetary growth model

In the one sector neoclassical monetary growth model, the balanced growth path under perfect foresight is a saddle point. The paper demonstrates that this instability problem can be resolved by entering real purchasing power into the liquidity preference function as well as into the consumption function. This process allows an additional mechanism based on income effects in money demand by which a change in real balances can influence the growth path. Stability now depends critically on the size of such income effects given wealth effects from money demand. If stability is restored, the nature of the traditional non-neutrality of money must be qualified.     

Stability of cycles and expectations

The actual dynamics of an economy depends on how agents forecast the future at every date as a function of their information on the past, while possibly learning the structure of their environment. We show in the case of a one-dimensional state variable that under mild conditions on expectations functions, a given cycle with perfect foresight that is stable in the actual dynamics is stable in a fictitious backward perfect foresight dynamics. We exhibit a restricted class of expectations functions for which the converse is true.     

Stability and limit cycles in one-dimensional dynamic optimisations of competitive agents with a market externality

This paper considers low dimensional (more precisely, one state variable) dynamic optimisation problems of competitive agents. These individual decisions lead to a dynamic externality for the evolution of the system. However, the impact of an individual and competitive agent is negligible and thus each agent considers this evolution as exogenous data. This leads, assuming rational expectations (perfect foresight due to the deterministic set up), to motions in the three dimensional space of state, costate and externality. Considering the fact that such externalities are widespread, e.g., R&D in the literature on new growth theory, pollution in environmental economics, etc., the incorporation of such externalities due to competitive markets is important, yet this incorporation may alter the stability of the system. Indeed, complex policies such as stable limit cycles are sustainable in such a low-dimensional economy, even for a separable and strictly concave model.     

Learning and Equilibrium Selection in a Monetary Overlapping Generations Model with Sticky Prices

We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model setup but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests one should analyse learning in stochastic models.     

On the dynamics of an endogenous growth model with learning by doing

Summary. The paper studies the local dynamics of an endogenous growth model with externalities of investment. It is demonstrated that, in case of sustained per capita growth, the competitve economy is characterized by a situation with a unique balanced growth path which is saddle point stable or by a situation with two balanced growth paths. If there are two balanced growth paths, the one with the higher growth rate is a saddle point whereas the path with the lower growth rate is either completely stable, with convergence to a rest point or limit cycle, or completely unstable. In the social optimum the existence of a balanced growth path implies that it is unique and that this path is a saddle point. Received: May 15, 2000; revised version: December 14, 2001     

Alternative passive monetary policies in an inflationary economy

This paper considers three alternative specifications of passive monetary policies in a simple dynamic macroeconomic model of an inflationary economy in which both the dynamics of wealth accumulation and the evolution of inflationary expectations play central roles. These policies include one in which the real stock of money is held fixed; one in which the rate of nominal monetary growth is held constant; and a third in which the real stock of government bonds is held fixed. We compare the dynamic behavior of the system as well as its steady state properties under these alternative policies. Two expectations hypotheses—the adaptive and perfect myopic foresight—are considered and their implications related at some length.     

Perfect myopic foresight and the effects of monetary and fiscal policy in a simple inflationary model: Some analytical and numerical results

This paper analyzes the effects of monetary and fiscal policies in a simple dynamic macroeconomic model under the assumption that inflationary expectations satisfy perfect myopic foresight. While many of its properties can be obtained analytically, a good deal of indeterminacy remains and further insights are obtained by supplementing the formal analysis with consistently constructed numerical examples. The dynamics of the system is critically dependent upon the financial policy chosen by the government to finance its deficit and several policies are considered. In some cases stability is consistent with continuous adjustment from some initial point: in other cases some initial discontinuous jump is required in order to ensure stability. Both types of adjustment are discussed, where appropriate.     

Inflation and distribution in a Keynes-Wicksell model of the business cycle

The paper integrates a Kaleckian hypothesis of markup pricing and markup adjustments into a dynamic IS-LM model of Keynes-Wicksell type. Local stability and instability are characterized by different speeds of adjustments in the adaptive expectations of inflation. Application of the Hopf bifurcation theorem proves existence of periodic orbits in the three-dimensional state space. The global dynamics is investigated by means of computer simulations. A suitable modification of the rule of adaptive expectations checks the explosive tendencies and gives rise to an apparently unique and stable limit cycle. It is sketched how the evolution of the most important variables over this growth cycle compares to empirical stylized facts.     

Money,national debt,and economic growth

This paper develops a dynamic model which allows for government spending, taxation, and the endogeneity of the money supply. As an example of an application of our framework, we consider the well known stability problem of the two asset (money and physical assets) neoclassical “money-and-growth” literature. We conclude, among other things, that the usual saddle-point instability result under myopic perfect foresight with proportional savings behavior can be reversed by introducing a third asset (securities). It is further argued that this result is “robust” as it holds under various policy rules (including the traditional case of national debt growing at a constant rate).     

History and Coordination Failure

An extensive literature discusses the existence of a virtuous circle of expectations that might lead communities to Pareto-superior states among multiple potential equilibria. It is generally accepted that such multiplicity stems fundamentally from the presence of positive agglomeration externalities. We examine a two-sector model in this class and look for intertemporal perfect foresight equilibria. It turns out that under some plausible conditions, positive externalities must coexist with external diseconomies elsewhere in the model, for there to exist equilibria that break free of historical initial conditions. Our main distinguishing assumption is that the positive agglomeration externalities appear with a time lag (that can be made vanishingly small). Then, in the absence of external diseconomies elsewhere, the long-run behaviour of the economy resembles that predicted by myopic adjustment. This finding is independent of the degree of forward-looking behavior exhibited by the agents.     

Rational thinking under costly information—Macroeconomic implications

The notion of optimized rational behavior in the formation of expectations is used in this note to study the dynamics of a simple macroeconomic model. In a setting where departures from stability are not possible under perfect foresight, the selection of an optimal degree of rationality may lead to the generation of long-term endogenous fluctuations.     

The Transition from Stagnation to Growth: An Adaptive Learning Approach

This article develops the first model in which, consistentwith the empirical evidence, the transition from stagnation toeconomic growth is a very long endogenous process. The modelhas one steady state with a low and stagnant level of incomeper capita and another steady state with a high and growing levelof income per capita. Both of these steady states are locallystable under the perfect foresight assumption. We relax the perfectforesight assumption and introduce adaptive learning into thisenvironment. Learning acts as an equilibrium selection criterionand provides an interesting transition dynamic between steadystates. We find that for sufficiently low initial values of humancapital—values that would tend to characterize preindustrialeconomies—the system under learning spends a long periodof time (an epoch) in the neighborhood of the low-income steadystate before finally transitioning to a neighborhood of the high-incomesteady state. We argue that this type of transition dynamic providesa good characterization of the economic growth and developmentpatterns that have been observed across countries.     

Optimal growth with many consumers

A method is described for constructing all Pareto-optimal allocations for a dynamic economy with many heterogeneous consumers, under certainty, in which both the technology and consumer preferences are recursive but preferences need not be additively separable over time. Optimal (perfect foresight competitive equilibrium) allocations are obtained through the study of a dynamic program. For an economy with one consumption good, sufficient conditions are given for the existence of a unique interior stationary distribution of consumption and wealth. For a two-person exchange economy, sufficient conditions are given for the global asymptotic stability of the unique interior stationary point.     

Time consistency and optimal government policies in perfect foresight equilibrium

This paper develops a framework for determining optimal monetary and fiscal policies in perfect foresight equilibrium. Such equilibria have the property that all underlying demand and supply functions are derived from optimizing behavior, expectations are realized, and all markets clear. The time consistency of optimal policies derived under such circumstances is analyzed for a variety of alternative optimal policy problems. The general conclusion is that time consistency will prevail with respect to the optimization of any single policy instrument which does not appear explicitly in the indirect utility functions; otherwise time inconsistency will result. Monetary instruments are generally examples of the former, and fiscal instruments examples of the latter.     

A Reinterpretation of Chapter 17 of Keynes's general Theory: Effective Demand Shortage Under Dynamic Optimization

This article is an attempt to formalize Chapter 17 of Keynes's General Theory using a continuous dynamic optimization model with perfect foresight. I present two subjective interest rates: the time preference rate and the liquidity premium that, respectively, govern the consumption-saving and portfolio decisions. Under optimal household behavior, they are equalized to the market rate of interest. In the monetary economy described by Keynes, however, the equality can be inconsistent with the condition of market equilibrium, in which case persistent stagnation occurs. A new analytic method based on dynamic optimization is proposed as an alternative to IS-LM analysis.     

Inflationary Expectations, Variable Output, and Exchange-Rate Dynamics

This paper develops a model of exchange-rate dynamics characterized by inflationary expectations held with perfect foresight, sticky wages, and sluggish output adjustment. In this framework monetary expansion initially lowers interest rates because of sluggish output and price adjustment but quite surprisingly produces exchange-rate overshooting or undershooting. Moreover, after its initial depreciation in the overshooting case, the domestic currency temporarily appreciates beyond its new long-run equilibrium level. In the undershooting case, the home currency temporarily appreciates away from its new long-run equilibrium level. Finally, the dynamic real exchange rate-real interest rate relationship at times becomes inverse.     

A note on Kaleckian lags in the Solow model

Building on a contribution by Paul Zak, we consider the modified Solow model with a time lag introduced in the Kaleckian spirit. This model produces endogenous cycles that can be interpreted as economic fluctuations. For reasonable parameter values it can generate empirically relevant cyclic variations in output. We prove the existence of a Hopf bifurcation and a limit cycle solution in the model. We find that there is only one solution with a period longer than the production lag. Additionally we calculate the period of this cycle.     

Equilibrium cycles in an overlapping generations economy with production

Perfect foresight equilibrium trajectories of an overlapping generations model with production may include stable or unstable invariant closed curves. These orbits are detected using the Hopf bifurcation theorem, where the parameter of bifurcation is purely technological. The paper also proves that there is a stabilization policy that completely eliminates the cycle. Finally, using a C.E.S. production function, it is shown that the range of values of the elasticity of substitution between capital and labor for which cycles may exist is bounded above.     

Multiplicity of Cournot Equilibria and Involuntary Unemployment

In an overlapping generations model with Cournot competition on the goods market it is shown that a continuum of stationary states and perfect foresight trajectories exists with unemployment at arbitrary low wages. Decisive for this is the influence that different forecast functions have on the objective demand curve, even though they are consistent with perfect foresight. With an example it is shown that simple adaptive and constant memory forecast rules generate such unemployment equilibria. The corresponding temporary equilibrium dynamics may display stable unemployment and unstable full employment equilibria.Journal of Economic LiteratureClassification Numbers: D43, D51, E24