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.     

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.     

Renewable Resource Use and Nonseparable Amenity Benefits

We incorporate amenity benefits into an overlapping generations model with a renewable resource as a factor of production, source of amenity benefits and store of value. Unlike the conventional renewable resource problems studied under the assumption of additive consumption and amenity benefits, we let amenity benefits affect the utility of consumers in a nonseparable fashion. We examine the role that weights given to consumption and amenities have for harvesting and the resource stock. We characterize dynamics and stability of steady state equilibria with a logistic resource growth function. We demonstrate in parametric and numerical models that the weights given to consumption and amenities in the utility function matter substantially for the steady state equilibrium stock and its stability and dynamics. Both conventional saddle point equilibria and indeterminacy with infinite number of equilibria and saddle-node bifurcation is possible depending on the weights given to consumption and amenities. In addition, we show that for each inefficient equilibrium stock, there is a unique subsidy rate that can move the economy from an inefficient equilibrium to an efficient one. The presence of indeterminacy provides a challenge to resource policies, because the system becomes unpredictable. Therefore, expectations and market psychology may play an important role in resource utilization and provision of amenities.     

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.     

What to stabilize in the open economy*

We consider the question how “best” to maintain price‐level stability in an open economy, and evaluate three possible policy choices: (a) a constant money growth rate rule; (b) a fixed exchange rate; and (c) a policy of explicit commitment to a price‐level target. In each case we assume that policy is conducted by injecting reserves into or withdrawing reserves from the “banking system.” In evaluating the three regimes, we adopt the criterion that the “best” policy should leave the least scope for indeterminacy and “excessive” economic volatility. In a steady‐state equilibrium, the choice of regime is largely irrelevant; any steady‐state equilibrium under one regime can be duplicated by an appropriate choice of the “control” variable under any other regime. However, we show that the sets of equilibria under the three regimes are dramatically different. When all countries follow the policy of fixing a constant rate of money growth, there are no equilibria displaying endogenously arising volatility and there is no indeterminacy of equilibrium. Under a regime of fixed exchange rates, indeterminacies and endogenously arising fluctuations are impossible if and only if the country with the low “reserve‐to‐deposit” ratio is charged with maintaining the fixed rate. Finally, when one country targets the time path of its price level, under very weak conditions, there will be indeterminacy of equilibrium and endogenously arising volatility driven by expectations.     

Capital market imperfections in a monetary growth model

Summary. We consider a monetary growth model essentially identical to that of Diamond (1965) and Tirole (1985), except that we explicitly model credit markets, a credit market friction, and an allocative function for financial intermediaries. These changes yield substantially different results than those obtained in more standard models. In particular, if any monetary steady state equilibria exist, there are generally two of them; one of these has a low capital stock and output level, and it is necessarily a saddle. The other steady state has a high capital stock and output level; either it is necessarily a sink, or its stability properties depend on the rate of money creation. It follows that monetary equilibria can be indeterminate, and nonconvergence phenomena can be observed. Increases in the rate of money creation reduce the capital stock in the high-capital-stock steady state. If the high-capital-stock steady state is not a sink for all rates of money growth, then increases in the rate of money growth can induce a Hopf bifurcation. Hence dynamical equilibria can display damped oscillation as a steady state equilibrium is approached, and limit cycles can be observed as well. In addition, in the latter case, high enough rates of inflation induce the kinds of “crises” noted by Bruno and Easterly (1995): when inflation is too high there are no equilibrium paths approaching the high-activity steady state. Received: November 18, 1995; revised version: March 26, 1996     

Hopf bifurcation and quasi-periodic dynamics in discrete multisector optimal growth models

This paper discusses the asymptotic stability of the steady state and the existence of a Hopf bifurcation in discrete time multisector optimal growth models. We obtain on the one hand a local turnpike theorem which guarantees the saddle point property for all discount rates. On the other hand, we provide a new proposition which gives some conditions ensuring local stability of the steady state if the impatience rate is not too high. A characterization of the boundδ*, above which the steady state is saddle-point stable, is also proposed in terms of indirect utility function's concavity properties. On this basis, some sufficient conditions for the existence of a Hopf bifurcation are stated. We thus prove the existence of quasi-periodic optimal paths in asymmetric models.     

Heterogeneous learning

There is by now a large literature characterising conditions under which learning schemes converge to rational expectations equilibria (REEs). It has been claimed that these results depend on the assumption of homogeneous agents and homogeneous learning. This paper analyses the stability of REEs under heterogeneous adaptive learning, for the class of self-referential linear stochastic models. Agents may differ in their initial perceptions about the evolution of the economy, the degrees of inertia in revising their expectations, or the learning rules they use. General conditions are provided for local stability of an REE. In general, it is not possible to show that stability under homogeneous learning implies stability under heterogeneous learning. To illustrate how to apply the results, several examples are provided.     

Inflation and growth in a disequilibrium macroeconomic model

The purpose of this paper is to study the dynamics of temporary equilibria in a disequilibrium growth model. Dynamics rests upon adjustment mechanisms of prices, capital stock, money balances, and labour supply. Wage dynamics is supposed to be influenced by indexation processes, and this question is related to the investment behaviour of firms. We give sufficient conditions for existence, unicity, and asymptotic stability of steady states of this model. We also show that steady states correspond to a long-run Phillips curve, which is vertical when inflationary expectations are fully reflected in wage and price changes.     

Liquidity traps, learning and stagnation

We examine global economic dynamics under learning in a New Keynesian model in which the interest-rate rule is subject to the zero lower bound. Under normal monetary and fiscal policy, the intended steady state is locally but not globally stable. Large pessimistic shocks to expectations can lead to deflationary spirals with falling prices and falling output. To avoid this outcome we recommend augmenting normal policies with aggressive monetary and fiscal policy that guarantee a lower bound on inflation. In contrast, policies geared toward ensuring an output lower bound are insufficient for avoiding deflationary spirals.     

Education,overlapping generations,and the existence of equilibrium

We describe a simple aggregative model, the essential features of which are that individuals are mortal (overlapping generations) and can invest in their own training (human capital). It is shown by example that if expectations are rational then there may be a unique steady state but no competitive path starting away from the steady state.     

Two‐level CES Production Technology in the Solow and Diamond Growth Models*

The two‐level CES aggregate production function—that nests a CES into another CES function—has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two‐factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital–skill complementarity.     

Is fiscal austerity really self-defeating?

This paper analyzes local and global equilibrium dynamics in an optimizing endogenous growth model under expenditure-based fiscal austerity feedback policies expressed relative to the private capital stock—prescribing spending cuts in reaction to public debt accumulation. Because the present value of equilibrium primary surpluses turns to be a nonlinear function of debt, two steady state equilibria are shown to emerge, one exhibiting low debt and high growth, one exhibiting high debt and low growth. Local analysis reveals that the low-debt/high-growth steady state is saddle-path stable while the high-debt/low-growth steady state is unstable—the latter thus indicating the possibility of self-defeating austerity, characterized by off-equilibrium upward spirals in debt because of persistent policy-induced adverse effects on growth dividends and fiscal revenues. However, when global nonlinear dynamics are taken into account, it is demonstrated that the two steady states are endogenously connected. In particular, global analysis reveals that even if the high-debt/low-growth steady state is locally unstable, there exists a unique and possibly nonmonotonic saddle connection making the economy converge to the low-debt/high-growth steady state. The existence of the saddle connection guarantees global determinacy of perfect foresight equilibrium should the high-debt/low-growth steady state be a node, ruling out multiple explosive paths incompatible with the government's intertemporal budget constraint and the private agents' transversality condition. The foregoing results are robust with respect to the adoption of an output-based—rather than a capital-based—policy function as long as the rule is nonlinear and sufficiently reactive to debt changes.     

Short-sighted managers and learnable sunspot equilibria

This paper assumes that firm managers make choices over a finite horizon while households plan over an infinite horizon. Following Shea (2013), I assume that labor exhibits firm-specific learning by doing so that newly employed labor is less productive than experienced labor. In the model, optimization requires that firm managers make conjectures about how their choices affect the labor demand choices of their successors. The model yields two steady states; one where the firm manager behaves as if she cares only about the present period and another where she is forward looking. The former (myopic) steady state usually exhibits higher output than the non myopic steady state. The non-myopic steady state also exhibits two regions of indeterminacy where extraneous, self-fulfilling expectational errors add volatility. One of these regions of indeterminacy is usually stable under adaptive learning while the other never is stable under learning.     

Determinacy and Stability under Learning of Rational Expectations Equilibria

This paper studies relationships between the local determinacy of a stationary equilibrium in the perfect foresight dynamics, and its local stability in dynamics arising from econometric learning procedures. Attention is focused on linear scalar economies where agents forecast only one period ahead, and with an arbitrary, but fixed, number of predetermined variables. In such a framework, it is well known that there are no clear links between the determinacy of the stationary state in the perfect foresight dynamics on the levels of the state variable, and its stability under learning. The paper emphasizes, however, that this is not the right perfect foresight dynamics to look at whenever agents try to learn the coefficients of the perfect foresight dynamics restricted to an eigenspace of lower dimension. Indeed the paper introduces a growth rate perfect foresight dynamics on these coefficients and proves equivalence between determinacy in that dynamics and stability under learning provided that a simple sign condition is satisfied. Journal of Economic Literature Classification Numbers: E32, D83.     

A two-sector Kaleckian model of growth and distribution with endogenous productivity dynamics

This study extends a two-sector Kaleckian model of output growth and income distribution by incorporating endogenous labour productivity growth. The model is composed of investment goods and consumption goods production sectors. The impact of a change in wage and profit shares on capacity utilisation and output growth rates at the sectoral and aggregate levels are identified. The study reveals short-run cyclical capacity utilisation rates and productivity growth dynamics. Even if the short-run steady state is stable, the capital accumulation rate in the consumption goods sector must decrease more than that in the investment sector for long-run stability. When simultaneous rises in profit shares in both the sectors affect long-run aggregate economic growth differently at a steady state, the distributional interests between the same class in different sectors may hamper the long-run economic growth. A policy message is that the effect of income distribution on industrial output growth is not always beneficial. These phenomena are specific to two-sector models and cannot be observed when using conventional aggregate growth models.     

Conventions and Economic Change: A Contribution toward a Theory of Political Economy

This essay presents a perspective on the growth of knowledge as the source of economic growth. After a critical examination of the reasons why the crucial issue has been neglected in the dominant tradition in economics, a concept of paradigm-seeking as the essence of decision making under uncertainty and learning is proposed. Behavioral implications of paradigm-seeking include the generation of conventions by which people stabilize their expectations and build a network of coordination and cooperation. The stability of conventions, however, generates a dynamic process of change, by creating unexploited opportunities. Entrepreneurial successes and their emulation amount to the process of social learning and growth of knowledge. It is further suggested that implications of the proposed perspective are consistent with other observed phenomena.     

Adaptive learning models of consumer behavior

In a model of dynamic duopoly, optimal price policies are characterized assuming consumers learn adaptively about the relative quality of the two products. A contrast is made between belief-based and reinforcement learning. Under reinforcement learning, consumers can become locked into the habit of purchasing inferior goods. Such lock-in permits the existence of multiple history-dependent asymmetric steady states in which one firm dominates. In contrast, belief-based learning rules must lead asymptotically to correct beliefs about the relative quality of the two brands and so in this case there is a unique steady state.     

Learning,estimation, and the stability of rational expectations

The stability of the rational expectations equilibrium of a simple asset market model is studied in a situation where a group of traders learn about the relationship between the price and return on the asset using ordinary least squares estimation, and then use their estimates in predicting the return from the price. The model which they estimate is a well-specified model of the rational expectations equilibrium, but a misspecified model of the situation in which the traders are learning. It is shown that for appropriate values of a stability parameter the situation converges almost surely to the rational expectations equilibrium.