Equilibrium selection in an experimental macroeconomy.

1. Introduction

One of the most influential literatures in economics is the theory of growth (for surveys see Azariadis 1993; Barro and Sala-i-Martin 1995; Romer 1996; Sala-i-Martin 2002). The basis of much of the literature is the Ramsey (1928)/Cass (1965)/Koopmans (1965) growth model. In this model the economy is assumed to behave like a benevolent social planner, who chooses capital stock and consumption levels over an infinite time horizon with the goal of maximizing the discounted utility of the consumption stream. The principal result of the model is that consumption and capital stock converge to unique optimal steady state levels that are independent of the initial endowment and the utility function of the social planner.

An implication of the model, therefore, is that different countries would converge toward a common income level even if their initial endowment of capital differed, provided that they have access to the same production technology. Relatively poor countries would exhibit higher growth rates than richer ones. These two predictions are testable with field data. However, field studies have generally failed to support the hypothesis of convergence toward a common income level (see Durlauf and Quah 1999; Temple 1999; and Islam 2003 for surveys). Rather, the data are more consistent with the alternative hypothesis of club convergence (Baumol 1986), which postulates that a small number of steady states exist, and that each country has a tendency to converge toward one of them. (1) Such a framework can explain the observed pattern over time of an increase in income differences between the Organisation for Economic Cooperation and Development countries and the developing world, as well as a decrease in the differences within each of the two groups.

The empirical support for club convergence has encouraged the development of theoretical models with multiple equilibria. While some countries may reach optimal equilibria, unfortunate countries might find themselves in low-income equilibria, which are often labeled as poverty traps. These countries are unable to reach a better equilibrium without coordination. Originally due to Rosenstein-Rodan (1943), the insight that the existence of multiple equilibria might provide an explanation of international income differences has led to a literature that considers a variety of growth models with multiple equilibria. For example, Azariadis and Drazen (1990) construct an overlapping generations model with two stable Pareto-rankable equilibria. In the inferior equilibrium, no agent trades with members of other generations. Murphy, Shleifer, and Vishny (1989) build a model with synergies between industries. Each industry is profitable only if other industries are operating and there are equilibria where all of the industries operate and other, Pareto-dominated equilibria where none operate. Galor and Zeira (1993) and Banerjee et al. (2001) show that inequality and differential access to credit can keep an economy in a Pareto-dominated equilibrium.

Recognizing whether or not an economy has multiple equilibria is important, because policy prescriptions differ depending on whether an economy is in an inferior equilibrium or whether it is in an equilibrium that is unique. Unfortunately, it is generally not possible to identify whether an economy has multiple equilibria (see Cooper 2005 for a discussion of the empirical issues involved). The underlying parametric structure of economies is typically unobservable, and in economies with multiple equilibria, the comparative statics are often ambiguous.

In this paper we take advantage of the fact that experimental methods allow the underlying parameters of the economy to be observed and manipulated, and we construct and study the behavior of dynamic laboratory macroeconomies that are known to have multiple, locally stable, Pareto-rankable stationary steady states. (2) As described in section 3, each steady state corresponds to a stationary competitive equilibrium, and therefore each steady state is a plausible attractor for the economy. The structure of the economies is one for which straightforward application of the Ramsey/Cass/Koopmans optimal growth model, which assumes that a benevolent social planner guides economic activity, makes a prediction that the economy will converge to the optimal of the steady states. These predictions provide null hypotheses about outcomes in our economies. However, another motivation of the paper is exploratory. We look for patterns in the data that might be characteristics of economies with multiple steady states, and that could be helpful in distinguishing between single and multiple steady state economies when the structure is unknown to the observer. While there is no ex ante reason to expect a difference between single and multiple steady state economies, there may be signatures in the economic data that reveal a uniqueness or multiplicity property of the underlying structure. This is potentially important because the right policy to promote growth or efficiency may differ in the two situations.

Two questions are posed with regard to model predictions. The first is whether or not a decentralized dynamic economy with multiple steady states will reach one of the steady states. To facilitate consideration of this question by allowing it to be interpreted within an existing framework, we use an institutional structure employed in Lei and Noussair (2002, hereafter LN), described in section 2, under which economies exhibit convergence to their optimal steady state in cases where the steady state is unique and stable. However, the situation considered here is different in that in economies with multiple steady states, a degree of coordination of actions and expectations is required to reach one of the steady states. We observe that the economy typically does operate at or very close to one of its steady states, and therefore coordination does occur in our dynamic economy.

The second question is whether, given that the economy attains a steady state, there exists any tendency to reach a steady state that is Pareto-dominated. In other words, do the economies fall into their poverty traps? Avoiding or exiting an inferior steady state involves a different and possibly more demanding coordination task than merely converging to some steady state. An ability of our economies to avoid inferior steady states would suggest that such coordination could occur in a natural way, even in economies with a decentralized structure such as ours. On the other hand, if our economies exhibit a tendency to reach inferior steady states, it illustrates that coordination problems are potentially consequential in macroeconomies. Furthermore, a result that the economy reaches inferior steady states is potentially useful for future research because it would create an arena in which different institutions could be introduced into the economy to identify those that might allow an economy to recoordinate on a better steady state. Indeed, we find that the economy often converges to a suboptimal steady state, and will typically do so if the initial endowment of capital is sufficiently low.

The exploratory analysis considers two topics. The first topic is whether an economy with multiple steady states exhibits behavior that is not characteristic of economies with a unique steady state. The existence of such behaviors might provide clues to observers who do not know the underlying parameters of the economy about whether or not the economy has multiple steady states. We study this question by comparing the patterns in our data with those observed by LN, who studied economies with a unique optimal steady state, and we find some suggestive evidence that economies with multiple steady states exhibit larger fluctuations from one period to the next and are more susceptible to severe downturns.

The second topic concerns the behavior of an economy with a similar underlying parametric structure under an idealized institutional arrangement. We consider the outcome when the economy is populated with agents who have incentives to act as benevolent social planners. All members of the economy possess full information about the structure of the economy and have an identical incentive to maximize the overall welfare of the economy. We explore the empirical patterns generated from the decisions of these social planners. We observe that a social planner, who faces no coordination problem, is not susceptible to poverty traps. On the other hand, the absence of trade means that no price information exists, making it difficult for the planner to identify the optimal sequence of consumption and investment.