Sufficient Conditions for the Existence of Sunspot Equilibria
This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects. Journal of Economic Literature Classification Number: 020.
This paper reports results on the character of the rational expectations equilibria of a stochastic overlapping generations model with heterogenous markets. The model considered is a stationary overlapping generations model in which the endowments of young agents are subject to i.i.d. random shocks. The main result shown is that if there is more than a single commodity traded in every period, then for most preferences, the rational expectations equilibrium stochastic process of prices and allocations necessarily exhibits serial correlation. This is in marked contrast to the one commodity model in which there always exists an equilibrium which is measure isomorphic to the endowment process. Journal of Economic Literature Classification Numbers: 021, 023.
In this paper, we analyze rational expectations equilibrium paths in a stochastic overlapping generations model. The work presented here builds on results of Spear (J. Econ. Theory 35 (1985), 251-275), where it is shown that in a model with multiple goods and time non- separable preferences, a stochastic steady state equilibrium will generically fail to exist. A stochastic steady state is deflned as an equilibrium in which the stochastic process of endogenously determined variables is measure isomorphic to the exogenous process driving the model. In this paper, we establish the existence of non-steady state equilibria and provide a characterization of their stochastic properties. Journal of Economic Literature Classification Numbers: 021, 022, 023.
In this paper, we analyze optimal contracts in an infinitely repeated agency model in which both the principal and agent discount the future. We show that there is a stationary representation of the optimal contract when the agent s conditional discounted expected utility is used as a state variable. This representation reduces the multi-period problem to a static variational problem which can be analyzed using standard variational techniques. This reduction is used to obtain several properties of the contract.
This paper presents a dynamic model of political competition between two "parties" with different policy preferences. A "party" is explicitly mode11ed as a sequence of overlapping generations of candidates, all of whom face finite decision horizons. In general, there is conflict between the interests of the individual policymakers and those of the "party", which includes subsequent generations of candidates. We characterize this conflict and suggest a scheme of "intergenerational transfers" within the party which can resolve or mitigate this conflict. The the paper shows how the "overlapping generations" model can be usefully applied to the political arena.
This paper establishes the existence and local uniqueness of stationary functional rational expectations equilibria for an open set of multi-good, multi-agent pure exchange overlapping generations models in which agents' endowments are random. Such equilibria are given by prices which are functions of one-period lagged prices and endowments, and of current endowments. Journal of Economic Literature Classification Numbers: 021, 026.
In this paper we consider how boundedly rational agents learn rational expectations. The assumption that agents are boundedly rational is made operational by imposing computability constraints on the economy: all equilibnum price functions or forecasts of future equilibnum prices are required to be computable. Computable functions are defined, as in the computer science literature, as functions whose values can be calculated using some finite algorithm.
The paper examines two learning environments. In the first, agents have perfect information about the state of nature. In this case, the theory of machine inference can be applied to show that there is a broad class of computable economies whose rational expectations equilibna can be learned by inductive inference.
In the second environment, agents do not have perfect information about the state of nature. In this case, a version of Godel's incompleteness theorem applicable to the theory of computable functions yields the conclusion that rational expectations equilibria cannot be learned.
This paper examines the concept of perfect foresight equilibrium in economies with informationally complex dynamics. The first part focuses on a typical example of such an economy, the two-sector neoclassical growth model. Recent results have shown that, for sufficiently small discount rates, this model exhibits optimal capital accumulation trajectories that are chaotic. Using a notion of informational complexity due to Kolmogorov, we quantify the informational burden imposed on agents by the requirement that they actually calculate the optimal trajectory. It is shown that when trajectories depend sensitively on initial conditions, informational complexity grows without bound as the trajectories become longer.
This analysis is then used to show that chaotic dynamics is not necessary for informationally complex dynamics to occur. Sensitive dependence on initial conditions alone is sufficient to generate informationally complex dynamics. We then observe that growing economies depend sensitively on initial conditions and, hence, require precise (and informationally complex) specification of inltial conditions for the calculation of perfect-foresight growth paths. These observations suggest the need for reevaluation of the role of frictions, such as measurement error, when the dynamics of an economy is informationally complex.
In this paper, I show the existence of stationary rational expectations equilibria in a simple two-island, overlapping generations model of the tvpe first considered bv Lucas, in which all uncertainty is endogenous. The result is obtained by first constructing sunspot equilibria on each island separately and then using the equilibrium pricing equations to eliminate the sunspot variable. In the resulting equilibrium, each island's prices serve as the sunspot for the other island. The constructed equilibrium is nontrivially stochastic.
In this paper, we consider the local uniqueness properties of stationary rational expectations equilibria (REE) in a stochastic overlapping generations (OLG) model. It is known that in non- stochastic OLG models, steady-state equilibria are locally isolated, although there may exist indeterminate non-stationary perfect foresight equilibria. We show by construction that in the stochastic model, even stationary equilibrium may be indeterminate. We also show that this result is robust in the sense that there exists a non-empty open set of economies for which the result is true. Journal of Economic Literature Classification Numbers: 021, 023, 131.
In this paper, we consider a simple model of neo-classical capital accumulation with production externalities, in which a continuum of identical infinitely lived agents produce output from a standard stationary neo-classical production technology, and choose their actions to maximize a discounted sum of single period utilities. Because of the presence of the externality in production, the model exhibits sunspot equilibria. Journal of Economic Literature Classification Numbers: 021, 111, 131.
Spatial models of voting are widely used in Economics and Political Science. Spatial theory is an attractive framework to analyze choice because Euclidean geometry is easy to visualize and the language of politics is full of spatial references. Empirical tests have generally supported the theory but the estimation methods employed to produce the spatial representations of voters have raised serious statistical issues which have not been fully resolved. One of these issues is determining the nurnber of dimensions. This is a difficult problem because the number of estimated parameters increases with the number of dimensions. We show a solution for this problem in this paper. We assume a uniform distribution of voters through an N-dimensional unit hypersphere with perfect spatial voting and equally salient dimensions. We then solve for the projection of this perfect voting onto one dimension and the resultant classification error. We derive the probability density function of the classification errors which can be used to calculate the likelihood that a sample of votes was drawn from an N-dimensional hypersphere. Our Monte- Carlo investigation into the properties of this likelihood function shows that it can be used reliably for low N with small sample sizes.
We analyze the canonical market game. There are l commodities, a single inside money, l markets in which commodities are exchanged for inside money, and n consumers. Each consumer's strategy is the nonnegative vector of his commodity offers and his money bids. Given endowments and sufficiently large offers, the set of interior Nash equilibrium strategies is finite and non-empty. Hence the set of interior Nash equilibria in strategy space is parametrized by the ln-dimensional vector of offers. In allocation space the manifold of Nash equilibrium allocations has generic dimension ln-l, which is also the dimension of the set of feasible allocations.
Recent work on general equilibrium models with incomplete financial markets has demonstrated that when assets pay off in units of account, equilibrium prices and allocations are indeterminate. The equilibria in such models are also generically constrained suboptimal. A central planner can typically reallocate assets in such a way as to Pareto dominate the competitive equilibrium. In this paper, we consider an overlapping generations model with incomplete markets in which one asset is fiat money. We show that when outside money has value in equilibrium, the stationary equilibrium prices and allocations are both locally isolated and constrained optimal.
We study the existence and robustness of expectationally driven price volatility in experimental overlapping generation economies. In the theoretical model under study there exist "pure sunspot" equilibria which can be "learned" if agents use some adaptive learning rules. Our data show the existence of expectationally driven cycles, but only after subjects have been exposed to a sequence of real shocks and "learned" a real cycle. In this sense, we show evidence of path-dependent price volatility. Journal of Economic Literature Classification Numbers: C62, C92.
