Stephen E. Spear

On Repeated Moral Hazard with Discounting

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 agents 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.

The market game: existence and structure of equilibrium

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 consumers 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.

When to fire a CEO: optimal termination in dynamic contracts

Abstract Existing models of dynamic contracts impose that it is both optimal and feasible for the contracting parties to bind themselves together forever. This paper introduces optimal termination in dynamic contracts. We modify the standard dynamic agency model to include an external labor market which, upon the dissolution of the contract, allows the firm to return to the labor market to seek a new match. Under this simple closure of the model, two types of terminations emerge. Under one scenario, the agent is fired after a bad output and he becomes too poor to be punished effectively. Under the second scenario, the agent is forced out after a good output and he becomes too expensive to motivate.

Learning Rational Expectations under Computability Constraints

In this paper, the author considers how boundedly rational agents learn rational expectations when all equilibrium price functions or forecasts of future equilibrium prices are required to be computable. 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 equilibria 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 Godels incompleteness theorem implies that rational expectations equilibria cannot be learned. Copyright 1989 by The Econometric Society.

Rational expectations in the overlapping generations model

Abstract 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 are l > 1 commodities 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.

Indeterminacy of stationary equilibrium in stochastic overlapping generations models

Abstract 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.

Growth, externalities, and sunspots

Abstract 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.

The Electricity Market Game

Abstract This paper examines the effects of imperfect competition in unregulated electricity markets from a general equilibrium perspective, and demonstrates that horizontal market power can explain both the large peak-period price spikes observed recently in California and elsewhere, and the marked reduction in addition to capacity that have also occurred during the transition to competitive markets.

Stationary Equilibria with Incomplete Markets and Overlapping Generations

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, the authors consider an overlapping generations model with incomplete markets in which one asset is fiat money. They show that when outside money has value in equilibrium, the stationary equilibrium prices and allocations are both locally isolated and constrained optimal. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Markov Rational Expectations Equilibria in an Overlapping Generations Model

Abstract In this paper, we analyze rational expectations equilibrium paths in a stochastic overlapping generations model. The work presented here builds on results of S. E. Spear ( J. Econ. Theory 35 (1985), 251–275), where is 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 defined 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.