Showing papers in "Economic Theory in 1994"

A simple model for study of the determination of the price level and the interaction of monetary and fiscal policy

Abstract: A representative-agent model with money holdings motivated by transactions costs, a fiscal authority that taxes and issues debt, no production, and a convenient functional form for agents' utility is presented. The model can be solved analytically, and illustrates the dependence of price determination on fiscal policy, the possibility of indeterminacy, even stochastic explosion, of the price level in the face of a monetary policy that holdsM fixed, and the possibility of a unique, stable price level in the face of a monetary policy that simply pegs the nominal interest rate at an arbitrary level. In a rational expectations, market-clearing equilibrium model with a costlessly-produced fiat money that is useful in transactions, the following things are true under broad assumptions. - A monetary policy that fixes the money stock may (depending on the transactions technology) be consistent with indeterminacy of the price level—indeed with stochastically fluctuating, explosive inflation. - A monetary policy that fixes the nominal interest rate, even if it holds the interest rate constant regardless of the observed rate of inflation or money growth rate, may deliver a uniquely determined price level. - The existence and uniqueness of the equilibrium price level cannot be determined from knowledge of monetary policy alone; fiscal policy plays an equally important role. Special case models with interest-bearing debt and no money are possible, just as are special cases with money and no interest-bearing debt. In each the price level may be uniquely determined. Determinacy of the price level under any policy depends on the public's beliefs about what the policy authority would do under conditions that are never observed in equilibrium. These points are not new. Eric Leeper [1991] has made most of them within a single coherent model. Woodford [1993], in a representative agent cash-in-advance model, has displayed the possibility of indeterminacy with a fixed quantity of money and the possibility of uniqueness with an interest-rate pegging policy. Aiyagari and Gertler [1985] use an overlapping generations model to make many of the points made in this paper, without discussing the possibility of stochastic sunspot equilibria. Sargent and Wallace [1981] and Obstfeld [1983] have also discussed related issues. This paper improves on Leeper by moving beyond his analysis of local linear approximations to the full model solution, as is essential if explosive sunspot equilibria are to be distinguished from explosive solutions to the Euler equations that can be ruled out as equilibria. It improves on the other cited work by pulling together into the context of one fairly transparent model discussion of phenomena previously discussed in isolation in very different models. We study a representative agent model in which there is no production or real savings, but transactions costs generate a demand for money. The government costlessly provides fiat money balances, imposes lump-sum taxes, and issues debt, but has no other role in the economy. We make restrictive assumptions about the form of the utility function and the form of a transactions cost term in the budget constraint. The model could be extended to include production, capital accumulation, non-neutral taxation, productive government expenditure, and a more general utility function without affecting the conclusions discussed in this paper. Indeed the model I informally matched to data in an earlier paper [1988] makes some such extensions. While such an extended model is more realistic, it is harder to solve. The version in my earlier paper [1988] was solved numerically and simulated. The bare-bones model of this paper allows an explicit analytic solution that may make its results easier to understand.

Monetary policy and price level determinacy in a cash-in-advance economy*

Abstract: Summary. The paper considers the determinacy of the equilibrium price level in the cash-in-advance monetary economy of Lucas and Stokey (1983, 1987), in the case of deterministic "fundamentals". The possibilities both of a multiplicity of perfect foresight equilibria and of "sunspot equilibria" are considered. Two types of monetary policy regimes are considered and compared, one in which the money supply grows at a given exogenous rate (that may be positive or negative), and one in which the nominal interest rate on one-period government debt is pegged at a given non-negative level. In the case of constant money growth rate regimes, it is shown that one can easily have both indeterminacy of perfect foresight equilibrium and existence of sunspot equilibria; indeed, in the case of negative rates of money growth (as called for by Friedman (1969)), both types of indeterminacy necessarily occur. On the other hand, sufficient conditions for uniqueness of equilibrium (and non-existence of equilibria other than a deterministic steady state) are also given, and a class of cases is identified in which a sufficiently high rate of money growth guarantees this. Thus there may be a conflict between the aims of choosing a rate of money growth that results in a high level of welfare in the steady state equilibrium and choosing a rate that makes this steady state the unique equilibrium.) In the case of the interest rate pegging regimes, sufficient conditions are given for uniqueness of equilibrium (and impossibility of sunspot equilibria), and it is shown that these necessarily hold in the case of any low enough nominal interest rate. Thus the nominal interest rate peg allows simultaneous achievement of price level determinacy and a high level of welfare in the unique (steady state) equilibrium. In this paper I consider the consequences of alternative choices of the monetary policy regime for the determinacy of the rational expectations equilibrium value of money, and in particular for the existence or not of "sunspot" equilibria, i.e., rational

On the structure and diversity of rational beliefs

Abstract: The paper proposes that the theory of expectations be reformulated under the assumption that agents do not know the structural relations (such as equilibrium prices) of the economy. Instead, we postulate that they can observe past data of the economy and form probability beliefs based on the data generated by the economy. Using past data agents can compute relative frequencies and the basic assumption of the theory is that the system which generates the data is stable in the sense that the empirically computed relative frequencies converge. It is then shown that the limit of these relative frequencies induce a probability on the space of infinite sequences of the observables in the economy. This probability is stationary. Abelief of an agent is a probability on the space of infinite sequences of the observable variables in the economy. Such a probability represents the “theory” or ∌ypothesis” of the agent about the mechanism which generates the data. A belief is said to becompatible with the data if under the proposed probability belief the economy would generate the same limit of the relative frequencies as computed from the real data. A theory which is “compatible with the data” is a theory which cannot be rejected by the data. A belief is said to be aRational Belief if it is (i) compatible with the data and (ii) satisfies a certain technical condition. The Main Theorem provides a characterization of all Rational Beliefs.

On rational belief equilibria

Abstract: We study equilibria in which agent's belief are rational in the sense of Kurz [1994]. The market is formulated by specifying a stochastic demand function and a continuum of producers, each with a quadratic cost function who must select their output before knowing prices. Holding Rational Beliefs about future prices, producers maximize expected profits. In a Rational Belief Equilibrium (RBE) agents select diverse forecast functions but each one is rational in the sense that it is based on a theory which cannot be rejected by the data. It is shown that there exists a continuum of RBE's and they could entail very different patterns of time series for the economy and consequently different aggregate levels of longterm volatility. Since the model contains exogenously specified random variables, the difference in the level of long-term volatility of prices among the different RBE's arises endogenously as an “amplification” of the volatility of exogenous variables. The paper derives exact bounds on the possible levels of such “amplification.”

Top dominance and the possibility of strategy-proof stable solutions to matching problems

Abstract: This paper explores the possibility of designing strategy-proof mechanisms yielding satisfactory solutions to the marriage and to the college admissions problem. Our first result is negative. We prove that no strategy-proof mechanism can always choose marriages that are individually rational and Pareto efficient. This strengthens a result by Roth (1982) showing that strategy-proof mechanisms cannot always select stable marriages. The result also applies, a fortiori, to college admissions. Since finding difficulties with strategy-proofness is quite an expected result, we then address a second question which is classical within the incentives literature. Are there restrictions on the preferences of agents under which strategy-proof and stable mechanisms do exist? We identify a nontrivial restriction on the domain of preferences, to be called top dominance, under which there exist strategy-proof and stable mechanisms for both types of matching problems. The mechanisms turn out to be exactly those that derive from the most classical algorithms in the literature; namely, the women's optimal, the men's optimal and the student's optimal. Finally, top dominance is shown to be essentially necessary, as well as sufficient, for the existence of strategy-proof stable matching mechanisms.

Expectations and learning under alternative monetary regimes: an experimental approach

Abstract: We design and analyze experimental versions of monetary overlapping generations economies under alternative policy regimes. Economies with a constant level of real deficit financed through seignorage, economies in which the level of deficit is adapted in order to follow a monetary policy with a target rate of inflation, and economies with preannounced changes in deficit levels are reported here. We also examine the behavior of an economy with no stationary competitive equilibrium. Our time series are compared to rational expectations equilibrium paths and to adaptive learning dynamics.

Market architectures, institutional landscapes and testbed experiments

Abstract: Designer markets are becoming a reality. A merger of theory and experimental work is setting stages for a different kind of economics. The modern theory of mechanisms suggests that it is possible to design markets and/or decentralized mechanisms that can perform tasks that were thought to be impossible. The mechanisms themselves can become active participants with computers solving complex optimization or coordination problems based on "messages" submitted to the system by decentralized agents. Competition becomes utilized in new ways in the context of what are becoming known as "smart markets." Testbed experiments are demonstrating that such processes can be developed beyond purely theoretical discussions. Paper processes, mechanisms found only as ideas on the pages of a journal, are being transformed to operating processes with a physical presence that can be studied and modified by practical considerations. Policy research has expanded to incorporate the ideas; and traces of such modern theorizing can be found in institutions that are being put into place. The five papers contained in this issue represent different stages of the new approach to economic research.

The demand commitment bargaining and snowballing cooperation

Abstract: A multi-person bargaining model based on sequential demands is studied for coalitional games with increasing returns to scale for cooperation. We show that for such games the (subgame perfect) equilibrium behavior leads to a payoff distribution which approaches the Shapley value as the money unit approaches 0. Subgame consistency and strategic equilibria are the main tools used in the analysis. The model is then applied to study a problem of public good consumption.

Fertility, human capital and the wealth of families*

Abstract: An overlapping generations model with parental altruism is examined. The existence of the optimal value function in a model with an endogenous discount rate is proven. Two development regimes are produced: a high fertility, low income and no growth steady state, and a perpetual growth equilibrium with low fertility and rising income.

Ergodic chaos in optimal growth models with low discount rates

Abstract: Whether or not erratic economic behavior can be explained by models of infinitely-lived rational agents has been discussed in the economic literature for some years. A positive answer to this question was provided first by Deneckere and Pelikan (1986) and Boldrin and Montrucchio (1986); that is, optimal paths of capital accumulation may behave chaotically. Until recently, however, the possibility of chaotic optimal dynamics has been established only for the case in which future utilities are discounted extremely heavily. This fact is in line with the intuition obtained from the turnpike literature, namely, that weak myopia tends to simplify the dynamic behavior of optimal growth paths (see, e.g, Brock and Scheinkman (1976), Cass and Shell (1976), McKenzie (1976, 1983), Scheinkman (1976), Yano (1990)). In Sorger (1992a,b, 1995) this intuition is further strengthened by the minimum impatience theorems which demonstrate that for any given dynamical system generating complicated dynamics there is an upper bound for the set of those discount factors with which that system is the optimal policy function of an optimal growth model. These results, however, do not exclude the possibility of chaotic optimal dynamics for arbitrary low myopia.

The local bifurcation of Ramsey equilibrium

Abstract: The hypothesis that aggregate fluctuations may represent an endogenous feature of dynamic competitive economies with incomplete markets has been advanced in several papers.1 The role of incomplete markets seems essential for the appearance of cycles in one sector models.2 Becker and Foias (1987) and Woodford (1988a) have pointed out that the elasticity of substitution of the production function plays a fundamental role in the existence of cyclic equilibrium paths. In those papers cycles are generated if the substitutability between capital and labor is not too great. Heterogeneity of households is also a crucial component of their fluctuation theories.

Dynamics of endogenous growth

Abstract: Summary. We present an overlapping generations model of endogenous fertility and growth. The cost of child rearing and the effect of population size on total factor productivity determine the dynamics of competitive equilibrium path of our model. The non-linear dynamics of the model generates a plethora of outcomes (depending on the functional forms, parameters and initial conditions) that include not only the neo-classical steady state with exponential growth of population with constant per capita income and consumption, but also growth paths which do not converge to a steady state and are even chaotic. Exponential, and even super exponential, growth of per capita output are possible in some cases.

On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy and Sunspots

Abstract: In this chapter we demonstrate the possibility of periodicity and indeterminacy of perfect foresight equilibrium under borrowing constraints in a dynamic one-sector economy with infinitely-lived heterogeneous households. As a consequence of indeterminacy we can also prove the existence of sunspot equilibria in this economy. The Ramsey model we consider is basically the same as the one used by Becker (1980), Becker and Foias (1987, 1994), and Becker et al. (1991). It differs from standard neoclassical growth models in two aspects, namely, that households are heterogeneous and that markets are incomplete which prevents households from using their discounted future income to finance present consumption.

Why are credit card rates sticky

Abstract: This paper investigates credit card rate stickiness using a screening model of consumer credit markets. In recent years, while the cost of funds has fallen, credit card rates have remained stubbornly high, spurring legislators to consider imposing interest rate ceilings on credit card rates. The model incorporates asymmetric information between consumers and banks, regarding consumers' future incomes. The unique equilibrium is one of two types: separating (in which low-risk consumers select a collateralized loan and high-risk consumers select a credit card loan), or pooling (in which both types of consumers choose credit card loans). I show that a change in the banks' cost of funds can have an ambiguous effect on the credit card rate, so that the credit card rate need not fall when the cost of funds does. Usury ceilings on credit card rates are detrimental to consumer welfare, so would be counter to their legislative intent.

Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects

Abstract: We examine a discrete-time aggregative model of discounted dynamic optimization where the felicity function depends on both consumption and capital stock. The need for studying such models has been stressed in the theory of optimal growth and also in the economics of natural resources. We identify conditions under which the optimal program is monotone. In our framework, the optimal program can exhibit cyclic behavior for all discount factors close to one. We also present an example to show that our model can exhibit optimal behavior which is chaotic in both topological and ergodic senses.

Cotenancy and competition in an experimental auction market for natural gas pipeline networks

Abstract: This research investigates the use of a "smart" computer-assisted auction mechanism for the allocation of resources within a network of commodity flows. The type of network that we examine has many of the economic properties of the natural gas pipeline industry. In fact this research was originally motivated by specific concerns about the impact of federal regulation on the economic performance of the natural gas industry. However, we believe that the ideas developed here have potential application in other network environments such as electricity generation and transmission, the provision of various transportation and communication services, and scheduling in multiprocessing computing environments.1 Here are some prominent features of the gas industry:

Optimal multilateral contracts

Abstract: The purpose of this paper is to derive the structure of optimal multilateral contracts in a costly state verification model with multiple agents who may be risk averse and need not be identical. We consider two different verification technology specifications. When the verification technology is deterministic, we show that the optimal contract is a multilateral debt contract in the sense that the monitoring set is a lower interval. When the verification technology is stochastic, we show that transfers and monitoring probabilities are decreasing functions of wealth. The key economic problem in this environment is that optimal contracts areinterdependent. We are able to resolve this interdependency problem by using abstract measure theoretic tools.

An experimental examination into the design of decentralized methods to solve the assignment problem with and without money

Abstract: An experimental examination of the assignment problem, matching individuals to positions or slots, is conducted in which various assignment mechanisms are analyzed. Generalized versions of both the Vickrey and English auctions are designed to solve the assignment problem along with oridinal ranking mechanisms (serial dictator and “funny” money system). The generalized auctions result in efficient allocations. In contrast, the ordinal ranking mechanisms, which require no monetary transfers, are significantly less efficient in their assignments. However, the efficient allocations obtained from the competitive bidding processes are at the expense of consumers' surplus since demanders retain significantly larger profits with the ordinal ranking mechanisms.

Fictitious play in 2×2 games: A geometric proof of convergence

Abstract: This paper provides a new proof of Miyasawa's (1961) result showing the convergence of fictitious play in 2×2 games. The novelty of the approach used here is that it rests entirely on the geometric properties of the best-response correspondence. The geometric approach greatly shortens the exposition, and it suggests some possible extensions to more difficult convergence conjectures.

Bayesian learning leads to correlated equilibria in normal form games

Abstract: Consider an infinitely repeated normal form game where each player is characterized by a “type” which may be unknown to the other players of the game. Impose only two conditions on the behavior of the players. First, impose the Savage (1954) axioms; i.e., each player has some beliefs about the evolution of the game and maximizes its expected payoffs at each date given those beliefs. Second, suppose that any event which has probability zero under one player's beliefs also has probability zero under the other player's beliefs. We show that under these two conditions limit points of beliefs and of the empirical distributions (i.e., sample path averages or histograms) are correlated equilibria of the “true” game (i.e., the game characterized by the true vector of types).

Experimentation with heteroskedastic noise

Abstract: The direction of information with respect to the choice variable can easily change under a general class of distributions. The implication is that, when information is a function of the choice variable, the result of a model may be an outcome of the structure of the uncertainty and not of the existence of uncertainty. Thus, incomplete information does not always have such a clear effect on an agent's decision as previous models have suggested. If such results are key to the conclusions, then the structure of the model should be examined. The model presented here can be used to determine the relationship between information and the choice variable and to derive basic insights into the particular model being examined. It can also be used to eliminate the informational aspect of decisions so as to examine other aspects of a model, e.g., the incentive for information transmission (jamming) and other dynamic aspects (e.g., capital accumulation). Finally, the functional form of the unknown function as well as the error function are inportant in determining the direction of increased information, as the direction of increased noise can be the direction of experimentation.

Bounded rationality and learning* Introduction

Abstract: Many have objected to the use of the Nash equilibrium (or more generally, Bayesian Nash equilibrium) concept in game theory, and similarly to the use of the rational expectations concept in the theory of competitive markets, on the grounds that the theory assumes too much sophistication and coordination of beliefs on the part of decision-markers. The papers in this volume are among those which study the implications of relaxing those assumptions. To provide a suitable context to describe the papers in this symposium, we will begin with a slight digression. Consider a repeated stage game where at each stage there are finitely many players, each with finitely many actions. First consider the case where each player seeks to maximize his expected utility at each date (i.e., he has a zero discount factor) given specified beliefs about the play of his opponents. Let us suppose that we have eliminated all dominated actions within the stage game. This means, in particular, that for each of the actions of each player there is a set of beliefs that a player could have on the actions of the other players which would rationalize that action as a best response for that player. If the stage game were to be played only once, each outcome to the game could be rationalized as the outcome of maximizing behavior under some beliefs of agents. Maximizing behavior by itself imposes absolutely no restriction on the outcome of the oneshot stage game! This is true even when the payoff matrices of the players are common knowledge. Introducing imperfect information over the payoffs does not diminish the set of possible utility maximizing outcomes. Indeed, by allowing type-dependent correlations in behavior, the introduction of imperfect information over payoffs may actually increase the set of possible (probability distributions of) outcomes. Instead of a zero discount factor, let us now suppose that the players have a positive discount factor and seek to maximize the expected sum of their discounted payoffs. Then, even without eliminating strategies which are dominated in the normal form game, we may show via folk-theorem-type arguments that without placing restrictions on the beliefs of players we can rationalize just about a n y

Efficiency and determinacy of equilibrium under inflation targeting

Abstract: There is increasing interest in conducting monetary policy so as to achieve a given target inflation rate (or price level path). Several policies that have been advocated for this purpose are evaluated on the following criteria: (a) are they consistent with the existence of an equilibrium for a variety of targets? (b) do they support only equilibria with the desired price level behavior, or are other equilibria also possible? (c) even if only the desired price level path is possible, are indeterminacies avoided on other dimensions? (d) if there is a unique equilibrium, does it support an allocation that can be Pareto dominated in equilibrium by an alternative policy mechanism? None of the policies examined performs well on the basis of all these criteria.

Optimal chaos, nonlinearity and feasibility conditions

Abstract: This chapter presents a new characterization of chaotic optimal capital accumulation by which a chaotic optimal path can be constructed in a simple systematic manner. In the existing literature, it has been demonstrated that optimal capital accumulation may be chaotic in the sense of Li and Yorke (1975); see Boldrin and Montrucchio (1986b) and Deneckere and Pelikan (1986).1 As Scheinkman’s survey (1990) discusses, this finding indicates that the deterministic equilibrium model of a dynamic economy may explain various complex dynamic behaviors of economic variables. And, in fact, the search for such explanations has already begun.2 In the existing literature, however, not much as been revealed with respect to the circumstances under which optimal accumulation exhibits complex nonlinear dynamics.3

A simple proof of K-K-M-S theorem*

Abstract: We give a simple proof of the K-K-M-S theorem based on the Kakutani fixed point theorem, the separation theorem for convex sets and the Berge maximum theorem.

Chaotic dynamical systems: an introduction

Abstract: In his Memoirs, Stigler (1988, p. 78) observed that economic "theorists like new and strange constructs that create a new world or change the way of looking at the current one". I f this is a correct description of the preferences of economic theorists, one ought to expect continued interest in the fascinating development of the literature on dynamical systems and complexity. The literature certainly offers a variety of 'new and strange constructs ' , and forces us to look at some of the old issues f rom a different perspective. The advances over the last two decades have been due to truly multi-disciplinary efforts, and have benefited f rom a collaboration between the more 'abstract ' analytical work and a careful exploration of 'concrete ' examples through increasingly sophisticated computer experiments. The first "break through" for dynamic economic theory and stability analysis "probably occurred during the twenties and thirties thanks to economists such as Frisch, Tinbergen, Kalecki, Robertson, Lundberg and Hicks;" and Samuelson's Foundations also played its role " to set the stage for further theoretical work" [Lindbeck (1970)]. A useful compendium of the trade cycle models of Hicks, Samuelson, Goodwin, Kalecki and Phillips was available in Allen (1956), and a number of the classic papers were compiled in Cass and McKenzie (1974). Subsequent research in dynamic economics continued in several directions, involving descriptive models of growth and market disequilibrium as well as models involving intertemporal optimization with their duals interpreted as intertemporal equilibria. By now we have a relative abundance of examples which generate complex

Monotonicity and envyfree assignments

Abstract: Given any problem involving assignment of indivisible objects and a sum of money among individuals, there is an efficient envyfree allocation (namely the minmax money allocation) which can be extended monotonically to a new efficient envyfree allocation for any object added or individual removed, and another (the maximin value allocation) extendable similarly for any object removed or person added. Still, the efficient envyfree solution is largely incompatible with the resource and population monotonicity axioms: The minmax money and maxmin value allocations are unique in being extendable.

Commodity money in the presence of goods of heterogeneous quality

Abstract: The aim of this paper is to demonstrate that uncertainty about the quality of a particular commodity does not necessarily exclude it from emerging as commodity money. This is shown in the context of the model of a simple economy with specialized agents and decentralized trade described in Kiyotaki and Wright (1989). In order to derive this result, considerations about marketability of the different goods are taken into account.

Bounded rationality, neural network and folk theorem in repeated games with discounting

Abstract: The perfect folk theorem (Fudenberg and Maskin [1986]) need not rely on excessively complex strategies. We recover the perfect folk theorem for two person repeated games with discounting through neural networks (Hopfield [1982]) that have finitely many associative units. For any individually rational payoff vector, we need neural networks with at most 7 associative units, each of which can handle only elementary calculations such as maximum, minimum or threshold operation. The uniform upper bound of the complexity of equilibrium strategies differentiates this paer from Ben-Porath and Peleg [1987] in which we need to admit ever more complex strategies in order to expand the set of equilibrium outcomes.

Fiscal rules and extrinsic uncertainty

Abstract: This paper analyzes the effect of two fiscal policy regimes on the set of equilibria. A general equilibrium model with public goods is used to re-examine Friedman's [9] proposal for fiscal reform. The issue is whether a constraint upon fiscal policy requiring budget balance under all contingencies increases the stability of the economy. Stability is modelled in terms of neutralizing extrinsic uncertainty or sunspots. The government consists of bureaus providing public goods. The budgetary rules entail fixed shares of revenues and arrangements for budget balancing. Existence of equilibrium and properties of the equilibrium set are established. The Friedmanite rules permit extrinsic uncertainty to affect outcomes, while a policy that allows the bureaus greater discretion in the pursuit of their objectives neutralizes it.