Non-parametric counterfactual analysis in dynamic general equilibrium

In this paper, we examine non-parametric restrictions on counterfactual analysis in a dynamic stochastic general equilibrium model. Under the assumption of time-separable expected utility and complete markets all equilibria in this model are stationary. The Arrow-Debreu prices uniquely reveal the probabilities and discount factor. The equilibrium correspondence, defined as the map from endowments to stationary (probability-free) state prices, is identical to the equilibrium correspondence in a standard Arrow-Debreu exchange economy with additively separable utility. We examine possible restriction on this correspondence and give necessary as well as sufficient conditions on profiles of individual endowments that ensure that associated equilibrium prices cannot be arbitrary. Although restrictions on possible price changes often exist, we show that results from a representative-agent economy usually do not carry over to a setting with heterogeneous agents.     

Macroeconomic Interdependence with Trade and Multinational Activities

This paper examines how differences in the integration strategies followed by firms active in foreign markets affect the way productivity and policy shocks spread their effects worldwide. The analysis incorporates costly trade and local sales by multinational firms in a general-equilibrium open economy macroeconomic model. The mode of foreign market access is found to play a major role in the international business cycle, affecting the dimension of consumption and output spillovers worldwide. We show that despite financial markets being effectively complete, consumption risks may not be fully insured in the world economy as long as multinational firms discriminate prices across markets. Furthermore, cross-country differences in firms' integration strategies can account for extensive asymmetries in the way country-specific and global shocks are transmitted in the world economy. We argue that this may have relevant consequences for the welfare implications of monetary and trade policies.     

Non-existence and inefficiency of equilibria with American options

Summary We analyze two examples of economies with incomplete financial markets. In the first model we consider a stock and an American put option on the stock. Although there is only one commodity and asset payoffs therefore do not depend on spot prices, we derive robust non-existence of equilibria. In the second model we consider an economy where a stock is the only asset available for trade. We show that it is impossible to complete the market by introducing American put options and that equilibria are inefficient. This example is also robust.We wish to thank Jonathan Berk, Virginia France, Flavio Menezes and a referee of this journal for useful comments. This research was partially funded by the National Science Foundation (SES-8821723).     

New financial markets: who gains and who loses

Summary. We evaluate the effects of new financial markets in a two-period incomplete markets model with heterogenous agents. For analytical tractability, we focus on the special case where utility is exponential and risks are normally distributed. We provide a complete characterization of life-cycle consumption and portfolio choice. The effect of new financial markets on individual welfare equals the sum of what we call the portfolio effect and the price effect. The portfolio effect is proportional to the square of the difference between the average exposure to the new asset in the economy and an individual investors exposure adjusted for risk aversion. The portfolio effect is always positive and measures the improved ability of investors to transfer consumption across states. The price effect captures the effect on individual welfare of changes in asset prices. We show that new financial markets drive down the prices of all assets which raises the interest rate and thus affects the ability of investors to transfer consumption across time. The price effect is positive for net savers but can be negative for net borrowers. For net borrower households, the price effect can wipe out the portfolio effect and lead to welfare reductions.Received: 24 July 2003, Revised: 22 March 2004, JEL Classification Numbers: D31, D52, G11, G12.Paul Willen: Thanks to Viral Acharaya, Alberto Bisin, Steve Davis, John Geanakoplos and a thoughtful anonymous referee for helpful comments and suggestions. Thanks also to seminar audiences at Stanford, Berkeley and at the 2001 Stony Brook workshop on incomplete markets for comments and suggestions. I gratefully acknowledge research support from the Graduate School of Business at the University of Chicago.     

Incomplete Markets, Allocative Efficiency, and the Information Revealed by Prices

We compare rational expectations equilibria with different degrees of information revelation through prices. These equilibria arise in a two-period exchange economy with finitely many states and signals, multiple commodities and incomplete financial markets for nominal assets. We show that there are always equilibria where information is redundant in the sense of being of no value to the uninformed traders. We give conditions under which for a generic set of economies, parametrized by endowments and utilities, there exist open sets of equilibria for which allocative and informational efficiency are independent, with implications for monetary policy. Journal of Economic Literature Classification Numbers: D52, D60, D82, E52.     

On persistent disequilibrium

Consider a standard model of a Walrasian economy where the time derivative of price change is a sign preserving function of excess demand. The only steady states of such a system are the Walrasian equilibria. For if the system is not at a Walrasian equilibrium then there must be excess demands or supplies in some market and thus those prices must be changing. Walras' law implies that all prices cannot change in the same direction, and thus relative prices must change.However, it seems that in real world economies there have been states of persistent disequilibrium. How can this be? How can there be stationary states of an economy that are not Walrasian equilibria?The answer presented in this paper goes something like this: the demands actually presented to the market, i.e., the demands that affect price movements, are not the Walrasian demands. Rather, these demands, the effective demands, are a function of both price and quantity signals. There is no reason why there cannot be equilibria of the effective demand system that are not equilibria of the Walrasian demand system.In this paper, I present a simple abstract model of effective demand systems and given a condition for this system to have non-Walrasian equilibria. I also present a simple example of this phenomena. Finally I discuss the real world implications of this model. Related concepts of effective demand are discussed in [A1H], [2], [3], [L5], and [L6].     

The speed of convergence of prices in random exchange economies

We examine the behaviour of prices in an economy in which preferences and endowments are random, and in which no contingent commodity markets exist. Prices are random vectors which produce equilibrium in almost all states of the world. First we prove a result on the speed of convergence of the price vector, as the stochastic economy increases in size, to the equilibrium price vector in a deterministic limit economy. Then we prove a result on the speed of convergence to zero of the error of normal approximation to the random price vector.     

Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. Aggregate and idiosyncratic shocks follow a joint Markov process. Conditional on the aggregate state, idiosyncratic shocks are independently distributed over time and identically distributed across households. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exists a recursive equilibrium for which equilibrium prices (returns) only depend on the exogenous aggregate shock variable (the wealth distribution is not a relevant state variable). Moreover, the allocation associated with this recursive equilibrium is identical to the equilibrium allocation of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.I would like to thank for helpful comments Peter Howitt, Bob Lucas, Michael Magill, Tomo Nakajima, Herakles Polemarchakis, Martine Quinzii, Kevin Reffett, an anonymous referee, and seminar participants at various universities and conferences.     

Non-Walrasian equilibria and the law of one price

We present a market game which features multiple posts for each commodity. We use this framework to illustrate the idea that in non-Walrasian markets, where individual activities influence market clearing prices, there are equilibria where commodities are exchanged simultaneously in two posts at different prices, thus defying the ‘law of one price’. Such equilibria are compatible with an apparent arbitrage possibility, which dissipates whenever individuals try to take advantage of it.     

Market crashes,speculation and learning in financial markets

A natural conjecture is that if agents’ beliefs are almost correct then equilibrium prices should be close to rational expectations prices. Sandroni (J Econ Theory 82:1–18, 1998) gives a counterexample in an economy with sunspots and complete markets. We extend Sandroni’s result by showing that the conjecture is generically true for economies with complete markets. We consider a standard General Equilibrium model with large but finite horizon and complete markets. We show that, for almost every such economy, if conditional beliefs eventually become correct along a path of events then equilibrium prices of assets traded along this path converge to rational expectations equilibria in the sup-norm. Moreover, we establish that, generically, there exist along any such path local diffeomorphisms between individual beliefs and equilibrium prices. I would like to thank C. Ewerhart and A. Kirman for their comments, as well as the seminar participants at the University of Minho, the General Equilibrium Workshop 2005 in Zurich, and the 15th Asian General Equilibrium Conference 2007 in Singapore. An anonymous referee also provided very valuable comments.     

Real indeterminacy in incomplete financial market economies without aggregate risk

Summary We analyze an exchange economy with incomplete financial markets and assets whose returns are fixed in units of account. Moreover, we assume absence of aggregate risk, i.e., that individual preferences and total resources are constrained to be invariant across different states of the world. In this framework we show that the set of (commodity) price-endowment equilibria is diffeomorphic to a Euclidean space. We then exploit this global parameterization to prove that the set of equilibrium allocations associated with each endowment in a generic set contains a smooth manifold, whose dimension is equal to the number of missing assets.     

Asset markets and the information revealed by prices

Summary When nominal assets serve to transfer revenues across states of the world, noninformative rational expectations equilibria exist. At noninformative prices, the restricted information under which individuals optimize can be modelled as restricted participation of the individuals in asset markets. When assets are nominal, the indeterminacy of equilibrium prices, and, generically, allocations as well, which characterizes economies with restricted participation guarantees that noninformative equilibrium prices exist.This work was supported in part by grant No 26 from the program Pole d' Attraction Interuniversitaire — Deuxieme phase of the Belgian government of CORE, Universite' Catholique De Louvain. The second author acknowledges the generous support of the Graduate School of Business of Columbia University. We wish to thank David Cass for very helpful comments.     

Financial frictions and the futures pricing puzzle

In perfect capital markets, the futures price of an asset should be an unbiased forecast of its realized spot price when the contract matures. In reality, futures prices are often higher for some assets and lower for others. However, there is no stability in the relationship between futures prices and the realized spot prices. This instability has been a puzzle in the existing financial literature. The key to this puzzle may lie in the nature of the model and the lack of market imperfections. In this study, we take a theoretical approach in a dynamic multi-period environment. We incorporate competition between disparate economic agents and impose financial frictions (i.e., imperfections) that are in the form of hedging and borrowing limits on them. Our model gives rise to multiple equilibria, each with unique market clearing prices, with the market switching between these equilibria. Our analysis incorporates a comprehensive consideration of the risks faced by the futures markets participants (i.e., speculators and hedgers) and leads to a better understanding of the puzzle.     

Core and equilibrium in incomplete markets

Conclusions The classical foundation of general equilibrium analysis by the cooperative concept of the core has been extended to an economy with incomplete trading possibilities. This has been accomplished by restricting the exchange possibilities of coalitions of traders in accordance with the available market structure. However, compared with the classical result, the present foundation of rational expectations equilibria may appear much weaker. The reason is that in reality consumers may sign contracts which are more complex than the existing market structure. Therefore, it may happen that prices cannot decentralize all cooperative transactions by markets, in spite of perfect competition. With an incomplete set of markets, therefore, a cooperative exchange of commodities by individual contracts may coexist with trading in non-cooperative, competitive markets.I wish to thank Martin Hellwig for helpful comments and suggestions. Of course, I remain responsible for all shortcomings of the paper.     

‘Double dipping’: the combined effects of social security and civil service pensions on employee retirement

How do macro variables such as aggregate consumption, aggregate money demand, prices, and interest rates vary in response to government attempts to redistribute income across agents through selective tax-transfer policies? This question is investigated for an overlapping generations model consisting of heterogeneously endowed three-period lived agents. In the presumably most favorable case for invariance (identical log-linear utility functions), it is shown that positive interest rate macro equilibria are invariant with respect to redistributions in social security benefits if and only if all agents initially exhibit qualitatively identical liquidity preference behavior, i.e. positive money holding only in youth, only in middle-age, or never.     

Stochastic equilibria with incomplete financial markets

We demonstrate the existence of equilibria with incomplete financial markets for stochastic economies whose information structure is given by an event tree, restricting attention to purely financial securities, those paying in units of account (e.g., “dollars”). Financial markets may be incomplete: some consumption streams may be impossible to obtain by any trading strategy. Securities may be individually precluded from trade at arbitrary states and dates. Sufficient conditions for the existence of stochastic equilibria are: continuous, convex, strictly monotonic preferences and strictly positive aggregate endowments. These conditions are weakened. A corollary states that any regime of security prices precluding arbitrage can be embedded in an equilibrium.     

Non-existence of competitive equilibria with dynamically inconsistent preferences

This paper shows the robust non-existence of competitive equilibria even in a simple three period representative agent economy with dynamically inconsistent preferences. We distinguish between a sophisticated and naive representative agent. Even when underlying preferences are monotone and convex, at given prices, we show by example that the induced preference of the sophisticated representative agent over choices in first-period markets is both non-convex and satiated. Even allowing for negative prices, the market-clearing allocation is not contained in the convex hull of demand. Finally, with a naive representative agent, we show that perfect foresight is incompatible with market clearing and individual optimization at given prices.     

The Effectiveness of Distributive Policy in a Competitive Economy

I consider an abstract social system made of individual owners endowed with nonpaternalistic interdependent preferences, who interact by means of individual gifts and by exchanges on competitive markets. The existence of equilibrium is established. I identify the set of allocations that are decentralizable in the sense that they are general equilibria for some vectors of market prices and initial endowments. This set is characterized in a simple way from the social endowment and individual market and distributive preferences. Decentralizable allocations are all accessible to distributive policy, unless public transfers are confined to some neighborhood of 0. In the latter case, distributive policy remains free to perform local redistributions of wealth across the components of the graph of equilibrium gifts.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

Regulating collateral-requirements when markets are incomplete

In this paper we examine the effects of default and collateral on risk sharing. We assume that there is a large set of assets which all promise a risk less payoff but which distinguish themselves by their collateral requirements. In equilibrium agents default, the assets have different payoffs, and there are as many linearly independent assets available for trade as there are states of the world. We derive necessary and sufficient conditions for equilibria to be Pareto-efficient in the presence of uncertainty. We explore some examples for which the collateral equilibrium allocation is identical to the Arrow–Debreu allocation, either when agents have a high preference for the durable good, or when the endowment distribution of the durable good is relatively homogeneous. We examine a series of examples to understand which collateral-levels prevail in equilibrium and under which conditions there is scope for regulating margin-requirements, that is, restricting the sets of tradable assets through government intervention. In these examples equilibrium is always sub-optimal but regulation never leads to a Pareto-improvement. While the competitive equilibria are constrained efficient, there do exist regulations which make large groups of agents in the economy better off. These regulations typically restrict all trades to take place in the low-collateral loans and benefit the poor and the rich agents in the economy through their effects on the equilibrium interest rate and the equilibrium prices of the durable goods.