Unawareness and bankruptcy: A general equilibrium model

Summary. We present a consistent pure-exchange general equilibrium model where agents may not be able to foresee all possible future contingencies. In this context, even with nominal assets and complete asset markets, an equilibrium may not exist without appropriate assumptions. Specific examples are provided. An existence result is proved under the main assumption that there are sufficiently many states that all the agents foresee. An intrinsic feature of the model is bankruptcy, which agents may involuntarily experience in the unforeseen states. Received: April 23, 1997; revised version: May 19, 1997     

Search and endogenous concentration of liquidity in asset markets

We develop a search-based model of asset trading, in which investors of different horizons can invest in two assets with identical payoffs. The asset markets are partially segmented: buyers can search for only one asset, but can decide which one. We show the existence of a “clientele’’ equilibrium where all short-horizon investors search for the same asset. This asset has more buyers and sellers, lower search times, and trades at a higher price relative to its identical-payoff counterpart. The clientele equilibrium dominates the one where all investor types split equally across assets, implying that the concentration of liquidity is socially desirable.     

Regularity and Pareto improving on financial equilibria with price-dependent borrowing restrictions

We consider a pure exchange, general equilibrium model, with two periods and a finite number of states, commodities, numeraire assets, and households. Participation in the asset markets is restricted in a household specific manner, imposing upper bounds on the amounts of borrowing which can be obtained using assets. Those bounds are assumed to depend on asset and commodity prices. After establishing existence of equilibria, we show that, generically in the set of the economies, equilibria are finite and regular. Then, we restrict our attention to the significant set of economies in which some associated equilibria exhibit a sufficiently high number of strictly binding participation constraints. We prove that, generically in that set, those equilibria are Pareto improvable through a local change of the participation constraints.     

State prices,liquidity, and default

We show, in a monetary exchange economy, that asset prices in a complete markets general equilibrium are a function of the supply of liquidity by the Central Bank, through its effect on default and interest rates. Two agents trade goods and nominal assets to smooth consumption across periods and future states, in the presence of cash-in-advance financing costs that have effects on real allocations. We show that higher spot interest rates reduce trade and as a result increase state prices. Hence, states of nature with higher interest rates are also states of nature with higher risk-neutral probabilities. This result, which cannot be found in a Lucas-type representative agent model, implies that the yield curve is upward sloping in equilibrium, even when short-term interest rates are fairly stable and the variance of the (macroeconomic) stochastic discount factor is 0. The risk-premium in the term structure is, therefore, a monetary-cost risk premium.     

Asset price bubbles in Arrow-Debreu and sequential equilibrium

Summary. Price bubbles in an Arrow-Debreu equilibrium in an infinite-time economy are a manifestation of lack of countable additivity of valuation of assets. In contrast, the known examples of price bubbles in a sequential equilibrium in infinite time cannot be attributed to the lack of countable additivity of valuation. In this paper we develop a theory of valuation of assets in sequential markets (with no uncertainty) and study the nature of price bubbles in light of this theory. We define a payoff pricing operator that maps a sequence of payoffs to the minimum cost of an asset holding strategy that generates it. We show that the payoff pricing functional is linear and countably additive on the set of positive payoffs if and only if there is no Ponzi scheme, provided that there is no restriction on long positions in the assets. In the known examples of equilibrium price bubbles in sequential markets valuation is linear and countably additive. The presence of a price bubble means that the dividends of an asset can be purchased in sequential markets at a cost lower than the asset's price. We present further examples of equilibrium price bubbles in which valuation is nonlinear, or linear but not countably additive.     

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.     

Ambiguity,uncertainty aversion and equilibrium welfare

Summary. In order to analyse the effect of ambiguity and uncertainty aversion on equilibrium welfare, a two period, pure exchange one good economy is considered. Agents are Choquet-expected-utility maximizers with same convex capacity and strictly concave utility index. It is proven that equilibrium is indeterminate whenever several probabilities in the core of the capacity minimize the expected value of aggregate endowment and not all agents have same expected endowments under those probabilities. It is further shown that small changes in aggregate endowment may have drastic welfare implications. A more general model is considered in the case of no aggregate uncertainty: agents have a set of priors and are uncertainty averse as modelled by Gilboa-Schmeidler [1989]. In the case of complete markets, it is shown that assets have a spread of equilibrium prices similar to the spread of no-arbitrage prices compatible with absence of arbitrage in markets with imperfections.Received: 2 June 2000, Revised: 27 March 2003, JEL Classification Numbers: D46, D59,D60, G12.I have benefited from conversations with L. Epstein, F. Magnien and J. M. Tallon.     

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.     

Aggregation of heterogenous beliefs,asset pricing,and risk sharing in complete financial markets

Given a competitive equilibrium in complete asset markets, we propose a method that aggregates heterogeneous individual beliefs into a single “market probability,” which, if commonly shared by investors, generates the same marginal valuation of assets by the market as well as by each individual investor. As a result of the aggregation process, the market portfolio may have to be scalarly adjusted, upward or downward, a reflection of an aggregation bias due to the diversity of beliefs. From a dual viewpoint, the standard construction of an expected utility-maximizing aggregate investor designed to represent the economy in equilibrium, is shown to be also valid in the case of heterogeneous beliefs, modulo the above scalar adjustment of the market portfolio, thereby generating an Adjusted version of the Consumption based Capital Asset Pricing Model (ACCAPM). We analyze how the allocation of aggregate and individual risks relates to deviations of individual beliefs from the aggregate market probability. Finally, we identify the channels through which the distribution of beliefs and other microeconomic characteristics (incomes, attitudes toward risk) across investors impact the pricing of risky assets an may contribute to explaining the equity premium puzzle.     

General equilibrium, wariness and efficient bubbles

Wary consumers overlook gains but not losses in remote sets of dates or states. As preferences are upper but not lower Mackey semi-continuous, Bewley?s (1972) [4] result on existence of equilibrium whose prices are not necessarily countably additive holds. Wariness is related to lack of myopia and to ambiguity aversion (and, therefore, to Bewley?s (1986) [6] work on Knightian uncertainty). Wary infinite lived agents have weaker transversality conditions allowing them to be creditors at infinity and for bubbles to occur in positive net supply assets completing the markets. There are efficient allocations that can only be implemented with asset bubbles.     

Incomplete financial markets and differential information

We provide a model of an incomplete markets economy where private restrictions on consumption are interpreted as lack of information. We prove existence of an equilibrium where agents are unable to infer any additional information from prices. When assets are nominal, these non-enlightening equilibrium prices result in a reduction of the degree of real indeterminacy.     

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.     

Valuation in infinite-horizon sequential markets with portfolio constraints

Summary. We develop a theory of valuation of assets in sequential markets over an infinite horizon and discuss implications of this theory for equilibrium under various portfolio constraints. We characterize a class of constraints under which sublinear valuation and a modified present value rule hold on the set of non-negative payoff streams in the absence of feasible arbitrage. We provide an example in which valuation is non-linear and the standard present value rule fails in incomplete markets. We show that linearity and countable additivity of valuation hold when markets are complete. We present a transversality constraint under which valuation is linear and countably additive on the set of all payoff streams regardless of whether markets are complete or incomplete. Received: March 9, 2000; revised version: February 13, 2001     

国际投资组合选择理论研究进展

国际投资组合选择理论研究的是在一定的假设条件下,当经济实现均衡时,投资者所应持有的本国与外国金融资产的比例。它的发展有5个特征:从追求金融市场的局部均衡到追求经济的一般均衡;从不考虑投资者的存在到考虑投资者个人效用的最大化;从单纯的理论模型构建到结合现实数据进行实证检验;从假设金融市场完全到考虑金融市场不完全的情况;从假设金融市场一体化到考虑金融市场存在分割的情况。     

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.     

When Borch's Theorem Does Not Apply: Some Key Implications of Market Incompleteness,with Policy Relevance Today

Markets are incomplete when the assets available to the agents do not span the space of future contingencies. In that case, competitive equilibria on the markets for assets and commodities fail (generically) to be constrained efficient. Pareto‐superior allocations can be implemented through price/wage rigidities and quantity constraints. However, nominal rigidities are conducive to multiple equilibria, implying endogenous macroeconomic uncertainties that compound the primitive (exogenous) uncertainties. This paper defines a temporary general equilibrium for which there exists a set of equilibria defining an inflation – unemployment locus. Various policy implications are drawn, with relevance to the current crisis.     

Incomplete markets and individual risks

Summary This paper studies the incomplete markets model with financial assets when the only missing markets are for individual risks. There are no aggregate risks in the economy. Assuming the individual risks are only privately observable, the only equilibria that are implementable by anonymous mechanisms are those in which prices do not vary across states of the world. Such equilibria always exist. Generically, they are locally unique and depend continuously on the parameters of the economy, just like complete-markets equilibria. Generically, there is also an infinite-dimensional manifold of equilibria in which prices do vary across states of the world. These equilibria are isomorphic to sunspot equilibria.I am grateful to Dave Cass for several helpful discussions and to Darrell Duffie for his comments on an earlier draft.     

Sunspots,indeterminacy and Pareto inefficiency in economies with incomplete markets

Summary. We consider two periods economies with both intrinsic and extrinsic uncertainty. Asset markets are incomplete in the certainty economy. If assets are nominal, there are enough commodities and the number of agents is greater than two and smaller than the total number of states of nature tomorrow (minus one), then a sunspot-invariant equilibrium is generically Pareto dominated by some sunspot equilibria. When assets are real, and there are enough commodities, if there are sunspot equilibria, there are sunspot equilibria Pareto dominating sunspot-invariant equilibria under the same restriction on the number of agents (and stronger restrictions on the number of commodities).Received: 20 October 2003, Revised: 1 April 2004, JEL Classification Numbers: D52.I wish to thank Paolo Siconolfi for helpful suggestions and comments. I aknowledge the financial support of M.I.U.R. and the kind hospitality of C.C.D.R. in Summer 2003.     

Temporary financial equilibrium

Summary. In a two-period pure exchange economy with financial assets, a temporary financial equilibrium is an equilibrium of the current spot and security markets given forecast functions of future prices and payoffs. The temporary equilibrium model can then be interpreted as an Arrow-Debreu economy where preferences depend on prices. This identification implies, among other consequences, the existence and the generic determinateness of the financial temporary equilibria associated with given forecast functions. Received: December 29, 1999; revised version: December 20, 2001     

Information and the operation of markets: tests based on a general equilibrium model of land leasing in India

This paper develops an estimable general equilibrium model of land leasing to test the extent to which information is commonly held in a village and whether village markets are efficient. Information regarding the relative farming skill of households is found to be widespread, but the assumption of perfectly efficient markets within the village is rejected. These results have ramifications for the estimation of agricultural household models and for our understanding of rural institutions. The model is derived from the primitives of the production technology, the extent of information and the distributions of assets and several household unobservables. Simultaneity and selection issues are dealt with explicitly in a two-stage maximum likelihood estimation procedure using panel data from India.