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Dynamic Equilibrium with Liquidity Constraints

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  • Jérôme B. Detemple

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  • Angel Serrat
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    Abstract

    We consider an intertemporal economy with liquidity constrained and unconstrained individuals. A liquidity constraint prevents marketability of future income and thus endogenously generates market incompleteness. In contrast with the existing literature on portfolio constraints, our liquidity constraints arise naturally whenever agents may default and have a finite horizon. Liquidity constrained individuals optimally (i) postpone consumption in early age and (ii) experience permanent consumption increases whenever the constraint binds. The equilibrium interest rate and asset prices are characterized under very general assumptions on preferences and endowment processes. In the presence of liquidity constraints, the cumulative interest return is reduced. In addition, the CCAPM holds, even when the basic market structure is incomplete. With homogeneous relative risk aversion market incompleteness reinforces the effect of liquidity constraints and further reduces the riskless return. However, we show that neither incompleteness nor liquidity constraints can explain the empirical magnitude of the Sharpe ratio for admissible levels of risk aversion, independently of preferences and endowment assumptions. Additional contributions of the paper include (i) a new characterization of the consumption-portfolio problem of constrained individuals leading to an explicit solution, (ii) a constructive approach to the determination of equilibrium, and (iii) a numerical procedure to handle the forward-backward path-dependent computational problem arising with a liquidity constraint. Cet article examine une économie intertemporelle avec contraintes de liquidité. Celles-ci empêchent la monétisation des revenus futurs et génèrent une incomplétude endogène des marchés financiers. En contraste avec la littérature récente sur les contraintes d'investissement, nos contraintes de liquidité émergent naturellement lorsque les agents peuvent déclarer faillite et ont un horizon fini. Un individu, dont la contrainte de liquidité sature, decide optimalement (i) de déférer sa consommation en période de jeunesse,0501s (ii) de l'augmenter lorsque la contrainte est active. Le taux d'intérêt et les prix des actifs financiers d'équilibre sont caractérisés sous des conditions générales sur les préférences et les dotations. En présence de contraintes de liquidité le rendement de l'actif non risqué décroît. De plus le CAPM par rapport à la consommation est valide, même lorsque la structure de base du marché est incomplète. Lorsque l'aversion relative par rapport au risque est homogène et constante l'incomplétude du marché renforce l'effet des contraintes de liquidité et réduit encore davantage le rendement non risqué. Cependant, ni la contrainte d'incomplétude, ni celles de liquidité ne nous permettent d'expliquer le niveau empirique du ratio de Sharpe pour des valeurs raisonables du taux d'aversion au risque. D'autres contributions de cet article comprennent (i) une caractérisation nouvelle du problème de consommation-portefeuille d'un individu sous contrainte conduisant a une solution explicite, (ii) une approche constructive de détermination de l'équilibre, et (iii) une procédure numérique qui nous permet d'aborder les problèmes de calcul qui se posent dans ce contexte.

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    Bibliographic Info

    Paper provided by CIRANO in its series CIRANO Working Papers with number 98s-41.

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    Date of creation: 01 Nov 1998
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    Handle: RePEc:cir:cirwor:98s-41

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    Keywords: Equilibrium; liquidity constraints; incomplete markets; heterogeneity; consumption; interest rate; equity premium; backward stochastic differential inequality; numerical method; Équilibre; contraintes de liquidité; marchés incomplets; hétérogénéité; consommation; taux d'intérêt; prime de risque du marché; inégalité différentielle stochastique récursive; méthode numérique;

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    Cited by:
    1. Basak, Suleyman & Pavlova, Anna, 2004. "A Dynamic Model with Import Quota Constraints," Working papers 4230-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Paul Ehling, 2004. "Consumption, Portfolio Policies and Dynamic Equilibrium in the Presence of Preference for Ownership," Econometric Society 2004 North American Winter Meetings 311, Econometric Society.

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