Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

Non-existence of recursive equilibria on compact state spaces when markets are incomplete

This paper analyzes one-good exchange economies with two infinitely lived agents and incomplete markets. It is shown that there are no recursive (Markov) equilibria for which borrowing (debt) constraints never bind if the state space of exogenous and endogenous variables is a compact subset of . Moreover, for large enough (but finite) borrowing limits, no recursive equilibrium with compact state space exists. These non-existence results hold for any economy satisfying the following standard assumptions: preferences are additively separable across time and states; the one-period utility function is time- and state-independent and unbounded from below; endowments are bounded and follow a Markov chain with stationary transition matrix; there is some idiosyncratic risk and no aggregate risk.     

On the non-neutrality and optimality of monetary policy when financial markets are incomplete: a macroeconomic perspective

We study in this paper a simple model of a two-period economy, with two states of the world in the second period, two agents and one good. Financial markets are incomplete since only inside money is available. We show that outside money, which is introduced in the model through its role as a medium of exchange, is non-neutral, in the sense that it has an effect on the equilibrium allocation. We then discuss whether a monetary policy that would aim at state-independent price levels is desirable. We illustrate that discussion with a few examples. The possible sub-optimality of a constant-across-states inflation rates target for monetary policy is to be contrasted with results from representative agent macroeconomic models.     

International outsourcing when labour markets are unionized

Abstract. We consider the implications of international outsourcing in a simple general equilibrium model where the wage rate is the outcome of negotiations between a firm and a trade union. The effects of potential, but non‐realized, international outsourcing, is a reduction in the wage rate and an increase in employment. Aggregate welfare increases, but the trade union becomes worse off while owners of capital become better off. Realized international outsourcing gives rise to an increase in the wage rate and a reduction in employment. Aggregate welfare decreases, but the trade union becomes better off, while owners of capital become worse off.     

Sequentially complete markets remain incomplete

We show by means of an example that the result of Arrow [Arrow, K.J. (1953), Le rôle des valeurs boursières pour la répartition la meilleure des risques, Econométrie, 41–47, CNRS, Paris; translated as The role of securities in the optimal allocation of risk bearing, Review of Economic Studies, 31, 91–96] is problematic when there exist multiple equilibrium continuations to the initial-period component of an intertemporal equilibrium.     

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.     

Optimal use of futures markets when input and output prices are uncertain

The purpose of this paper is to extend the analysis of the use of futures markets by a competitive firm facing an uncertain market price for its output to the case where both input and output prices are uncertain.     

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.     

Information, trade and incomplete markets

The no-trade result of Milgrom and Stokey, J Econ Theory 26:17–27 (1982), states that if rational traders begin with an ex-ante Pareto optimal allocation then the arrival of information cannot generate trade. This paper allows traders to trade before and after the arrival of information. If there are enough securities to hedge against all payoff relevant risk, then the preinformation-arrival allocation is Pareto optimal and information arrival has no effect. This no-retrade result is the competitive analog of the no-trade result of (1982). However, information generically generates trade when markets are state-contingent incomplete.We thank seminar participants at Cambridge, Carnegie Mellon,Cornell, Essex, London, Maastricht, USC, and York and participants at the 2003 SITE, the 2003 SAET and the Fall 2002 Cornell–Penn State Macro Conference. We also thank Karl Shell and a referee for this journal for useful comments     

Regulating internal markets for hospital care

Internal markets have been created in an attempt to shift power from producers to consumers in a context where consumers have very weak incentives to seek out low-cost producers and have little knowledge about the quality of health care. The idea is that by establishing public agencies to act as the sole purchasers on behalf of consumers in their area of jurisdiction, the asymmetry of information can be moderated and a more competitive environment created in which costs will be minimized and quality enhanced. Whether these aspirations can be fulfilled will depend on how the internal market is organized. In this article the cost-minimizing properties of alternative market structures where hospitals do not share the same objectives are examined. The scheme is designed from the standpoint of a benevolent regulator that provides services using two hospitals with fixed locations. The paper shows that price discrimination is a superior instrument. Finally some market forms are always dominated and should be avoided.

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Regulating regulators in transitionally competitive markets

During the course of the first thirty CRRI conferences, we have gained considerable insight about how to design regulatory policy in the presence of developing competition. The insight to date has focused on how to harness competitive forces to motivate incumbent suppliers to serve the best interests of consumers. This paper stresses the importance of considering the incentives of regulators and explores the associated changes in standard recommendations for regulatory policy design in the presence of developing competition.     

Endogenous trading constraints with incomplete asset markets

This paper endogenizes the borrowing constraints on capital in a production economy with incomplete markets. We find that these limits get looser with income, a property that is consistent with US data on credit limits. The framework with endogenous limits is then used to study the effects of a revenue neutral tax reform that eliminates capital income taxes. Our results illustrate that it is very important to take into account the effects of tax policies on the limits. Throughout the transition, these effects can be big enough to change the overall conclusion about the desirability of a tax reform.     

Risk sharing and retrading in incomplete markets

At a competitive equilibrium of an incomplete-markets economy agents’ marginal valuations for the tradable assets are equalized ex-ante. We characterize the finest partition of the state space conditional on which this equality holds for any economy. This leads naturally to a necessary and sufficient condition on information that would induce agents to retrade, if such information was to become publicly available after the initial round of trade.     

On constrained optimal allocations with incomplete markets

Summary We provide an example of an economy with incomplete asset markets in which there is no constrained optimal allocation.I would like to thank Ramon Marimon for many helpful discussions, and to an anonymous referee for useful comments.     

Equilibrium in economies with incomplete financial markets

This paper analyses an exchange economy in the absence of Arrow-Debreu complete markets. It is assumed that trading takes place in the sequence of spot markets and futures markets for securities payable in units of account. Unlimited short-selling in securities is allowed. A general equilibrium in such an economy is a set of current and future prices (contingent on uncertain events) and a set of individual plans such that all markets are cleared. The existence of such an equilibrium is proved under usual assumptions. This is in contrast to the case of futures markets for contingent futures commodities where an equilibrium may not exist. The optimality of equilibrium allocations is also discussed.     

Pareto improving financial innovation in incomplete markets

Summary. In this paper we develop a differential technique for investigating the welfare effects of financial innovation in incomplete markets. Utilizing this technique, and after parametrizing the standard competitive, pure-exchange economy by both endowments and utility functions, we establish the following (weakly) generic property: Let S be the number of states, I be the number of assets and H be the number of households, and consider a particular financial equilibrium. Then, provided that the degree of market incompleteness is sufficiently larger than the extent of household heterogeneity, S−I≥2H−1 [resp. S−I≥H+1], there is an open set of single assets [resp. pairs of assets] whose introduction can make every household better off (and, symmetrically, an open set of single assets [resp. pairs of assets] whose introduction can make them all worse off ). We also devise a very simple nonparametric procedure for reducing extensive household heterogeneity to manageable size, a procedure which not only makes our restrictions on market incompleteness more palatable, but could also prove to be quite useful in other applications involving smooth analysis. Received: August 14, 1995; revised version: April 14, 1997     

Belief heterogeneity and survival in incomplete markets

In complete markets economies (Sandroni in Econometrica 68:1303–1341, 2000), or in economies with Pareto optimal outcomes (Blume and Easley in Econometrica 74:926–966, 2006), the market selection hypothesis holds, as long as traders have identical discount factors. Traders who survive must have beliefs that merge with the truth. We show that in incomplete markets, regardless of traders’ discount factors, the market selects for a range of beliefs, at least some of which do not merge with the truth. We also show that impatient traders with incorrect beliefs can survive and that these incorrect beliefs impact prices. These beliefs may be chosen so that they are far from the truth.     

Complete and incomplete markets with short-sale constraints

Summary. This paper argues that the introduction of a short-sale constraint in the Arrow-Radner framework invalidates standard definitions of complete and incomplete markets. Two threshold values with familiar properties arise in this constrained set-up. If short sales are not allowed on some security, then financial markets will be incomplete in the standard sense. Beyond a particular level of the short-sale bound, financial markets are “complete”, since the short-sale constraint is not effective. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called “technically incomplete markets”, exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto-dominated by those of the non-restricted complete markets equilibrium. Received: November 28, 2000; / revised version: November 9, 2001     

Optimal taxation with endogenously incomplete debt markets

Empirical analyses of labor tax and public debt processes provide prima facie evidence for imperfect government insurance. This paper considers a model in which the government's inability to commit to future policies or to report truthfully its spending needs renders government debt markets endogenously incomplete. A method for solving for optimal fiscal policy under these constraints is developed. Such policy is found to be intermediate between that implied by the complete insurance (Ramsey) model and a model with exogenously incomplete debt markets. In contrast to optimal Ramsey policy, optimal policy in this model is consistent with a variety of stylized fiscal policy facts such as the high persistence of labor tax rates and debt levels and the positive covariance between government spending and the value of government debt sales.     

Regulating a risk-averse firm under incomplete information

We examine the optimal regulatory policy for a risk-averse firm when the firm is imperfectly informed about its efficiency parameter for a project at the time of contracting. The firm’s risk aversion shifts the optimal regulatory policy from a fixed-price contract to a cost-plus contract. The optimal regulatory policy entails undereffort by an inefficient firm as in Laffont and Tirole (J Polit Econ 94(3):614–641, 1986) and the effort distortion increases as the firm becomes more risk-averse. Further, the regulator benefits from sequential contracting with the firm where the firm chooses contract terms gradually as it acquires information, albeit the benefit diminishes as the firm becomes more risk-averse.