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     

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     

A characterization of inefficiency in stochastic overlapping generations economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies of overlapping generations. With respect to the established body of results in the literature, we allow for sequentially incomplete markets and we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, based entirely on observable prices and independent of the length of the horizons of generations. For sequentially incomplete markets, we introduce a notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete. Furthermore, our analysis shows that the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency.     

Natural Oligopolies: A Vertical Differentiation Model

This article contains a more complete characterization of conditions under which vertically differentiated markets are or are not natural oligopolies than has been found previously in the literature. Specifically, previous results on markets in which firms have cost functions with constant returns are incomplete; these results are expanded. Moreover, results are provided for markets with firms having increasing or decreasing marginal cost functions.     

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.     

Debt and deficit fluctuations and the structure of bond markets

We analyse the implications of optimal taxation for the stochastic behaviour of debt. We show that when a government pursues an optimal fiscal policy under complete markets, the value of debt has the same or less persistence than other variables in the economy and it declines in response to shocks that cause the deficit to increase. By contrast, under incomplete markets debt shows more persistence than other variables and it increases in response to shocks that cause a higher deficit. Data for US government debt reveals diametrically opposite results from those of complete markets and is much more supportive of bond market incompleteness.     

Public investment criteria,insurance markets,and income taxes

The evaluation of small government investments is studied in a one-commodity, two-period world with risk and income taxation, assuming both complete and incomplete insurance markets. When marginal personal tax rates differ or markets are incomplete, there are at least two interpretations of the assumption that the distribution of income is optimal. The correct discount rate for riskless investment depends on which interpretation is chosen. The correct adjustment for risk generally does not. The use of nonmarket information - relating the returns from the proposed investment to those from ongoing activities - to compute this adjustment is explored.     

Information Revelation and Market Incompleteness

This paper introduces a theory of market incompleteness based on the information transmission role of prices and its adverse impact on the provision of insurance in financial markets. We analyse a simple security design model in which the number and payoff of securities are endogenous. Agents have rational expectations and differ in information, endowments, and attitudes toward risk. When markets are incomplete, equilibrium prices are typically partially revealing, while full relevation is attained with complete markets. The optimality of complete or incomplete markets depends on whether the adverse selection effect (the unwillingness of agents to trade risks when they are informationally disadvantaged) is stronger or weaker than the Hirshleifer effect (the impossibility of trading risks that have already been resolved), as new securities are issued and prices reveal more information. When the Hirshleifer effect dominates, an incomplete set of securities is preferred by all agents, and generates a higher volume of trade.     

Dynamic versus one-period completeness in event-tree security markets

We show that in event-tree security markets dynamic completeness does not coincide with one-period completeness unless the law of one price is explicitely assumed. We do so by means of a simple example of a dynamically complete market with an incomplete one-period sub-market.     

Collective fineness of stock prices and efficiency of financial markets

Recent literature exploring the efficiency properties of options has examined the conditions under which incomplete financial markets would be equivalent to the Arrow-Debreu model. A usual assumption made in establishing such an equivalence is that some security price is ‘fine’ on the state space. This assumption is relaxed. Under more realistic assumptions it is shown that any portfolio is fine and options written on it can bring about complete markets.     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 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.     

Equity home bias,incomplete financial markets,and nominal rigidities

Abstract This paper analyzes optimal portfolio decisions in a monetary open‐economy framework. It is found that market completeness and the specific form of nominal rigidities, namely, nominal price vs. nominal wage rigidities, matter for justifying the observed structure of equity holdings. When markets are complete, sticky prices generate a negative correlation between the non‐diversifiable labour income and the profit of domestic firms with respect to the productivity shocks, which explains why households invest little abroad. In contrast, when markets are incomplete, rigidities in goods prices result in a counterfactual ‘super home bias’, because domestic equities provide a good hedge against not only the labour income risk but also the relative price risk. Wage rigidities, however, have the opposite effect. Therefore, nominal rigidities in both goods prices and wage rates are needed to address the empirical composition of gross equity positions under incomplete markets.     

Market Sharing Agreements and Collusive Networks*

We analyze reciprocal market sharing agreements by which firms commit not to enter each other's territory in oligopolistic markets and procurement auctions. The set of market sharing agreements defines a collusive network. We characterize stable collusive networks when firms and markets are symmetric. Stable networks are formed of complete alliances, of different sizes, larger than a minimal threshold. Typically, stable networks display fewer agreements than the optimal network for the industry and more agreements than the socially optimal network. When firms or markets are asymmetric, stable networks may involve incomplete alliances and be underconnected with respect to the social optimum.     

Can Markets Learn to Avoid Bubbles?

One of the most striking results in experimental economics is the ease with which market bubbles form in a laboratory setting and the difficulty of preventing them. This article re-examines bubble experiments in light of the results of an earlier series of market experiments that show how learning occurs in markets characterized by an asymmetry of information between buyers and sellers, such as found in Akerlof's lemons model and Spence's signaling model. Markets with asymmetric information are incomplete because they lack markets for specific levels of product quality. Such markets either lump all qualities together (lemons) or using external indications of quality to separate them (signaling). Similarly, the markets used in bubble experiments are incomplete in that they are lacking a complete set of forward or futures markets, depriving traders of the information supplied by the prices in those markets. Preliminary experimental results suggest that the addition of a single forward market can sometimes mitigate bubble formation and this article suggests more extensive research in this direction is warranted. Market bubbles outside of the laboratory usually are found in markets in which forward and futures markets are either legally restricted or otherwise limited. Experimentation in markets with asymmetric information also indicates that the ability of subjects to learn how to send and receive signals can be enhanced by changing the way that market information is presented to them. We explore how this result might be used to help asset markets learn to avoid bubbles     

企业的性质:要素使用权交易合约之履行过程

本文对企业的性质进行了分析 ,发现企业的性质在于 ,企业是市场中由要素所有者签订的一组不完备的要素使用权交易合约的履行过程。要素使用权交易合约的履行过程包括要素投入、要素使用权 (核心是剩余控制权 )的行使以及要素增值的分配 (核心是剩余索取权的行使 )以及企业组织资本与组织资产的创造和使用等 ,这一过程融交易功能与生产功能于一体。该组合约的关键内容就在于企业剩余索取权与剩余控制权的安排。作为要素使用权交易合约的履行过程 ,企业与市场是不能截然对立分离的 ,即要素市场、资产及服务市场等与要素使用权交易合约的签订与履行是互为基础 ,互相促进的。     

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.     

Incomplete Insurance and Non-expected Utility

This paper shows that the estimation of non-expected utility (Kreps–Porteus preference) based on the representative agent model is less robust with respect to the departure from complete markets than is the expected utility for the following reasons. First, the precautionary saving caused by uninsured shocks may be evaluated incorrectly. Second, the portfolio held by individual household includes not only marketable assets, but also non-marketable assets (e.g. human capital) in the context of incomplete markets. Third, returns on marketable assets may not provide sufficient information for recovering relevant parameters. The estimated parameters available from the existing empirical research are consistent with the biasedness of parameters implied by this study.
JEL Classification: E44, G12.     

International asset markets and real exchange rate volatility

The real exchange rate is very volatile relative to major macroeconomic aggregates and its correlation with the ratio of domestic over foreign consumption is negative (Backus–Smith puzzle). These two observations constitute a puzzle to standard international macroeconomic theory. This paper develops a two country model with complete asset markets and limited enforcement for international financial contracts that provides a possible explanation of these two puzzles. The model performs better than a standard incomplete markets model with a single non-contingent bond unless very tight borrowing constraints are imposed in the latter. With limited enforcement for both domestic and international financial contracts, the model's asset pricing implications are brought into line with the empirical evidence, albeit at the expense of raising real exchange rate volatility.     

A bargaining theory of the firm

Suppose that a firm has several owners and that the future is uncertain in the sense that one out of many different states of nature will realize tomorrow. An owner’s time preference and risk attitude will determine the importance he places on payoffs in the different states. It is a well-known problem in the literature that under incomplete asset markets, a conflict about the firm’s objective function tends to arise among its owners. In this paper, we take a new approach to this problem, which is based on non-cooperative bargaining. The owners of the firm play a bargaining game in order to choose the firm’s production plan and a scheme of transfers which are payable before the uncertainty about the future state of nature is resolved. We analyze the resulting firm decision in the limit of subgame-perfect equilibria in stationary strategies. Given the distribution of bargaining power, we obtain a unique prediction for a production plan and a transfer scheme. When markets are complete, the production plan chosen corresponds to the profit-maximizing production plan as in the Arrow–Debreu model. Contrary to that model, owners typically do use transfers to redistribute profits. When markets are incomplete, the production plan chosen is almost always different from the one in a transfer-free Drèze (pseudo-)equilibrium and again owners use transfers to redistribute profits. Nevertheless, our results do support the Drèze criterion as the appropriate objective function of the firm.