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     

State-price densities under heterogeneous beliefs, the smile effect, and implied risk aversion

It has been widely noted in the empirical literature that state-price densities implicit in financial asset prices are not log-normal. This paper shows that this phenomenon can be caused by heterogeneity in investors’ beliefs. It derives the state-price density under heterogeneous beliefs in closed form and demonstrates that heterogeneous beliefs can give rise to multimodal state-price densities. Consequences for the “smile effect” in implied option volatility and for measures of risk aversion inferred from empirical state-price densities are discussed.     

The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibrium when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of some agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.     

The effect of heterogeneous beliefs on mergers and acquisitions

This article investigates the effect of heterogeneous beliefs on firms’ mergers and acquisitions (M&A) decisions. Using data of China’s financial market, which is featured with great heterogeneity of belief, we find that heterogeneous beliefs are positively associated with the occurrence of M&A transactions, and firms with greater heterogeneous beliefs are more likely to pay the transactions with stock. Moreover, we show that government intervention, measured by state ownership, weakens the effect of heterogeneous beliefs on firms’ M&A decisions.     

Monetary policy with heterogeneous agents and borrowing constraints

We show that the long-run neutrality of inflation on capital accumulation obtained in complete market models no longer holds when households face binding credit constraints. Borrowing-constrained households are not able to rebalance their financial portfolio when inflation varies, and thus adjust their money holdings differently compared to unconstrained households. This heterogeneity leads to a new precautionary savings motive, which implies that inflation increases capital accumulation. We quantify the importance of this new channel in an incomplete market model where the traditional redistributive effects of inflation are also introduced. We show that this model provides a quantitative rationale for the observed hump-shaped relationship between inflation and capital accumulation.     

Welfare effects of unbundling under different regulatory regimes in natural gas markets

In this paper, we develop a theoretical model that enriches the literature on the pros and cons of ownership unbundling vis-à-vis lighter unbundling frameworks in the natural gas markets. For each regulatory framework, we compute equilibrium outcomes when an incumbent firm and a new entrant compete à la Cournot in the final gas market. We find that the entrant’s contracting conditions in the upstream market and the transmission tariff are key determinants of the market structure in the downstream gas market (both with ownership and with legal unbundling). We also study how the regulator must optimally set transmission tariffs in each of the two unbundling regimes. We conclude that welfare maximizing tariffs often require free access to the transmission network (in both regulatoy regimes). However, when the regulator aims at promoting the break-even of the regulated transmission system operator, the first-best tariff is unfeasible in both regimes. Hence, we study a more realistic set-up, in which the regulator’s action is constrained by the break-even of the regulated firm (the transmission system operator). In this set-up, we find that, for a given transmission tariff, final prices in the downstream market are always higher with ownership unbundling than with legal unbundling.     

Market stability switches in a continuous-time financial market with heterogeneous beliefs

By considering a financial market of fundamentalists and trend followers in which the price trend of trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examine the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. These interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, sufficient conditions on the stability and global existence of the periodic solution are obtained.     

Welfare implications of growth under quotas

Using the standard trade model, it is shown that growth under quotas always improves welfare. This result is contrary to Johnson's (1967) result on the possibilities of immeserizing growth in the presence of tariffs.     

Welfare effects of tied food aid

An important part of the overall U.S. aid program is Public Law 480 food aid. The design of the program seeks to satisfy numerous and often conflicting objectives. Several constraints have been placed on the use by recipient countries of that aid to insure that the intentions of the program are achieved. This paper examines the implications for recipient country welfare of both the traditional and the proposed restrictions on PL480 aid. It also seeks to clarify the interpretation of empirical work on the effects of this aid. It is shown that the net value of such commodity tied aid is simply the grant component of the subsidized sale and may easily be realized by substituting food aid imports for commercial imports. Restrictions which prevent aid recipients from doing so are costly to the recipient and could lead even to immuserization. Empirical evidence obtained by others is consistent with the notion that such restrictions are circumvented, where possible, by food aid recipients. The results presented indicate that a ‘Schultzian’ disincentive effect is characteristic of a closed economy. Typical interventions on the part of recipient country governments do not effectively reclose the economy. Hence, open economy models are more appropriate frameworks for evaluating the effects of PL480 aid.     

Portfolio delegation under short-selling constraints

Summary. In this paper we study delegated portfolio management when the manager’s ability to short-sell is restricted. Contrary to previous results, we show that under moral hazard, linear performance-adjusted contracts do provide portfolio managers with incentives to gather information. We find that the risk-averse manager’s effort is an increasing function of her share in the portfolio’s return. This result affects the risk-averse investor’s choice of contracts. Unlike previous results, the purely risk-sharing contract is now shown to be suboptimal. Using numerical methods we show that under the optimal linear contract, the manager’s share in the portfolio return is higher than what it is under a purely risk sharing contract. Additionally, this deviation is shown to be: (i) increasing in the manager’s risk aversion and (ii) larger for tighter short-selling restrictions. As the constraint is relaxed the deviation converges to zero.Received: 25 July 2002, Revised: 12 December 2004, JEL Classification Numbers: D81, D82, J33.Juan-Pedro Gómez: Correspondence toAn earlier version of the paper was circulated under the title “Providing Managerial Incentives: Do Benchmarks Matter?” We are grateful to an anonymous referee whose comments helped to improve the paper. We also thank comments by Viral Acharya, Alexei Goriaev, Ernst Maug, Kristian Rydqvist, Neil Stoughton, Rangarajan Sundaram, Fernando Zapatero and seminar participants at the 1999 SED meetings in Sardinia, the 1999 Workshop in Mutual Fund Performance at EIASM, Brussels, the 2000 EFA meetings in London, the Bank of Norway, the Stockholm Schools of Economics, the Norwegian School of Management and the 2001 WFA meetings in Tucson. Sharma gratefully acknowledges financial support from the Asociacion Mexicana de Cultura.     

Voting by committees under constraints

We consider social choice problems where a society must choose a subset from a set of objects. Specifically, we characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters’ preferences are separable or additively representable.     

Welfare effects of the euro cash changeover

Using merged data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel (SOEP), this paper applies a parametric difference-in-differences approach to assess the real effects of the introduction of the euro on subjective well-being. A complementary nonparametric approach is also used to analyze the impact of difficulties with the new currency on well-being. The results indicate a loss in well-being associated with the introduction of the new currency, with the predicted probability that a person is contented with his/her household income diminishing by 9.7 percentage points. We calculate a compensating income variation of approximately one-third. That is, an increase in post-government household income of more than 30% is needed to compensate for the clear decline in well-being. The reasons for the negative impact are threefold. First, perceived inflation overestimates the real increase in prices resulting in suboptimal consumption decisions. Second, money illusion causes a false assessment of the budget constraint. Third, individuals have to bear the costs from the conversion and the adjustment to the new currency. Moreover, it is thought that losses are higher for persons who have difficulties with the new currency. However, the impact of difficulties in using and converting the new currency is rather small, and the initial problems were overcome within one year of the introduction of euro cash.     

Consumption dynamics under information processing constraints

This paper studies how “rational inattention” (RI)—a type of information processing constraint proposed by Sims [Sims, C.A., 2003. Implications of rational inattention, Journal of Monetary Economics 50 (3), 665–690]—affects the joint dynamics of consumption and income in a permanent income model with general income processes. Specifically, I propose an analytical approach to solve the multivariate permanent income model with RI and examine its implications for optimal consumption, saving, and welfare. It is shown that RI can affect the relative volatility of consumption and provide an endogenous propagation mechanism that disentangles the short-run and long-run responses of consumption to exogenous income shocks. I also explore how aggregation reduces the impact of the RI-induced endogenous noise on consumption and thus increases the smoothness of aggregate consumption. Finally, I compare RI with four alternative hypotheses (habit formation, signal extraction, robustness, and inattentiveness) by examining their implications for the joint behavior of consumption and income.     

Technical Improvements and Welfare under International Duopoly

It is now common wisdom that a free-trading country with perfectly competitive markets might be hurt by its own technical improvement of that country's export industry, and that an improvement in the import-competing industry never impoverishes the country if no commodity is inferior for that country. This paper examines the welfare effects of technical progress in a perfectly competitive industry and in an internationally duopolistic market in a two-country, two-good, one-factor trading model. It will be shown that the above propositions are severely qualified in our setting with duopolistic industry.     

Credit contracting and bidding under wealth constraints

Summary. We model credit contracting and bidding in a first-price sealed-bid auction when bidder valuation and wealth are private information. An efficient separating equilibrium exists only if the wealth levels of both bidder types are sufficiently different. If not, high-valuation bidders signal by borrowing more and using less of their wealth – this is inefficient as wealth is a cheaper source of funds. An increase in the amount of borrowing required to signal does not necessarily decrease seller expected revenue. In contrast to separating equilibria, high-valuation bidders adopt pure strategy bids in pooling equilibria. Conditions are identified under which the lower bound on winning bids is higher in pooling than separating equilibria. Received: January 22, 2001; revised version: August 28, 2001     

Evaluating international financial integration under leverage constraints

The global financial crisis has undermined many economists' views about the benefits of open financial markets. Anecdotal evidence seems to indicate that financial linkages may propagate shocks during crises. This paper develops a simple two-country model in which financial liberalisation across countries takes place in the presence of credit market distortions within countries. Countries may be subject to macro risk coming from productivity shocks and direct shocks to the credit system (‘financial shocks’). Three different degrees of financial linkages between countries are examined. It is shown that the type of financial integration is critical for both macroeconomic outcomes and welfare. In particular, financial integration in bond markets alone may increase aggregate consumption volatility and reduce welfare. Financial integration in both bond and equity markets generates high positive co-movement across countries, but is welfare-improving.     

Coalition-proof supply function equilibria under capacity constraints

Whereas in the absence of capacity constraints the Cournot outcome is the unique coalition-proof supply function equilibrium outcome, the presence of capacity constraints may enlarge the set of equilibrium outcomes. Interestingly, if capacities are sufficiently asymmetric the new equilibrium prices are below the Cournot price. These results have important implications for merger and privatization policies: specifically, capacity divestiture will not necessarily imply lower market prices.This article is based on the second chapter of my PhD dissertation. I benefited from the comments and suggestions of Diego Moreno and Bill Hogan. I thank three anonymous referees for helpful comments. Seminar audiences at Carlos III and Harvard are gratefully acknowledged. The author is currently a Repsol YPF fellow at the Harvard John F. Kennedy School of Government. I am grateful to the Repsol YPF-Harvard Fellowship Program for financial support.