Jordi Caballé

Imperfect Competition in a Multi-security Market with Risk Neutrality

THE CENTRAL PURPOSE OF THIS PAPER is to develop a model of insider trading (i.e., trading based on private information) in the context of an imperfectly competitive multi-security market with risk-neutral agents. Imperfect competition allows us to consider strategic behavior, and a multi-security market lets us study the effect of a correlated environment on equilibrium. We employ the informational assumption that market makers can observe all order flows, and so portfolio diversification arises in this model for strategic reasons. Given correlated fundamentals, market makers can potentially learn about every security from each order flow. This causes even a risk neutral trader who does not face short-selling restrictions to refrain from determining the demand for each security independently. This contrasts with traditional multi-asset models, which focus on the incentive to reduce portfolio variance, or the effect of short-selling restrictions or budget constraints. Under imperfect competition, correlation has two effects. One, ceteris paribus, it allows the uninformed to learn from additional variables since each order flow could potentially have information about all payoffs. On the other hand, it creates an incentive for informed traders to restrict what others can learn from public information. Thus, our analysis can be viewed as an application to the multi-security, heterogeneous-information model in Admati (1985) of the imperfectly competitive equilibrium concept which Kyle (1985) first applied to the single-security, homogeneous-information model of Grossman and Stiglitz (1980). Our principal results include an explicit characterization of a linear equilibrium as a function of three general covariance matrices associated with payoffs, noise trading, and errors in private signals. Under general covariance structures, we show that there always exists an equilibrium in which the relationship between the vector of prices and the vector of order flows is governed by a symmetric positive definite matrix. The plan of the paper is as follows. In Section 2, we introduce our model. We derive the equilibrium in Section 3, and Section 4 comments on the properties of the equilibrium. The proofs of the results are in the Appendix.

Speculating against an overconfident market

We distinguish two components of self-confidence in a financial market: private confidence measures the self-confidence level of speculators, while public confidence measures the confidence level they attribute to their competitors. We then study how independent changes in these components affect the equilibrium trading strategies. We conduct the analysis in a financial market with imperfect competition where investors submit limit orders We calculate the unique linear symmetric equilibrium as well as the major indicators of the market. In addition to providing a partial explanation for the excess volatility of asset prices as well as for trading volume unexplained by the arrival of new information, our model highlights the differences between the effects of public versus private confidence.

Growth Effects of Taxation under Altruism and Low Elasticity of Intertemporal Substitution

An increase in the tax rate on capital income may raise the rate of economic growth when the elasticity of intertemporal substitution is low and intergenerational transfers are absent. Since the strength of the bequest motive depends on tax rates, this paper provides conditions under which taxing capital income, and then reducing the labor income tax, is more growth enhancing than the classical policy of zero taxes on capital income, and vice versa.

Welfare Implications of the Interaction between Habits and Consumption Externalities

We analyze the welfare properties of the equilibrium path of a growth model where both habits and consumption externalities affect the utility of consumers. Our analysis highlights the crucial role played by complementarities between externalities and habits in order to generate an inefficient dynamic equilibrium. In particular, we show that the competitive equilibrium is inefficient when consumption externalities and habit adjusted consumption are not perfect substitutes.

Stochastic Dominance and Absolute Risk Aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Pay-as-you-go Social Security and the Distribution of Altruistic Transfers

This paper studies the impact of an unfunded social security system on the distribution of altruistic transfers in a framework where savings are due to both life cycle and random altruistic motivations. We show that the effect of social security on the distribution of these transfers depends crucially on the strength of the bequest motive in explaining savings behaviour. We measure this strength by the expected weight that individuals attach to the utility of future generations. On the one hand, if the bequest motive is strong, then an increase in the social security tax raises the bequests left by altruistic parents. On the other hand, when the importance of altruism in motivating savings is sufficiently low, the increase in the social security tax could result in a reduction of the bequests left by altruistic parents under some conditions on the attitude of individuals toward risk and on the relative returns associated with private saving and social security. Some implications concerning the transitional effects of introducing an unfunded social security scheme are also discussed. Copyright 2003, Wiley-Blackwell.

Effects of Aspirations and Habits on the Distribution of Wealth

We analyze how the introduction of habits and aspirations affects the distribution of wealth when the labor productivity of individuals is subject to idiosyncratic shocks and when bequests arise from a joy-of-giving motive. In the presence of either bequests or aspirations, labor income shocks are transmitted intergenerationally, and this transmission, together with contemporaneous shocks, determines the distribution of wealth. We show that the introduction of aspirations (habits) decreases (increases) the average wealth, and increases (decreases) both its intragenerational variability and the degree of intergenerational mobility. Therefore, a distinction between aspirations and habits is relevant because they involve different implications for the distribution of wealth.

Pay-as-you-go Social Security and the Distribution of Bequests

This paper studies the impact of an unfunded social security system on the distribution of bequests in a framework where savings are due both by life cycle and by random altruistic motivations. We show that the impact of social security on the distribution of bequests depends crucially on the importance of the bequest motive in explaining savings behavior. If the bequest motive is strong, then an increase in the social security tax raises the bequests left by altruistic parents. On the other hand, when the importance of bequests in motivating savings is sufficiently low, the increase in the social security tax could result in a reduction of the bequests left by altruistic parents under some conditions on the attitude of individuals toward risk and on the relative returns associated with private saving and social security. Some implications concerning the transitional effects of introducing an unfunded social security scheme are also discussed.

Social rents, interest rates, and growth

Abstract We present a simple OLG model with a convex technology in which physical capital exhibits a productive externality, and workers receive part of the social rents generated by that externality. This setup allows for sustained growth without incurring poverty traps. Moreover, every equilibrium path displays constant interest rates as suggested by some empirical evidence.

Consumption composition and macroeconomic dynamics

Abstract We analyze the transitional dynamics of an economic model with heterogeneous consumption goods where convergence is driven by two different forces: the typical diminishing returns to capital and the dynamic adjustment in consumption expenditure induced by the variation in relative prices. We show that this second force affects the growth rate if the consumption goods are produced with technologies exhibiting different capital intensities and if the intertemporal elasticity of substitution is not equal to one. Because the aforementioned growth effect of relative prices arises only under heterogeneous consumption goods, the transitional dynamics of this model exhibits striking differences with the growth model with a single consumption good. We also show that these differences in the transitional dynamics can give raise to large discrepancies in the welfare cost of shocks.