A note on decomposing the Malmquist productivity index by means of subvector homotheticity

Summary. This paper introduces a decomposition of the Malmquist productivity index into component indexes. The motivation is to derive an analogue of the decomposition of the T?rnqvist index into productivity and quality change provided by Fixler and Zieschang (1992) to the Malmquist index. Since we employ no second order approximations, this decomposition requires additional structure, namely a generalized version of Shephard's (1970) inverse homotheticity, which we dub subvector homotheticity. We show that subvector homotheticity is necessary and sufficient for our decomposition. Received: July 10, 1998; revised version: August 11, 1999     

On Input and Output Translation Homotheticity

This note determines necessary and sufficient conditions for a production technology to exhibit both input translation homotheticity and output translation homotheticity without invoking joint efficiency.     

Biased Technical Change and Parallel Neutrality

The Luenberger productivity indicator has many attractive features to evaluate productivity, technical and efficiency changes. Paralleling Färe et al. (1997), this paper shows that the technical change indicator can be expressed as the sum of a magnitude indicator and a bias indicator that is the sum of two bias indicators input and output oriented respectively. Using a recent concept of ``parallel neutrality'' introduced by Briec et al. (2006), some conditions under which each bias indicator makes no contribution to productivity change are established. Among the key contributions of this paper is a new linear programming model involving a graph translation homotheticity property.     

Translation homotheticity

Summary. The concept of translation homotheticity is introduced and defined. It is demonstrated that translation homotheticity is necessary and sufficient for: disposable surplus to be independent of the reference utility, Luenberger's compensating and equivalent benefits to be independent of the reference utility and always equal to one another, the risk premium to be independent of reference-level utility, absolute indexes of income inequality to be reference free, and social-welfare functionals to satisfy invariance with respect to the choice of a common origin. Translation homotheticity is also sufficient for Hicks' many-market consumer surplus measure to be a second-order approximation to disposable surplus, compensating benefit, and equivalent benefit. If preferences are translation homothetic and appropriately quadratic, Hicks, many-market consumer surplus measure is exact for these welfare measures. Received: October 24, 1996; revised version: March 3, 1997     

Determinacy with nominal assets and outside money

Summary. We build a finite horizon model with inside and outside money, in which interest rates, price levels and commodity allocations are determinate, even though asset markets are incomplete and asset deliveries are purely nominal.Received: 2 July 2003, Revised: 1 December 2004 JEL Classification Numbers: D50, E40, E50, E58.Correspondence to: J. Geanakoplos     

COMMENT: TESTING FOR INVERSEHOMOTHETICITY: A NONPARAMETRIC APPROACH*

This paper starts from Fukuyama and Weber's (2004 ) work on testing for inverse homotheticity to show that the equality of the output gain function and the Zieschang output gain function is not equivalent to inverse homotheticity. Hence, testing for the equality of these gain functions cannot prove that a technology is inverse homothetic. Moreover, it is established that the gain functions are equal if and only if the direct and indirect isoquant and the corresponding efficient set are equal, which does not depend on inverse homotheticity.     

Asset price bubbles and crashes with near-zero-intelligence traders

Summary. We examine whether a simple agent-based model can generate asset price bubbles and crashes of the type observed in a series of laboratory asset market experiments beginning with the work of Smith, Suchanek and Williams (1988). We follow the methodology of Gode and Sunder (1993, 1997) and examine the outcomes that obtain when populations of zero-intelligence (ZI) budget constrained, artificial agents are placed in the various laboratory market environments that have given rise to price bubbles. We have to put more structure on the behavior of the ZI-agents in order to address features of the laboratory asset bubble environment. We show that our model of near-zero-intelligence traders, operating in the same double auction environments used in several different laboratory studies, generates asset price bubbles and crashes comparable to those observed in laboratory experiments and can also match other, more subtle features of the experimental data.Received: 15 July 2003, Revised: 28 September 2004, JEL Classification Numbers: D83, D84, G12. Correspondence to: John DuffyWe would like to thank an Anonymous referee, Guillaume Frechette, David Laibson, Al Roth and participants in Harvard Experimental and Behavioral Economics Workshop for their comments, and Charles Noussair for providing his data set.     

Computing equilibria in finance economies with incomplete markets and transaction costs

Summary. Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria.Received: 2 December 2002, Revised: 15 November 2004, JEL Classification Numbers: C61, C62, C63, C68, D52, D58, G11, G12. Correspondence to: P. Jean-Jacques HeringsThis research started when Jean-Jacques Herings enjoyed the generous hospitality of the Cowles Foundation for Research in Economics at Yale University. His research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organisation for Scientific Research. We thank audiences at Stanford University, UC San Diego, and Venice for discussions on the subject. We are very grateful to an anonymous referee for very helpful comments on an earlier draft.     

Testing revealed preferences for homotheticity with two-good experiments

It is shown that for two dimensional commodity spaces any homothetic utility function that rationalizes each pair of observations in a set of consumption data also rationalizes the entire set. The result is used to provide a simplified nonparametric test for homotheticity of demand and a measure for homothetic efficiency. The article thus provides a useful tool to screen data for severe violations of homotheticity before estimating parameters of homothetic utility functions. The new test and measure are applied to previously published data.     

Asset trading volume in a production economy

Judd et al. (J Finance 63: 2203–2217, 2003) show that the stationary Lucas tree model cannot generate nontrivial asset trading: Heterogenous agents will optimally choose a fixed portfolio after initial rebalancing. This paper explores asset trading volume in production economies with heterogeneous agents and dynamically complete market structures. We establish a recursive version of the Negishi approach to prove the existence of a competitive equilibrium. Furthermore, we develop a general method to solve for equilibrium portfolios in production economies within a fairly general set of complete market structures. We thus establish the theoretical reasons why production economies in general generate a nontrivial volume of asset trading even if heterogeneity of the agents is kept to a minimum. We would like to thank W. Brock, D. DeJong and, especially, H. Ennis for comments and suggestions. We also thank seminar participants at Di Tella and San Andrés Universities (Argentina), the Institute for Advanced Studies (Austria), SED Meetings 2005 (Budapest) and SAET Conference 2005 (Vigo).     

New financial markets: who gains and who loses

Summary. We evaluate the effects of new financial markets in a two-period incomplete markets model with heterogenous agents. For analytical tractability, we focus on the special case where utility is exponential and risks are normally distributed. We provide a complete characterization of life-cycle consumption and portfolio choice. The effect of new financial markets on individual welfare equals the sum of what we call the portfolio effect and the price effect. The portfolio effect is proportional to the square of the difference between the average exposure to the new asset in the economy and an individual investors exposure adjusted for risk aversion. The portfolio effect is always positive and measures the improved ability of investors to transfer consumption across states. The price effect captures the effect on individual welfare of changes in asset prices. We show that new financial markets drive down the prices of all assets which raises the interest rate and thus affects the ability of investors to transfer consumption across time. The price effect is positive for net savers but can be negative for net borrowers. For net borrower households, the price effect can wipe out the portfolio effect and lead to welfare reductions.Received: 24 July 2003, Revised: 22 March 2004, JEL Classification Numbers: D31, D52, G11, G12.Paul Willen: Thanks to Viral Acharaya, Alberto Bisin, Steve Davis, John Geanakoplos and a thoughtful anonymous referee for helpful comments and suggestions. Thanks also to seminar audiences at Stanford, Berkeley and at the 2001 Stony Brook workshop on incomplete markets for comments and suggestions. I gratefully acknowledge research support from the Graduate School of Business at the University of Chicago.     

Welfare-improving financial innovation with a single good

Summary. We show that at any equilibrium of almost every single-good incomplete markets economy, it is possible to find an asset which when introduced makes every agent better-off. Diamond (1967) has shown, however, that such economies are constrained suboptimal, so it is of course impossible to find a new asset which makes all agents worse-off. This contrasts with the case of multiple consumption goods, for which Cass and Citanna (1995) and Elul (1995) demonstrate that equilibrium utilities may be arbitrarily perturbed via financial innovation. Proving our result requires us to exploit not changes in equilibrium prices, but rather the gains to trading the new asset. In particular, we find an asset which when introduced does not change the existing asset prices even though it is traded by every agent – by a revealed preference argument it must therefore make everyone better-off. Received: May 28, 1997; revised version: July 1, 1997     

Insurance with Frequency Trading: A Dynamic Analysis of Efficient Insurance Markets

This paper extends existing insurance results on the type of insurance contracts needed for insurance market efficiency to a dynamic setting. It introduces continuously open markets that allow for more efficient asset allocation. It also estimates the role of preferences and endowments in the classification of risks, which is done primarily in terms of the actuarial properties of the underlying risk process. The paper further extends insurability to include correlated and catastrophic events. Under these very general conditions the paper defines a condition that determines whether a small number of standard insurance contracts (together with aggregate assets) suffice to complete markets or one needs to introduce such assets as mutual insurance. Journal of Economic Literature Classification Numbers: D81, D99, G11.     

Informational efficiency: ranking markets

Summary. The paper studies informational properties of three types of imperfectly competitive markets: a one-signal speculative market (OSS market) in which agents have only private information about the fundamental value (v) of the risky asset traded, a two-signal speculative market (TSS market) in which agents have private information about both v and the asset supply, and a market in which agents are endowed with both information about v and shares of the risky asset traded. In this last market (JA market), agents have joint activities: they trade for both speculative and hedging purposes. It is shown that (i) the JA market and the OSS market are the most and the least efficient, respectively, and (ii) the levels of informational efficiency in the three markets are inversely correlated with the intensities with which traders use their private information about the fundamental value of the asset. Received May 28, 1999; revised version: May 28, 1999     

Financial price fluctuations in a stock market model with many interacting agents

Summary. We consider a financial market model with a large number of interacting agents. Investors are heterogeneous in their expectations about the future evolution of an asset price process. Their current expectation is based on the previous states of their neighbors and on a random signal about the mood of the market. We analyze the asymptotics of both aggregate behavior and asset prices. We give sufficient conditions for the distribution of equilibrium prices to converge to a unique equilibrium, and provide a microeconomic foundation for the use of diffusion models in the analysis of financial price fluctuations.Received: 16 April 2003, Revised: 1 March 2004, JEL Classification Numbers: D40, D84, G10.I thank Peter Bank, Dirk Becherer, Hans Föllmer, Peter Leukert, José Scheinkman, Alexander Schied, Ching-Tang Wu, and seminar participants at various institutions for many suggestions and discussions. Thanks are due to two anonymous referees and the editor, C.D. Aliprantis, for valuable comments which helped to improve the presentation of the results. Financial support of Deutsche Forschungsgemeinschaft via SFB 373, Quantification and Simulation of Economic Processes, Humboldt-Universität zu Berlin, and DFG Research Center Mathematics for Key Technologies (FZT 86) is gratefully acknowledged.     

The structure of consumer preferences,Federal Republic of Germany, 1950–1973

Summary The objective of this paper is to analyze the structure of consumer preferences and changes in preferences over time. Consumer preferences are represented by an indirect translog utility function with time-varying preferences that is quadratic in the logarithms of its arguments. We consider a system of demand functions associated with parameter restrictions consistent with the theory. We characterize groupwise separability and groupwise homotheticity of preferences and derive for each set of restrictions on preferences parametric restrictions on the corresponding system of demand functions. Empirical results of the tests, based on time series data for FRG consumption expenditures on three commodity groups — durables, non-durables, and energy — are presented.     

The Production Possibility Frontier as a Maximum Value Function: Concavity and Non-increasing Returns to Scale

This paper makes both a methodological as well as a substantive contribution to the literature on the concavity of the production possibility frontier (PPF). Rather than using the standard, calculus‐based techniques, the method here relies on the fact that the PPF is a maximum value function. The consequent simplification in analysis makes it possible to demonstrate that the conditions which are sufficient to guarantee global concavity of the PPF are considerably less stringent than those stated in the literature. Existing analyses have assumed that production functions are (a) concave and homothetic, or (b) display non‐increasing returns to scale (NIRS) and homogeneity. This paper shows that concavity without homotheticity, or NIRS and quasiconcavity without homogeneity (or even homotheticity) are sufficient, thus greatly increasing the generality of existing results. The analysis can be extended to include situations in which the input set includes industry‐specific factors.     

Monetary confidence and asset prices

Three issues are studied in this paper: the existence of sunspot equilibria; the excessive volatility of asset prices; and the possibility that assets may be undervalued relative to their market fundamentals. We show that (i) stationary sunspot equilibria exist in a very general environment; (ii) asset prices may fluctuate despite a constant stream of dividends; and (iii) assets may be undervalued. JEL: 021, 023, 131.     

Excess price volatility and financial innovation

Summary. In a three-period finite exchange economy with incomplete financial markets and retrading, we study the effects of the degree of incompleteness and of changes in the financial structure on asset price volatility. In what are essentially no aggregate risk economies, asset price volatility is a sunspot-like phenomenon. If markets are completed by financial innovation, asset price volatility reduction is generic. With aggregate risk, changes in the financial structure affect asset price volatility through a pecuniary externality. Financial innovation which decreases equilibrium price volatility can be crafted under conditions of sufficient market incompleteness. Numerical examples illustrate the role of risk aversion for volatility changes and show that, with or without aggregate risk, reducing the degree of incompleteness per se is not necessarily associated with a volatility reduction.Received: 10 October 2003, Revised: 3 June 2004, JEL Classification Numbers: C60, D52, G10. Correspondence to: Alessandro CitannaThis research project stems from and expands previous work circulated as Financial innovation and price volatility, GSIA Working Paper #1996-E30 and Controlling price volatility through financial innovation, Kellogg Working Paper #2002-1338. We thank Herakles Polemarchakis and Chris Telmer for their comments. We are grateful to an anonymous referee for careful reviews of earlier versions. The first author thanks also GSIA - Carnegie Mellon University for the kind hospitality during Fall 2002, when part of this project was completed.     

Strategic Information Acquisition in Capital Markets*

A simple model of an asset market is presented, where agents are asymmetrically informed and hence information is transmitted through the price system. Prior to the trading period, a group of traders is given the opportunity to decide in a collusive arrangement whether they want to undertake a (costless) analysis which yields information about the future dividends of a risky asset. It will be shown that the fully rational and risk-averse insiders can do better without the information, if the dividend volatility of the risky asset is sufficiently low.
JEL Classification Numbers: D82, G14.