No unbounded arbitrage,weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions

Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162] prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page [Page, F.H., 1987. On equilibrium in Hart’s securities exchange model. Journal of Economic Theory 41, 392–404], is equivalent to the existence of a no arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. [Allouch, N., Le Van, C., Page F.H., 2002. The geometry of arbitrage and the existence of competitive equilibrium. Journal of Mathematical Economics 38, 373–391] extend the NAPS introduced by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418] and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart [Hart, O., 1974. On the existence of an equilibrium in a securities model. Journal of Economic Theory 9, 293–311]. They mention that this result implies the one given by Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162]. In this note, we show that all these conditions are equivalent.     

Inconsequential arbitrage

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, prove that inconsequential arbitrage is sufficient for existence of equilibrium. Moreover, with a slightly stronger condition of nonsatiation than that required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that inconsequential arbitrage, the existence of a Pareto optimal allocation, and compactness of the set of utility possibilities are equivalent. Thus, when all equilibria are Pareto optimal — for example, when local nonsatiation holds — inconsequential arbitrage is necessary and sufficient for existence of an equilibrium. By further strengthening our nonsatiation condition, we obtain a second welfare theorem for exchange economies allowing short sales.Finally, we compare inconsequential arbitrage to the conditions limiting arbitrage of Hart [Hart, O.D., 1974. J. Econ. Theory 9, 293–311], Werner [Werner, J., 1987. Econometrica 55, abs1403–1418], Dana et al. [Dana, R.A., Le Van, C., Magnien, F., 1999. J. Econ. Theory 87, 169–193] and Allouch [Allouch, N., 1999. Equilibrium and no market arbitrage. CERMSEM, Universite de Paris I]. For example, we show that the condition of Hart (translated to a general equilibrium setting) and the condition of werner are equivalent. We then show that the Hart/Werner conditions imply inconsequential arbitrage. To highlight the extent to which we extend Hart and Werner, we construct an example of an exchange economy in which inconsequential arbitrage holds (and is necessary and sufficient for existence), while the Hart/Werner conditions do not hold.     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Unbounded exchange economies with satiation: How far can we go?

We unify and generalize the existence results in Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55 (6), 1403–1418], Dana et al. [Dana, R.-A., Le Van, C., Magnien, F., 1999. On the different notions of arbitrage and existence of equilibrium. Journal of Economic Theory 87 (1), 169–193], Allouch et al. [Allouch, N., Le Van, C., Page Jr., F.H., 2006. Arbitrage and equilibrium in unbounded exchange economies with satiation. Journal of Mathematical Economics 42 (6), 661–674], Allouch and Le Van [Allouch, N., Le Van, C., 2008. Erratum to “Walras and dividends equilibrium with possibly satiated consumers”. Journal of Mathematical Economics 45 (3–4), 320–328]. We also show that, in terms of weakening the set of assumptions, we cannot go too far.     

Proper preferences and quasi-concave utility functions

It is shown that preferences which are continuous, convex and uniformly proper [Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented by a quasi-concave utility function which is defined on a larger domain with non-empty interior. This utility function may be chosen to be either upper or lower semi-continuous on its domain, and continuous at each point of the positive cone. Conversely, any preference relation on the positive cone which is monotone and arises from such a utility function is shown to satisfy a condition which is slightly weaker than uniform properness but which (in the presence of appropriate compactness assumptions) is sufficient to establish the existence of quasi-equilibria. An example is presented to illuminate the role played by the uniformity requirement.     

No-arbitrage condition and existence of equilibrium with dividends

In this paper we first give an elementary proof of existence of equilibrium with dividends in an economy with possibly satiated consumers. We then introduce a no-arbitrage condition and show that it is equivalent to the existence of equilibrium with dividends.     

Federal budget deficits and long-term interest rates in USA

We investigate whether the emergence of high inflation rates after 1965 and large budget deficits after 1980s caused the financial market agents to become more sensitive to the outlooks for inflation and budget deficits. Our approach is parametric and our models fully account for possible presence of ARCH effects in the data.Our results show a statistically significant positive link between the budget deficits and the slope of the yield curve which is more pronounced in the later sub-sample period. These results are in line with Reinhard and Sack [Reinhard, V., & Sack, B. (2000). The economic consequences of disappearing government debt. Brooking Papers of Economic Activity, 163–209] but in sharp contrast with Evans [Evans, P. (1985). Do large deficits produce high interest rates? American Economic Review, 7, 68–87] and Evans [Evans, P. (1987). Do budget deficits raise nominal interest rates? Journal of Monetary Economics, 20, 281–300].     

New evidence on the dynamic wage curve for Western Germany: 1980–2004

Blanchflower and Oswald [Blanchflower, David G. and Oswald, Andrew J., 1994a, The Wage Curve, (Cambridge, MA, MIT Press), Blanchflower, David G. and Oswald, Andrew J., 1994b, Estimating a Wage Curve for Britain 1973–90, The Economic Journal 104, 1025–1043. Eine praktische Einführung, Nürnberg] reported that they have found an ‘empirical law of economics’ — the Wage Curve. Our paper reconsiders the western German Wage Curve using disaggregated regional data and is based on almost one million employees drawn from the Federal Employment Services of Germany over the period 1980–2004. We find that the wage equation is highly autoregressive but far from unit root. The unemployment elasticity is significant but relatively small: only between ? 0.02 and ? 0.04. We also check the sensitivity of this elasticity for different population groups (young versus old, men versus women, less educated versus highly educated, German native versus foreigner), confirming that it is stronger the weaker the bargaining power of the particular group.     

The return to schooling: Estimates from a sample of young Australian twins

This study uses a sample of young Australian twins to examine whether the findings reported in [Ashenfelter, Orley and Krueger, Alan, (1994). ‘Estimates of the Economic Return to Schooling from a New Sample of Twins’, American Economic Review, Vol. 84, No. 5, pp.1157–73] and [Miller, P.W., Mulvey, C and Martin, N., (1994). ‘What Do Twins Studies Tell Us About the Economic Returns to Education?: A Comparison of Australian and US Findings’, Western Australian Labour Market Research Centre Discussion Paper 94/4] are robust to choice of sample and dependent variable. The economic return to schooling in Australia is between 5 and 7 percent when account is taken of genetic and family effects using either fixed-effects models or the selection effects model of Ashenfelter and Krueger. Given the similarity of the findings in this and in related studies, it would appear that the models applied by [Ashenfelter, Orley and Krueger, Alan, (1994). ‘Estimates of the Economic Return to Schooling from a New Sample of Twins’, American Economic Review, Vol. 84, No. 5, pp.1157–73] are robust. Moreover, viewing the OLS and IV estimators as lower and upper bounds in the manner of [Black, Dan A., Berger, Mark C., and Scott, Frank C., (2000). ‘Bounding Parameter Estimates with Nonclassical Measurement Error’, Journal of the American Statistical Association, Vol. 95, No.451, pp.739–748], it is shown that the bounds on the return to schooling in Australia are much tighter than in [Ashenfelter, Orley and Krueger, Alan, (1994). ‘Estimates of the Economic Return to Schooling from a New Sample of Twins’, American Economic Review, Vol. 84, No. 5, pp. 1157–73], and the return is bounded at a much lower level than in the US.     

A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core

In 2004, Predtetchinski and Herings [A. Predtetchinski, P.J.J. Herings, “A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game”, Journal of Economic Theory 116 (2004) 84–92] provided a necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game. In this paper, we extend this theorem to its counterpart in fuzzy games and give a necessary and sufficient condition for a non-transferable utility fuzzy game to have a non-empty fuzzy core. As a consequence, we derive a necessary and sufficient condition for non-emptiness of the fuzzy core of a TU fuzzy game.     

Generalized weak transfer continuity and the Nash equilibrium

This paper introduces the notion of generalized weak transfer continuity and establishes that a bounded, compact locally convex metric quasiconcave and generalized weak transfer continuous game has a Nash equilibrium. Our equilibrium existence result neither implies nor is implied by the existing results in the literature such as those in [Carmona, G., 2011. Understanding some recent existence results for discontinuous games. Economic Theory 48, 31–45], [Prokopovych, P., 2011. On equilibrium existence in payoff secure games. Economic Theory 48, 5–16], [Carmona, G., 2009. An existence result for discontinuous games. Journal of Economic Theory 144, 1333–1340], and [Reny, P.J., 1999. On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056].     

Erratum to “Walras and dividends equilibrium with possibly satiated consumers”

The main contribution of the paper is to provide a weaker nonsatiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points in the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends (see Aumann, R.J., Drèze, J.H., 1986. Values of markets with satiation or fixed prices. Econometrica 54, 1271–1318; Mas-Collel, A., 1992. Equilibrium theory with possibly satiated preferences. In: Majumdar, M. (Ed.), Equilibrium and Dynamics: Proceedings of the Essays in Honour of David Gale. MacMillan, London, pp. 201–213) is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner’s (1987) assumption.     

Coasian equilibrium

We consider a general equilibrium economy with public goods and externalities. Following Boyd and Conley (1997), we treat externality markets directly instead of indirectly through Arrovian commodities. Because such direct externality markets are not subject to the nonconvexities that Starrett [Starrett, D., 1972. Fundamental nonconvexities in the theory of externalities. Journal of Economic Theory 4, 180–199] shows are fundamental to Arrow’s externality markets, this new approach admits the use of largely standard methods to prove welfare and existence theorems in an economy with externalities. We extend the Boyd and Conley model to allow firms to benefit from public goods and be damaged by externalities, and to allow consumers to produce externalities. We state a first welfare theorem and prove the existence of a competitive equilibrium. Taken together, this can be viewed as a type of general equilibrium Coase theorem. Considered as a special case, these theorems also represent a significant generalization of existing results for pure public goods economies.     

Arbitrage pricing theory and risk-neutral measures

Abstract We consider a market with countably many risky assets and finite factor structure, as in the “arbitrage pricing theory” of Ross (1976). We prove necessary and sufficient conditions in terms of parameters for the existence of an equivalent risk-neutral measure, i.e., a measure under which each asset return has zero expected value. We relate these conditions to a certain absence of arbitrage property of the model. Mathematics Subject Classification (2000): 91B24, 91B28 Journal of Economic Literature Classification: G10, G12     

A Note on Some Properties of STUR Processes*

This note presents some properties of the stochastic unit‐root processes developed in Granger and Swanson [Journal of Econometrics (1997) Vol. 80, pp. 35–62] and Leybourne, McCabe and Tremayne [Journal of Business & Economic Statistics (1996) Vol. 14, pp. 435–446] that have not been or only implicitly discussed in the literature.     

The no-arbitrage condition and financial markets with heterogeneous information

This paper examines the role of the no-arbitrage condition in financial markets with heterogeneous expectations. We consider a single-period, state-contingent claims model, withM risky securities andS states. There exist two types of heterogeneously informed investors, where the information heterogeneity is defined with respect to either the security payoff matrix, the state probability vector, or state partitions. When the information heterogeneity is defined with respect to either the security payoff matrix or state partitions, the no-arbitrage condition imposes a constraint on the dispersion of information between informed and uninformed investors. Further, the no-arbitrage condition is useful in ascertaining the patterns of heterogeneity among investors that are consistent with equilibrium. However, when the information heterogeneity is defined with respect to state probabilities, the role of the no-arbitrage condition is severely restricted. Finally, the no-arbitrage condition may have important implications for the (necessary and sufficient) conditions for the existence of an equilibrium price vector in financial markets with heterogeneous expectations.     

Limited arbitrage is necessary and sufficient for the existence of an equilibrium

In Chichilnisky (Working Paper No. 586, 1991), Chichilnisky (Working Paper No. 650, 1992) and Chichilnisky (Economic Theory, 1995, 5, 79–108), I introduced the concept of a global cone and used it to define a condition on endowments and preferences, ‘limited arbitrage’, which I showed to be necessary and sufficient for the existence of a competitive equilibrium. In response to a comment (Monteiro et al., Journal of Mathematical Economics, 1997, 26, 000-000), I show here that the authors misunderstood my results by focussing on brief announcements which cover other areas, social choice (Chichilnisky, American Economic Review, 1994, 427–434 and algebraic topology (Chichilnisky, Bulletin of the American Mathematical Society, 1993, 29, 189–207), rather than on the publication which contains may proofs on equilibrium. The comment's example is irrelevant to my results in Chichilnisky (Economic Theory, 1995, 5, 79–108) because it starts from different conditions. Limited arbitrae is always necessary and sufficient for the existence of a competitive equilibrium, with or without short sales, with the global cones as I defined them, and exactly as proved in Chichilnisky (Economic Theory, 1995, 5, 79–108).     

Iterated weak dominance and subgame dominance

In this paper, we consider finite normal form games satisfying transference of decisionmaker indifference. We show that any set of strategies surviving k rounds of elimination of some weakly dominated strategies can be reduced to a set of strategies equivalent to the set of strategies surviving k rounds of elimination of all weakly dominated strategies in every round by (at most k) further rounds of elimination of weakly dominated strategies. The result develops work by Gretlein [Gretlein, R., 1983. Dominance elimination procedures on finite alternative games. International Journal of Game Theory 12, 107–113]. We then consider applications and demonstrate how we may obtain a unified approach to the work by Gretlein and recent results by Ewerhart [Ewerhart, C., 2002. Iterated weak dominance in strictly competitive games of perfect information. Journal of Economic Theory 107, 474-482] and Marx and Swinkels [Marx, L.M., Swinkels, J.M., 1997. Order independence for iterated weak dominance. Games and Economic Behavior 18, 219-245].     

A Note on the Theme of Too Many Instruments*

The difference and system generalized method of moments (GMM) estimators are growing in popularity. As implemented in popular software, the estimators easily generate instruments that are numerous and, in system GMM, potentially suspect. A large instrument collection overfits endogenous variables even as it weakens the Hansen test of the instruments’ joint validity. This paper reviews the evidence on the effects of instrument proliferation, and describes and simulates simple ways to control it. It illustrates the dangers by replicating Forbes [American Economic Review (2000) Vol. 90, pp. 869–887] on income inequality and Levine et al. [Journal of Monetary Economics] (2000) Vol. 46, pp. 31–77] on financial sector development. Results in both papers appear driven by previously undetected endogeneity.