Contract enforcement and incentive compatibility in large economies with differential information: the role of exact feasibility

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy, Moreno and Shitovitz (2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis, Muir and Yannelis (2002)). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (2001) are still valid without free-disposal. Then we define an incentive compatibility property motivated by the issue of contracts’ execution and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of a competitive or core allocations are enforceable.

On the Impossibility of an Exact Imperfect Monitoring Folk Theorem

It is shown that, for almost every two-player game with imperfect monitoring, the conclusions of the classical folk theorem are false. So, even though these games admit a well-known approximate folk theorem, an exact folk theorem may only be obtained for a measure zero set of games. A complete characterization of the efficient equilibria of almost every such game is also given, along with an inefficiency result on the imperfect monitoring prisoner s dilemma.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Exact arbitrage, well-diversified portfolios and asset pricing in large markets

: In a model of a nancial market with an atomless continuum of assets, we give a precise and rigorous meaning to the intuitive idea of a \well-diversi ed" portfolio and to a notion of \exact arbitrage". We show this notion to be necessary and su cient for an APT pricing formula to hold, to be strictly weaker than the more conventional notion of \asymptotic arbitrage", and to have novel implications for the continuity of the cost functional as well as for various versions of APT asset pricing. We further justify the idealized measure-theoretic setting in terms of a pricing formula based on \essential" risk, one of the three components of a tri-variate decomposition of an asset's rate of return, and based on a speci c index portfolio constructed from endogenously extracted factors and factor loadings. Our choice of factors is also shown to satisfy an optimality property that the rst m factors always provide the best approximation. We illustrate how the concepts and results translate to markets with a large but nite number of assets, and relate to previous work.

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.