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Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?

Econometrica 2002 70(1), 285-329
This paper analyzes the complexity of the contraction fixed point problem: compute an e-approximation to the fixed point V * = Γ(V * ) of a contraction mapping r that maps a Banach space B d of continuous functions of d variables into itself. We focus on quasi linear contractions where Γ is a nonlinear functional of a finite number of conditional expectation operators. This class includes contractive Fredholm integral equations that arise in asset pricing applications and the contractive Bellman equation from dynamic programming. In the absence of further restrictions on the domain of Γ, the quasi linear fixed point problem is subject to the curse of dimensionality, i.e., in the worst case the minimal number of function evaluations and arithmetic operations required to compute an e-approximation to a fixed point V * e B d increases exponentially in d. We show that the curse of dimensionality disappears if the domain of Γ has additional special structure. We identify a particular type of special structure for which the problem is strongly tractable even in the worst case, i.e., the number of function evaluations and arithmetic operations needed to compute an e-approximation of V * is bounded by Ce -p where C and p are constants independent of d. We present examples of economic problems that have this type of special structure including a class of rational expectations asset pricing problems for which the optimal exponent p = 1 is nearly achieved.

The ultimate ownership of Western European corporations

Journal of Financial Economics 2002 65(3), 365-395
We analyze the ultimate ownership and control of 5,232 corporations in 13 Western European countries. Typically firms are widely held (36.93%) or family controlled (44.29%). Widely held firms are more important in the UK and Ireland, family controlled firms in continental Europe. Financial and large firms are more likely widely held, while non-financial and small firms are more likely family controlled. State control is important for larger firms in certain countries. Dual class shares and pyramids enhance the control of the largest shareholders, but overall there are significant discrepancies between ownership and control in only a few countries.

A Commodity Price Process with a Unique Continuous Invariant Distribution Having Infinite Mean

Econometrica 2002 70(3), 1213-1219 open access
Americanae nace como un proyecto conjunto que surge dentro de la Red Europea de Información y Documentación sobre América Latina (REDIAL), y que ha afrontado la Biblioteca de la Agencia Española de Cooperación Internacional para el Desarrollo (AECID). Esta nueva biblioteca virtual hace más accesibles los libros digitales de tema americanista a los investigadores y usuarios interesados de cualquier parte del mundo.

Real Investment Implications of Employee Stock Option Exercises

Journal of Accounting Research 2002 40(2), 359-393
This paper examines a real cost of awarding employee stock options. Based on the observation that managers are extremely concerned about earnings‐per‐share dilution in equity related compensation, we predict and find that firms experiencing significant employee stock option (ESO) exercises shift resources away from real investments towards the repurchase of their own stocks. We further find weak evidence of a decline in subsequent firm performance (as measured by return on assets) for several years following the cut in discretionary investments as a result of stock option exercises, though this result is sensitive to the metric used to measure performance. Collectively, our findings indicate that ESO exercises potentially impose a real cost on the firm in terms of foregone investment opportunities.

Sidelined Investors, Trading-Generated News, and Security Returns

Review of Financial Studies 2002 15(2), 615-648
This article studies information blockages and the asymmetric release of information in a security market with fixed setup costs of trading. In this setting, “sidelined” investors may delay trading until price movements validate their private signals. Trading thereby internally generates the arrival of further news to the market. This leads to (1) negative skewness following price run-ups and positive skewness following price rundowns (even though the model is ex ante symmetric), (2) a lack of correspondence between large price changes and the arrival of external information, and (3) increases in volatility following large price changes.

On the Global Convergence of Stochastic Fictitious Play

Econometrica 2002 70(6), 2265-2294
We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities.