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.     

The asymptotic codifference and covariation of log-fractional stable noise

Many econometric quantities such as long-term risk can be modeled by Pareto-like distributions and may also display long-range dependence. If Pareto is replaced by Gaussian, then one can consider fractional Brownian motion whose increments, called fractional Gaussian noise, exhibit long-range dependence. There are many extensions of that process in the infinite variance stable case. Log-fractional stable noise (log-FSN) is a particularly interesting one. It is a stationary mean-zero stable process with infinite variance, parametrized by a tail index α$\alpha$ between 1 and 2, and hence with heavy tails. The lower the value of α$\alpha$, the heavier the tail of the marginal distributions. The fact that α$\alpha$ is less than 2 renders the variance infinite. Thus dependence between past and future cannot be measured using the correlation. There are other dependence measures that one can use, for instance the “codifference” or the “covariation”. Since log-FSN is a moving average and hence “mixing”, these dependence measures converge to zero as the lags between past and future become very large. The codifference, in particular, decreases to zero like a power function as the lag goes to infinity. Two parameters play an important role: (a) the value of the exponent, which depends on α$\alpha$ and measures the speed of the decay; (b) a multiplicative constant of asymptoticity c$c$ which depends also on α$\alpha$. In this paper, it is shown that for symmetric α$\alpha$-stable log-FSN, the constant c$c$ is positive and that the rate of decay of the codifference is such that one has long-range dependence. It is also proved that the same conclusion holds for the second measure of dependence, the covariation, which converges to zero with the same intensity and with a constant of asymptoticity which is positive as well.     

Informativeness of experiments for meu

The celebrated Blackwell’s theorem demonstrates the equivalence of a notion of statistical informativeness and economic valuableness for the class of preferences that are represented by the subjective expected utility. This note shows that this equivalence holds for a larger class of preferences, namely maxmin$maxmin$ expected utility.     

Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification

Since the 1990s, the Akaike Information Criterion (AIC) and its various modifications/extensions, including BIC, have found wide applicability in econometrics as objective procedures that can be used to select parsimonious statistical models. The aim of this paper is to argue that these model selection procedures invariably give rise to unreliable inferences, primarily because their choice within a prespecified family of models (a) assumes away the problem of model validation, and (b) ignores the relevant error probabilities. This paper argues for a return to the original statistical model specification problem, as envisaged by Fisher (1922), where the task is understood as one of selecting a statistical model in such a way as to render the particular data a truly typical realization of the stochastic process specified by the model in question. The key to addressing this problem is to replace trading goodness-of-fit against parsimony with statistical adequacy as the sole criterion for when a fitted model accounts for the regularities in the data.     

Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects

This paper develops an asymptotic theory for test statistics in linear panel models that are robust to heteroskedasticity, autocorrelation and/or spatial correlation. Two classes of standard errors are analyzed. Both are based on nonparametric heteroskedasticity autocorrelation (HAC) covariance matrix estimators. The first class is based on averages of HAC estimators across individuals in the cross-section, i.e. “averages of HACs”. This class includes the well known cluster standard errors analyzed by Arellano (1987) as a special case. The second class is based on the HAC of cross-section averages and was proposed by Driscoll and Kraay (1998). The ”HAC of averages” standard errors are robust to heteroskedasticity, serial correlation and spatial correlation but weak dependence in the time dimension is required. The “averages of HACs” standard errors are robust to heteroskedasticity and serial correlation including the nonstationary case but they are not valid in the presence of spatial correlation. The main contribution of the paper is to develop a fixed-b asymptotic theory for statistics based on both classes of standard errors in models with individual and possibly time fixed-effects dummy variables. The asymptotics is carried out for large time sample sizes for both fixed and large cross-section sample sizes. Extensive simulations show that the fixed-b approximation is usually much better than the traditional normal or chi-square approximation especially for the Driscoll-Kraay standard errors. The use of fixed-b critical values will lead to more reliable inference in practice especially for tests of joint hypotheses.