Abstract. We propose a computationally feasible way of deriving the identified set of parameter values in models with multiple equilibria, with particular emphasis on oligopoly entry models. This is achieved through an equivalence result between the existence of an equilibrium selection mechanism compatible with the observed data and a set of inequalities, and through an appeal to efficient linear programming techniques.
We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks, and signs, based on canonical transportation maps between a distribution of interest on IR d and a reference distribution on the d-dimensional unit ball. The new depth concept, called Monge-Kantorovich depth, specializes to halfspace depth for d = 1 and in the case of spherical distributions, but, for more general distributions, differs from the latter in the ability for its contours to account for non convex features of the distribution of interest. We propose empirical counterparts to the population versions of those Monge-Kantorovich depth contours, quantiles, ranks, signs, and vector quantiles and ranks, and show their consistency by establishing a uniform convergence property for empirical (forward and reverse) transport maps, which is the main theoretical result of this paper.
London School of EconomicsSemiparametric estimates of long memory seem useful in the analysis of long financial time series because they are consistent under much broader conditions than parametric estimates+ However, recent large sample theory for semiparametric estimates forbids conditional heteroskedasticity+ We show that a leading semiparametric estimate, the Gaussian or local Whittle one, can be consistent and have the same limiting distribution under conditional heteroskedasticity as under the conditional homoskedasticity assumed by Robinson~1995, Annals of Statistics 23, 1630-61!+ Indeed, noting that long memory has been observed in the squares of financial time series, we allow, under regularity conditions, for conditional heteroskedasticity of the general form introduced by Robinson~1991, Journal of Econometrics 47, 67-84!, which may include long memory behavior for the squares, such as the fractional noise and autoregressive fractionally integrated moving average form, and also standard short memory ARCH and GARCH specifications+
We consider partial identification of finite mixture models in the presence of an observable source of variation in the mixture weights that leaves component distributions unchanged, as is the case in large classes of econometric models. We first show that when the number J of component distributions is known a priori, the family of mixture models compatible with the data is a subset of a J(J − 1)dimensional space. When the outcome variable is continuous, this subset is defined by linear constraints, which we characterize exactly. Our identifying assumption has testable implications, which we spell out for J = 2. We also extend our results to the case when the analyst does not know the true number of component distributions and to models with discrete outcomes.
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