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This article presents a large class of probability densities f(x, θ) for which, with positive probability, the maximum likelihood estimator based on a sample of size 2 is non unique, and the possible values of do not form an interval. Such a density f(x, θ) can even be chosen to be unimodal, and one such example is the Cauchy density with a location parameter. A discrete version of the argument gives examples in which the nonuniqueness of the maximum likelihood estimator persists for samples of arbitrary size.     

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Selection processes that are inherent in litigation complicate policy-oriented research of medical malpractice tort reforms. In regard to their deterrent impact, the range of potential inferences based on analyses of claim frequency is limited because plaintiffs only file a subset of potential claims. In regard to their impact on litigation costs, researchers often analyze data on claim disposition, but it is difficult to determine whether effects attributed to tort reforms reflect changes in litigant behavior or their influence on the selection of claims. In this article, we evaluate these problems and report results of our study of the effects of medical malpractice reforms on claim disposition.     

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ABSTRACT

In the class of stochastic volatility (SV) models, leverage effects are typically specified through the direct correlation between the innovations in both returns and volatility, resulting in the dynamic leverage (DL) model. Recently, two asymmetric SV models based on threshold effects have been proposed in the literature. As such models consider only the sign of the previous return and neglect its magnitude, this paper proposes a dynamic asymmetric leverage (DAL) model that accommodates the direct correlation as well as the sign and magnitude of the threshold effects. A special case of the DAL model with zero direct correlation between the innovations is the asymmetric leverage (AL) model. The dynamic asymmetric leverage models are estimated by the Monte Carlo likelihood (MCL) method. Monte Carlo experiments are presented to examine the finite sample properties of the estimator. For a sample size of T = 2000 with 500 replications, the sample means, standard deviations, and root mean squared errors of the MCL estimators indicate only a small finite sample bias. The empirical estimates for S&;P 500 and TOPIX financial returns, and USD/AUD and YEN/USD exchange rates, indicate that the DAL class, including the DL and AL models, is generally superior to threshold SV models with respect to AIC and BIC, with AL typically providing the best fit to the data.     

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Thanks and congratulations to all of the discussants for covering a wide array of important topics. Since space does not permit attention to all of the points that have been raise, this reply will concentrate on trying to dispell confusion on important matters that might remain.     

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Beginning with the 1990 Census and the January 1992 Current Population Survey (CPS), the Bureau of the Census changed the emphasis of its educational-attainment question from years of education to degree receipt. Using a matched sample from the 1991 and 1992 March CPS, this article addresses how to reconcile the old and new questions. The effects of those methods on the estimated return(s) to education are then examined. Both the estimated linear return and the estimated college–high-school wage differential are slightly larger using information from the new question.     

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Statistics and Computing -     

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Many of the recently developed alternative ecocometric approaches to the construction and estimation of life-cycle consistent models using individual data can be viewed as alternative choices for conditioning variables that summarise past decisions and future anticipations. By ingenious choice of this conditioning variable and by exploitation of the duality relationships between the alternative specifications, many currently available micro-data sets can be used for the estimation of life-cycle consistent models. In reviewing the alternative approaches their stochastic properties and implicit preference restrictions are highlighted. Indeed, empirical specifications that are parameterised in a form of direct theoretical interest often can be shown to be unnecessarily restrictive while dual representations may provide more flexible econometric models. These results indicate the particular advantages of different types of data in retrieving life-cycle consistent preference parameters and the appropriate, most flexible, econometric approach for each type of data. A methodology for relaxing the intertemporal separability assumption is developed and the advantages and disadvantages of alternative approaches in this framework are considered.