Flavio Cunha; James Heckman.May, 2007.The technology of skill formation,Report,ChicagoAmerican Economic Association,17

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The Technology of Skill Formation

Generalized Linear Models (2nd ed.)

This article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical Bayes viewpoint, particularly in the case of parametric prior distributions. Some successful applications of major importance are considered. Recent results concerning estimates of error and confidence intervals are described and illustrated with data.

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Parametric Empirical Bayes Inference: Theory and Applications

Nonlinear relationships are common in economic theory, and such relationships are also frequently tested empirically. We argue that the usual test of nonlinear relationships is flawed and derive the appropriate test for a U-shaped relationship. Our test gives the exact necessary and sufficient conditions for the test of a U shape in finite samples in a large class of models.

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With or Without U? The Appropriate Test for a U-Shaped Relationship*

A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

Statistical Size Distributions in Economics and Actuarial Sciences

In this paper we consider the issue of performing statistical inference for Lorenz curve orderings. This involves testing for an ordered relationship in a multivariate context and making comparisons among more than two population distributions. Our approach is to frame the hypotheses of interest as sets of linear inequality constraints on the vector of Lorenz curve ordinates, and apply order-restricted statistical inference to derive test statistics and their sampling distributions. We go on to relate our results to others which have appeared in recent literature, and use Monte Carlo analysis to highlight their respective properties and comparative performances. Finally, we discuss in general terms the issue and problems of framing hypotheses, and testing them, in the context of the study of income inequality, and suggest ways in which the distributional analyst could best proceed, illustrating with empiricalexamples.

http://www.vcharite.univ-mrs.fr/PP/lubrano/atelier/dardanoni.pdf

Inference for Lorenz curve orderings

For data in a two-way contingency table with ordered margins, we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities. This leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log-likelihood ratio tests. The usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases. In particular, for each of these three orderings we determine the transformation required to apply the estimation algorithm; we then consider testing the hypothesis that the rows are identically distributed against the alternative that they are stochastically ordered, as well as testing each stochastic order against an u...

https://www.jstor.org/stable/info/2669854

A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context

We extend Bergsma and Rudas (2002)'s hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continu- ation type which may be more suitable with ordinal data. We introduce a general definition of marginal interaction parameters and show that this parameterization constitutes a link function so that linear models defined by equality and inequality constraints may be fitted and tested by extending the methods of Colombi and Forcina (2001). Computation and asymptotic properties of maximum likelihood estimators are discussed, and the asymptotic distribution of the likelihood ratio test is derived.

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An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints

Given a set of discrete response variables, some of which are ordinal, and an arbitrary set of discrete explanatory variables, we propose a simple matrix formulation for parameterising the saturated model as in Glonek (1996). This is such that, within a hierarchical structure, marginal logits and log-odds ratios of various possible types, together with the remaining log-linear interactions of high order, may be modelled by equality and inequality constraints. Inequality constraints are particularly relevant for specifying models of positive association. Efficient algorithms are provided for computing maximum likelihood estimates under such constraints. The asymptotic distribution of the likelihood ratio test is derived and an extension of the usual analysis of deviance is outlined which incorporates inequality constraints.

Marginal regression models for the analysis of positive association of ordinal response variables

The aim of this study was to review the usefulness of clinical and instrumental evaluation in individuals with disorders of consciousness (DOC). Thirteen subjects with severe acquired brain injury (ABI) and a diagnosis of DOC were evaluated using the Coma Recovery Scale in its revised version (CRS-R) and a new global disability index, the Post-Coma Scale (PCS). These instruments were administered both by a neutral examiner (professional) and by a professional in the presence of a caregiver. All patients were also scored using the International Classification of Functioning, Disability and Health (ICF). A statistically significant correlation between CRS-R and PCS was demonstrated. However, there also emerged significant differences in responsiveness between professional versus caregiver+professional assessment using the two scales. The emotional stimulation provided by significant others (caregivers) during administration of DOC evaluation scales may improve the assessment of responsiveness.

Vegetative state, minimally conscious state, akinetic mutism and parkinsonism as a continuum of recovery from disorders of consciousness: An exploratory and preliminary study

Antonio Forcina

Papers

Inference for Lorenz curve orderings

A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context

An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints

Marginal regression models for the analysis of positive association of ordinal response variables

Vegetative state, minimally conscious state, akinetic mutism and parkinsonism as a continuum of recovery from disorders of consciousness: An exploratory and preliminary study