Stochastic monotonicity in intergenerational mobility tables
SUMMARY The aim of this paper is to test for stochastic monotonicity in intergenerational socio-economic mobility tables. In other words, we question whether having a parent from a high socio-economic status is never worse than having one with a lower status. Using existing inferential procedures for testing unconditional stochastic monotonicity, we first test a set of 149 intergenerational mobility tables in 35 different countries and find that monotonicity cannot be rejected in hardly any table. In addition, we propose new testing procedures for testing conditional stochastic monotonicity and investigate whether monotonicity still holds after conditioning on a number of covariates such as…
Regression models for multivariate ordered responses via the Plackett distribution
AbstractWe investigate the properties of a class of discrete multivariate distributions whose univariate marginals have ordered categories, all the bivariate marginals, like in the Plackett distribution, have log-odds ratios which do not depend on cut points and all higher-order interactions are constrained to 0. We show that this class of distributions may be interpreted as a discretized version of a multivariate continuous distribution having univariate logistic marginals. Convenient features of this class relative to the class of ordered probit models (the discretized version of the multivariate normal) are highlighted. Relevant properties of this distribution like quadratic log-linear e…
A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context
Abstract 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. I…
Inference for Lorenz curve orderings
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 gener…
Testing for Asymmetric Information in Insurance Markets: A Multivariate Ordered Regression Approach
The positive correlation (PC) test is the standard procedure used in the empirical literature to detect the existence of asymmetric information in insurance markets. This article describes a new tool to implement an extension of the PC test based on a new family of regression models, the multivariate ordered logit, designed to study how the joint distribution of two or more ordered response variables depends on exogenous covariates. We present an application of our proposed extension of the PC test to the Medigap health insurance market in the United States. Results reveal that the risk–coverage association is not homogeneous across coverage and risk categories, and depends on individual so…