Stochastic monotonicity in intergenerational mobility tables

Abstract

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. We then propose new testing procedures for testing conditional stochastic monotonicity, and investigate how a number of covariates such as education, cognitive and non-cognitive skills can be used to investigate whether monotonicity still holds after conditioning on these variables. Based on the NCDS cohort data from the UK, our results provide evidence that monotonicity holds even conditionally. Moreover, we do not find large differences in our results when comparing social class and wage class mobility.

Distribution-free tests of stochastic monotonicity

“…stochastic monotonicity of the distribution of Y given X . Recently, Dardanoni et al (2012) has considered the same testing problem using a different data set.…”

“…having a parent from a high social-economic status is never worse than having one with a lower status. This testing problem has been considered by LLW and Dardanoni et al (2012) using different data sets. Many theories in finance also imply monotonic patterns in expected returns and other financial variables, see e.g.…”

Measurement error and rank correlations

“…This result is in line with Proposition 2.3, as stochastic monotonicityin this context, that the conditional distribution function of child income given parent income is increasing in parent income -is likely to hold in intergenerational relationships. Dardanoni, Fiorini, and Forcina (2012) test 149 tables of intergenerational class mobility covering 35 countries, and find that stochastic monotonicity can be rejected in only four cases. Delgado and Escanciano (2012) propose a distribution-free test of stochastic monotonicity, and fail to reject the null hypothesis of stochastic monotonicity in the association between child and parent income in the Panel Study of Income Dynamics.…”

Testing for Asymmetric Information in Insurance Markets: A Multivariate Ordered Regression Approach

“…This defines a multinomial likelihood conditional on covariates that may be maximized by the regression algorithm (see Evans and Forcina, ); essentially, at each step, the algorithm maximizes a quadratic approximation of the log‐likelihood under a log‐linear approximation of the constraints implied by the model. The algorithm is an extension of the one formulated by Aitchison and Silvey () and it has also been used by Dardanoni, Fiorini, and Forcina () to model the joint distribution of father and son social class conditional on individual covariates.…”