Using copulas to estimate reduced-form systems of equations

This paper introduces a new approach to measuring the association between health and socioeconomic status. Measuring inequalities in health is difficult when health is measured qualitatively, specifically on an ordinal scale. This paper demonstrates a rank-based dependence measure - the copula - that is invariant to both the scale and any monotonic transformations of its dimensions. Accordingly, the copula measure of association between health and income is robust under different cardinal scales for health as well as different income distributions, and can be used for ordering countries. The copula is also used to generate contingency tables of joint probability, which illustrate how this ordering can be due to polarity in the distributions of health and income, as well as stronger association between the distributions of health and income.