Alternative methods for estimating systems of (health) equations

This paper considers the simultaneous explanation of mortality risk, health and lifestyles, using a reduced-form system of equations in which the multivariate distribution is defined by the copula. A copula approximation of the joint distribution allows one to avoid usually implicit distributional assumptions, allowing potentially more robust and efficient estimates to be retrieved. By applying the theory of inference functions the parameters of each lifestyle, health and mortality equation can be estimated separately to the parameters of association found in their joint distribution, simplifying analysis considerably. The use of copulas also enables estimation of skewed multivariate distributions for the latent variables in a multivariate model of discrete response variables. This flexibility provides more precise estimates with more appropriate distributional assumptions, but presents explicit trade-offs during analysis. Information that can be retrieved concerning distributional assumptions, skewness and tail dependence require prioritisation such that different needs could generate a different ’best’ model even for the same data.