# Economic theory as a guide for the specification and interpretation of empirical health production functions

*Working Papers.*

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We employ a model of utility maximization with health production to derive precise interpretations of estimated effects of observable inputs on health outcomes when some other inputs are not observed. We show that if omitted or unobserved inputs are not properly accounted for, then estimated marginal products of health inputs cannot be easily interpreted. Using a general theoretical model, we propose empirical specifcations to control for the omitted inputs. The resulting "effects" one can estimate using such specifcations do not correspond exactly to the marginal products of the observed inputs on health. One can, however, establish some likely bounds on the \true" marginal products of the observed inputs when one uses empirical specifcations compatible with economic theory. This bound is equivalent to the effect one can estimate with an experimentally assigned input. We also discuss approaches for obtaining more informative bounds if one believes that

particular separability assumptions in the utility function are reasonable and demonstrate their performance in a simulation exercise. We present empirical evidence demonstrating the issues raised in our theoretical analysis using data on children's growth from the Russian

Longitudinal Monitoring System of HSE (RLMS-HSE)

JOUR

Mityakov, Sergey

Mroz, Thomas

2013

Working Papers

2185