We estimate a health investment equation, derived from a health capital model that is an extension of the well-known Grossman model. Of particular interest is whether the health production function has constant returns to scale, as in the standard Grossman model, or decreasing returns to scale, as in the Ehrlich-Chuma model and extensions thereof. The model with decreasing returns to scale has a number of theoretically and empirically desirable characteristics that the constant returns model does not have. Although our empirical equation does not point-identify the decreasing returns to scale curvature parameter, it does allow us to test for constant versus decreasing returns to scale. The results are suggestive of decreasing returns and in line with prior estimates from the literature. But when we attempt to control for the endogeneity of health by using instrumental variables, the results become inconclusive. This brings into question the robustness of prior estimates in this literature.