Does sport affect health and well-being or is it the other way around? A note on reverse-causality in empirical applications

Estimating the causal impact of sport or physical activity on health and well-being is an issue of great relevance in the sport and health literature. The increasing availability of individual level data has encouraged this interest. However, this analysis requires dealing with two types of simultaneity problem: (1) between exercise and response variables; and (2) across the different response variables. This note discusses how the previous literature has dealt with these two questions with particular attention paid to the use of seemingly aseptic econometric models proposed by some recent empirical papers. Regardless of the approach, identification necessarily requires the use of untestable hypotheses. We provide some recommendations based on analyzing the robustness of the estimation results to changes in the adopted identification assumptions.