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.