Sports facilities as substitutes for exercise-induced well-being: Evidence from four-wave CFPS panel data

Background The relationship between sports participation and psychological well-being is well-documented, yet empirical evidence regarding the moderating role of community sports facilities remains inconclusive. This study tests whether facilities amplify or attenuate the well-being returns to exercise, using four-wave panel data from China (CFPS 2014, 2018, 2020, 2022). Methods Linear regression models with individual fixed effects were constructed using China Family Panel Studies data (CFPS 2014, 2018, 2020, and 2022; the 2016 wave was excluded because its happiness item reached only 2.5% of adults). The analytical sample comprised 71,326 observations from 23,818 individuals. Self-rated happiness (0−10 scale) was regressed on binary exercise participation, community sports facility count (0−5+), and their interaction, controlling for age and log household income. Robustness was tested via instrumental variable estimation (community mean exercise rate) and propensity score matching. Results Exercise positively predicted happiness (β = +0.074, p < 0.001) in the baseline fixed-effects model. The exercise × facility interaction was directionally consistent with the substitution hypothesis but not statistically significant (β = −0.022, p = 0.075). Marginal exercise effects declined from +0.095 in zero-facility communities (p < 0.001) to non-significance where three or more facility types were available. Instrumental variable estimation results (first-stage F = 3231.25; second-stage β = −0.158, p = 0.117). The IV estimate did not reach statistical significance, providing limited evidence on treatment effect heterogeneity. Four-wave balanced panel estimates confirmed the baseline finding (β = +0.074, p < 0.01). CES-D mediation accounted for only approximately 4.6% of the total effect. Conclusions Exercise benefits subjective well-being most where community sports facilities are least available—a directionally consistent substitution pattern. Facility investment may yield greater marginal returns when targeted at underserved communities.