Population aging, long-term care insurance, and economic growth: theoretical and empirical evidence from an OLG model and a quasi-natural experiment

Population aging poses a fundamental challenge to China’s long-run economic development. As a key institutional mechanism for insuring disability risk and strengthening the multi-tiered social security system, long-term care insurance (LTCI) warrants rigorous examination of its growth effects and transmission channels. This paper develops an overlapping-generations (OLG) model that incorporates disability risk and LTCI contribution rules, and derives qualitative predictions through steady-state comparative statics. Using panel data covering 48 prefecture-level cities from 2011 to 2019, we estimate treatment effects with the Callaway–Sant’Anna estimator for staggered adoption (CSDID), supplemented by two-way fixed-effects difference-in-differences (TWFE-DID), a Goodman–Bacon weight decomposition, and a Heckman two-stage procedure. Point estimates are positive in most specifications—the CSDID average treatment effect for the 2016 pilot cohort is 0.36 and the TWFE estimates range from 0.29 to 0.57—although the cohort-specific CSDID estimates are not uniformly positive (the 2012 Qingdao cohort point estimate is negative), and the principal CSDID estimates are statistically imprecise under the reported inference. Because conventional significance is attenuated under city-clustered and wild-cluster-bootstrap inference in this 48-city design, we interpret the evidence as suggestive of a positive policy effect that is concentrated in the short run. An entropy-weighted policy-intensity index suggests positive moderation, with the institutional effect estimated to turn positive only above intermediate intensity levels—a threshold pattern that is likewise suggestive rather than definitive. Intermediate-outcome regressions are consistent with transmission through financial deepening and innovation investment, although they do not by themselves identify full causal mediation. Formal interaction tests indicate that the growth-enabling effect is significantly stronger under universal coverage. The OLG framework characterizes long-run steady-state relationships, whereas the 2011–2019 window empirically captures effects concentrated around implementation and the short run, so the long-run empirical implications remain suggestive. The study extends the economic analysis of LTCI to the macro-productivity dimension and informs the differentiated nationwide expansion of the scheme.