Abstract Background We analyze the effects of the Mexican universal health insurance program, Seguro Popular, on key variables associated with the provision of healthcare services. Given that the program was introduced gradually over a period that lasted more than a decade, the dynamics of the roll-out of the program and its reaction to the expansion of healthcare services it caused should be accounted for when evaluating the program. Methods We present a new semiparametric procedure to analyze time-varying continuous interventions. This is accomplished by bringing together the literatures on continuous and on dynamic treatments. Our approach allows the researcher to estimate mean and quantile dose-response functions by applying local regression methods to appropriately weighted samples that control for time-dependent confounding. Results Using administrative data, we show compelling evidence that Seguro Popular has incremented the human and physical resources available for healthcare services over the period 2001–2013. Moreover, we show that these effects have been heterogeneously distributed. Conclusions The program has proven most helpful in less vulnerable territories, leaving behind those in greater need.