We develop a stochastic overlapping-generations model with heterogeneous beliefs on the degree of inflation protection that can be provided by markets versus the monetary authority. A distinct feature is that it incorporates adaptive learning from inflation history and imperfect empathy in the cultural transmission of individual beliefs, allowing social beliefs to evolve endogenously. Analytical results on endogenous inflation beliefs and socially-optimal inflation are derived first in a within-generation voting equilibrium that defines a particular degree of inflation aversion of a society's monetary institution. Then, the intergenerational dynamics of inflation and inflation beliefs are analyzed, providing insights into the long-run evolution of population types and social institutions. The framework allows exploring the interactions of three mechanisms: the persistence of inflation, the degree of inflation aversion of the central bank and the recurrent irregular cycles of agent type proportions (and subsequent majority switches). It is thus shown how the endogenous transmission of inflation beliefs and monetary institutions in a stochastic economic environment can be understood as a process of intergenerational learning from history, combined with a political economy mechanism that amends legislation, and a socialization process that transmits experienced knowledge.