We study how learning from experience affects stock market participation in overlapping generations. During episodes of market exuberance and low risk premiums, the unexperienced enter the market often with high leverage exposing them to the risk of abruptly losing wealth, with the consequence being exit. On the contrary, experienced cohorts typically remain in the market despite pessimism. These patterns generate procyclical participation and feedback effects between participation and learning, amplifying fluctuations in interest rates and market volatility and lead to large welfare losses. Importantly, the model reproduces empirical evidence on participation, entry and exit from multiple countries.

This paper studies the implications of a simple theorem, which states that for arbitrary underlying dynamics and diffusive information flows, the cumulants of Bayesian beliefs have a recursive structure: the sensitivity of the mean to news is proportional to the variance; the sensitivity of the nth cumulant to news is proportional to the n+1th. The specific application is the US aggregate stock market, because it has a long time series of high-frequency data along with option-implied higher moments. The model qualitatively and quantitatively generates a range of observed features of the data: negative skewness and positive excess kurtosis in stock returns, positive skewness and kurtosis and long memory in volatility, a negative relationship between returns and volatility changes, and predictable variation in the strength of that relationship. Those results have a simple necessary and sufficient condition, which is model-free: beliefs must be negatively skewed in all states of the world.

We identify desirable/undesirable inflation outcomes under subjective beliefs by comparing survey-based and risk-adjusted distributions of inflation. Intuitively, investors dislike inflation at both extremes, preferring a range in the middle. This "good inflation" region, which investors associate with lower-than-average marginal utility, varies substantially over time in position and width, revealing time-varying preferences across inflation ranges. Different ranges contribute to the inflation risk premium with mixed signs, offsetting each other and often masking important insights into the pricing of inflation risk. We rationalize these empirical patterns using a model where investors learn and update beliefs about hidden deflationary and inflationary recession states.