Explaining the Stock Price-Inflation Puzzle : Inflation as a Signal for a Rare-Event

This paper explains the negative correlation between realized inflation and real stock prices under a rare-event framework. Agents make use of realized inflation rates to update their beliefs on the time-varying probability of a rare-event (stagflation or hyperinflation). A higher stagflation probability implies a higher correlation between inflation and real stock prices (dividend yield). I show that for a Bayesian belief-updating agent, the expectation on the Fed commitment to low inflation is key in order to explain the magnitude of the correlation. To test the model predictions, I perform a Markov Regime switching estimation and identify two statistically different regimes: one regime in which agents expect a strong commitment to low inflation by the Fed; and another regime in which they expect a low commitment to low inflation. Inflation correlates higher with stock prices in the second regime than in the first one. Finally, I show that the rare-event approach is more robust than the money illusion approach a-là Modigliani and Cohn (1979)