The paper develops a model of bubbles that can be taken to the data and explain the behavior of asset prices and their statistics. We depart from the rational expectations framework and assume that investors are only boundedly rational. They observe the price process, but do not fully understand how its volatility and expected returns are determined in equilibrium. Investors learn about the market by looking at past prices. When they observe unexpectedly high returns, they infer that the asset must currently have a high Sharpe ratio, and therefore, allocate a higher share of their wealth to the asset, further increasing the asset price. The interaction of this feedback effect with investors’ wealth effect determines the price dynamics and evolution of investors’ beliefs in the model. We fit the model to cryptocurrency markets and show that it can successfully explain many empirical facts in these markets.
