Paper: A Simple Model of Bubbles and Crashes
This paper generates bubbles and crashes in a simple linear asset pricing model with adaptive learning. The existence of recurrent bubbles in a model with adaptive learning has been an open question in macroeconomics. Our central insight is that in an environment in which traders are risk averse and boundedly rational, in the sense that they know the reduced form of the actual law of motion governing prices but not the parameters, then they must forecast both the conditional mean and the conditional variance of stock returns.
We show that, when agents adopt constant-gain econometric learning, the qualitative nature of the dynamics can generate frequent deviations from the fundamentals solution taking the form of bubbles and crashes.
We identify two roles for real-time learning of risk.
First, occasional shocks can lead agents to revise their estimates of risk in dramatic fashion. A sudden decrease in the estimated risk of a stock can propel the system away from the efficient-markets fundamentals equilibrium and into a bubble.
Second, along a bubble path, risk estimates will increase until eventually the perceived risk is so high that asset demand will collapse and stock prices will crash. Thus, risk in an adaptive learning setting plays a central role in triggering and collapsing asset price bubbles. These results are intuitive and provide insights into the role adaptive learning and bounded rationality play in large swings in asset prices.
Learning about Risk and Return: A Simple Model of Bubbles and Crashes
William A. Branch and George W. Evans