Rational and Near‐Rational Bubbles Without Drift

Abstract

This paper derives a general class of intrinsic rational bubble solutions in a standard Lucas-type asset pricing model. I show that the rational bubble component of the pricedividend ratio can evolve as a geometric random walk without drift. The volatility of bubble innovations depends exclusively on fundamentals. Starting from an arbitrarily small positive value, the rational bubble expands and contracts over time in an irregular, wholly endogenous fashion, always returning to the vicinity of the fundamental solution. I also examine a near-rational solution in which the representative agent does not construct separate forecasts for the fundamental and bubble components of the asset price. Rather, the agent constructs only a single forecast for the total asset price that is based on a geometric random walk without drift. The agent's forecast rule is parameterized to match the moments of observable data. In equilibrium, the actual law of motion for the price-dividend ratio is stationary, highly persistent, and nonlinear. The agent's forecast errors exhibit near-zero autocorrelation at all lags, making it di¢ cult for the agent to detect a misspeci…cation of the forecast rule. Unlike a rational bubble, the near-rational solution allows the asset price to occasionally dip below its fundamental value. Under mild risk aversion, the near-rational solution generates pronounced low-frequency swings in the price-dividend ratio, positive skewness, excess kurtosis, and time-varying volatility-all of which are present in long-run U.S. stock market data. An independent contribution of the paper is to demonstrate an approximate analytical solution for the fundamental asset price that employs a nonlinear change of variables.

House Price Dynamics: Fundamentals and Expectations

“…We emphasize that although we show that the near rational bubble model described in Lansing (2010) is consistent with some key characteristics of the housing market, we do not claim that the data is only consistent with this model. Other factors, alone or in conjunction with non fully rational expectations, might play a role in determining the evolution of house prices and price-rent series.…”

“…Then, in section 2.3 and 2.4 we will relax the assumption of rational expectations and consider two extrapolative expectations models developed by Lansing (2006Lansing ( , 2010 for the analysis of the stock market.…”

“…In particular we follow the approach developed in Lansing (2006Lansing ( , 2010 for the study of the stock market and assume that agents In the models that assume extrapolative behavior of the agents, expectations are related to past realizations through an extrapolation coe¢ cient which de…nes the weight agents put on past observations to generate their expectations. This expectation mechanism introduces persistence in the equilibrium price-rent ratio and ampli…es the ‡uctuations of the price-rent ratio around the mean.…”

“…Although the model can explain the sample average of the price-rent ratio, it does not generate the volatility and persistence observed in the data. Then, we consider an intrinsic bubble model and two models of extrapolative expectations developed by Lansing (2006Lansing ( , 2010 in applications to stock prices: one that features a constant extrapolation parameter and one in which the extrapolation coefficient depends on the dividend growth process. We show that these last two models are equally good at matching sample moments of the data.…”

House price dynamics: Fundamentals and expectations

“…Même si le modèle parvient à restituer la moyenne empirique du ratio, il ne génère pas la volatilité et la persistance observées dans les données. Les auteures considèrent ensuite un modèle de bulle intrinsèque ainsi que deux modèles dotés d'anticipations extrapolatives mis au point par Lansing (2006Lansing ( et 2010 …”