Intrinsic Bubbles in Stock Prices Under Persistent Dividend Growth Rates

Abstract

We extend the constant discount factor model with intrinsic bubbles developed in Froot and Obstfeld (1991) to account for serial correlation in dividend growth rates. We derive an exact analytical expression for both the present value stock price and an intrinsic bubble component when dividend growth rates evolve as a Gaussian first-order autoregressive process. We estimate the model with two sets of annual U.S. stock prices and dividends data, namely the DJIA and the S&P 500 series, over the last century. Hypotheses tests reject an AR(0) process for dividend growth rates in favor of an AR(1) process for both data series. Likelihood ratio tests also favor the AR(1)-based model developed here for price-dividends ratios to the AR(0)-based model considered in Froot and Obstfeld (1991). Hypotheses tests also reject the absence of a bubble component in both series. This inference is robust to whether or not the parameters governing the intrinsic bubbles process are restricted to values implied by our model or freely estimated. Incorporating the bubble component into our model provides a significant improvement in fit to observed P/D ratios and stock prices as compared to the present value stock prices alone.