Media Briefings

'Near-Rational' Bubbles: Making Sense Of Repeated Booms And Busts In Asset Prices

  • Published Date: December 2010

If economic policy-makers are to take deliberate steps to prevent or deflate asset price bubbles, they need a realistic model of a bubble. In a study published in the December 2010 issue of the Economic Journal, Kevin Lansing contributes to this effort by developing a model that matches many quantitative features of long-run US stock market data.

In Lansing’s ‘near-rational’ bubble model, investors fit a simple extrapolative forecast rule to observable stock market data. The resulting price-dividend ratio exhibits pronounced upward and downward swings, giving rise to the excess volatility that has been all too common in real world asset markets.

‘Nowhere does history indulge in repetitions so often or so uniformly as in Wall Street,’ observed legendary stock market speculator Jesse Livermore way back in 1923.

History has proven him right. The dramatic run-up and crash of the US stock market in the late 1920s was followed decades later by twin bubbles and crashes in Japanese real estate and stocks during the late 1980s and early 1990s.

This episode was later followed by the US technology stock mania of the late 1990s, which ended abruptly in March 2000. Most recently, a global housing bubble during the mid-2000s nearly brought down the world’s financial system when, like all preceding bubbles, it ultimately burst.

An important unsettled policy question in economics is whether policy-makers should take deliberate steps to prevent or deflate asset price bubbles. Progress on this question requires a realistic model of a bubble.

Despite the long history of speculative bubbles in financial markets, the economics profession has generally preferred models where investors set prices on stocks according to fundamentals, as measured by the discounted stream of expected future dividends or cash flows.

Bubble models are often dismissed because of their unrealistic long-run predictions. For example, so-called ‘rational bubble’ models say that investors are fully cognisant of the fundamental stock price, but nevertheless they may be willing to pay more than this amount. This can occur if expectations of future price appreciation are large enough to satisfy the rational investors’ required rate of return.

In a rational bubble model, an asset is valued not for its cash flows, but rather for its potential to deliver capital gain – a feature that seems to fit the prevailing psychology during historical bubble episodes.

But to sustain a rational bubble, the stock price must grow faster than dividends (or cash flows) in perpetuity – that is, the price-dividend ratio must exhibit ‘positive drift’. But this is not what is seen in the data. Instead, the price-dividend ratio in the real world exhibits irregularly spaced run-ups and crashes.

This study develops a model of stock price bubbles that is exempt from the typical criticisms and is successful at matching numerous quantitative features of long-run US stock market data. The framework is a standard asset pricing model where a representative investor can purchase shares of stock to transfer wealth from one period to another.

The study shows that the standard model admits rational bubble solutions where the average drift rate (or growth rate) of the bubble is zero in the long run. In these solutions, the short-term prospects for capital gain derive solely from the high volatility of the bubble component in stock prices.

Starting from an arbitrarily small value, a driftless rational bubble exhibits irregularly spaced episodes of rapid expansions and contractions, which can be viewed as stylised bubbles and crashes. Stock return volatility increases dramatically during these episodes.

Rational bubble models assume that investors always know the size of the bubble – to the point of constructing separate forecasts for the fundamental and bubble components of the stock price. Real world investors may be inclined to construct only a single forecast that attempts to predict the movement of the total stock price (fundamental plus bubble).

Adopting this set-up, the study goes on to develop a ‘near-rational’ bubble model in which investors fit a simple extrapolative forecast rule to observable stock market data. The resulting price-dividend ratio exhibits pronounced upward and downward swings, giving rise to excess volatility, but the ratio always returns to the vicinity of a long-run average.

The near-rational solution does a good job of matching many quantitative features of US stock market data and allows the stock price occasionally to dip below the fundamental price.

ENDS

Notes for editors: ‘Rational and Near-Rational Bubbles without Drift’ by Kevin J Lansing is published in the December 2010 issue of the Economic Journal.

Kevin Lansing is a senior economist at the Federal Reserve Bank of San Francisco (homepage: http://www.frbsf.org/economics/economists/staff.php?klansing).

For further information: contact Kevin Lansing on +1-415-974-2393 (email: kevin.j.lansing@sf.frb.org); or Romesh Vaitilingam on +44-7768-661095 (email: romesh@vaitilingam.com).