A rational expectations model in initial public offerings.

Abstract

This thesis constructs a rational expectations model in which an observation of "coarse" market signal introduces additional noise to a fully revealing rational expectations framework. The resulting equilibrium is similar to a noisy rational expectations model with supply noise. Grossman's paradox is avoided because the imperfect aggregation of market information by the market system induces investors to have incentives to collect private information. The new issue market is investigated as an example. The degree of subscription to a new issue works as a market signal. The magnitude of subscription is observed if the issue is oversubscribed; this is not observed if the issue is undersubscribed. The fact that the investors only know that the degree of subscription for the undersubscribed issue is less than or equal to unity adds noise to the system. It is shown that under fairly general conditions there exists a rational expectations equilibrium where the equilibrium is linear for a certain range of the market signal but is non-linear for the remaining range of the market signal. Thus, information about the market signal is not sufficient to infer the true value of the new issue. If the signal is exactly observed, the true value is correctly inferred; if it is observed as a range, the true value is not correctly inferred. This model has a general application to the market in which the observation of the market equilibrium price is restricted. Government interventions like price ceilings in the goods market and minimum wages in the labor market are examples of such restrictions. Under the price ceiling policy, for example, consumers observe the competitive equilibrium price when the ceiling is not binding but observe the ceiling price instead when the ceiling is binding. The latter signal is coarse in the sense that the observation of the ceiling price only indicates that the competitive equilibrium price is at least as high as the ceiling price. The major implication of the model, viz., that an undersubscribed issue experiences more ex post uncertainty than an oversubscribed issue is tested. Initial public offerings in the years 1975-84 are investigated. Three measures of ex post uncertainty are adopted: the time series variance of the portfolio daily returns, the error mean of squares of the simple regression based on the market model, and the error mean of squares of the regression incorporating three-month slope dummies. For each of the three measures, the volatility of the undersubscribed subgroup is significantly higher than that of the oversubscribed subgroup. The robustness of our empirical results suggests policy implications that requiring revelation of the degree of undersubscription may enhance the efficiency of the aftermarket.