The costs of shortages and rationing are not captured by standard consumer price indices. Thus the change in real GDP per capita is an overestimate of welfare losses in transition economics. In this study virtual prices are used to calculate new cost-of-living indices (CLIs). The results for Polant show that from 1987 to 1992 the CLI ignoring the rationing effects is biased upward from 1.53 to 3.71 percentage points per year. Compared to the estimates of welfare loss that neglect the rationing effects during the prereform period, the estimated welfare losses that reflect the rationing are reduced by 50% using Hausman' virtual prices and by 75% using external proxy virtual prices.

A model that includes bounded price variation and rational expectations by producers is estimated for the U.S. corn market. The resulting model specification is highly nonlinear though, since the probability of market equilibrium must be determined endogenously. Unlike previous research, the cross-equation restrictions implied by the rational expectations hypothesis are incorporated in the bounded prices model by using Fair and Taylor's (1983) procedure for obtaining maximum likelihood estimates of nonlinear rational expectations models. The resulting model is compared against a standard equilibrium model with naive expectations. The results show the bounded prices model is a superior specification.