A method is developed for imputing missing values when the probability of response depends upon the variable being imputed. The missing data problem is viewed as one of parameter estimation in a regression model with stochastic censoring of the dependent variable. The prediction approach to imputation is used to solve this estimation problem. Wages and salaries are imputed to non-respondents in the Current Population Survey and the results are compared to the nonrespondents' IRS wage and salary data. The stochastic censoring approach gives improved results relative to a prediction approach that ignores the response mechanism.