We use the longitudinal structure of earnings of trainees and a comparison group to estimate the effectiveness of training for participants in the 1976 CETA programs. We fit a components-of-variance model to earnings of the comparison group and use a simple model of program participation to predict the earnings histories of the trainees. These predictions provide an estimate of the effect of training and an overidentification test of the model. Our program estimates are very sensitive to the model of participation (ranging from 200 to 2000), and we conclude that randomized clinical trials are necessary to reliably determine program effects.