The author presents estimates of the union wage effect controlling for unmeasured individual effects, and subjects the conventional fixed-effects model to specification tests. For Panel Study of Income Dynamics men, the union wage effect is 5-8 percent after controlling for person effects, as opposed to 20 percent in cross-section. Omnibus tests based on an unrestricted reduced form and instrumental variables tests based on differencing are consistent with conventional models. Tests based on comparing those who enter and leave union coverage provide evidence against the usual model. The author finds evidence for interactions between union status and other variables even after controlling for person effects. Copyright 1991 by The Review of Economic Studies Limited.