Proxy variables are frequently used in economics to control for unavailable variables in a linear regression setting. For example, AFQT scores have been used to control for human capital accumulation in measuring black-white wage differentials. This practice may bias the coefficient estimates for the correctly measured variables as well. This paper models proxy variables as a measurement error process and derives bounds for the coefficients on the correctly measured variables under a variety of assumptions. The results show that the coefficient on race in a linear regression is an overstatement of the actual black-white wage gap. Sensitivity analysis suggests that if human capital could be correctly measured it would be unlikely that the coefficient on black would be negative.