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.

Earnings nonresponse in the Current Population Survey is roughly 30% in the monthly surveys and 20% in the March survey. If nonresponse is ignorable, unbiased estimates can be achieved by omitting nonrespondents. Little is known about whether CPS nonresponse is ignorable. Using sample frame measures to identify selection, we find clear-cut evidence among men but limited evidence among women for negative selection into response. Wage equation slope coefficients are affected little by selection, but because of intercept shifts, wages for men and, to a lesser extent, women are understated, as are gender gaps. Selection is least severe among household heads.