Wage Gap Estimation with Proxies and Nonresponse

Earnings nonresponse in the Current Population Survey (CPS) is about 30% in the monthly surveys and 20% in the annual March surveys. Half of CPS earnings records rely on “proxy” respondents, among whom nonresponse is particularly high. Even if nonresponse is random, severe bias attaches to wage equation coefficient estimates on non-match (and some imperfectly matched) imputation attributes. If nonresponse is ignorable (i.e., conditional missing at random), unbiased estimates can be achieved by omitting imputed earners. In this paper, we use selection models and longitudinal analysis to examine whether CPS nonresponse is ignorable and how proxy responses affect reported earnings. Based on reasonable instruments to identify selection, we conclude there is negative selection into response for men and, to a far lesser extent, women. 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 wage gaps. Longitudinal results reinforce the qualitative conclusion that imputation understates earnings, but gender differences are less clear-cut. Cross-sectional estimates of proxy effects on reported earnings suggest large differences in the effects of spouse and non-spouse proxies. These results are driven by heterogeneity, with panel analysis suggesting that both spouse and non-spouse proxy respondents report about 2% less than do self respondents. For most wage equation analyses, response bias and proxy reports are of second order importance and the simple exclusion of imputed earners provides a reasonable first-order approach.