Addressing Potential Concerns with Cost of Living Measures

In Column 4, we add to the sample 40 women without observed wages whose spousal earnings fall between the 75 th and 89 th percentiles in the distribution of earn- ings. We continue to fi nd a positive and statistically signifi cant black wage premium. Thus, we conclude that the black- wage premiums documented in the prior literature remain after accounting for selection. We now examine whether the estimated pre- mium is robust to including two important omitted variables: cost of living and years of education. Subsequent rows of Table 3 present wage gap estimates that also control for the cost of living in an area and a respondent’s years of education. In Table 1, we showed that blacks live in CZs characterized by higher cost of living, whether we consider mean housing rents or higher wages paid to the least mobile occupations. We now present estimates that control for either of these two measures of cost of living. This is similar to the approach that DuMond, Hirsch, and Macpherson 1999 took for individuals residing in a MSACMSA. In Panel 2a of Table 3, we add a control for the average monthly rent in the CZ where the respondent lives. We fi nd that the black wage pre- mium estimate falls substantially in all specifi cations Columns 1–4. As Lang and Manove 2011 show, relative wages of black workers are overstated when we control for AFQT score but not years of education. In the third results row of Table 3, we control for years of education in addition to local costs of living. The additional control for education completely erases the estimated black wage premium. For the OLS results in Column 1, the coeffi cient on black turns slightly negative a wage penalty, although the conditional racial wage gap is essentially zero. The same result holds in our median regression estimates that account for selection in Columns 3 and 4: Controls for cost of living and education in addition to quadratics in age and AFQT score yield no evidence of a black wage premium. We note that the 95 percent confi dence intervals for the conditional wage gap are somewhat large, and we are unable to reject substantial wage premiums as high as 0.087, in Column 2 or wage penalties as low as –0.089, in Column 4. Nevertheless, these specifi cations show clearly that the very large black wage premiums estimated in prior studies are not at all robust to reasonable controls for cost of living and education. In Panels 3a and 3b of Table 3, we show that results are similar when we instead control for cost of living with a measure of average wages in “low- mobility” occupa- tions. Differential cost of living for black and white women explains away a large share though not all of the estimated black wage premium. When we also control for a respondent’s years of education, we again fi nd no evidence of a wage premium. 21

A. Addressing Potential Concerns with Cost of Living Measures

A possible concern with our two cost of living measures is that we might not be cap- turing price differences across areas but are instead controlling for public sector em- ployment. This concern arises since blacks are more likely to work in the public sector than whites U.S. Department of Labor 2012 and public sector jobs pay more see, for example, Congressional Budget Offi ce 2012, especially in urban areas Brueckner observed in our sample 156. 21. The 95 percent confi dence interval is quite large and we are unable to reject wage premiums as large as 0.08 in Column 2 or wage penalties as small as –0.077 in Column 4. and Neumark 2011. In Table 4, Column 1 we replicate the coeffi cient estimates from Column 4 of Table 3, for comparison. In Column 2, we exclude respondents living in commuting zones where the share of public employees is above the 90 th percentile 21.6 percent and present the corresponding coeffi cient estimates. The same qualita- tive conclusion is upheld: The estimated wage premium disappears once we control for cost of living and education. Therefore, we do not believe that our measure merely proxies for public sector employment. A second concern with the cost of living measure is that it might proxy for local school quality instead of local prices, because many of the areas with the highest cost of living have poorly performing public schools for example, large cities. In response, we show that our main results hold when we also control for proxies of school quality inputs to the respondents’ high school such as the share of teachers with higher degrees. These results are in Columns 3 and 4 of Table 4. In Column 3, we present results for the sample of respondents with valid school input measures as a baseline note that this results in the loss of more than half the sample. 22 In Column 4, we include school input variables and fi nd the same pattern as our main result: Controlling for cost of living and years of education erases the black- wage premium. Although we observe these measures of school quality, employers may not know the quality of schools for workers who have relocated since high school. Therefore, in Column 5 we restrict the sample to workers who lived in the same CZ in 2006 and age 14 since employers likely have a sense of school quality in their current location. Again, the qualitative conclusions are upheld, suggesting that our controls for cost of living are not merely picking up school quality.

B. Alternative Controls for Cost of Living