Checks of Robustness with Employer Characteristics in the First-Step Regressions
| Second-Step Coefficient of the Check of Robustness (103 Local Labor Markets) | Log Agglomeration Measure in Regression for the Labor Supply Elasticity | Log Agglomeration Measure in Regression for the Urban Wage Premium When Not Conditioning on the Labor Supply Elasticity | Log Agglomeration Measure in Regression for the Urban Wage Premium When Conditioning on the Labor Supply Elasticity | Labor Supply Elasticity in Regression for the Urban Wage Premium (Instrumented) |
|---|---|---|---|---|
| Baseline | 0.1486 | 0.0283 | 0.0181 | 0.0374 |
| (0.0658) | (0.0050) | (0.0061) | (0.0103) | |
| Alternative agglomeration measures | ||||
| Log population density in 1985 | 0.1325 | 0.0276 | 0.0177 | 0.0381 |
| (0.0632) | (0.0048) | (0.0058) | (0.0105) | |
| Log population density in 2010 | 0.1530 | 0.0289 | 0.0191 | 0.0364 |
| (0.0698) | (0.0051) | (0.0063) | (0.0098) | |
| Log population (controlling for log area separately) | 0.1397 | 0.0308 | 0.0213 | 0.0357 |
| (0.0895) | (0.0056) | (0.0070) | (0.0094) | |
| Log employment density | 0.1612 | 0.0266 | 0.0164 | 0.0383 |
| (0.0745) | (0.0044) | (0.0057) | (0.0109) | |
| Including imputed wage observations | 0.1481 | 0.0266 | 0.0162 | 0.0387 |
| (0.0646) | (0.0048) | (0.0063) | (0.111) | |
| Using share of job exits into nonemployment as instrument | 0.1486 | 0.0283 | 0.0185 | 0.0358 |
| (0.0658) | (0.0050) | (0.0059) | (0.0100) | |
Notes: IEB and BHP, 1985–2010. The first column shows the coefficient of the agglomeration measure in the second-step regression (Equation 5) where the first-step separation equation includes worker controls, employer controls, and a worker–region-specific baseline hazard—akin to Model II in Table 2. The second column gives the estimated urban wage premium when not conditioning on the labor supply elasticity as in Equation 7, where the first-step wage equation includes worker controls and fixed effects, as well as employer controls—akin to Model IV in Table 3. The last two columns present the corresponding estimates when conditioning on the labor supply elasticity as in Equation 8, where we instrument the elasticity as in Panel C of Table 3. In the final row, we use the share of job exits into nonemployment as instrumental variable; the F-statistic of the first-stage regression underlying this row is 22.77. Robust standard errors are given in parentheses.