JUE Insight: Using the mode to test for selection in city size wage premia

The causal effect of city size on urban wage premia has been difficult to measure because unusually skilled workers may select into large city labor markets. We propose a new approach to this challenge. For single-peaked wage distributions, if individuals left of the mode disproportionately select out of large city labor markets, the CDF evaluated at the mode shrinks as city size increases. Among college trained, white full-time US workers, evidence of selection is present even after conditioning on extensive observable attributes. Among individuals with a high school degree or less, selection is absent. Additional estimates indicate that for college trained workers, 3.5% is an upper bound on the modal worker's wage elasticity with respect to city size. For those with limited education we can be more precise: modal wage elasticity is 3.9% for men and 5.2% for married women.