The Fallacy of Crowding-Out: A Note on "Native Internal Migration and the Labor Market Impact of Immigration"

In "Native Internal Migration and the Labor Market Impact of Immigration," George Borjas (2006) identifies a strong negative correlation between immigration and native-born employment in the US using local area data. This relationship is particularly strong at the metropolitan area level, weaker but still significant at the state level, and weakest at the Census region level. In this note, we show that Borjas’s negative correlation arises due to the construction of the dependent and explanatory variables rather than from any true negative association between the employment growth of immigrants and natives. Borjas regresses log native employment, ln(Nt), on the share of foreign-born employment, pt = Mt/(Mt + Nt), across skill-state-year cells. The specification therefore includes native employment in the numerator of the dependent variable and in the denominator of the explanatory variable. This builds a negative correlation into the model that is particularly strong if the variance of Nt relative to Mt is large. To illustrate, we first show that state and city level regressions of the standardized native employment change, (Nt+10−Nt)/(Mt+Nt), on standardized immigration, (Mt+10 −Mt)/(Mt+Nt), always find a positive and mostly significant correlation between the two. Second, we randomly simulate changes in the native and foreign-born workforce with a data generating process that has zero or positive correlation between the shocks ΔMt and ΔNt (i.e., so that immigration is associated with either no change or an increase in native employment). Borjas specifications employing this simulated data estimate large and significantly negative coefficients as long as the variance of ΔNt is larger than the variance of ΔMt, which is true in observed state-level and city-level data.