Research

Working Papers

Novel Shift-Share Instruments and Their Applications

Shift-Share (Bartik) instruments are among the most important tools for causal identification in economics. In this paper, I crystallize main ideas underlying Shift-Share instruments - their core structure, distinctive claim to validity as instruments, history, uses, and wealth of varieties. I argue that the essence of the Shift-Share approach is to decompose the endogenous explanatory variable into an accounting identity with multiple component parts; preserve that which is most exogenous in the accounting identity, and neutralize that which is most endogenous. Following this framework, I show clearly how several variants in the literature are related. I then develop formulas for several new variants. Particularly, I show how to develop Shift-Share instruments for distribution summaries beyond the mean - the variance, skew, absolute deviation around a central point, and Gini coefficient. As an empirical application that highlights the themes of the paper, I measure the effect of earnings inequality on rates of single parenting in the U.S., comparing results using each of various alternative instruments for the Gini coefficient.

The Distinct Roles of Poverty and Higher Earnings in Motivating Crime (with Lia Yin)

Does inequality lead to more crime? We develop a new model that articulates how Poverty (the lower tail of the earnings distribution) and Earnings (the upper tail) enter into equilibrium crime rates. In our model, individuals in Poverty have less to lose in the context of criminal punishment, so are less averse to committing crimes in general. The presence of high Earnings (therefore things worth stealing) heightens the expected gain to offenders per crime - but specifically in terms of financial gain, not emotional gain. We estimate our model on a comprehensive panel of U.S. Commuting Zones (1980-2016), deploying novel Shift-Share instruments to correct for reverse causality (of crime on the earnings distribution). Corroborating our hypothesis, we find that high Earnings plays a much larger role in driving crimes that yield financial gain to the offender (various forms of theft) than it does for crimes of emotional gain; while Poverty is a driving force equally across both types of crime. In each case, not accounting for reverse causality would underestimate both effects, often by more than double.

How Women and Men Choose Where to Live Based on Each Other's Expected Earnings

Might the earnings potential of prospective spouses drive migration choices? Migrants who flock to places with high-earning prospective partners can cause sex ratios to become unbalanced. Shortages of men have been shown to increase single parenthood, and shortages of women to increase crime. Past attempts to answer this question have been limited to brief windows in time, and have lacked causal identification. I build a 7-decade panel of U.S. Commuting Zones from Census and American Community Survey data, computing gender-specific shift-share (Bartik) instruments in order to isolate exogenous variation in women's and men's expected earnings. I find that both women and men place at least twice as much priority weight on men's expected earnings as they do on women's, indicating a gender asymmetry in preferences. This asymmetry slightly erodes over time from 1970 to 2019, consistent with a shift in norms. Because women and men prioritize men's earnings over women's by about the same amount, gender differences in earnings play little role in driving sex ratio imbalance. However, women place more weight than men do on the sum of women's and men's earnings, so that the ratio of women to men increases by about 1% per 10% increase in earnings. More balanced sex ratios may follow from policies that reduce overall (gender neutral) inequality, such as between urban and rural areas.