Table 1.

Associations between friending bias, exposure and upward income mobility across areas

Dependent variable	log[upward income mobility]						log[causal upward income mobility]
	ZIP codes				Counties
	(1)	(2)	(3)	(4)	(5)	(6)	(7)
log[EC]	0.236***		0.227***		0.272***
	(0.01)		(0.01)		(0.02)
log[high-SES exposure]		0.248***		0.224***		0.286***	0.116***
		(0.01)		(0.02)		(0.03)	(0.02)
log[1 − friending bias]		0.185***		0.236***		0.142*	0.339***
		(0.03)		(0.04)		(0.08)	(0.07)
County FEs	No	No	Yes	Yes	No	No	No
Observations	24,200	24,200	24,200	24,200	2,986	2,986	2,136
R2	0.42	0.43	0.71	0.71	0.38	0.39	0.03

Estimates from OLS regressions of log[upward income mobility] on log[EC] and other covariates. The coefficients can be interpreted as the elasticity of upward mobility with respect to the relevant covariate. In columns 1–6, upward income mobility is obtained from the observational measures in the Opportunity Atlas²³, and is defined as the predicted household income rank in adulthood for children with parents at the 25th percentile of the national income distribution. Columns 1–4 present regressions at the ZIP-code level. In column 1, the only independent variable is log[EC], defined here as the product of mean high-SES exposure and 1 − mean friending bias in the ZIP code (Supplementary Information B.5). In column 2, the independent variables are the log of mean high-SES exposure and the log of 1 − mean friending bias (Supplementary Information B.5). We start from individual-level statistics to compute ZIP-code-level and county-level means of exposure and friending bias (Supplementary Information B.5). At the individual level, exposure is defined as the weighted average of two times the fraction of above-median-SES members of the groups in which an individual with below-median SES participates, weighting each group by the individual’s share of friends in that group. Friending bias is defined as one minus the weighted average of the ratio of the share of friends with high SES to the share of peers with high SES in the groups in which a low-SES individual participates, again weighting each group by the individual’s share of friends in that group. Columns 3 and 4 replicate columns 1 and 2 adding county fixed effects. Columns 5 and 6 replicate columns 1 and 2 at the county level instead of ZIP-code level. Column 7 replicates column 6 using counties’ causal effects on upward mobility, defined as the mean predicted household income rank in adulthood for children with parents at the 25th percentile of the income distribution overall in the United States plus 20 times the raw annual causal exposure effect of growing up in the county reported in ref. ³². Regressions in columns 1-6 are weighted by the number of individuals in the primary analysis sample with below-median SES in the county or ZIP code. The regression in column 7 is weighted by the inverse of the squared standard error of the estimated annual causal exposure effect of growing up in that county³². Standard errors (reported in parentheses) are clustered at the commuting-zone level for county-level regressions and at the county level for ZIP-code-level regressions. Asterisks indicate the level of significance; *10%, **5%, ***1%.