OLS	IV: SNAP+ SNAP2+SNAP policy index
Variables	Coeff. of WIC participation	S. E	P-value	Coeff. of WIC participation	S. E	P-value	Identification test‡-
ALL	−0.063	0.008	< 0.001	−0.039	0.322	0.902	O
Boy	−0.069	0.010	< 0.001	0.347	0.402	0.388	O
Girl	−0.059	0.011	< 0.001	−0.302	0.512	0.556	UWO
Non-H White	−0.091	0.010	< 0.001	0.680	1.089	0.533	O
Non-H Black	−0.052	0.021	0.015	0.675	0.811	0.405	UO
Hispanic	−0.024	0.014	0.087	0.543	0.283	0.055	O
Other	−0.038	0.020	0.061	−0.211	0.420	0.616	UWO

^†Controlling state dummy, sex, race/ethnicity, education, child’s age, maternal age, maternal marital status, number of people in the household, interview language, birth year, TANF/Temporary Assistance for Needy Families enrollment rate (# of enrolled participants/# of state population), CHIP/Children’s Health Insurance Program enrollment rate (# of enrolled children/# of children 18 or under in the state), and state unemployment rate. IV Variables including SNAP enrollment rates (SNAP, # of SNAP participants in that year/# of state population in that year), square of SNAP enrollment rates (SNAP²), and SNAP policy index.

^‡U means the under-identification test P < 0.05. Stock–Yogo tabulations based on the Cragg–Donald statistic were used for the weak identification test; W means the F statistic of the weak identification test > 10% maximal IV relative bias or > 10% maximal IV size. O means over-identification test > 0.05.(O could not be tested in the first stage).