We show that our results remain robust to a wide range of values of _δ_ up to at least 0.04 in Appendix Figure O10, which is double our back-of-the-envelope estimate. To illustrate this, we plot the estimated coefficients and their confidence intervals against different levels of _δ_ under various methods in Conley et al. (2012). The three methodologies are the union of confidence interval approach with a support of [0 _,_ 0 _._ 08], the local-to-zero approach with a standard deviation of 0.02, and the local-to-zero approach with a standard deviation of _δ_ .<sup>64</sup>

# **F Auxiliary Data**

Population data are available from the Census Bureau. Data on housing prices are obtained from the Federal Housing Finance Agency (FHFA), which produces housing price indices at the state level from 2006 to 2015. County housing-price indices from 2006 to 2015 are also obtained from CoreLogic through the Fama-Miller Center at the University of Chicago Booth School of Business. Results are presented using state-level housing prices from FHFA, whereas results are robust to using county level housing prices. Labor force and demographic variables are obtained from the BLS and the Census. Tobacco tax data are available from the industry-funded annual report _Tax Burden on Tobacco, 2017_ and are assembled by _Campaign for Tobacco-Free Kids_ . SNAP-recipient characteristics are obtained from SNAP QC data described above. Energy controls, which include annual state-level total energy, electricity, LPG, and natural gas quantities consumed and prices for the residential sector, are obtained from the State Energy Data System (SEDS) maintained by the US Energy Information Administration (EIA). Data on monthly temperature by state are obtained from Berkeley Earth. Data on policy controls refer to state-year measures of amounts paid out by transfer programs available from the BEA. The transfer amounts are logged and these programs include social security, other retirement and disability insurance transfers, Medicare, Medicaid and other vendor payments, military medical insurance, SSI, EITC, other income maintenance programs such as TANF and WIC, state unemployment insurance, other unemployment insurance, Veterans’ benefits, education and training assistance, other government transfers, transfers from nonprofit institutions, and transfers from businesses. Measures of grocery industry concentration, which include the number of establishments per population and the HHI, are obtained from the County Business Patterns (CBP) made available by the Census Bureau. The HHI is calculated using the mid-point of available employment size brackets.

# **G Graphical Evidence**

We present some graphical evidence that suggests the identifying assumption of parallel trends is satisfied as an alternative graphical illustration of parallel pre-trends. Appendix Figure O3 plots the revenue-weighted average grocery store price indices by the quantile of change in residualized log synthetic benefits per population, our IV, for states above and below the median, respectively. To obtain these quantiles, a state-month panel of log synthetic benefits per population is regressed on the set of control variables as well as

> 64To implement the local-to-zero approach, we dropped a few control variables to ensure the covariance matrix would remain non-singular. The point estimates are robust to such changes in the set of controls.

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