around the Farm Bill and the ARRA where substantial variation exists in SNAP-benefit disbursement. Our results are robust to using the entire sample period of 2006-2015.

# **4.1 Retail Stores**

We estimate the contemporaneous effect of SNAP-benefit increases on prices and real sales using equation (3). We first show the estimated price effects for grocery stores in Table 2. Without controls, the OLS estimate is statistically insignificant, because endogenous counter-cyclical variations in program scale induce a negative bias on the coefficient. The IV is also weak without controls. We argue that this is because the disturbance term in the SNAP-benefit series overwhelms the IV’s idiosyncratic signal. Economic variables such as housing prices help to net out some of this disturbance term, improving relevance and sharpening the observable alignment between the benefit series and the IV. When a set of economic variables such as housing prices are included to control for recessionary shocks and disturbance terms, the effect of raising SNAP benefits is positive and significant. The effect remains positive and significant with further addition of controls such as the state-level tobacco tax, which strongly affected tobacco prices over this period. Other controls include economic characteristics of SNAP recipients, energy quantities consumed and energy prices, all of which affect benefits per recipient as shown in Section 2 and Appendix Section C.1.<sup>28</sup> Regarding our IV approach, the first-stage F-test passes standard thresholds benchmarked in the literature.<sup>29</sup> We report the first stage and reduced form in Appendix Table N2 and N3, respectively. The first-stage coefficients are larger than 1 (although 1 is included in their confidence intervals), suggesting that idiosyncratic increases in intensive-margin program generosity encouraged more people to take up the program and raised program scale on the extensive margin.<sup>30</sup> Even with the full set of controls included, the size of the IV coefficient is larger than the OLS coefficient by almost a factor of four, which is consistent with the hypothesis that local macroeconomic trends not fully controlled for in the OLS specification were driving SNAP benefits up and prices down. A 1% increase in benefits per population increases prices across goods in grocery stores by about 0.08%. Because the average change in benefits was about 15% for the two events, we can infer that prices were raised by 1.2% by each event. Given

> 28Appendix Figure O5 plots the observations (collapsed into 50 bins) used in the estimation in a binned scatter plot, which shows the data support a log-log specification with most of the observations lying close to the regression line.

> 29According to Lee et al. (2021), a first-stage F-statistic of 20.682 in column (6) requires a standard error adjustment factor of about 1.32, at which the point estimates remain statistically significant.

> 30Hence, the two-stage least squares procedure downscales the reduced-form coefficient to give the response per 1% increase in total benefits per population. We also show in Appendix Figures O6 and O7 how the changes in the synthetic-benefit series track changes in the actual series with and without controls.

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