in Section 5.2, this term can be thought of as the vertical upward shift in the aggregate demand curve caused by a marginal change in benefits affecting SNAP consumers’ demand. For the demand elasticity for food ( _εD_ ), we obtain from the data directly an estimate of -0.709, which falls within the typical range reported in the literature as summarized by Andreyeva et al. (2010).<sup>43</sup> We obtain from USDA data the proportion of sales accounted for by SNAP recipients (<sup>_<u>pQ</u>_</sup> _pQ_<sup>_D,S_):</sup> 0.168. Combining these numbers together with the aforementioned estimates for _εQD,S ,b_ , we obtain a range of [0.0802, 0.124].

In order to calibrate the benefit pass-through elasticity ( _ερ_ ), we consider the last two remaining terms: the unit-subsidy pass-through elasticity and the slope effect from equation (8). For the unit-subsidy pass-through elasticity, we calibrate the term at 0.5 based on Besanko et al. (2005).<sup>44</sup> For the slope effect, which reflects incremental pricing power that producers can exercise based on the benefit-induced change in the slope of aggregate demand, we assume this is close to zero. This assumption follows as a corollary to our previous assumption in Section 5.4 that the inverse aggregate-market-demand curve _p_ ( _Q, b_ ) shifts up by a constant amount in response to a benefit increase.<sup>45</sup> Multiplying the shift-magnitude range by 0.5, we arrive at a range of [0.0401, 0.062]. Comparing the range [0.0401, 0.062] with our reduced-form estimate 0.0724 and its standard error 0.0269 in Table 6, we see that the range falls well within the confidence interval of our reduced-form estimate.<sup>46</sup> We now present the calibration of the quantity response, which is straightforward based on the discussion above and equation (9).<sup>47</sup> Plugging in the estimates for the MPC elasticity, proportion of SNAP sales, demand elasticity, and the calibrated price elasticity, we obtain a range of [0.028, 0.044]. If we use our reduced-form estimate for the price elasticity, with the MPCF from HS instead of the calibrated price elasticities, we obtain 0.036. All these numbers are close to our reduced-form point estimate for the real-sales response reported in Table 6:

> 43See column (3) of Appendix Table N16 (and discussion in Appendix Section L), where we regress log real sales on log price indices with store and period fixed effects. Results are nearly identical using Hausman IVs (average of other stores in the same chain) following DVG. Both DVG and Hitsch et al. (2017) estimate product-level elasticities using panel variation and find that these estimates are similar to those obtained using IVs and other alternative methods. We follow Hitsch et al. (2017) and use 3-digit zip-code-period fixed effects; estimates are similar using period or market-period fixed effects. Note that this approach estimates the residual demand elasticity for the store as opposed to the market demand elasticity, which is the object of interest. The magnitude of the residual demand elasticity may be an upper bound for the magnitude of the market demand elasticity. Hence, the calibrated shift effect may represent a lower bound.

> 44In fact, as shown in in Appendix Section L, we also obtain a similar unit-subsidy pass-through rate of 0.49 by estimating the curvature of demand, subject to caveats.

> 45Assuming that<sup>_∂p_</sup> _∂b_<sup><u>(</u></sup><sup>_x,b_</sup><sup><u>)</u></sup> is constant in _x_ implies _∂b∂Q∂_<sup>2</sup> _<u>p</u>_<sup>= 0,whichimplies</sup><sup>_ε|p′|,b≡_</sup> _∂b∂Q∂_<sup>2</sup> _<u>p</u> ∂p/∂Qb_<sup>= 0.</sup>

> 46One potential explanation for why the point estimate itself is slightly higher than the calibrated bounds—while this is stretching what we can say with statistical confidence—is a small positive slope effect. Based on the differences, the slope effect would be [0.011, 0.032] which, if _θ_ is around 0.2 as discussed further below, would imply _ε|p′|,b_ within [0.075, 0.229].

> 47We do not report this in Table 8 for brevity.

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