Accounting for the Distribution of Redemption Rates

The redemption rates for WIC foods in the revised set of food packages are based on a distribution of redemption practices among WIC participants that ranged from no redemption of a food to partial redemption to full redemption of the package allotment. In 2012, Altarum conducted a study of redemption rates in three states (Kentucky, Michigan, and Nevada) (USDA/ERS, 2014) that provided basic information on the redemption distribution. All three states had implemented EBT issuance systems. The study classified redemption practices in three groups: full redemption, partial redemption and nonredemption. As stated in the Altarum report:

The amount redeemed in a given month was subtracted from the amount issued to all participants in the family for that benefit month; if the remaining amount was zero or less than an approved minimum size food item, then the redemption was considered a full redemption. (USDA/ERS, 2014)

If the amount remaining was greater than the approved minimum amount but less than the amount issued, this was considered partial redemption. If none of the amount issued was redeemed, this was nonredemption. The redemption amounts were calculated for more than 14 individual food categories, for each of the food categories, and over all of the categories. Overall, 12.6 percent of the families receiving WIC benefits redeemed all of their benefits.

The information on redemption rates by product category from Altarum's report can also be used to develop data-based assumptions for redemption behaviors, specifically those used to guide committee choices of redemption rates to apply for the revised packages. The committee used a combination of the Altarum and FNS data to develop a range of revised redemption rates, and the final rates used were close to the implied new FNS-based rates with some adjustments.

WIC-participating families that did not redeem a food category in the current food package (the nonredemption group) were assumed not to redeem under the revised package if there was no change to the food category or if the only change was to change the amount offered. This seems like a plausible assumption given that there was relatively little change in the type of foods offered for each food group. If WIC-participating families fully redeemed foods in the category (the full redemption group), the families were assumed to continue to fully redeem the benefits in the food category with the revised packages as long as the amount offered was less than in the current package. This was also the case if the amount of the food provided increased, as in the case of the CVV, the full redemption rate was assumed to stay approximately unchanged. The CVV is the main category with a large increase in the amount of food provided. If there were partial redemption in the food category, the committee compared the revised amount offered in the package with the average partial redemption amount of the food before the change. (The average partial redemption amount redeemed can be derived from the redemption rates, the full amount offered, and the total average amount redeemed.) If the revised package amount was less than the average partial redemption amount, the partial redeemers were treated as were the full redeemers and assumed to fully redeem the revised package. If the revised amount was more than the average partial redemption amount, then a new implied average redemption rate consistent with the other numbers was calculated. The degree to which partial redemption affects the projected redemption rates can be derived from the available information.

Application of the Altarum Redemption Distributions (None, Partial, Full): Assumptions

To apply the Altarum redemption distribution information to estimate the revised redemption rates, several assumptions were applied, as listed below:

• The redemption rate patterns follow the distributions—full, partial, and none—observed in the Altarum study.
• The redemption patterns are constant and independent of the overall percentage redemption observed. That is, the Altarum distribution of rates of no, partial, and full redemption was applied to all redemption rates assumed for each food item, including the redemption rates based on the FNS redemption data provided to the committee as well as the observed state average rates included in the current food package consensus rates.²
• Implied adjustments occur because of changes in quantities only; adjustment for changes attributable to new products or available substitutions are made separately from the adjustments to the quantities.

The committee was interested in obtaining estimates for the implied new redemption rate (Redemption%New) for each food item. The relationship observed from Altarum is:

• Redemption%Alt = (Partial%Alt × PartialAmtAlt + Full%Alt × FullAmt) /FullAmt

Where:

• Redemption%Alt = the overall redemption rate observed in Altarum
• PartialAmtAlt = the implied average partial redemption amount in Altarum
• FullAmt = the full amount issued
• Partial%Alt = the % (share) with partial redemption from Altarum
• Full%Altarum = the % (share) with full redemption from Altarum.

In this equation, all of the numbers are known from the data except PartialAmtAlt. Solving for PartialAmtAlt (the implied average partial redemption amount in Altarum):

• Redemption%Alt = (Partial%Alt × PartialAmtAlt + Full%Altarum × FullAmt) /FullAmt
• Redemption%Alt × FullAmt = (Partial%Alt × PartialAmtAlt + Full%Altarum × FullAmt)

Rearranging terms:

• Partial%Alt × PartialAmtAlt = [(Redemption%Alt – Full%Altarum) × FullAmt]
• PartialAmtAlt = [(Redemption%Alt – Full%Altarum) × FullAmt] /Partial%Alt

Similarly, the committee knows the overall average redemption rates in the FNS (or state average) data and can combine it with the no, full, and partial rates from the Altarum data to calculate the implied average partial redemption amounts assumed for the FNS data as well (PartialAmtAssumed). As the same redemption shares are assumed to hold for different overall redemption levels across all locations, the value Redemption%Assumed can be substituted in the below calculation for the overall redemption rate observed in the Altarum study (Redemption%Alt) to solve for PartialAmtAssumed if this leads to nonnegative amounts. In this case, replacing Redemption%Alt, the reported overall Altarum redemption rate, with Redemption%Assumed, the FNS reported (consensus) redemption rate, yields:

• PartialAmtAssumed = [(Redemption%Assumed − Full%Altarum) × FullAmt] /Partial%Alt

As long as the PartialAmtAssumed, our calculated assumed partial redemption amount on average is positive, this calculation is not inconsistent with observed patterns and yet incorporates the distribution of redemptions rates across full, no, and partial rates.

Now when the implied partial amount assumed is nonnegative, we use this calculation of the assumed Partial Amount (PartialAmtAssumed) to adjust our overall redemption rate for the revised package. Then we consider a further adjustment to our revised rates to account for whether the distribution of full and partial redeemers (based on the mean) is above the newly projected amount in the new package. If the revised amount is below the current amount and the current average redeemed partial amount, we assume the new redemption rate is 1 minus the share that has no redemption (that is, all participants except the nonredemption group will redeem the revised full amount). However, if the revised full amount is more than the current amount redeemed by partial redeemers, then the redemption amount is down-weighted to incorporate their lower levels.

Following this procedure generates implied new redemption rates based on the changes between the current and revised food packages (see Table R-5). These implied rates do not account for behavioral changes, such as those resulting from the offering of new substitutions. Slight adjustments were made (see the “Revised” column, Table R-5) to account for these changes.

TABLE R-5

Redemption Rates Applied to Generate the Set of Cost-Neutral Food Packages.