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Buyer Alliances as Countervailing Power in WIC Infant-Formula Auctions


State agencies in infant-formula procurement auctions receive lower bids when they are in buyer alliances than when they are unallied. The Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) uses an auction to procure infant formula. Manufacturers bid on the right to be an agency’s sole supplier by offering a rebate on formula sold through WIC. Agencies frequently join together in buyer alliances. An empirical estimation shows that bids are lower to alliances and that lower prices result because alliances are heterogeneous. Results suggest that when heterogeneity is not controlled, bids decline with alliance size, which has policy implications because Congress recently limited alliance size.

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  1. Limiting alliance size apparently was intended to promote competition for contracts: “\(\ldots \)an unintended consequence of large alliances is that competition is diminished because not all infant formula manufacturers may be able to compete for larger State alliance contracts due to production capacity. The Department believes that limiting the size of State alliances will help to maintain competition among infant formula manufacturers by ensuring all manufacturers can compete for rebate contracts” (Federal Register, 3/3/2008).

  2. The total per-unit cost to WIC is the net price plus the retail markup over the wholesale price.

  3. See Oliveira et al. (2001) for a more complete discussion of the history of the WIC infant formula rebate system.

  4. There is no provision in Federal regulations for monitoring wholesale prices, but agencies are required to monitor retail prices. The wholesale price is a useful benchmark to compare rebate bids, but actual wholesale prices that are charged to retailers may vary. Manufacturers offer volume discounts, ordering a truckload size volume offers the largest discount, and different retailers may order different volumes.

  5. See Davis (2008) for a complete description of WIC infant-formula alliances and their member agencies.

  6. In rebate auctions at most four manufacturers have bid for the sole-source contracts, and in many auctions only two manufacturers bid. Wyeth is a fourth firm that was active in WIC infant formula auctions until the mid-1990s.

  7. I call the equation a reduced form to distinguish it from a structural model of bids. The equation is not a true reduced form since it includes endogenous variables as regressors.

  8. Plant locations for Mead Johnson (Evansville, IN, Zealand, MI, and Springfield, MO), Ross (Casa Grande, AZ, Columbus, OH, Sturgis, MI, and Alta Vista, VA), and Wyeth (Mason, MI and Georgia, VT) are noted in the Handbook of American Business History (Powell 1997). Carnation’s only infant formula plant in the US is in Eau Claire, WI.

  9. The weight for agency i is \((\textit{WIC}\,\textit{Infants}_{{i}} +0.5*Non\textit{WIC}Infants_{i})/(\Sigma _{i\in A}(\textit{WIC}Infants_{{i}}+0.5*Non\textit{WIC}Infants_{i})\) where the sum is over all agencies in an alliance. I use a 0.5 weight for non-WIC infants to capture the spillover effect. I also experimented with weights of 0 and 0.7; the choice of weights did not meaningfully affect regression results.

  10. Firms do not know which of their rivals will bid in an auction. Consequently, Rival Distance is always the distance of a firm’s rival that is closest to the agency. I assume that firms bid as if they always expect their rival that is nearest the agency to bid.

  11. Infant-formula manufacturers provide their customers with price catalogs of all of their various products. The wholesale prices in these data are taken from those catalogs.

  12. Powdered bids are adjusted to equal the amount of reconstituted formula (26 fluid ounces) produced by a 13-ounce can of liquid concentrate.

  13. I estimate what Wooldridge calls “Chamberlain’s random effects probit” and include time-averaged values for all right-hand-side variables (Wooldridge 2002, p. 487). Specification tests suggest that the random-effects model is the appropriate model. A chi-square test for the joint significance of the time-averaged variables rejected the null hypothesis that their coefficients were jointly zero at the 5 % level.

  14. I follow the procedure that is suggested by Wooldridge (2002, pp. 567–68) to test for sample-selection bias using two-stage least squares.

  15. Below, I consider the number of agencies in an alliance (Number in Alliance) as an alternative variable to measure alliance effects. The count of agencies includes Indian Tribal Organizations. If an agency is not in an alliance, the variable takes a value of 1.

  16. Some auctions include bids for both liquid-concentrate and powder. While the bids are based on the same 26 reconstituted ounces, including them both in a regression may bias standard errors since errors are likely correlated across observations (Moulton 1986, 1990). I adjust for arbitrary correlation within agencies by using cluster-robust standard errors. Because the powder/liquid concentrate level of clustering is nested within the higher agency level, it is necessary only to adjust standard errors at the higher-level cluster (Cameron et al. 2011).

  17. Initially the bidder dummies do not seem to suggest lower bids when there are more bidders. But the coefficients are imprecisely estimated; and because the coefficients are estimates, the best that we can conclude is that the true value is within its 95 % confidence interval. For example, from column (1) the true effects could be: for two bidders \(-\)0.85, three bidders \(-\)1.0, and four bidders \(-\)1.2. All of these values are within the 95 % confidence interval of the estimated coefficients. The imprecision is likely due to the small sample, and to the small number of auctions that have more than two bidders.

  18. Of course alliance size might still matter if costs decrease with size.

  19. Note that infant counts are for all participating infants and is not restricted to non-breastfeeding infants, which is the measure of infants used in regressions.

  20. The results reported are not sensitive to the choice of weight that is placed on non-WIC infants. I experimented with weights of 0 and 0.7, and regression results were largely unaffected.

  21. As robustness checks I experimented with other heterogeneity measures. I used an Atkinson Index in place of the Gini, and conclusions were unchanged. I also created a measure that is similar to a Hefindahl-Hirschman Index. I defined each agency’s share of an alliances as \((WIC\,Inflants_{{i}} +.5*nonWIC\,Inflants_{{i}})/\Sigma _{{i\in \hbox {A}}}(WIC\,Inflants_{{i}}) +0.5*\Sigma _{i\in A}(nonWIC\,Inflants_{{i}}))\), then squared each share and summed the squared shares. The regression results were similar to those reported using the Gini index, but the Gini results were more consistently statistically significant.

  22. I ran all models in Table 6 including Gini as a regressor; the coefficients on WIC Infants, WIC Infants Sq., AlliancexWIC Infants, and AlliancexWIC Infants Sq. were not statistically significant, jointly or individually.

  23. The alliance with the largest number of participating WIC infants was the Texas, Minnesota, Iowa alliance with about 279,000 infants in 2007.


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Thanks to Victor Oliveira for providing helpful comments. The paper benefited from the direction of two anonymous reviewers, and the journal editor. Linda Clarke at FNS and personnel at the Center for Budget and Policy Priorities provided valuable assistance compiling rebate bid data. Funding assistance for this research was provided by the Economic Research Service of USDA, Cooperative Research Agreement No. 58-4000-2-0113. The views expressed in this article are those of the authors and are not necessarily those of ERS or USDA.

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Correspondence to David E. Davis.

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Davis, D.E. Buyer Alliances as Countervailing Power in WIC Infant-Formula Auctions. Rev Ind Organ 45, 121–138 (2014).

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  • Auctions
  • Food assistance
  • Countervailing power
  • Buyer concentration
  • Oligopoly
  • WIC

JEL Classification

  • L13
  • D43
  • D44
  • Q18
  • I18