Within- and Cross-Auction Geographic License Complementarities in FCC Spectrum Auctions

Geographic complementarities across licenses being offered within a single FCC spectrum auction have been previously identified (Ausbel, Cramton, McAfee, and McMillian, 1997; Moreton and Spiller, 1998; Fox and Bajari, 2013; Xiao and Yuan, 2021) and have influenced the design of FCC auctions. Here, we estimate geographic complementarities between licenses being offered in the same auction (within-auction complementarities), as well as, complementarities between licenses currently held by bidders and new licenses being offered in an auction (cross-auction complementarities). These complementarities are important for FCC auction design at two levels. Both within-auction and cross-auction complementarities impact the optimal choice of the size of geographic market designations for new licenses, as well as what predetermined package bidding offers should optimally be offered in an FCC auction. We adapt the structural estimation method introduced by Fox and Bajari (2013) to estimate the deterministic component of bidder valuations in FCC spectrum auctions based on a pairwise stability condition: two bidders cannot exchange two licenses in a way that increases the sum of their valuations. We expand their modeling of license complementarities to include geographic complementarities between licenses being offered in an auction and licenses already owned by bidders at the time of the auction. Applying this approach to PCS C Block auctions 22, 35 and 58, we find evidence of significant geographic complementarities between licenses both within and across these auctions. Moreover, in these three auctions, estimated cross-auction license complementarities are larger than within-auction license complementarities. The introduction of cross-auction geo-complementarities improves the fit of the estimator, allowing for more accurate estimation of the likely efficiency of these auctions. To our knowledge, this is the first paper to empirically estimate such cross-auction license complementarities within a structural model. The magnitude of the estimated cross-auction license complementarities highlights the importance of market designation choices in FCC auctions