Complements and Substitutes in Sequential Auctions: The Case of Water Auctions

We study sequential auctions in which bidders demand multiple units. We collect a novel data set on sequential water auctions for the empirical study. Although water units are identical, two features from the empirical setting create a trade-off whereby units of water end up being complements or substitutes. First, there is a water loss that is only incurred for the first unit, generating a sunk cost. Second, subsequent units of water exhibit decreasing marginal returns. Units of water are complements or sub- stitutes depending on the relative importance of the sunk cost and decreasing returns. Weather seasonality provides us with the required variation (in sunk costs relative to de- creasing returns) to perform the empirical investigation. When units are complements, one bidder wins all units by paying a high price for the first unit, thus deterring others from bidding on subsequent units. When units are substitutes, different bidders win the units with positive probability and pay prices of similar magnitude, even when the same bidder wins all units. We analyze this stark pattern of outcomes not investigated in the literature before. We recover individual demand consistent with this pricing behavior and confirm it is not collusive, but consistent with non-cooperative behavior. Demand estimates are biased if one ignores these features.