Complements and substitutes in sequential auctions: the case of water auctions

• Author: José‐Antonio Espín‐Sánchez,Javier D. Donna
• DOI: http://doi.org/10.1111/1756-2171.12221
• Date: 01 March 2018
• Published date: 01 March 2018

RAND Journal of Economics

Vol.49, No. 1, Spring 2018

pp. 87–127

Complements and substitutes in sequential

auctions: the case of water auctions

Javier D. Donna∗

and

Jos´

e-Antonio Esp´

ın-S´

anchez∗∗

We use data on sequential water auctions to estimate demand when units are complements or

substitutes. A sequential English auction model determines the estimating structural equations.

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, paying prices similar in magnitude. We recover

individual demand consistent with this stark pattern of outcomes and confirm it is not collusive

but consistent with noncooperative behavior. Demand estimates are biased if one ignores these

features.

∗The Ohio State University; donna.1@osu.edu.

∗∗Yale University; jose-antonio.espin-sanchez@yale.edu.

We are indebted to our advisors and members of our dissertation committees’ helpful discussions, guidance,

and support. Donna: Rob Porter (committee chair), Meghan Busse, Aviv Nevo, and Florian Zettelmeyer. Esp´

ın-

S´

anchez: Joel Mokyr (committee chair), Joseph Ferrie, Regina Grafe, and Rob Porter. Discussions with Jason

Blevins, Jia-Young (Mike) Fu, Matt Gunden, Jim Peck, Bill Rogerson, Ron Siegel, Rick Steckel, Alex Torgov-

itsky, Greg Veramendi, and comments from anonymous referees, the Editor, Marc Rysman, as well as semi-

nar participants at the International Industrial Organization Conference (2013), the Jornadas de Economia Indus-

trial (XXVIIth edition), the Meetings of the European Association for Research in Industrial Economics (EARIE

2012), the North American Summer Meetings of the Econometric Society (2012), the Second Annual UTDT

Economics Conference, the World Economic History Congress (XVIth edition), the Midwest Economics Associa-

tion Annual Meeting (2013), Aarhus University, Analysis Group, Arizona State University, Bates White, Charles

River Associates, Centro de Estudios Monetarios y Financieros (CEMFI), Compass Lexecon, Johns Hopkins

University, Northwestern University (Industrial Organization and History Workshops), The Ohio State University, and

Universidad Carlos III have greatly benefited this work.We would also like to express our gratitude to Fernanda Donna

and Antonio Esp´

ın for superb research assistance, to the librarians from the archive of Mula for valuable help in ac-

cessing the historical files, and to Maja Butovich, Kelly Goodman, Elizabeth Lenaghan, and Melissa Petruzzello for

editorial advice. We thank the AEMET for providing us with the meteorological data. Donna acknowledges financial

support from the CSIO at Northwestern University, the allocation of computing time from the Ohio Supercomputer

Center, and financial support from the SBS at The Ohio State University. Esp´

ın-S´

anchez also acknowledges financial

support from Fundaci´

on Caja Madrid. A version of this article was part of Donna’s PhD. dissertation at Northwest-

ern University. All errors are involuntarily. The online web Appendix for this article is http://www.jdonna.org/water-

auctions-web.

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88 / THE RAND JOURNAL OF ECONOMICS

1. Introduction

There are many instances in the real world where severalunits of the same or similar goods

are allocated sequentially or periodically using auctions. Examples include timber, procurement

of public goods, electromagnetic spectrum, and treasury bills. The nature of the goods at auction

and the firms bidding determine whether the goods are complements (increasing marginal returns,

or IMR) or substitutes (decreasing marginal returns, or DMR). In many cases, IMR arise because

firms incur fixed costs to realize the full value of purchased goods. This is the case of the

machinery and workers needed to fell trees or build highways. Firms might experience DMR

due to limited capacity to hire more workers or buy more machinery. DMR may also arise as a

consequence of the downward sloping demand for the firms’ final products, for example, once

a firm has a valid spectrum for a given county, the value of another tranche of the spectrum

decreases substantially. Firms would face IMR if the first effect dominates, DMR if the second

effect dominates, and hill-shaped marginal returns if both effects are important.

By affecting the valuation of subsequent units, fixed costs and decreasing returns determine

bidder behavior and price dynamics. Price dynamics are central to connect observed bids to the

underlying distributions that characterize individual demand, which is fundamental to discuss

positive and normative questions. For instance, variation in prices caused by a high sunk cost

will affect even relatively simple tasks, such as measuring the dispersion in individuals’ private

valuations. Moreover,in such a case, a competitive environment could be incorrectly interpreted

as collusive.

The existing literature on sequential auctions has provided little empirical evidence on the

effect that complementarities and substitutabilities in the valuation of subsequent units have on

price behavior within the same market. The main reason for this lack of evidence is the challenge

of finding sufficient variation in the degree of complementarity within the same market. Our aim

is to address this empirical gap. To that end, we examine a unique panel data set from sequential

water auctions from a self-governed community of farmers in Mula, Spain.1Admittedly, few

industrial organization economists will find water auctions from farmers in southeastern Spain

interesting per se. Westudy this empirical setting because it allows us to exploit a unique scenario

where a market exhibits periodic switches or reversionsbetween regimes of complementarity and

substitutability, that is, regimes where identical units may complement and substitute within the

same market and for the same bidder. Weather conditions in Mula generate large changes in the

degree of complementarity across seasons: variation in the importance of sunk costs relative to

decreasing returns, as described in Section 3. We use this variationto (i) analyze bidding behavior

in sequential auctions in which buyers’ preferences for multiple units exhibit both sunk costs

and DMR, and (ii) investigate its implications for price dynamics and price competition. This

empirical setting allows to analyze a stark pattern of outcomes not previously documented in

the literature. Sometimes, winning prices exhibit a standard competitive pattern. In this scenario,

winning prices are similar in magnitude, regardless of whether the same or different bidders

(farmers in our case) win the sequential units. Other times, one farmer wins all the units, pays

a high price for the first unit, deters other farmers from entering subsequent auctions, and thus

pays a very low price for the remaining units. We call this the deterrence effect.We show that this

pattern of outcomes is consistent with a noncooperative equilibrium, where the observed price

dynamics are competitive, not collusive.

The data in this article come from all water auctions in Mula, Spain, from January 1954

through August 1966—when the last auction was run—and the allocation system switched to

a bargaining system, as described in Section 2. The data for our analysis consist of individual

winning bids and auction covariates. These covariates include the amount of rainfall. The basic

unit of sale is the right to use three hours of water (432,000 liters) for irrigation. For each weekday,

eight units are sold for each schedule: four for daytime (7 a.m.–7 p.m.) and four for nighttime

1The four main fruit trees grown in the region are oranges, lemons, peaches, and apricots.

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IN-S ´

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(7 p.m.–7 a.m.) irrigation. The auctioneer sells first the 20 units corresponding to nighttime and

then the 20 units corresponding to daytime. This leaves 10 four-units sets of auctions that are

sold in order. (The 10 sets of four-units auctions are: Monday–nighttime, Tuesday–nighttime,

and so on, until Friday–daytime.) Thus, the relevant unit of analysis for investigatingindividuals’

demand and the pattern of outcomes is four-units auctions. However, units within each four-units

set are not conditional-independent, due to the friction created by the presence of sunk costs.

Observing the winner’s identity allows us to estimate the model, as outlined in Section 4. Local

weather conditions determine the relevant agricultural irrigation technology and, hence, water

demand. Additionally,as less rain falls in summer than in winter in southern Spain, the presence of

seasonalities provides us with the variation in sunk costs relative to decreasing returns necessary

to perform the empirical investigation.

We incorporate two features fromour empirical setting. First, a sunk cost is incurred for the

first unit bought because water flows through a channel dug into the ground. Some water is lost

when the channel is dry (the first unit), but the loss is negligible for subsequent units. Engineers

have estimated that 20 percent of the water of the first unit that travels through a dry channel

was lost ( G´

omez-Esp´

ın, Gil-Meseguer, and Garc´

ıa-Mar´

ın, 2006). Second, DMR are present for

subsequent units because the amount of irrigated land is fixed. We model the environment as

a sequential ascending price English auction along the lines of von der Fehr (1994) in which

bidders, by incurring a participation cost, decide whether to attend each sale.

The relative importance of sunk costs and DMR generates a trade-off, whereby buyers’

bidding behavior depend on whether different units are complements or substitutes. When goods

are complements, the same bidder wins all the objects, paying a high price for the first unit equal

to the valuation for the whole bundle (four times the second highest valuation for the first unit,

adjusted for the complementarity effect and participation cost). By doing this, the winner of the

first unit deters others from bidding on the remaining three units, allowing this bidder to pay very

low prices (close to zero) for the remaining three units. The resulting price pattern, along with

the same bidder winning all the units, may lead to an incorrect collusive interpretation. When

goods are substitutes, different bidders win the objects with a positive probability and pay prices

of similar magnitude, even when the same bidder wins all the objects. We provide empirical

evidence for the key features of our model: participation and sunk costs.

The price patterns predicted by the model provide a straightforward method to determine

the regime—complements or substitutes—being played. When goods are complements, very low

prices are paid by the same winner (the winner of the first unit) for the second, third, and fourth

units; thus, the difference between the price paid for the first and the remaining units is large.

When goods are substitutes, the units might be bought by different bidders and the prices of all

four units are similar; thus, the difference between the price paid for the first and the remaining

units is negligible. This allows to determine the regime by looking at (i) the identities of the

winner (i.e., whether the same bidder bought all the four units), and (ii) the difference between

the price paid for the first and the remaining units (see Section 4).

We estimate the distribution of private valuations by maximum likelihood using an expo-

nential distribution and the English structure for the auction. To estimate sunk cost and DMR, we

form moment conditions based on the structural equations of the model. We infer participation

costs using data from auctions in which bidders were present, but no one placed bids. This method

gives us bounds on participation costs.

Our empirical work establishes three main results. First, we recover individual demand—

characterized by private valuationsand the model’s structural parameters—that is consistent with

the described price patterns and the deterrence effect, in particular. Second, the equilibrium

price dynamics are consistent with competitive behavior. Noncooperative behavior is not only

consistent with the deterrence effect, but also predicts such price differentials. Incentives to

deviate from a collusive strategy are higher in spring and summer, when water is more valuable.

However, it is in spring and summer when we observe noncooperative behavior more often.

Finally, we show that estimates that ignore the importance of participation and sunk costs will

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