Bidding behavior in sequential cattle auctions

Int. J. Ind. Organ. 27Organization (2009) 33–42 International Journal of Industrial 27 (2009) 33–42

Contents lists available at ScienceDirect

International Journal of Industrial Organization j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / i j i o

Bidding behavior in sequential cattle auctions Christine Zulehner ⁎ University of Vienna, Department of Economics, BWZ-Brünner Strasse 72, A-1210 Vienna, Austria

a r t i c l e

i n f o

Article history: Received 14 September 2007 Received in revised form 1 March 2008 Accepted 2 March 2008 Available online 18 May 2008 JEL classification: D4 L1 Q1

a b s t r a c t This paper studies the institutional characteristics of sequential cattle auctions and their effects on prices. It examines the effects of the order of sale according to quality, secret reserve prices, bidders' multi-unit demands and certain characteristics of the bidders. Theory predicts declining prices when sellers are allowed to reject the outcome of the auction, and increasing prices when bidders demand more than one unit. I find evidence that observed declining prices are caused by the order of sale according to quality and the secret reserve prices. I also find that bidders consider the strategic effect of sequential auctions and multi-unit demand. © 2008 Elsevier B.V. All rights reserved.

Keywords: Sequential auctions Private values Secret reserve price Multi-unit demand

1. Introduction Standard models of auctions predict constant prices when identical units of a good are offered sequentially to bidders who demand at last one unit (Milgrom and Weber, 2000; Weber, 1983). In reality, we often observe declining prices in some auctions, increases in others, and still other patterns.1 One explanation for these different price patterns might be that characteristics of the auctions do not completely match the assumptions of the theoretical models. Declining prices might arise when the order of sale is determined by product quality (Beggs and Graddy, 1997), supply uncertainty (Jeitschko, 1999) or participation cost (von der Fehr, 1994). If bidders demand more than one unit, we expect them to shade their bids for earlier units and prices to increase over an auction day (Donald et al., 2006).2 This paper is an empirical study of bidding behavior in sequential cattle auctions.3 The objective is to analyze the effects of the institutional characteristics of auctions on prices. The effects of the order of sale ⁎ Tel.: +43 1 4277 37481. E-mail address: [email protected]. 1 Examples of declining prices are wine auctions (Ashenfelter, 1989), art auctions (Beggs and Graddy, 1997), or rose auctions (van denBerg et al., 2001). Examples for increasing prices are rare book auctions (Deltas and Kosmopoulou, 2004). Auctions of eggplants in France have exhibited an inverse U-shaped pattern (Laffont et al., 1997). 2 Deltas and Kosmopoulou (2004) provide a detailed list of assumptions under which prices decrease, stay constant or increase. A detailed examination of sequential auctions is given in Krishna (2002). 3 For surveys of empirical studies of auctions see Hendricks and Paarsch (1995) or Laffont (1997). For a survey on nonparametric identification and estimation of auction models see Athey and Haile (2005). 0167-7187/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2008.03.001

according to quality, secret reserve prices, bidders' multi-unit demands and the characteristics of the bidders are examined. In Amstetten, a small city in Austria, dairy cattle of different quality are sold in a sequence of ascending auctions. Each animal is offered by a different seller, who may reject the auction price immediately after it has been hammered down by the auctioneer. Bidders are either representatives of wholesale firms, i.e. traders, or farmers from nearby regions. We observe two distinct price patterns. Prices decline over auction days and traders pay on average lower prices than farmers. The main questions addressed are whether the observed decline in prices is caused by ordering sales according to quality, or by the secret reserve prices that introduce uncertainty into the supply. I further investigate, whether bidders consider the strategic effects generated by the sequential auctions and multi-unit demand, and whether the price differential between traders and farmers is caused by differences in their preferences or in their strategic behavior. To answer these questions, I test the predictions of various bidding models by estimating hedonic price equations. To assess the relative contributions of the institutional characteristics in explaining price declines over auction days and price differences between traders and farmers, I employ decomposition techniques. I utilize a large data set covering 95 auction days from 1995 until 2003 with more than 25,000 dairy cattle offered. Because all important characteristics of the cattle are contained in the auction catalogue, I can employ those bidding models that assume independent private values.4 The most important characteristic of a

4 For an analysis of whether private or common value models best fit the data see Paarsch (1992).

34

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

dairy cow is the amount of milk it produces. Sellers must guarantee this information, and based on it cattle are placed into different quality classes. Since the price of milk is known, so too is the value of an individual cow. Bidders also tend to agree on various other characteristics of the cattle (Engelbrecht-Wiggans and Kahn, 1999). As a consequence, bidders' preferences can be assumed to be of a purely private nature. Each bidder ranks the different characteristics of a cow in a particular order depending on her breeding program's goals. Besides milk production, these characteristics can include an animal's behavior in the stable, how easy it is to milk, or how well it fits to a farmer's other cows. These judgments are based on a farmer's preferences and experience. The second group of bidders are traders. They are agents of resale firms and buy cattle on behalf of their firms. Traders may also buy on behalf of farmers who do not attend the auction, and place orders for particular animal(s) at specific prices before the market opens. These prices are then the valuations of the traders in the auction (Laffont et al., 1995). When traders bid on behalf of their firms, their valuations are dependent on demand in the resale market, which may be correlated with demand in the current auction market. Firms buy for geographically distinct markets, however, which I assume to be independent.5 In ascending auctions with private values, the dominant strategy is to “stay in” the auction as long as the price is lower than one's own valuation (Vickrey, 1961). This also true of sequential ascending auctions (Milgrom and Weber, 2000). The optimal stopping rule determines the price of each unit and we expect constant prices. If bidders demand more than one unit, they shade their bids for earlier units and increasing prices are expected (Donald et al., 2006). If the seller may reject the outcome of the auction, rational bidders adjust their strategic behavior to influence the probability that the seller rejects the outcome and guard themselves against a lower probability of winning by bidding more aggressively for earlier units. By adjusting the model of Jeitschko (1999), I show that prices decline over an auction day and depend on the probability of rejection.6 This paper's contributions are to estimate the effects of a secret reserve price and multi-unit demand on prices in sequential auctions, to empirically disentangle their opposite effects on prices, and to provide evidence on bidders' behavior in sequential auctions. I do not follow a structural approach like Paarsch (1997) or Donald et al. (2006), but take similar to Beggs and Graddy (1997) and Deltas and Kosmopoulou (2004) the models' predictions to the data and test for bidders' behavior. I find that the declining prices are caused by ordering sales according to quality and the secret reserve price. I also find that bidders consider the strategic effect of sequential auctions and multi-unit demand. The remainder of the paper is organized as follows. Section 2 describes the auction market in Amstetten and the data. Section 3 discusses the sequential bidding process and its predictions on prices. Section 4 presents the empirical model. Section 5 gives estimation and decomposition results. Section 6 concludes. 2. Description of the market and data The auctions in Amstetten are conducted as ascending auctions. Cattle are offered sequentially with 200–300 animals sold during a typical auction day. Both dairy cows and stock bulls are auctioned. Since stock bulls are largely a complement to the cows, only the sale of dairy cows is investigated in this paper. Auctions take place eleven times a year with each one lasting two days. On the first day potential buyers have the opportunity to view 5 Halie (2001) provides an analysis of timber auctions, where firms bid for harvesting contracts in U.S. forests and can resell their contracts later. 6 For empirical studies of (secret) reserve prices in static auctions see Elyakime et al. (1994), Paarsch (1997), or Eklöf and Lunander (2003).

the animals and a catalogue with detailed descriptions of every animal is available at a low price. The descriptions of the cattle include various quality criteria such as milk production, milk components, the animal's owner, its date of birth, names of its parents and grandparents as well as some of their quality characteristics. The cattle are divided mainly by age into three categories — young female calves, female calves and mature cows.7 There are two different breeds. Fleckvieh have spotted coats, and Braunvieh have brown coats. The cattle are also characterized by two quality criteria. The first has five different classifications. For mature cows and female calves it gives the minimum requirements for their milk's output and structure (fat, protein). In the case of young female calves, it gives the minimum requirements for their mother's milk. The second quality criterion has three divisions and is a subclass of the other quality criterion. Medical checks are carried out during the animals' stay in the auction stables and the results are published on the morning of the second day. Female calves and mature cows are also milked the evening of the first day and morning of the second. These results are published as well.8 The auctions take place on the second day with the order of sale sorted according to breed, age category and the two quality criteria. Within each group the order is random. The auctioneer starts the auction at a given price and raises the price by fixed amounts. Each bidder has a paddle (so-called Winker) with a number on its front. By raising the paddle, a bidder indicates to accept an announced price.9 The auction lasts until no one is willing to accept the next highest bid. When the bidding stops, the sale animal is “hammered down,” but is not necessarily sold as the seller has the option of rejecting the price. In this market, sellers are farmers and buyers are representatives of wholesale firms, i.e. traders, or farmers from nearby regions. All bidders arrive at the auction with trucks, as the cattle must be brought away from the market within the next day. Although bidders' overall capacities to buy cattle are likely to depend, of course, on the size of their firms or farms, the sizes of their trucks determine their capacity on an auction day.10 Traders tend to bid for pregnant or young cattle, as lactating cattle cannot be transported long distances. Most farmers need cows for immediate production and therefore tend to bid for lactating cows. The data, which were kindly provided by “Nö Genetik”, cover 95 auction days from 1995 till 2003. For each animal the winning bid, breed, age category, two quality criteria, weight, date of the auction, (anonymous) identity of the seller, and (anonymous) identity of the winning bidder (number on the Winker) are known. A seller's identity can be traced across auction days, a bidder's only within an auction day. The data also identify which of the four possible outcomes of an auction occurred — sold in the auction, sold after the auction, seller did not accept the price obtained in the auction, and no bidder accepted the initial price. Finally, for each auction day the order of sale is known. Table 1 presents summary statistics. From 1995 until 2003, 27,183 dairy cows were registered for sale; 25,125 (92%) were sold, for 1497 (6%) the seller rejected the auction's outcome, and for 561 (2%) the initial offer was not accepted. The average winning bid was euro 1275.11 When the seller rejected the offer or there was no initial offer, the winning bid equals the last submitted offer. The average winning 7 The label “female calves” is slightly misleading as these animals have already given birth. 8 If the milking output does not coincide with the information provided by the seller, the auction house depreciates the quality of the cattle to the lowest quality and announces this before the auctions take place. 9 When stock bulls are auctioned, bidders sometimes also outcry their bids. I did not observe this phenomenon when dairy cows were auctioned. See Avery (1998) for a theoretical analysis of jump bidding. 10 In this context I do not consider the exclusion of stock bulls to be problematic. Bulls have to be transported with an extra truck due to their sometimes aggressive behavior. On a particular auction day, therefore, most bidders only buy either dairy cows or stock bulls. 11 Prices are constant as of 1996. Prices before the euro's introduction are divided by 13.7603, the reference value for the Austrian schilling at the euro currency board.

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

35

Table 1 Summary statistics for winning prices (winning bids) Variable

Number of observations

Percent of sample

Mean

Standard error

Minimum

Maximum

All outcomes Animals sold in the auction Animals sold after the auction Seller did not accept the price Initial offer was not accepted

27,183 25,036 89 1497 561

100.0 92.1 0.3 5.5 2.1

1275.2 1296.0 1380.5 1064.8 892.0

271.1 263.4 323.4 222.8 174.3

85 427 753 239 85

4798 4798 2695 3125 1623

Notes: Prices are constant as of 1996. Prices before the euro's introduction are divided by 13.7603, the reference value for the Austrian schilling at the euro currency board.

bid of the animals sold in the auction equaled 1296 euro, and the average winning bid of cows sold after the auction was 1381 euro.12 Within an auction day, bidders can be identified by their Winker. With the help of this variable I define two groups of bidders. Because representatives of wholesale firms usually get a Winker number ending in zero like 10 or 20, such bidders are defined as traders. The other bidders are defined as farmers. 8982 animals were sold to traders and 16,143 to farmers. The average winning bids of the two groups differ and are presented in Table 2. Traders paid on average 1197 euro, farmers 1352. The price difference of about 12% is significantly different from zero using a t-test. This is also true for cattle of different breeds, age categories, qualities, and groups.13 Additionally, we observe that farmers paid higher prices on 92 out of 95 auction days. To investigate the evolution of prices, each auction day was divided into ten intervals. Mean prices decreased from 1263 euro in the morning to 1054 in the afternoon, a price difference of roughly 17%. Prices declined on 89 out of 95 auction days. The price decline of traders equaled 5%, whereas for farmers it was about 22%. Furthermore, farmers paid on average significantly higher prices than traders during nearly the whole auction day. Table 3 presents bidders' demand schedules. Most bidders bought one or two animals. Within this group most buyers were farmers. Most traders buy between 11 and 40 cows per auction day. They pay lower prices and the prices they pay are (relatively) constant for additional animals. Most farmers buy one cow and those, who buy a second one, pay a lower price for it. The descriptive statistics show a falling price sequence. It may be caused by the order of sale according to observed product characteristics or by bidders' strategic behavior. These statistics further show that there are bidders with multi-unit demands, and that sellers reject the outcome of the auction at a nonnegligible rate. The next section studies bidders' strategic behavior taking into account these observations. 3. Theoretical considerations I now discuss the strategic considerations of bidders and sellers and their influence on price levels, and how prices are expected to evolve over an auction day. The relevant factors are the sequential nature of the auctions and bidders' demands (Section 3.1), and the possibility for sellers to reject the outcome of the auction (Section 3.2). The basic game is a sequence of ascending button auctions.14 There are for simplicity only two units for sale, l = 1, 2, and i = 1,…, I risk neutral bidders who demand at least one unit. Let di be bidder i's 12 A few animals were sold after the auction. In these cases the seller usually accepted an outside offer. 13 The two most often offered cattle groups were Fleckvieh, female calves of quality 2B and Fleckvieh, female calves of quality 3A. They account for 62% and 14% of the overall sample. 14 There are some forms of ascending auctions. Milgrom and Weber (1982, 2000) describe button (clock, Japanese) auctions when they analyze this format. There, the price rises continuously and bidders press a button as long as they wish to stay in the auction. Once they leave the auction, they must stay out. As described above, in Amstetten one cannot perfectly observe whether another bidder has already dropped out of an auction or is still participating. I assume, however, that the button auction is a sufficient model of the Amstetten auctions. See Halie and Tamer (2003) for an incomplete model of ascending auctions.

capacity on an auction day as determined by the size of i's truck, which thus determines bidder i's demand on this auction day. It can I be equal to one or two. Total demand is denoted by D = Σi = 1 di. Let vil be bidder i's valuation for the l-th unit. It is a function of her private valuation vi and the number of units qil i has bought until l, such that vil = γi(vi, qil) if qil ≤ di and zero otherwise. γi is decreasing in qil to account for a decreasing marginal utility for further units, and the valuation of the first unit is equal to vi, i.e. γi(vi, 0) = vi. The values vi are independent draws from a continuous probability distribution G. Each unit for sale is offered by a different seller. Let rl be seller l's valuation of the l-th unit, which is an independent draw from a continuous probability distribution H. 3.1. One-unit vs. multi-unit demand If bidders demand only one unit, Milgrom and Weber (2000) show that the optimal strategy in a sequence of ascending auctions is to bid up to one's own valuation for each unit, i.e. bopt = vil, ∀l.15 An optimal stopping rule determines the price of each unit. The bidders with the two highest valuations are going to obtain one unit, and pay a price equal to the valuation of the third highest bidder. The sequence of winning bids is equal to a sequence of third-order statistics of the distribution function G, i.e. bwl = v[3:I], ∀l.16 Prices are expected to be constant over an auction day and to depend negatively on the number of offered units. If bidders demand more than one unit, there are in general multiple equilibria. However, it is still a dominant strategy to bid up to one's valuation in the second auction. This valuation is equal to bidder i's first valuation vi, if i loses the first unit, and equals γi(vi, 1), if i wins the first unit. In the first auction, bidder i stays in to a price that equals the expected second highest valuation among the (D positive) valuations of all other participants, conditional on having the highest valuation (Black and de Meza, 1993; Katzman, 1999; Donald et al., 2006). Bidders shade their first bid even more than when they demand one unit. Should they win both units, their incentive is to bid less than their true valuation on the first unit as they expect a lower price for the second unit. If there are two different winners, we observe on average constant prices and a sequence of winning bids equal to bwl = v[3:D], ∀l. If the same bidder wins both units, we observe increasing prices; bwl = (γ− w(v[3:D]), v[3:D]) with γ− w to be the residual supply that the winning bidder faces. Prices are expected to increase on average, therefore, and to increase for winning bidders. 3.2. Secret reserve price In contrast to bidders, each seller faces a static decision problem. Seller l optimally rejects the outcome of the l-th auction, if the price bwl is lower than his valuation rl, and accepts it, if it is equal to or higher than his valuation rl. The possibility for sellers to reject auction outcomes affects the number of units offered and adds uncertainty to total supply. Rational bidders are aware of this. If they shade their bids for earlier units too much or, put differently, leave the auction too 15

The same is true when there is only one unit for sale (Vickrey, 1961). In general, it is a sequence of L + 1-th order statistics, where L is the number of offered units. 16

36

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

Table 2 Differences in winning prices between traders and farmers Variable

All Traders Farmers Difference pbidders in percent value

All animals Breed Braunvieh Fleckvieh Age category Female calves Young female calves Mature cows Quality Quality 1B Quality 2A Quality 2B Quality 3A Quality 3B Selected cattle groups Fleckvieh, female calves, quality 2B Fleckvieh, female calves, quality 3A Order of sale Decile 1 (Morning) Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9 Decile 10 (Afternoon)

1296.3

1196.7

1351.7

11.5

0.00

1249.2 1301.9

1147.2 1203.9

1323.1 1354.7

13.3 11.1

0.00 0.00

1305.7 765.8 1072.3

1208.5 769.5 1046.1

1359.2 758.0 1077.4

11.1 −1.5 2.3

0.00 0.41 0.53

1849.6 1649.9 1319.3 1105.7 902.9

1863.3 1571.3 1229.1 1120.1 889.0

1848.3 1660.7 1361.1 1085.6 923.4

−0.8 5.4 9.7 −3.2 3.7

0.76 0.00 0.00 0.00 0.16

1315.2 1100.4

1239.9 1147.0

1369.3 1101.5

9.4 −4.1

0.00 0.00

1263.4 1347.2 1426.7 1437.0 1372.5 1300.0 1255.5 1192.2 1106.6 1053.4

1174.3 1142.2 1300.4 1337.2 1274.4 1231.4 1221.3 1194.7 1145.2 1110.6

1352.1 1490.0 1477.7 1475.2 1423.1 1340.9 1296.3 1217.1 1115.6 1051.7

13.1 23.3 12.0 9.3 10.4 8.2 5.8 1.8 −2.6 −5.6

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Notes: Prices are constant as of 1996. Prices before the euro's introduction are divided by 13.7603, the reference value for the Austrian schilling at the euro currency board. The p-value in the last column originates from a two-sided t-test testing the significance of the mean price difference between traders and farmers.

early — compared to a model without a secret reserve price, sellers with high valuations will reject the auction's outcome and fewer units will be available. Bidders therefore adjust their strategic behavior to influence the probability of rejection. The sequence of winning bids changes due to the change in bidders' optimal behavior. If bidders demand only one unit, bidder i's optimal strategy in the second auction is still to bid up to her valuation vi. Bidder i's expected profit π2 in the second auction is equal to      π2 ðvi Þ = ρ2 vi −ρ1 E v½3:I jvi = v½2:I −ð1−ρ1 ÞE v½2:I jvi = v½1:I ;

ð1Þ

where ρl is the probability that the outcome of the l-th auction is not rejected, i.e. ρl =H(rl b bwl). The probabilities ρ1 and ρ2 are in general not equal and each ρl depends on the respective outcome of the auction bwl, and the distribution function H. Bidder i's profit in the second auction is equal to i's valuation vi minus the price paid in the second auction, given that a second unit is sold. This price is a weighted average of the thirdorder and second-order statistics. The weight is equal to the probability that the first unit is sold, i.e. ρ1. If the first unit is sold, then the price in the second auction equals the third-order statistic. If the first unit is not sold, then the price in the second auction is equal to the second-order statistic. The second unit is sold with a probability equal to ρ2. Bidder i's optimal strategy in the first auction is to bid her valuation vi minus the expected payoff in the second auction (Eq. (1)):   b1 ðvi Þ = vi −π2 ðvi Þ = ð1−ρ2 Þvi + ρ2 fρ1 E v½3:I jvi = v½2:I   + ð1−ρ1 ÞE v½2:I jvi = v½1:I g:

ð2Þ

To guard against a lower probability of winning, bidders react by bidding more aggressively in the first auction. They bid a weighted average of their valuation vi and the price in the second auction, i.e.

ρ1E[v[3:I]|vi = v[2:I]] + (1 − ρ1)E[v[2:I]|vi = v[1:I]]. There are two effects. The first effect accounts for the seller of the first unit as an additional player. The second effect accounts for the possibility that the second unit is not sold. The higher are the rejection probabilities, the more aggressively bidders bid, as otherwise some of the bidders do not obtain a unit, although their valuation is higher than that of the seller. If the probabilities of rejection are very large, bidders stay in the first auction even until the bidder with the second highest valuation has left.17 If the outcomes of both the first and second auction are not rejected by the respective sellers and both units are sold, we can show that the price of the second unit is expected to be lower than the price of the first unit, and the sequence of winning bids bwl is equal to  bwl =

ð1−ρ2 Þv½2:I + ρ2 v½3:I v½3:I

if l = 1 ; if l = 2

ð3Þ

where the price in the first auction equals a weighted average of the second-order and third-order statistics. If the outcomes of both auctions are rejected, then in both cases the winning price is zero. Prices are expected to decline over an auction day and to depend positively on the probability of rejection in the second auction (1 −ρ2).18 If sellers may reject the outcome of the auction and bidders demand more than one unit, then there are two opposing effects. Bidders bid more aggressively in the first auction to account for the possibility that the seller rejects the outcome. They shade their bids in the first auction to account for their multi-unit demand. On average these effects may cancel out. It is then an empirical question to determine the dominant effect. The data allow us to identify both effects and assess the magnitude of each. 4. Empirical bidding model The theoretical considerations suggest that prices are determined by the sequential nature of the auctions, bidders' demand, and the secret reserve price. To formally test the theoretical predictions and assess the effect of bidders' preferences and strategies on prices, I estimate hedonic price equations using ordinary least squares. To model the probability of rejection, I also use data on units for which sellers rejected the outcome of the auction and estimate a probit model. I construct the inverse Mill's ratio and use it in the pricing equations. To account for differences in bidders' preferences, the price equations are estimated separately for traders and farmers, and to explore the determinants of the price patterns in more detail, I decompose the price difference between traders and farmers with techniques developed by Blinder (1973) and Oaxaca (1973). These techniques are used to analyze wage differentials and distinguish between differences in human capital endowment and differences in the valuation of human capital across groups of individuals. Here, they help to understand whether price differences across bidders can be explained by differences in preferences or in strategic behavior. 4.1. Price equations For the price equations, I use the logarithm of the winning price as the dependent variable. Characteristics of the cattle and variables that describe the sequential nature of the auctions, bidders' demands, and

17 Jeitschko (1999) formally describes the equilibrium price paths of a model that is close to the situation in Amstetten. With some probability ρ ∈ [0, 1] that is common knowledge there is no second auction. In the second auction, bidders bid up to their valuation vi, and in the first auction, they bid a weighted average of their valuation vi and the price in the second auction, i.e. the third-order statistic v[3:I]. Beggs and Graddy (1997) obtain a similar outcome. The order of sale is according to quality and bidders' valuations are assumed to decline with a common factor ρ ∈ [0, 1]. 18 The proof that prices decline is analogous to the proof in Jeitschko (1999).

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42 Table 3 Demand schedules Number of units bought on one auction day

Number of bidders All

Traders

Farmers

All

Traders

Farmers

1–10 1 2 11–20 21–30 31–40 41–50 51–60 61–100 Total

15,811 9910 3882 1612 3462 2645 679 327 589 25,125

465

15,346 9888 3860 266 498 33

1352.1 1378.0 1338.0 1213.0 1198.0 1191.9 1199.9 1240.5 1214.5 1296.3

1118.9

1359.2 1378.7 1339.8 1207.7 1211.2 1154.3

1346 2964 2612 679 327 589 8982

Mean price in euro

16,143

1214.1 1195.8 1192.4 1199.9 1240.5 1214.5 1196.7

1351.7

Notes: Prices are constant as of 1996. Prices before the euro's introduction are divided by 13.7603, the reference value for the Austrian schilling at the euro currency board.

the secret reserve price, are explanatory variables. The choice of these variables is based on the sequences of winning bids described in Sections 3.1 and 3.2. These sequences depend on order statistics to account for the strategic effect of the number of bidders. In Amstetten, the number of bidders is usually high and the effect of the order statistics can therefore be considered as negligible.19 I also include cattle group-specific, auction day-specific and seller-specific fixed effects.20,21 To test the strategic effect of sequential auctions, I use the number of offered units. This variable is constant within an auction day, but varies over auction days. Its effect can only be tested, therefore, if there are a sufficient number of auction days. To test for the strategic effect of multi-unit demand, I use the total number of units bought by the winning bidder on an auction day, the cumulative number of units bought by the winning bidder and the cumulative number of units bought by other bidders. The first variable measures a (winning) bidder's fulfilled demand on an auction day. It is constant on an auction day, but varies over bidders. Its effect can be tested, if there is enough variation across bidders. The second variable equals zero for the first unit bought by each (winning) bidder on an auction day, one for the second unit and, so on. As bidders can only buy one animal at a time, it is a bidder-specific trend on an auction day and measures the effect of bid shading in auctions of earlier units. Therefore, it can be used to measure deviations from on average declining prices. Identification comes from variation across bidders and times of day. The third variable is other bidders' cumulated demand on an auction day. It measures the residual supply each winning bidder faces, and varies across bidders and auction days. To test the effect of the secret reserve price, I use the order of units and the probability of rejection. The order of units on a particular auction day measures the relative time elapsed on that day. The number of units offered varies across auction days. I normalize them to one and construct a variable equal to zero before the auction starts, and that linearly increases over the course of an auction day equaling one at its end. 4.2. Probability of rejection To model the probability of rejection, I also use data for the 1497 rejected outcomes. I estimate a probit model with a dependent variable equal to one for unsold cows and zero otherwise. The

19 In general, I do not know the number of bidders. There is information for four auction days, however. In January, February, March and April 1996, there were 249, 209, 191 and 181 bidders. 20 The effect of the number of bidders on prices is measured by the auction dayspecific fixed effects. 21 I construct dummy variables for each of the six sellers who supplied more than 100 animals in the years 1995 to 2003. Another 80 sellers who sold between 50 and 100 cows are summarized in one dummy variable.

37

probability of rejection depends on the winning bid, and in the probit model, the only explanatory variable would then be the logarithm of the winning price. This variable is endogenous, however, as bidders strategically react to the probability of rejection. Therefore, I use proxy variables as explanatory variables — the same as in the price equations. The inverse Mill's ratio is then constructed for eventual use as an estimate for the probability of rejection in the price equations.22 To (economically) identify the probability of rejection, I use an indicator variable that is equal to one if the seller rejected the last offer and zero else as an instrument. As I know the seller's identity across auctions, the last offer can be from other auction days but also from the same auction day. This variable is a valid instrument as sellers can be assumed to have no dynamic considerations. However, one has also to assume that bidders do not remember whether the seller rejected an offer in the past. If the seller's decision is from another auction day, this is plausible. If it is from the same day, this seems to be still plausible as long as there are enough animals offered between the current and last offer for each seller. To validate these considerations, I calculated this number. The mean is equal to 1028.6; the median is equal to 353 and the 25 (10) percentile is equal to 79 (12). In 2% of the cases the difference is equal to one. As a robustness check, I also restrict the sample to observations for which this variable is larger than 12. 5. Estimation results In this section I report the estimation results for the basic and some additional specifications, and the decomposition results. Table 4 presents the estimation results for the basic specifications. Results for the probit model are in column 1. The model's explanatory power is 18%. The used instrument is highly correlated with the probability of rejection. If the seller rejected the last offer, the probability of rejection significantly increases by 2.3%. Higher quality and more weight also increase the likelihood of a sale. The more cows the bidders have already bought, the more likely it is that an animal stays unsold. Columns 2–8 present results for various specifications of the price equation. Column 2 uses data on all bidders, whereas all other specifications separate between traders and farmers. The first specification (columns 2, 3 and 4) includes animal characteristics and the order of units sold. The second specification (columns 5 and 6) adds variables that account for the strategic effect of sequential auctions and bidders' multi-unit demands. The third specification (columns 7 and 8) additionally includes the inverse Mill's ratio to account for the strategic effect of the secret reserve price. As in the probit model, cattle group-specific, auction day-specific and sellerspecific dummy variables prove to be highly significant in all specifications. To avoid potentially misclassifying traders and farmers, I drop observations when traders bought less than ten cows or when farmers bought more than two. The explanatory power of the regressions is between 62 and 70%. Comparing column 2 with columns 3 and 4, we observe that some estimated coefficients are different across bidders. A Chow test is used to test the statistical significance of the differences. The F-statistic of 24.29 (116, 22,148) rejects the null hypothesis of equal coefficients. It indicates the importance of distinguishing between traders and farmers in the regressions and that bidders' preferences are different. The estimated values for the constant lie between 5.73 and 5.77 for traders, and between 5.98 and 6.05 for farmers, and indicate that controlling for product quality does not necessarily explain price differences between traders and farmers. Traders pay between 20 and 30% less for a cow with the basic characteristics (Braunvieh, mature cow, quality 3B, subquality 3) than farmers do. Recall that the raw 22 For a discussion of the inverse Mill's ratio, see for example, Wooldridge (2001, chapter 17).

38

Table 4 Determinants of sale and prices Data set

Offered units

All bidders

Traders

Farmers

Traders

Farmers

Traders

Farmers

Number of observations

22,150

22,265

8517

13,748

8517

13,748

8016

12,705

0.69

0.62

0.70

0.62

0.68

0.61

(3)

(4)

(5)

(6)

(7)

(8)

0.18

0.64

Prob(rejection)

Ln(winning bid)

Variable

(1)

(2)

Constant Last offer rejected Fleckvieh Female calves Young female calves Quality 1B Quality 2A Quality 2B Quality 3A Sub-quality 1 Sub-quality 2 Weight Order of units Number of offered units Total number of units bought by the winning bidder Cumulative number of units bought by the winning bidder Cumulative number of units bought by other bidders Inverse Mill's ratio Cattle group-specific fixed effects (4) Auction day-specific fixed effects (94) Seller-specific fixed effects (7)

1.4585 (1.62) 0.0234 (5.18)⁎ −0.0038 (0.27) −0.0600 (2.30)⁎ −0.0365 (5.16)⁎ −0.0293 (2.62)⁎ −0.0267 (2.50)⁎ −0.0753 (3.12)⁎ −0.0372 (3.08)⁎ − 0.0146 (1.06) − 0.0160 (1.23) −0.1965 (8.88)⁎ − 0.0475 (2.14)⁎ −0.0002 (0.86) 0.0029 (28.39)⁎ −0.0016 (10.93)⁎ 0.0003 (5.55)⁎ Yes (5.76)⁎ Yes (271.51)⁎ Yes (36.90)⁎

5.9869 (202.86)⁎ 0.0644 (6.41)⁎ 0.2452 (14.38)⁎ −0.1740 (9.67)⁎ 0.5285 (34.75)⁎ 0.4412 (32.95)⁎ 0.2552 (19.10)⁎ 0.0858 (6.75)⁎ 0.1205 (10.18)⁎ 0.0367 (3.07)⁎ 0.6376 (31.69)⁎ −0.0724 (6.78)⁎

Yes (9.67)⁎ Yes (155.22)⁎ Yes (40.26)⁎

5.7658 (126.08)⁎

6.0501 (138.49)⁎

5.7695 (76.46)⁎

6.0126 (110.31)⁎

0.0289 (1.36) 0.2522 (7.49)⁎ − 0.0836 (2.86)⁎ 0.4751 (13.23)⁎ 0.3447 (15.46)⁎ 0.1436 (9.25)⁎ 0.0459 (3.31)⁎ 0.0752 (4.47)⁎ 0.0272 (1.64) 1.0847 (43.08)⁎ − 0.0322 (2.20)⁎

0.0806 (7.27)⁎ 0.2573 (13.28)⁎ − 0.1949 (6.81)⁎ 0.5452 (22.42)⁎ 0.4690 (20.02)⁎ 0.3106 (12.65)⁎ 0.1203 (4.67)⁎ 0.1221 (7.09)⁎ 0.0465 (2.66)⁎ 0.5127 (18.47)⁎ − 0.1336 (9.18)⁎

0.0307 (1.45) 0.2529 (7.51)⁎ −0.0832 (2.86)⁎ 0.4755 (13.34)⁎ 0.3450 (15.49)⁎ 0.1444 (9.28)⁎ 0.0469 (3.39)⁎ 0.0784 (4.64)⁎ 0.0291 (1.75) 1.0882 (43.42)⁎ 0.0103 (0.47) −0.0001 (0.31) 0.0004 (3.00)⁎ 0.0003 (1.59) −0.0002 (3.45)⁎

0.0820 (7.42)⁎ 0.2521 (13.01)⁎ −0.1964 (6.93)⁎ 0.5475 (22.49)⁎ 0.4720 (20.12)⁎ 0.3127 (12.72)⁎ 0.1208 (4.69)⁎ 0.1252 (7.19)⁎ 0.0486 (2.75)⁎ 0.5124 (18.55)⁎ − 0.0595 (2.75)⁎ 0.0002 (1.60) − 0.0264 (8.69)⁎ 0.0343 (8.24)⁎ − 0.0003 (5.28)⁎

Yes (3.05)⁎ Yes (95.95)⁎ Yes (4.97)⁎

Yes (5.76)⁎ Yes (86.89)⁎ Yes (32.19)⁎

Yes (3.25)⁎ Yes (88.72)⁎ Yes (4.98)⁎

Yes (6.05)⁎ Yes (76.11)⁎ Yes (32.88)⁎

5.7258 (66.16)⁎

6.1610 (42.04)⁎

0.0344 (1.52) 0.2463 (7.16)⁎ −0.1190 (3.77)⁎ 0.4761 (13.07)⁎ 0.3486 (14.82)⁎ 0.1502 (8.01)⁎ 0.0544 (3.06)⁎ 0.0754 (4.29)⁎ 0.0231 (1.32) 1.0698 (36.62)⁎ 0.0064 (0.28) −0.0001 (0.27) 0.0006 (2.25)⁎ 0.0001 (0.61) −0.0001 (2.51)⁎ 0.0722 (1.13) Yes (2.87)⁎ Yes (63.14)⁎ Yes (4.95)⁎

0.0773 (7.01)⁎ 0.2463 (12.29)⁎ −0.2498 (7.39)⁎ 0.5312 (19.28)⁎ 0.4586 (17.20)⁎ 0.2950 (10.46)⁎ 0.1017 (3.39)⁎ 0.1253 (6.99)⁎ 0.0461 (2.53)⁎ 0.4539 (15.24)⁎ −0.0540 (2.11)⁎ −0.0017 (10.96)⁎ −0.0249 (7.85)⁎ 0.0346 (4.82)⁎ −0.0002 (3.33)⁎ 0.6920 (3.49)⁎ Yes (4.31)⁎ Yes (51.57)⁎ Yes (31.95)⁎

Notes: Absolute values of t-statistics are shown in parentheses beside the parameter estimates. In the probit equation, the value of the χ2-statistic is shown for the fixed effects and in the hedonic price equations, it is the value of the F-statistic. In the probit model (column 1), the dependent variable is an indicator variable, which is equal to one when the seller rejected the offer and zero otherwise. Explanatory variables are animal characteristics, the order of units, number of offered units, total number of units bought by the winning bidder, cumulative number of units bought by the winning bidder and cumulative number of units bought by other bidders. An indicator variable that is equal to one if the seller has rejected the last offer and zero otherwise serves as an instrument. In the price equations (columns 2–8), the dependent variable is the logarithm of the wining bid. The first specification (columns 2–4) includes animal characteristics and the order of units; the second specification (columns 5 and 6) additionally includes the number of offered units, total number of units bought by the winning bidder, cumulative number of units bought by the winning bidder and cumulative number of units bought by other bidders; and the third specification (columns 7 and 8) additionally includes the inverse Mill's ratio. The reference group with respect to animal characteristics is Braunvieh, mature cows, quality 3B and subquality 3. All specifications are estimated with cattle group-specific, auction day-specific and seller-specific dummy variables. Standard errors and t-statistics are adjusted for heterogeneity and if necessary for the two step procedure. ⁎ Denotes a 95% level of significance.

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

Pseudo/adjusted R-squared Dependent variable

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

price differential is 12%, which might indicate that traders' valuations are on average lower than those of farmers. It may also indicate that traders' transportation costs are higher.23,24 We observe differences in the coefficients for age category, quality 2B and weight. The difference in the coefficient for young female calves may account for differences in bidders' willingness to pay, but also for differences in their attitudes towards risk. Traders seek to buy non-lactating cows and farmers cows that milk. Because young female calves do not give milk, we may interpret the difference in the estimated coefficients as a difference in bidders' willingness to pay. The quality of young female calves is based on their mothers' quality, and due to a small risk of infertility or an innate inability to give milk, it is associated with some uncertainty. We may also interpret the difference in the estimated coefficients, therefore, as a difference in risk aversion.25 The higher coefficient for quality 2B in the farmers' equation reflects their preference for this quality. The higher coefficient on weight in the traders' equation mirrors their preference for heavier cows. Because traders prefer pregnant cows, since lactating cows cannot be transported over long distances, the higher coefficient on weight may account for the additional value of an unborn calf.26 Both groups of bidders pay declining prices over an auction day, but the magnitude of the declines is greater for farmers. Everything else is equal, the average price a trader (farmer) pays for the first cow on an auction day is about 3% (13%) higher than he or she pays for the last cow (see columns 3 and 4). This result provides evidence that part of the raw price decline of 17% (5% for traders and 22% for farmers) can be explained by the fact that the order of sale is according to quality. When we add the variables that describe the strategic effect of sequential auctions and bidders' multi-unit demands, the estimated coefficient of the order of units changes to an insignificant positive value of 1% for traders (column 5). It decreases to a significant 5% for farmers (column 6). When we add the probability of rejection, the estimated coefficients of the order of units change only slightly (columns 7 and 8). These results indicate that the estimated price decline is actually less pronounced compared to a standard specification,27 once we take all institutional aspects of the auctions into account. For some bidders we now even do not observe any price decline. We also observe that prices depend on variables that explain bidders' strategic behavior with respect to the sequential nature of the auctions, bidders' multi-unit demands, and the secret reserve price. The coefficients on the number of offered units are insignificant for traders (columns 5 and 7). Depending on the specification, there is an insignificant positive or a significant negative effect for farmers (columns 6 and 8). Traders do no adjust their bids to different market situations. This may indicate that their aggregate demand function is highly elastic. Farmers, whereas, may lower their bids when more units are offered.

23 The latter option is explored in more detail by estimating the price equation for traders with a dummy variable for a trader who is from a region farther away than other traders. Traders usually obtain the same Winker number, but as the data cover a longer time period this cannot be said for sure. The estimated coefficient is negative and the estimated value for the constant increases. Thus, transport cost may matter. 24 Subsidies cannot explain the price difference between traders and farmers, because traders resell to other farmers who also obtain subsidies. 25 Due to the uncertainty, one may consider the assumption of private values to be violated. Talking to Johann Tanzler and farmers participating in the auctions, however, gave me the impression that farmers buy cattle according to their immediate needs for production. I therefore consider the second explanation to be of lesser importance. 26 I do not have data on whether an animal is pregnant. Therefore, I cannot explore the effect of pregnancy on prices in more detail. If pregnancy is positively correlated with traders' preferences, however, omitting a dummy variable for pregnancy biases the estimates of the constant and the coefficient on weight upwards. Thus, if we were able to control for pregnancy, the estimated constant in the regression for traders might be smaller and the difference between the estimated constants for traders and farmers even larger. The same might be true for weight. 27 See for example, Beggs and Graddy (1997) or Deltas and Kosmopoulou (2004).

39

The coefficient on the number of units bought by the winning bidder on an auction day is significantly positive for traders (0.0004), and significantly negative for farmers (−0.0264). The more units traders buy on an auction day, the higher is the price. Higher demand lets them bid more aggressively. The opposite is true for farmers. A reason for this result might be that there are only two groups of farmers buying either one or two units and, therefore, there might not be enough variation in the data to identify this variable's effect. The more units bidders have already bought within a day, the higher is the price. Bidders shade their bids and take the strategic effect of multiunit demand into account. The estimates imply a 1.0% elasticity for traders and a 0.2% elasticity for farmers (evaluated at the sample mean). The effect of bid shading is small.28 This is particularly the case when we compare these values to the estimated elasticities of the cumulative number of units bought by other bidders. The more cows other bidders have already bought, the lower the price. The coefficients imply a 3.2% elasticity for traders, and 4.0% for farmers (evaluated at the sample mean). The coefficient of the probability of rejection is positive and significant as expected. The higher the probability of rejection, the higher are the winning bids. Prices are expected to decline over an auction day, but if only the coefficient of the order of units is significant, declining prices are not explained by the secret reserve price, and might be due to other factors like participation cost. As columns 7 and 8 show, the coefficient of the probability of rejection is not significantly different from zero for traders, but significantly different for farmers. Traders do not adjust their bids to the secret reserve price, whereas farmers do. The higher the probability that the seller rejects the outcome of the auction, the higher the prices paid by farmers. In line with the predictions, the estimated price decline is at the same time insignificant for traders and significant for farmers. The joint occurrence of these results lets us believe that the only explanation for the price decline is the secret reserve price. To evaluate this hypothesis in more detail, I conduct robustness checks and estimate additional specifications to account for bidders' participation. 5.1. Further specifications Other reasons for declining prices may be declining participation due to the order of sale according to quality or to participation cost. Different quality cows are imperfect substitutes. If bidders' substitution patterns differ, quality differences may attract different numbers of bidders. Then ordering sales according to quality automatically induces decreasing participation, as bidders who only buy high quality do not bid for low quality. If there are participation costs, any order of sale induces decreasing participation.29 Both effects would be measured by the order of units. To control for bidders' participation, I estimate two additional specifications. The first adds the order of units multiplied with particular cattle groups to the last specification in Table 4. The second further includes the order of units multiplied by decile divisions of each auction day. The first set of variables tests for different participation behavior within particular cattle groups, whereas the second set tests whether participation is driven by the particular time of day. To support the hypothesis that declining prices are primarily caused by the secret reserve price, the previously obtained results 28 The cumulative number of units bought by the winning bidder could also measure learning effects or budget constraints. If either explanation was true, I would expect a negative sign for this variable. The more bidders learn, the lower the expected price for later units. If bidders are budget constrained, their valuations and prices for later units should be lower. However, we do not observe negative signs on the estimated coefficients. 29 For explicit models with participation costs see von der Fehr (1994) or Menezes and Monteiro (1997). For structural models that account for bidders' participation see Bajari and Hortacsu (2003) or Donald et al. (2006).

40

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

Table 5 Robustness checks Data set

Traders

Farmers

Traders

Farmers

Traders

Farmers

Number of observations

8016

12,705

8016

12,705

7247

11,577

Adjusted R-squared

0.68

0.62

0.68

0.62

0.68

0.61

Dependent variable

Ln(Winning bid)

Variable

(1)

(2)

(3)

(4)

(5)

(6)

Constant Fleckvieh Female calves Young female calves Quality 1B Quality 2A Quality 2B Quality 3A Sub-quality 1 Sub-quality 2 Weight Order of units Number of offered units Total number of units bought by the winning bidder Cumulative number of units bought by the winning bidder Cumulative number of units bought by other bidders Inverse Mill's ratio Order of units × Braunvieh Order of units × Fleckvieh, female calves, quality 2B Sub-quality 1 Sub-quality 2 Sub-quality 3 Order of units × Fleckvieh, female calves, quality 3A Order of units × Deciles (9)

5.7424 (64.20)⁎ 0.0585 (1.53) 0.2729 (6.34)⁎ −0.1267 (4.21)⁎ 0.4342 (8.18)⁎ 0.3130 (8.18)⁎ 0.1335 (5.85)⁎ 0.0457 (2.30)⁎ 0.0713 (3.69)⁎ 0.0178 (0.99) 1.0761 (36.68)⁎ −0.0505 (0.89) −0.0001 (0.34) 0.0002 (0.76) −0.0001 (2.60)⁎ 0.0006 (2.03)⁎ 0.0560 (0.89) −0.0855 (0.61)

6.3668 (40.02)⁎ 0.0933 (5.37)⁎ 0.2786 (12.76)⁎ −0.2725 (− 7.70)⁎ 0.4112 (6.66)⁎ 0.3433 (5.72)⁎ 0.2035 (3.44)⁎ 0.0456 (0.77) 0.0827 (4.12)⁎ 0.0273 (1.46) 0.4738 (15.96)⁎ −0.1985 (2.53)⁎ −0.0018 (11.09)⁎ 0.0340 (7.89)⁎ −0.0002 (3.53)⁎ −0.0247 (4.78)⁎ 0.5898 (2.99)⁎ − 0.6770 (3.73)⁎

5.7102 (61.80)⁎ 0.0603 (1.53) 0.2725 (6.34)⁎ −0.1237 (4.15)⁎ 0.4336 (8.14)⁎ 0.3131 (8.18)⁎ 0.1320 (5.74)⁎ 0.0450 (2.26)⁎ 0.0723 (3.74)⁎ 0.0174 (0.96) 1.0818 (37.15)⁎ −0.0079 (0.12) −0.0001 (0.30) 0.0002 (0.98) −0.0002 (2.83)⁎ 0.0005 (1.75) 0.0354 (0.58) −0.0645 (0.40)

6.4686 (42.60)⁎ 0.0813 (3.68)⁎ 0.2824 (12.96)⁎ − 0.2684 (7.62)⁎ 0.4035 (6.39)⁎ 0.3353 (5.45)⁎ 0.2002 (3.31)⁎ 0.0390 (0.64) 0.0836 (4.15)⁎ 0.0297 (1.58) 0.4835 (16.54)⁎ − 0.2252 (2.57)⁎ −0.0018 (11.03)⁎ 0.0342 (7.94)⁎ − 0.0002 (3.71)⁎ − 0.0249 (4.88)⁎ 0.4843 (2.55)⁎ − 0.7559 (3.91)⁎

5.7250 (64.58)⁎ 0.0274 (1.23) 0.2189 (8.29)⁎ −0.1545 (5.57)⁎ 0.4633 (12.47)⁎ 0.3316 (13.63)⁎ 0.1352 (7.14)⁎ 0.0458 (2.51)⁎ 0.0727 (3.36)⁎ 0.0204 (0.94) 1.0658 (33.78)⁎ 0.0031 (0.13) 0.0000 (0.03) 0.0001 (0.51) −0.0002 (2.46)⁎ 0.0008 (2.57)⁎ 0.1070 (1.58)

6.1421 (43.10)⁎ 0.0710 (6.18)⁎ 0.2200 (9.49)⁎ − 0.3242 (7.45)⁎ 0.5150 (16.83)⁎ 0.4424 (14.82)⁎ 0.2737 (8.63)⁎ 0.0809 (2.34)⁎ 0.1319 (6.06)⁎ 0.0533 (2.41)⁎ 0.4306 (13.50)⁎ − 0.0681 (2.04)⁎ − 0.0019 (11.29)⁎ 0.0368 (8.09)⁎ − 0.0002 (2.67)⁎ − 0.0246 (4.66)⁎ 0.8559 (4.20)⁎

0.1408 (2.29)⁎ 0.0050 (0.09) 0.0783 (1.11) 0.1468 (2.16)⁎ No

0.3654 (4.59)⁎ 0.0431 (0.54) − 0.2073 (2.28)⁎ 0.0694 (0.70) No

0.2181 (2.73)⁎ −0.0714 (1.04) 0.1478 (1.78) 0.1384 (1.61) Yes (2.62)⁎

0.3373 (3.79)⁎ 0.0883 (0.96) −0.1726 (1.60) 0.1233 (0.96) Yes (0.71)

No

No

Notes: Absolute values of t-statistics are shown in parentheses beside the parameter estimates. The value of the F-statistic is shown for the fixed effects. In all specifications, the dependent variable is the logarithm of the wining bid, and explanatory variables are animal characteristics, the order of units, number of offered units, total number of units bought by the winning bidder, cumulative number of units bought by the winning bidder and cumulative number of units bought by other bidders. Columns 1 and 2 additionally include the order of units multiplied with particular product groups; columns 3 and 4 additionally include the order of units multiplied with particular product groups, and the order of units multiplied by decile divisions of each auction day; and columns 5 and 6 restrict the samples to observations for which the number of offered cows between the current and last offer for each seller was larger than 12. The reference group with respect to animal characteristics is Braunvieh, mature cows, quality 3B and subquality 3. All specifications are estimated separately for traders and farmers, with cattle group-specific, auction day-specific and seller-specific dummy variables, and adjusted probit models in the first step. Standard errors and t-statistics are adjusted for heterogeneity and if necessary for the two step procedure. ⁎Denotes a 95% level of significance.

should be sustained. The added variables should be either insignificant or, if significant, should not change the signs and significance of the probability of rejection and order of units. Columns 1 and 2 of Table 5 present the results for traders and farmers when the order of units multiplied by particular cattle groups is added. We observe larger coefficients than previously for the price decline over an auction day, and significant price movements for each cattle group. The price decline over an auction day is 5.1% for traders, but is still insignificant. It is 19.9% and significant for farmers. The estimated coefficient of the inverse Mill's ratio is insignificant for traders and significant for farmers. Columns 3 and 4 of Table 5 present the second extended specification for traders and farmers. The coefficients of the order of units multiplied by the ten auction-day-time intervals are jointly significant for traders, but none of the coefficients is individually significant. The estimates are jointly and individually insignificant for farmers. These results support the hypothesis that declining prices are mainly caused by the secret reserve price. For both specifications, we observe an insignificant probability of rejection combined with an insignificant price decline for traders, and a significant probability of rejection combined with a significant price decline for farmers. The added variables do not change the previous results. The results further show, however, that different cattle groups attract different numbers of bidders. To test the validity of the instrument used in the probit model, I restrict the sample to observations for which the number of offered cows between the current and last offer for each seller was larger than 12. Herewith, I exclude those cases, where bidders may remember the

seller's behavior. The estimation results, presented in columns 5 and 6 of Table 5, show no differences compared to the results in columns 7 and 8 of Table 4. Table 6 Blinder–Oaxaca decomposition results Price difference

Total

Unexplained Explained

Distribution of reference: all bids Basic specification 0.120 31.1% Additional specifications With variables that describe strategic behavior 0.120 11.8% With variables that describe participation behavior 0.120 11.5% Contribution of selected variables Quality 2B 0.111 Weight −0.418 Order of units −0.028 Number of offered units −0.523 Inverse Mill's ratio 0.527

68.9% 88.2% 88.5% 0.040 −0.017 0.006 0.029 −0.002

Notes: The decomposition results are based on price regressions for traders and farmers. The dependent variable is the logarithm of the winning bid. The explanatory variables of the basic specification are the variables that describe bidders' preferences, i.e. constant, animal characteristics, cattle group-specific, auction day-specific and seller-specific fixed effects. The variables that describe the strategic behavior are the order of units, number of offered units, total number of units bought by winning bidder, cumulative number of units bought by winning bidder, cumulative number of units bought by other bidders, and the inverse Mill's ratio. Variables that describe participation behavior are the order of units multiplied with particular product groups and the order of units multiplied by decile divisions of each auction day. The reference group with respect to product characteristics is Braunvieh, mature cows, quality 3B and subquality 3. The distribution of reference is the distribution of all bids.

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

5.2. Decomposition results Three factors may explain the price difference between traders and farmers: bidders' preferences for particular animals, strategic behavior and participation. To assess the relative importance of these factors, I calculate the price decomposition for a basic specification using variables that describe bidders' preferences only and for two additional specifications. The first adds the variables that describe bidders' strategic behavior; and the second adds the variables that describe participation behavior. Bidders' preferences are measured by animal characteristics, cattle group-specific and seller-specific fixed effects. Strategic behavior is measured by the number of units offered, total number of units bought by the winning bidder, the cumulative numbers of units bought by the winning bidder and by other bidders, and order of units sold. Participation behavior is measured by the order of units multiplied by particular cattle groups, and by order of units multiplied with the time-of-day deciles. Table 6 presents the decomposition results. The results of the basic specification show that about two thirds of the raw price difference can be attributed to bidders' endowment, i.e. which product qualities bidders prefer. The other part is due to differences in coefficients that may reflect differences in the willingness to pay, strategic behavior or participation. The results for the two other specifications show that bidders' preferences are the most important source of the unexplained price difference between traders and farmers. Bidders' strategic behavior is the second most important source, whereas the contribution of the variables that describe bidders' participation is not given. Particular variables that contribute most to the unexplained price difference between traders and farmers are quality 2B, weight, the number of offered units, order of units and the inverse Mill's ratio. These results indicate that differences in strategic behavior are mainly driven by differences in bidders' reactions to changes in supply and uncertainty of supply. 6. Summary and concluding remarks This paper presented an empirical analysis of bidding behavior in sequential cattle auctions. The objectives were to investigate the effects of institutional characteristics on prices, where institutional characteristics denote the order of sale according to quality, a secret reserve price, bidders' multi-unit demands and the existence of two bidder groups, i.e. traders and farmers. The main results are as follows. Animal characteristics are the most important source of variation in prices. This finding is not astonishing when we keep in mind that the quality of a cow determines its value on the market. Nevertheless, institutional aspects and their effects on bidders' strategic behavior are nonnegligible determinants of prices. Declining prices are caused by the order of sale according to quality and the secret reserve price. This finding is in line with Beggs and Graddy (1997) and Deltas and Kosmopoulou (2004), who also explain observed price patterns by specific institutions. The evidence in this paper supports the hypothesis that bidders adjust their strategic behavior to influence the seller's probability of rejection, and that bidders react by bidding more aggressively for earlier units. Fehr's hypothesis that prices decline due to participation cost is not supported (von der Fehr, 1994). However, I cannot completely rule out risk aversion as a reason for declining prices (McAfee and Vincent, 1993). Furthermore, I find that bidders take the strategic effects of sequential auctions and multi-unit demand into account and shade their bids for earlier units. Bidders' incentive is to bid less than their true valuation on the earlier units as they expect lower prices for the later units. Disentangling the simultaneous effects of bidding more aggressively and shading bids in earlier auctions were only possible, because of the detailed data that include bidders' identity and history of an auction day.

41

The price difference between traders and farmers is mainly explained by differences in preferences and only to a lesser extent by differences in strategic behavior. Traders are in general more insensitive to institutional considerations. They react strategically to sequential auctions and multi-unit demand, but do not adjust their bids to the secret reserve price. Their prices are on average constant over auction days and their aggregate demand is highly elastic. Farmers react to all institutional characteristics, and in particular to the uncertainty of supply generated by the secret reserve price. Institutional aspects may have opposite effects on prices in sequential auctions. The empirical evidence provided in this paper shows that declining prices are caused by the order of sale according to quality and a secret reserve price, but also that bidders consider the strategic effect of sequential auctions and multi-unit demands. Acknowledgements The data were kindly provided by “Nö Genetik”. I am grateful to Johann Tanzler, manager at “Nö Genetik”, and Martin Graf, auctioneer in Amstetten, for their valuable information. I thank the coeditor Matthew Shum, an anonymous referee, Jason Abrevaya, René Böheim, Jesus Crespo-Cuaresma, Dennis C. Mueller, Ralph Siebert, Frank Verboven, Andrea Weber and Sepp Zuckerstätter as well as seminar participants at Purdue University and participants at the EARIE conference 2007 for their helpful comments and suggestions. I gratefully acknowledge support from the Austrian Science Foundation (grant J2481-N12) and also thank Purdue University and University of California Berkeley for their hospitality. All errors are mine. References Ashenfelter, Orly, 1989. How auctions work for wine and art. Journal of Economic Perspectives 3, 39–64. Athey, Susan, Haile, Phil, 2005. In: Heckman, J.J. (Ed.), Nonparametric Approaches to Auctions. . The Handbook of Econometrics, vol. 6. Elsevier Science. Avery, Christopher, 1998. Strategic jump bidding in English auctions. Review of Economic Studies 65 (2), 185–210. Bajari, Patrick, Hortacsu, Ali, 2003. The winner's curse, reserve prices and endogenous entry: empirical insights from eBay auctions. Rand Journal of Economics 34 (2), 329–355. Beggs, Alan, Graddy, Kathryn, 1997. Declining values and the afternoon effect: evidence from art auctions. Rand Journal of Economics 28 (3), 544–565. Black, Jane, de Meza, David,1993. Systematic price differences between successive auctions are no anomaly. Journal of Economics and Management Strategy 1, 607–628. Blinder, Alan S., 1973. Wage discrimination: reduced form and structural estimates. Journal of Human Resources 18 (4), 436–455. Deltas, George, Kosmopoulou, Georgia, 2004. ‘Catalogue’ vs. ‘order-of-sale’ effects in sequential auctions: theory and evidence from a rare book sale. Economic Journal 114, 28–54. Donald, Stephan D., Paarsch, Harry J., Robert, Jacques, 2006. An empirical model of the multi-unit, sequential, clock auction. Journal of Applied Econometrics 21, 1221–1247. Eklöf, Matia, Lunander, Anders, 2003. Open outcry auctions with secret reserve prices: an empirical application to executive auctions of tenant owner's apartments in Sweden. Journal of Econometrics 114, 243–260. Elyakime, Bernard, Laffont, Jean-Jacques, Ossard, Henry, Vuong, Quang, 1994. First-price sealed-bid auctions with secret reservation prices. Annales d'Econmie et de Statistique 34, 115–141. Engelbrecht-Wiggans, Richard, Kahn, Charles M., 1999. Calibration of a model of declining prices in cattle auctions. Quarterly Review of Economics and Finance 39 (1), 113–128. Halie, Phil, 2001. Timber auctions with resale markets. American Economic Review 91 (3), 399–427. Halie, Phil, Tamer, Elie, 2003. Inference with an incomplete model of English auctions. Journal of Political Economy 111 (1), 1–52. Hendricks, Ken, Paarsch, Harry J., 1995. A survey of recent empirical work concerning auctions. Canadian Journal of Economics 28 (2), 403–426. Jeitschko, Thomas D., 1999. Equilibrium price paths in sequential auctions with stochastic supply. Economic Letters 64, 67–72. Katzman, Brett, 1999. A two stage sequential auction with multi-unit demand. Journal of Economic Theory 86, 77–99. Krishna, Vijay, 2002. Auction Theory. Academic Press, San Diego. Laffont, Jean-Jacques, 1997. Game theory and empirical economics: the case of auction data. European Economic Review 41, 1–35. Laffont, Jean-Jacques, Ossard, Henry, Vuong, Quang, 1995. Econometrics of first-price auctions. Econometrica 63, 953–980.

42

C. Zulehner / Int. J. Ind. Organ. 27 (2009) 33–42

Laffont, Jean-Jacques, Loisel, Patrice, Robert, Jacques. Intra-day Dynamics in Sequential Auctions: Theory and Estimation. Mimeo, IDEI Toulouse, 1997. McAfee, R. Preston, Vincent, Daniel, 1993. The declining price anomaly. Journal of Economic Theory 60, 191–212. Menezes, Flavio M., Monteiro, Paulo K., 1997. Sequential asymmetric auctions with endogenous participation. Theory and Decision 43, 187–202. Milgrom, Paul R., Weber, Robert J., 2000. A theory of auctions and competitive bidding II. In: Klemperer, Paul (Ed.), The Economic Theory of Auctions. Edgar Elgar, pp. 179–194. Milgrom, Paul R., Weber, Robert J., 1982. A theory of auctions and competitive bidding. Econometrica 50, 1089–1122. Oaxaca, Ronald L., 1973. Male-female wage differentials in urban labor markets. International Economic Review 14, 693–709. Paarsch, Harry J., 1992. Deciding between the common and private value paradigms in empirical models of auctions. Journal of Econometrics 51, 192–215.

Paarsch, Harry J., 1997. Deriving an estimate of the optimal reserve price: an application to British Columbia timber sales. Journal of Econometrics 51, 333–357. van den Berg, Gerard J., van Ours, Jan C., Pradhan, Menno P., 2001. The declining price anomaly in Dutch Dutch rose auctions. American Economic Review 91 (4), 1055–1062. Vickrey, William, 1961. Counterspeculation, auctions and competitive sealed tenders. Journal of Finance 16, 8–37. von der Fehr, Nils-Henrik, 1994. Predatory pricing in sequential auctions. Oxford Economic Papers 46, 345–356. Weber, Robert J., 1983. Multiple-object auctions. In: Engelbrecht-Wiggans, Richard, Shubik, Martin, Stark, Robert M. (Eds.), Auctions, Bidding, and Contracting: Uses and Theory. New York University Press, New York, pp. 165–191. Wooldridge, Jeffrey M., 2001. Econometric Analysis of Cross Section and Panel Data. The MIT Press, Cambridge.