masterclass: recent empirical analysis of auction markets and bidding robert porter northwestern...

Masterclass:Recent Empirical Analysis of Auction

Markets and Bidding

Robert PorterNorthwestern University

CEMMAPInstitute for Fiscal Studies

University College London March 13 & 14 2008

Masterclass March 13 & 14, 2008 2

IntroductionAuctions have been the subject of a lot of good theory and good empirical

work.• Game is relatively simple, with well-specified rules.• Actions are observed directly.• Payoffs can sometimes be inferred.• Data sets are readily available. Market Structure: monopoly seller, heterogenous buyers. Why use an auction, instead of posting or negotiating a price? • Buyers’ willingness to pay is private information; an auction can be

efficient price discovery process.• Identity of highest value buyer is unknown; an auction can be an

efficient allocation mechanism. • Auctions can also be good at generating revenue. Information asymmetries are fundamental.


There are many possible auction mechanisms. • open outcry vs. sealed bid• highest bid vs. second-highest bid • reserve price, announced or secret• entry fees or subsidies In practice, most auctions are either first-price sealed bid (FPSB) or open

outcry, ascending price (English). Goals of Theory• Positive: describe how to bid rationally – Bayesian Nash equilibrium• Normative: characterize optimal (e.g., revenue maximizing or

efficient) selling mechanismGoals of Empirical Studies• Positive: what are the bid markups? Are buyers’ valuations correlated

and if so, what is the source of the correlation? Is observed bidding consistent with Bayesian Nash Equilibrium (BNE)? Is there evidence of buyer risk aversion? Do agents collude?

• Normative: recover value distribution, identify the revenue maximizing or efficient auction, simulate the effects of design changes.


There are many structural empirical papers which posit equilibrium bidding in the auction of a single item.

Recent surveys: Athey & Haile (Handbook of Econometrics, Vol. 6A, 2007)Hendricks & Porter (Handbook of IO, Vol. 3, 2007)Paarsch & Hong (MIT Press, 2006)

There has been considerable progress, but there remain important open issues.

In this class, I discuss the basic empirical model of a one shot, single item auction, and some recent developments that extend the basic model.

I describe some research directions that might be of interest.


Outline of Class

1. Standard Model and Notation2. The Structural Program

2A. Second-Price Auctions2B. First-Price Auctions

3. Tests of the Theory4. Revenues and Auction Design5. Collusion6. Seller Incentives7. Bidder Entry and Information Acquisition8. Dynamics9. Multi-Unit Auctions10. Conclusion


1. Standard Model and Notation

n = number of (potential) bidders

m = number of bids (“active” bidders)

Xi = private signal of bidder i

X = (X1, … , Xn)

V = common payoff component

Ui = u(Xi,V) bidder i utility if obtain one unit

F = joint distribution function of (X,V)

Yi = max{Xj, j i}

W = winning bid

i(x) bidder i’s (monotone) bid strategy

i(b) inverse bid function of bidder i


Main Assumptions

• Each bidder wants only one unit.

• Utility u is non-negative, continuous, and increasing in each argument, and common across bidders.

• Bidders are risk neutral.

• F(X,V) is symmetric in the signals X.

• (X,V) are affiliated.

• Xi is real-valued.

• F, n and u are common knowledge.

• The losing bidders don’t care who wins.


Special Cases

Private Values (PV): u(Xi,V) = Xi

Can normalize the signal Xi to be an unbiased estimator of expected valuation:

Xi = E[u(Xi,V)| Xi].

– IPV: Xi’s are iid, Fx is marginal distribution of Xi

– APV: Xi’s are affiliated.

If not PV, then say have Common Values (CV).– Pure Common Value: u(Xi,V) = V

– CICV: Xi’s are independent conditional on V.


A Fundamental Empirical Issue

Are values private or common? This issue is important for both positive and normative goals.

• In PV, more competition typically raises bids and revenues.

• In CV, this may not be the case. Argument: In a symmetric equilibrium, winner is the bidder

with the highest signal. But winning is “bad news”, since

E[V| Xi = x, Yi < x ] < E[V| Xi = x].Under private values, these expressions are equal. The difference is a measure of the “winner’s curse.” The

curse is more severe with higher n.


2. The Structural Program

Objective: Estimate F (and u) from bid data. Basic idea: Bayesian Nash equilibrium (BNE) maps

private signals into bids given F. Can we recover the primitives of the model from bid data?

Focus on symmetric BNE with increasing bid functions.

• Affiliation and symmetric payoff functions are sufficient conditions for existence.

• Many asymmetric models also have equilibria with increasing bid functions.

See Athey (2001), Krishna (2002).


2A. Second Price Auctions1. Is the Bayesian Nash equilibrium in increasing bid functions unique? If not, the likelihood function for the data is not well-defined. A vector of

signals maps into more than one outcome. The answer is typically no. In CV models:• There are many ways in which the n-2 losing bidders can drop out

(Bikhchandani, Haile & Riley (2002)).• Final subgame with 2 bidders has a continuum of asymmetric

equilibria (Milgrom (1981), Klemperer (1998), Bikhchandani & Riley (1991)).

In PV models:• Unique in SPSB and button English auctions; in fact, equilibrium is in

dominant strategies.• But most oral auctions are open outcry auctions; free form of bidding

allows many equilibria. E.g., serious participants may not bid. There may also be equilibria with jump bidding (Avery (1998)).


2. Fixing an equilibrium, is the model non-parametrically identified from bid data? That is, is there a one-to-one relationship between the joint distribution of bidder values, F, and the joint distribution of bids?

Athey & Haile (2002) have studied this issue for English and SPSB auctions.

• IPV models in which the winning bid can be interpreted as the realization of a second-order statistic are identified.

• APV models are generally not identified unless all bids are observed.• Most CV models are not identified.

Why demand non-parametric identification?• Main object of interest is the distribution of the idiosyncratic

component of payoffs, not the deterministic component. Private information is the source of rents and the focus of mechanism design.

• If identification is only by functional form, then a given parametric family of distributions may not approximate the true unknown distribution.


Empirical Studies

1. Bajari & Hortacsu (2003) study bidding in eBay coin auctions. They model the auction as a SPSB, pure common value auction with conditionally independent signals.

• Symmetric equilibrium: (x) = E[V|Xi = x , Yi = x] (No Regret Property)• Distribution of Xi conditional on V is normal. Thus, likelihood function is well-defined. Need to estimate numerically since

neither the inverse bid function nor its derivative are available in closed form.Use estimates of the parameters of F to study impact of different reserve policies.

2. Hong & Shum (2003) estimate a structural model of an asymmetric, ascending auction in a common value environment. The application is to PCS auctions.

Likelihood is well-defined but involves high dimensional integrals; use simulation nonlinear least squares method developed by Laffont, Ossard & Vuong (1995) for First-Price auctions.

• Need to infer bidders’ private values from the bids at which they drop out. But drop out bids are typically not observed. Even if they were, the theory cautions against drawing strong inferences.


3. Haile & Tamer (2003) study oral, ascending IPV auctions. Application is to timber auctions.

Likelihood function is not well-defined due to multiple equilibria problem.

In open ascending auctions, problem of interpretation of losing bids.They make two assumptions about bidding behavior, if bi is i’s highest

bid:1. Winner is willing to pay more than the final bid, and losing bidders do

not submit bids greater than their values, so xi ≥ bi for all i. 2. Losing bidders are not willing to raise the winning bid by the minimum

bid increment Δ, so xi ≤ w +Δ for all i but the winning bidder. These two assumptions provide upper and lower bounds on FX, without

fully specifying equilibrium play. Surprisingly, the bounds can be quite tight. The implied bounds on the revenue maximizing reserve price are also tight.

Assumption 2 is not innocuous. It is not necessarily satisfied by equilibria with jump bidding, nor if bidders collude. But the H&T estimation approach is a novel solution to a fundamental problem.


2B. First Price Sealed Bid Auctions1. Is the equilibrium unique? The answer is generally yes in symmetric models (Athey & Haile (2005))

and in asymmetric IPV models (Lebrun (1996, 1999), Maskin & Riley (2000a,b)).

2. Is the model non-parametrically identified from bid data?Yes for APV models, no for CV models. Laffont & Vuong (1996): any symmetric CV model with fixed number of

bidders and no reserve price is observationally equivalent to some symmetric APV model; true of asymmetric models as well.

Can distinguish between PV and CV models if • Reserve price is binding (Hendricks, Pinkse & Porter (2003))• Exogenous variation in number of bidders (Haile, Hong & Shum

(2004))Tests are important because if PV is not rejected, structural estimation is

viable.


Equilibrium Bidding in FPSB AuctionsExpected profits from bidding b, given a signal x:

π(b,x)=∫η(b) [w(x,y) - b] dFY|X(y|x)

where w(x,y) = E[u(V,X)| X=x, Y=y].

Differentiating with respect to b and imposing symmetry:

[w(x,x) – β(x)] fY|X(x|x) = β’(x)FY|X(x|x)

Laffont & Vuong idea: Let M = β(Y), the highest rival bid.

Let GM|B denote the distribution function, conditional on one’s own bid, and gM|B its p.d.f.

Then FY|X(y|x) = GM|B(β(y)|β(x)) and fY|X(y|x) = gM|B(β(y)|β(x)) β’(y).

Substitute into the FOC and evaluate at b = β(x), to obtain the inverse bid function:

w(η(b),η(b)) = b + (GM|B(b|b)/gM|B(b|b)) = (b,G)


Estimation Method for PV ModelsIn the PV model, w(x,x) = xIn the special case of IPV,

GM|B = Gn-1 and gM|B = (n-1)gGn-1

where G is the distribution of a random rival bid, and g its p.d.f. The inverse bid function becomes:η(b) = b + G(b)/[(n-1)g(b)] = (b,G)

Estimation proceeds in two steps, for the sub-sample where nt = n:1. Estimate GM|B and gM|B either parametrically or non-parametrically. Form valuation estimates:

xit = (bit , GM|B)This yields a sample of pseudo-values.

2. Use the data {bit, xit} to estimate F and/or β.Advantages of the first-order approach (Elyakime, Laffont, Loisel & Vuong

(1994)):• Does not rely on functional form assumptions• Computationally easy to implement• Can be extended to asymmetric IPV models


Extensions of the Standard Model

The inverse bid equation has been adapted to estimate several variations on the standard model.

• Unobserved heterogeneity– Non-parametric (Krasnokutskaya (2004))– Parametric (Athey, Levin & Seira (2004), Krasnokutskaya & Seim

(2007))• Asymmetric bidders

– Collusion (Bajari & Ye (REStat 2003))– Observable types (Athey, Levin & Seira)

• Risk averse bidders (Bajari & Hortacsu (JPE 2005))• Identification of the CV model using ex post payoff data (Hendricks,

Pinkse & Porter (RES 2003)) • Tests of PV vs. CV

– Variation in number of bidders (Haile, Hong & Shum (2003))– Binding reserve price (Hendricks, Pinkse & Porter)


3. Tests of The Theory

Basic Question: Do bidders bid as game theory says they should?

No strategic play in SPSB and English PV auctions, if each bidder has a dominant strategy to bid her valuation.

In FPSB auctions, two (overidentifying) tests:

T1: The inverse bid function (b,G) is increasing in b; and limb↓r(b,G) r.

T2: Fn, the empirical distribution of pseudo-values obtained from first-order conditions in auctions with n bidders, is non-decreasing in n.

• Both tests are joint tests of affiliation and equilibrium bidding. The latter requires n to be exogenous, a dubious assumption in most data sets.

• T2 also applies to bids in second-price auctions and to losing bids in English auctions.

Difficult to examine rationality in PV auctions using field data since valuations are private.


Bajari & Hortacsu (2005) use bid data from private value auctions experiments to distinguish between different models of preferences and behavior. Two big advantages:

• Variation in n is exogenous

• Bidder values and their distribution FX are known.

Result: Bayesian Nash equilibrium with risk averse bidders performs best.If u(x) = xθ , for 0 < θ ≤ 1, then η(b) = b + θG(b)/[(n-1)g(b)].

Rational bidding is easier to test in CV environments where ex post measure of V is often available. The question is often reformulated as: Do bidders take into account the winner’s curse?


Empirical Studies

1. Hendricks & Porter (1988), H, P & Wilson (1994) use OCS FPSB drainage auction data.• Drainage leases are adjacent to tracts where oil and gas deposits have been discovered.• Neighboring firms possess drilling information, as a consequence are better informed.• Given the information asymmetry, non-neighbor firms face a severe winner’s curse.• Neighbor firms can be identified and they behaved as a consortium.

Data: {bIt, bUt, rt , vt}. Here bIt is the informed bid, bUt is the maximum uninformed bid, rt the minimum bid, and vt a measure of ex post value. Theory argues that the number of uninformed firms is not relevant.

Testable Equilibrium Predictions1. Non-neighbor firms participate, but less than the neighbor firm.2. Neighbor firm is more likely to win than non-neighbor firms.3. Non-neighbor firms should earn zero profits.4. Distribution of BU should coincide with the distribution of BI above the upper bound of

the support of the (random) reserve price.Result: Data consistent with all four predictions.Conclusion: Non-neighbors are aware of the winner’s curse and bid strategically.


2. Hendricks, Pinkse & Porter (2003) study implications of rational bidding using data from OCS FPSB wildcat auctions.

• Wildcat tracts are located in areas that have not been drilled. Firms are allowed to conduct seismic studies prior to bidding, but cannot drill exploratory wells.

• Seismic studies yield noisy signals about the amount of oil and gas contained by the tract. Firms are more or less equally informed, but they may have quite different value estimates depending upon the content and analyses of the surveys.

Data: {{bit}, nt, rt, vt} plus covariates Zt for auctions where mt > 0.Use data to compute conditional expectations:

γ(b) = E[Vt |Bit = b](b) = E[Vt |Bit = b, Mit <b](b) = E[Vt |Bit = b, Mit = b]

These functions are estimated by locally linear regression. The difference γ(b) - (b) is a measure of the magnitude of the winner’s curse, assuming pure common values, and it is increasing in n.


Consider the following tests:

T1. Do bidders bid less than expected value: γ(b) – b > 0?

T2. Do bidders bid less than expected value conditional on winning: (b) – b > 0?

T3. Do bidders bid according to the first-order condition, (b) = (b,G)?

Results: Yes to T1 and T2, the basic rationality tests; Yes to T3 when competition is high (n>5); Some evidence of overbidding when competition is low. Bayesian Nash equilibrium, as reflected by T3, fits the data better

than the corresponding first order condition (or inverse bid function) for bidders who do not account for the winner’s curse: γ(b) = (b,G).


4. Revenues and Auction Design

Revenue Equivalence Theorem: Suppose the auction rules and equilibrium bidding are such that the highest type always wins and the lowest type has zero expected payoff. Then the expected payment to the seller by a bidder of type x is E[X(2) | X(1) = x].

Testable PredictionsFirst moments of revenue distributions from different auction mechanisms are

equal. Second and higher moments differ, but for particular auctions (e.g., FPSB vs. English) they may be ordered.

Empirical StudiesHansen (1986) compares revenues from English and FPSB auctions of timber

conducted by US Forest Service. Regresses winning bid on sale characteristics and an indicator variable that is

equal to 1 if auction t is FPSB.Accounts for selection bias – Forest Service’s selection rule was not randomCould not reject revenue equivalenceAthey, Levin & Seira (2004) find that, in more recent periods, revenues are higher

in FPSB, even correcting for sample selection.


Non-equivalence raises the following question:

Which of the many assumptions underlying IPV environments is responsible?

Haile argues that the presence of a resale market can explain FPSB superiority. Winning bid is a signal to potential buyers in the resale market of seller’s valuation.

Robinson argues that it may be easier for bidders to collude in English auctions. Participants are identified and deviations can be punished in the course of the auction.

Athey, Levin & Seira relax the symmetry assumption; mills have a stochastically higher willingness to pay than loggers who have to sell timber to mills. FPSB is less efficient and gives loggers a stronger incentive to enter more competitive auction.

Athey, Levin & Seira also explore the collusion hypothesis; they use structural estimates of entry costs and FX from FPSB auction data to predict average sale prices in oral auctions under competitive and collusive behavior mills are mildly more collusive in oral auctions.

Shneyerov (2005) uses estimates of pseudo-values obtained from FPSB data to predict revenue changes from switching to SPSB or English. Tests for PV vs. CV and rejects PV. Key insight: Even though F is not identified, the pseudo-values are estimates of the latent conditional expectation, w((b),(b)); this is the amount that a bidder with signal x = (b) would bid in a SPSB.


Theorem: Assume an IPV model and an auction in which k items are auctioned sequentially using a FPSB (or SPSB) auction. Then the prices form a martingale: E[wt] = wt-1 for t = 2, ..., k.

Empirical StudiesAshenfelter (1989) studies winning bids on identical cases of wine sold sequentially via

English auctions by an auction house.• Prices systematically and significantly decline over the sequence by a few percent.• Violates martingale property, and more general notion of no arbitrage opportunities.Donald, Paarsch & Robert (2006) study winning bids for sequential sales of Siberian timber

export permits.• Prices are initially decreasing and then increasing• Explain this result as a combination of risk aversion (decreasing) and affiliation

(increasing).Other studies: Ashenfelter & Genesove (1992), Beggs & Graddy (1997). Resolution of anomaly? Risk neutrality, IPV, unit demands • McAfee & Vincent (1993): need non-decreasing ARA – not plausible.• Milgrom & Weber (2000): affiliation causes price to increase; winner’s curse mitigated

as information is revealed.• Black & de Meza (1992): relaxing unit demand can offer explanation.No one has examined higher moments of the revenue distributions.


6. The Incentives of the Seller

Basic Question: What does the auction design reveal about the economic environment?

In most structural empirical analyses of the bidders’ problem, the mechanism choice, or the reserve price policy, is treated as exogenous.

But the optimal reserve price is a monotonic function of the seller’s valuation, which may be correlated with the buyers’ values, and it also depends on the distribution of buyers’ values.

More generally, the mechanism choice may depend on the distribution of bidders’ valuations, or on their behavior.

Examples: In an IPV setting, if bidders are risk averse, the FPSB auction yields higher revenues than SPSB. A seller may prefer SPSB or an oral ascending auction if CV (Milgrom & Weber’s linkage principle).FPSB is less vulnerable to collusion.


Laffont, Ossard & Vuong (Ecma 1995):Marmande Eggplants

Model bidding in eggplant auctions (descending price, or Dutch) as BNE of IPV model, treating the reservation price as exogenous.

There is a strong correlation between the reserve price and the winning bid (see Figure 3 in LOV).

If the variation in the reserve price r is exogenous, so that FX does not vary, the winning bid covaries with r in the BNE of the IPV model.

Here (x) = E[max{Y, r}| X = x, Y ≤ x], as in FPSB.But it is also possible that both the reserve price r and the location and/or

scale of the distribution of bidder values FX are correlated with some factor (or factors) that are not observed by the econometrician.

In the variation in r is exogenous, should see more instances of no sale when r is high.

Under an optimal reserve price policy, there is a positive probability of no sale in many environments.


Should be cautious in specifying seller rationality.The seller may have an objective other than static

revenue maximization.• If a government agency is the seller.• If the seller can re-offer unsold items.• If buyers can also go to competing sellers.

Nevertheless, if the reserve price is not exogenous, it may be informative about unobserved heterogeneity.

E.g., some authors deflate bids by the reserve price, to correct for proportional shifts in the mean valuation.

But need to be careful about higher order moments.E.g., is the dispersion in bids proportional to the value of

the item?


7. Bidder Entry & Information Acquisition

Auctions can be an important testing ground for studying entry.• Auctions are held repeatedly, firms have to make frequent entry

decisions. • A rich variety of settings for studying entry decisions.Much of the literature assumes that the number of bidders is fixed. But if

participation is costly, the number should be determined as part of the equilibrium to the game.

• Who chooses to be a potential bidder? • Which potential bidders choose to be active?• Which active bidders submit a bid?• In each instance, what do agents observe?Do auctions attract too many or too few bidders? This issue particularly

important when bidders are asymmetric since, in this case, Revenue Equivalence does not hold (e.g., Athey, Levin & Seira), or if there are common values. Then auction design matters.


Empirical problem: multiplicity of entry equilibria likelihood function is not well-defined. Strategies for dealing with this issue include:

• Restrict payoffs so that number of entrants in set of pure strategy equilibria is unique and define likelihood in terms of this event. (Bresnahan & Reiss (RES 1990), Berry (Ecma 1992))

• Change game form: sequential entry, or private entry cost information (Seim (RAND 2006))

• Bound the probabilities of the outcomes (Tamer (RES 2003), Ciliberto & Tamer (2004))

• Append a set of selection rules and estimate joint distribution over outcomes and selection rules (Bajari, Hong & Ryan (2004)).

Auctions provide a natural context for implementing these strategies. Sealed bid auctions – simultaneous move. Oral auctions – sequential move.


Entry Models

Standard model:

All potential bidders are active; they submit a bid in the FPSB or SPSB, or participate in the open outcry auction, if their signal is above a threshold.

PV: Bid if x ≥ r.

CV: Bid if x ≥ x*(r,n),

where x*(r,n) = inf{x| E[u(X,V)| X=x, Y<x] ≥ r}

and x*(r,n) > r is increasing in r and n.

In the PV case, x*(r,n) = r.


Athey, Levin & Seira (2004): Timber Sales

Fixed number of potential bidders (of two types).Bidders are endowed with a private signal, their bid preparation cost.Bidders (simultaneously) choose to become active if this cost is below

some threshold.ALS consider the type symmetric pure strategy equilibrium, where

bidders take as given the (binomial) distribution of the number of active rivals of each type.

Bidders then observe their private value, independent of their bid preparation cost, and they observe the number of active bidders.

Bidders submit a bid if their value is above the reserve price, as in the standard model.

The first stage is analogous to Seim’s (RAND 2006) entry model.The bidding game is that of Maskin & Riley (RES 2000), with a

preceding round of entry decisions.


Bajari & Hortacsu (RAND 2003): eBay Coins

Model is in the spirit of Levin & Smith (AER 1994).Large number of potential bidders, with a common bid preparation cost.They (simultaneously) choose to become active.BH consider the symmetric mixed strategy equilibrium.Active bidders then observe their private signal of the common value, but

not the number of active rival bidders.Bidders take as given the (Poisson) distribution of the number of active

rivals.Bidders submit a bid if their signal is above the CV threshold, where this

is the zero profit signal, taking expectations over the number of active rivals.

The bidding game is SPSB with an unknown number of rivals.The common entry probability is uniquely determined by a zero ex ante

profit condition.


Krasnokutskaya & Seim (2007): California Highway Procurement

KS consider two entry models.In the first variant, firms observe a private bid preparation cost. This model is essentially that of Athey, Levin & Seira, also with two bidder

types.In California, qualified small bidders are favored. The lowest small bidder

wins if their bid is not 5% higher than the lowest large firm bid. KS are interested in the effect on entry and bid levels for each bidder type.In the second model, firms have a common bid preparation cost.Firms randomize in their entry decisions, with type specific entry

probabilities. They observe the number of rivals of each type, which are distributed

binomial.Because values are assumed to be private, active bidders submit a bid if

their signal is above the reserve price.Active bidders choose bid levels in the FPSB, given the numbers of active

rivals of each type, according to asymmetric PV BNE.


Hendricks, Pinkse & Porter (RES 2003): Offshore Oil & Gas

Model similar to McAfee & Vincent (AER P&P 1992).Fixed number of potential bidders, with private signal of common value.They (simultaneously) choose whether to become active.Consider the symmetric pure strategy equilibrium.Active bidders then observe a better signal of the common value, but not

the number of active rival bidders.Bidders’ initial signals are informative about the number of active rivals.Active bidders submit a bid if their second (better) signal is above the CV

threshold, where this is the zero profit signal taking expectations over the number of active rivals.

The bidding game is FPSB, with an unknown number of rivals.The active entry threshold is uniquely determined by a zero profit

condition.Here the entry decision is not independent of the bid level.


Endogenous Information Precision?

Almost all papers take the precision of information as given. Potential bidders may not only choose whether to acquire information, but

also the accuracy of their signals.In offshore oil and gas auctions, firms choose how much to invest in

analyzing seismic data.Firms’ entry and bidding strategies will depend on their perceptions of

how many serious rival bidders they face. Information acquisition will be influenced by the auction mechanism

(e.g., Compte & Jehiel (RAND 2007)).A related issue: Much of the literature compares mean revenues. But in

some instances bid dispersion varies with the mean bid level (e.g., offshore oil lease bidding).

This variation may be driven by variation in the level of competition. But the entry decision, and decisions about the precision of information

acquisition, may vary with the expected value of the item.


8. Dynamics

Aguirregabiria & Mira (Ecma 2007), Bajari, Benkard & Levin (Ecma 2007), Pakes, Ostrovsky & Berry (RAND 2007), and Pesendorfer & Schmidt-Dengler (RES 2008) have developed feasible estimators for dynamic games, extending the Hotz & Miller (RES 1993) approach to estimating dynamic decision problems.

Restrictive conditions: repeated stage game played in a stationary environment in which unobservables are independent across time and players.

Private value auctions, e.g., highway procurement auctions, can come close to meeting these conditions.


Most of empirical literature assumes that bidders treat auctions as static games, choosing bids to maximize profits in that auction.

Plausible in environments with no learning or payoff linkages, if the time interval between auctions is sufficiently long.

But when time between auctions is short, the current auction outcome can affect the state of play in future auctions. • Winner of current auction may not be able to participate in future auctions, or have stochastically lower valuations.• Losers are then more likely to win future auctions.

As a result, bidding is less aggressive, which must be accounted for in estimating the distribution of valuations.


Jofre-Bonet & Pesendorfer (2003): California Highway Procurement

Extend the Laffont & Vuong approach to the dynamic setting. The inverse bid equation in a PV setting has an additional term:

η(b,c) = b + GM(b|c)/gM(b|c) + β ∂V/∂b

where c is the vector of firm costs, which are increasing in backlog, V is the expected continuation value, and β the discount factor.

Here ∂V/∂b > 0, as losing bidders have relatively lower future costsHence bidding is less aggressive than in the static case (higher markups). One issue: The distribution of valuations F(x|c) is identified only for a

fixed discount rate β. Thus one cannot distinguish between myopic and forward-looking

behavior. Conjecture: Use variation in time between contracts to identify β, and

thereby distinguish bidder myopia from foresight.


9. Multi-Unit Auctions

In many instances, multiple units are sold or procured simultaneously, rather than sequentially.

Examples: treasury bills, wholesale electricity, spectrum licenses.An important issue is optimal mechanism design. For identical items:

Discriminatory auctions, in which winning bidders pay their own bids, vs. Uniform price auctions, in which winning bidders all pay the same price (such as the lowest winning bid, or the highest losing bid).

Ausubel & Cramton (2002) show that there is no clear ranking of the two according to expected seller revenues. The revenue maximizing choice is an empirical issue.

A recent literature proposes structural estimation methods to estimate the distribution of valuations, and so draw inferences about the consequences of changes in the selling procedure. Buyers may value more than one of the multiple units being sold.

For non-identical items, there is also an issue of whether and how to bundle items, or allow package bids, to reflect complementarities.


Recent Studies of Treasury Bill AuctionsHortacsu (2002) studies discriminatory Turkish auctions.Model based on Wilson’s (QJE 1979) analysis of share auctions, in which

bid schedules are continuous.Assume private values, real valued signals.(Euler-LaGrange) necessary condition to demand q units at bid price b:

vi(q,x) = b + Gi(b,q)/(∂Gi(b,q)/∂b),where vi(q,x) is the marginal value at q given x, and Gi(b,q) is the probability that the bid b is accepted.Here vi(q,x) is smooth, decreasing in q and increasing in x.

Analogous to the inverse bid equation in the single item case. Uses resampling methods to estimate Gi, and hence recover vi(q,x).Hortacsu treats vi(q,x) as an upper bound on the bid schedule in a uniform

price auction, to bound revenues from above, and compare with revenues in the discriminatory format.


Kastl (2007) studies uniform price Czech auctions.Explicit recognition of bids as step functions, not continuous.Bidders are limited to at most 10 steps.

In his sample this constraint is never binding.Larger bidders average 2.5 steps, small bidders 1.1 steps.

Allows common values, assumes real valued signals, plus an independent (and private) cost per bid point.

Bidders choose the number of bid points, and (b,q) for each point.With step bid functions, ties are a possibility.Assume rationing is pro-rata on the margin (as is typical in practice).If values are private, ties have zero probability in equilibrium. PV bidders may bid b(q) > vi(q,x), but not above average valuation.Thus marginal valuation vi(q,x) is not a valid upper bound on the bid

schedule in a uniform price PV auction.Kastl shows that in the Czech data this is a practical concern.


Chapman, McAdams & Paarsch (2006) study discriminatory Canadian cash reserve auctions.

Also consider bids as step functions.Quantity increments are taken as fixed, as with a finite number of identical

discrete units for sale. Bids are price offers for a given number of units (and prices are chosen

from a fixed grid). Assume affiliated private values, but signals are vectors of length equal to

the number of quantity grid points. Marginal values are only required to be non-increasing. Characterization of equilibrium is daunting.Build on work of McAdams, to derive bounds on values implied by

equilibrium; essentially focus on necessary conditions for bid prices.Look for bid patterns that are inconsistent with equilibrium.Bidders do not appear to deviate in an important way from equilibrium

predictions.


10. Conclusion

Empirical analysis of auction markets continues to be a fertile research area.

My focus today has been on methods that extend the standard model for single item auctions.

In some instances, the extensions involve relatively straightforward adaptations of existing methods.

But some extensions are not so simple.

Institutional details and the available data play a large role in the choice of research method.

masterclass: recent empirical analysis of auction markets and bidding robert porter northwestern...

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