Can Affirmative Action Be Cost Effective? An ExperimentalExamination of Price-Preference Auctions

By ALLAN CORNS AND ANDREW SCHOTTER*

One of the most controversial questions fac-ing our economy and society in recent years isthe question of affirmative action. The debatecenters around an issue of minority represen-tation in which the rights of the majority aredepicted as being compromised by affirmativeaction programs set up to increase the welfareof minorities. Implicit in this discussion is theassumption that all affirmative action pro-grams must be cost increasing. This result, itis claimed, follows trivially from economictheory since any interference into the compet-itive process which prevents the most capablefrom being chosen must be wasteful andcostly.

In this paper we challenge this claim withexperimental results, demonstrating that price-preference auctions, in which high-cost mi-nority firms are given preferential treatment inthe awarding of contracts in such a way that itis possible for these firms to win a contract butnot have submitted the lowest bid, can be pro-grams that both enhance minority representa-tion and are cost effective in that they decreasethe cost of government procurement. In thetheoretical literature on asymmetric auctions(Eric Maskin and John Riley, 1995) and theoptimal auction literature (Roger Myerson,1981 ) it has been shown that in asymmetricauctions, in which firms draw their costs from

* Departmenl of Economics. New York University,269 Mercer Street. New York, NY 10003. The authorswould like lo express their ihanks to Huagang Li for hiscomputational assistance. We would also like to thank J,P. Benoit, and John Riley for sharing his BIDCOMP^ pro-gram with us. In addition, the research assistance of JiaLu Yin, Gautam Barua. and Jeff Davis is gratefully ac-knowledged, as is the financial assistance of the C. V. Stan-Center for Applied Economics at New York University.We have also benefitted from comments received from theNYU/C. V. Starr Micro Workshop and the Economic Sci-ence Association. We would also like to thank two anon-ymous referees for their suggestions and insight.

different probability distributions, it is not al-ways optimal to award the good to the lowest-cost firm. In fact, in a paper on internationaltrade, R. Preston McAfee and John McMillan(1989) ask a question identical to the one in-vestigated here. Our analysis follows theirsclosely.

Our experiments indicate that the imposi-tion of a price-preference rule can lead toan increase in both minority representationand cost effectiveness if the degree of price-preference is chosen correctly, but can leadto a decrease in cost effectiveness if theprice-preference is too great. In our exper-imental auction in which a 5-percentprice-preference was used, the cost of pur-chasing for the laboratory auctioneer de-creased while at the same time the frequencywith which high-cost (minority) firms wona contract increased as compared to the 0-percent preference case. For the auctions runusing a 10-percent or 15-percent price-preference there was additional increase inminority representation but it came at a costof higher purchasing prices for the labora-tory auctioneer. These results are consistentwith theoretical predictions however, indi-cating that if a government purchasing agenthas some accurate prior information aboutthe distributions from which the cost of buy-ers are drawn, then it is possible to choosea price-preference which will be costeffective.

In this paper we will proceed as follows. InSection I we will review the incidence ofprice-preference auctions among governmentagencies as well as the empirical work in thefield. In Section II we present the theory thatunderlies these experiments, while in SectionIII we present our experimental design. In Sec-tion IV we give the results of our experiments.Finally, in Section V we offer someconclusions.

291

292 THE AMERICAN ECONOMIC REVIEW MARCH 1999

I. Price-Preference Auctions—Their Usein Practice

A. The Incidence of Price-PreferenceAuctions

Auctions in which some form of preferenceis given to minority bidders have been a com-mon feature of the American economy formany years. Probably the most famous use ofminority preference auctions, at least for econ-omists, has been their use in the recent FederalCommunications Commis.sion (FCC) auctionof radio spectrum licenses. In setting up thisauction the government's concern for minorityrepresentation led it to devise a preference pro-gram where minority- and women-ownedfirms (designated entities) were given a 40-percent bidding preference.' In addition, anumber of surveys have been conducted by theNational Institute of Governmental Purchasing(1993) and the National Association of StatePurchasing Officials (1994), whose purpose isto summarize the purchasing practices of var-ious governmental agencies. The results indi-cate that 2 percent of the 402 federal, state,city, and administrative bodies responding in-dicated that they used minority price-preferences in their procurement programs. Infact, of all minority preference programs ex-isting about 8 percent are price-preference pro-grams with the remainder split betweenset-aside and goal-based programs. Further, ofthe 50 .states. 15 had some form of in-stateprice-preference program with percentagesranging from 2 percent to 5 percent. On thefederal level there is a long history of the"Buy-American" purchasing preference pro-gram (starting with the Buy-America Act of1933) with price-preferences ranging from 6percent to 12 percent. On defen.se contracts,however, the price-preference can he as higha.s 50 percent. Because these price-preference

' In authorizing these auctions. Congress required theFCC to '"ensure that , . businesses owned by membersof minority groups and women are given the opportunityto participate in the provision nf spectrum-based services.and for such purposes, consider the use of tax certificates,bidding preferences, and other procedures." [IJ.S.C,309(j)(4)(D); Ian Ayres and PeterCramton ( 1996).]

programs are seen as creating substantial har-riers to trade, their validity has often beenchallenged.

B. A Review of the Empirical Literature

Despite their common use, we are not awareof any study which investigates the procure-ment cost consequences of minority prefer-ence auctions except for the recentinvestigation by Ayres and Cramton (1996) ofthe FCC auction data. The reason for this lackof attention is that in all of the studies we haveseen which mention minority preference pro-grams, it has been assumed that these pro-grams are put in place strictly for minorityrepresentation purposes with the tacit assump-tion that higher purchasing costs for the gov-ernment will inevitably result.

While little attention has been focused onminority price-preference programs, there hasheen some research on the related, and theo-retically identical, issue of "StaCe-Preference"and "Buy-American" programs of state andfederal purchasing authorities. When studyingstate and federal price-preference programs,there seems to be an Implicit ad hoc method-ology hinted at of simply laking all contractsawarded by an in-state preference and esti-mating the cost of the preference as the dif-ference between the lowest hid and the actualprice that the contract was awarded. This viewof what industry seems to think of as the costof a price-preference program is summarizedhy Donald E. Jordan (1978 p. 215): ' The ma-jor effect of such laws is to increase the costof government. Indeed, an obvious cost is anyamount which must be paid in excess of thelowest bid from non-residents."

This naive accounting approach, which wewill call the "Naive Cost" approach, does notconsider the effect of the price-preference ruleon bidding behavior. For example, in comput-ing the cost of instituting an jr-percent prefer-ence auction, one must not look at thedifference between the low bid and price paidwithin Ihe .v-percent preference auction whenthe preference is binding in determining thewinner, but rather the difference between theprice paid in the .r-percent preference auctionand what the price paid would have been hadthe auctioneer employed a 0-percent prefer-

VOL 89 NO. 1 CORNS AND SCHOTTER: PRICE-PREFERENCE AUCTIONS 293

ence auction instead. The key ingredient in aproper cost-accounting system is to take intoaccount the change in equilibrium behaviorthat would be invoked by the change in rulesof the auction. This is what we do later whenwe discuss the "Real Cost" accountingmethod.

II. Some Theory

A. Price-Preference Auctions

While not optimal, it is possible that bychoosing the right preference percentage agovernment might be able to use price-preferences to both reduce its cost of purchas-ing and increase the probability that highercost, minority-owned firms win contracts.' Tounderstand why price-preferences work, con-sider an auction with two high-cost firms andfour low-cost firms. By low cost and high costwe mean that the low-cost firms draw theircosts from a uniform distribution with support[c', c''], while the high-cost firms draw theircosts from a uniform distribution with support[\c', \ t ' ' ] , where \ > 1.'We assume through-out that minority-owned firms are high-costfirms and non-minority-owned firms are lowcost. This cost difference may be attributed topast discrimination, which preventedminority-owned firms from acquiring the sameexperience and human capital through learn-ing by doing that non-minority-owned firmswere able to gain through the winning of pastcontracts.'*

Note the asymmetry in the situation. Whilehigh-eost firms face one other high-cost firmand four low-eost firms, low-cost firms faceonly three low-cost firms and two high-eost

- Especially in the uniform distribution case, price-preference rules might be quite successful in approximat-ing both the allocation and purchasing prices of Iheoptimal auction.

' Nute in this specification that while the absolute val-ues of Ihe mean and standard deviation of the bidders'uniform distribuliuiis have increased by a tactor K iroin(he low-cust to high-cost firms, the coefficient of variation(standard deviation/mean) remains the same.

^ Obviously, if minority fimis were also low-cost pro-ducers, then, if the auction were run fairly, there would beno need for a price preference program to assi-st them.

firms. In other words, low-cost firms face lesscompetition than high-cost firms. When price-preferences are instituted, it makes high-costfirms look more like low-cost firms and as aresult of this increase in "effective" compe-tition, the low-cost firms bid more aggres-sively, i.e., they bid closer to their cost. Byanalogy, high-cost timis now face less com-petition and hence bid less aggressively. If thepreference is chosen correctly, the reductionin bids by low-cost firms (the firms which aremore likely to have lower costs of production)more than compensates for the increased bidsof high-cost firms.

To see this more formally, assume that thereis a single contract to be awarded in a price-preference, first-price, sealed-bid auction. Let:Ar= | 1 , ... , n} be the set of bidders for thiscontract. A subset containing k < n of thesebidders is assumed to be of Type A. The restof the bidders are of Type B. Each bidder pri-vately draws an individual-specific cost, c, offulfilling the contract" from his own type-specifie probability distribution over costs,G, (•), I = A, B; G, (•) is be assumed to be acontinuous, differentiable distribution, definedover the interval [£i,c,], i = A, B, with den-sity function gA-). It will be assumed that cT,> CH and £,, > Q , so Type A bidders will bethe high-cost bidders. Each individual bidderknows his own type, how many bidders ofeach type are present, his own private costdraw, and the distributions of costs faced byall other bidders.

Given the assumptions on the supports ofthe cost draws for each type, if it is true thatfor any given cost, c, which lies jointly in bothsupports, / /B(C) > H^c) where

(1)

then bidders of Type B have a cost advantageover bidders of Type A. In other words, givenany cost level, c, contained in either interval,there is a higher probability that a bidder ofType B will draw a cost lower than t than ofa bidder of Type A drawing a cost lowerthan c.

^ We drop subscripts for simplicity.

294 THE AMERICAN ECONOMIC REVIEW MARCH 1999

What separates the price-preference aue-tion from the simple asymmetric case is thatbidders of Type A are given a bidding ad-vantage in the auction for purposes ofawarding the contract. After all bids are sub-mitted, the auctioneer adjusts all Type B bidsby multiplying them by one plus the amountof the preference (we will denote this sumas B) to form the comparison bids for biddersof Type B. The bids of Type A remain un-changed for purposes of comparison, so forall Type A bidders, the submitted bid andcomparison bid will be identical. The bidderwho submits the lowest comparison bid willthen be awarded the contract at a price equalto his submitted bid. Therefore, the adjust-ment procedure only determines the winnerof the auction and does not affeet the ex postpayoff of the winner.

B. Equilibrium Bid Functions^

The problem facing a bidder / of Type A isto maximize expected profits given his eostdraw, c,. This can be written as

(2)

We ean rewrite the optimization problem fac-ing a member of Type A as

(3a) maK(b-c){l - G.(:v,{i)) )*" 'b

•l-k

given that there are n total bidders, k ofwhich are of Type A. Analogously, we candefine the problem faced by members ofType B as

(3b)

X ( 1 -

Taking first-order conditions and simplify-ing with equation (1), we get the followingsystem of nonlinear, first-order, differentialequations:

(4a)1

We do not know the distributions of bids forthe types, but we do know the distributions ofcosts and that the bid functions are strictlymonotonic. Therefore, we can define the in-verse bid functions for both types as

(4b)

" To be able to find the equilibrium bid functions of thetwo types, one must prove that the bid functions are mono-tonically increasing and that they are defined over a closedand bounded interval. Once these two facts are estab-lished, it follows that the bid functions are differentiablealmost everywhere on that interval. Differentiability al-lows us to take the firsi-order conditions for optimizationof expected profits for both types. Solving these two equa-tions simultaneously yields the equilibrium bid functionsof each type. Since the proofs of these two prerequisitesare easily available elsewhere, we will simply proceed byassuming monotonicity for the bid functions as well asdifferenliability.

y',(bHn-k-l).

It is this system of differential equationsthat needs to be solved, given appropriateboundary conditions, to yield the symmetric,within-type equilibrium bid functions. Theupper boundary conditions of the system forboth Type A and Type B firms can be deter-mined analytically and can serve as terminal

VOL 89 NO. I CORNS AND SCHOTTER: PRICE PREFERENCE AUCTIONS 295

conditions to pin down the equilibrium bidfunctions. The termitial conditions dependon whether ft> > c^ or Ocg < c^ J Derivationof the system of differential equations andthese terminal conditions can be found in anAppendix to Corns and Schotter (1996) ,available from the authors on request. It isimportant to note that in the case when OCB> CA, Type B bidders cannot win if theydraw a cost in the range {Cfl,l6, QJ] and when(^CH < CA, Type A bidders cannot win if theydraw costs in the range [OCB, C^]. Equilih-rium behavior in these "no-win" ranges canbe arbitrary but for simplicity we assumethat in these regions bidders will bid theircost.

As with most systems of nonlinear differ-ential equations, it is not possible to find aclosed-form solution for the inverse bidfunctions, and thereby for the actual bid func-tions themselves. We used the algorithm ofJohn Riley and Li Huagang (1993) to numer-ically solve for the equilibrium bid functionsin our auction."*

111. Experimental Design

The experiments performed were a straight-forward implementation of a price-preferenceauction. Students were recruited by announce-ment in undergraduate economies classes dur-ing the summer and fall of 1995. Volunteerswere told to come to a classroom that was re-served for the experiment. Upon arrival sixstudents were then randomly selected for eachexperimental session. Four subjects were ran-domly assigned to be Type B subjects and twowere randomly assigned to be Type A subjects.Type B bidders independently drew their costs

'' Let fc,. (• = A, B be the upper bound to the domain ofV, (•) in the system of differential equations. Also, lei h,,i = A. Bbe the maximum bid issued by both types. Thenit will be true that if Oct > c^, then b^ = 6^ = c^ andh,,= cJO. so terminal conditions are >'A(t^) = ^A and >H(t~i/0) = cj(f^ If it is the case that Oc^ < Q , then b^ ^ Oc^and bn = bn = Ca, SO terminal conditions iti this case arey^(fO() = **("« and ynicu) = O,.

" Here again let us take the opportunity to thankHuagang Li for all of his time and effort in helping us usethis algorithm and for the actual time he took in workingon this problem.

in all rounds ofthe experiment from a unifortndistribution with support IIOO, 200]. Type Asubjects drew their costs from a uniform dis-tribution with support 1110, 220] . Hence,Type A subjects were high-cost bidders whileType B subjects were low-cost bidders.

After subjects read the instructions to them-selves and then had them read out loud by theexperimental administrator, any questions thesubjects had were answered and the experi-ment began.'* In the beginning of each roundof the experiment (there were 20 rounds in all)an experimental administrator walked aroundthe room with two hags marked A and B. Ineach bag was a number of chips representinguniform distributions for the integers in thesupports of the two types of distributions. Thebag identities were hidden from the subjectsso that no one in the room knew who amongthem was a low- or high-cost type. If a subjectwas an A type {B type), the administratorwould give him or her the A bag (B bag) andhe or she would pull out a chip with a numberwritten on it. This number would be the costfor the subject in that round.

After a cost was drawn, each subject wouldrecord that cost on his or her work sheet andthen take out one of their 20 bid slips uponwhich they would write their bid. These bidswere then collected by the experimental ad-ministrator and then, depending on the rulesof the auction run, a winner would be deter-mined. The experimental administrator wouldthen write on the blackboard the number of thesubject who had won, the price he or she wonat, and whether that subject was an A or J5 type.Subjects would then record their payoffs andthe next round would start in an identical man-ner. In each experiment the final payoff to sub-jects was the sum of their payoffs over theentire 20-round history of the experiment plusa $5.00 bonus for showing up. Subjects werepaid at the end of the experiment and dis-missed. A postexperimental questionnaire wasalso administered in 13 out of the 20 experi-mental sessions run. The results of this ques-tionnaire are available upon request from theauthors.

' Instructions for the 10 percent preference experimentare contained in the Appendix to this paper.

296 THE AMERICAN ECONOMIC REVIEW MARCH 1999

TABLb 1—EXPERIMENTAL DKSIGN

Preference experimentNumber of

groups Types CostsNumber of

subjects

0 percent

5 pcrccni

10 percent

15 percem

2 A types4 B types2 A types4 B types2 A types4 B types2 A types4 B types

. , e (110. 220]c « e 1100.200]^•,€[110.2201f sG [100.2001c^e [110.220]CBG (100.200]r^ G [110. 220]( B G [100.200]

30

30

30

30

Table 1 describes our design. Four treat-ments which differed only with respect to thepreference rule used were run. The preferencerules used were a 0-pcrcent, 5-percent. 10-percent, and 15-percenl preference for Type A.After aJI bids were submitted, the bids of theB types were increased by the appropriatepercentage for the treatment before any com-parison of bids was made. The lowest postpre-ference bid was then awarded the contract atthe price of the submitted bid and the experi-ment proceeded to the next round. Includingthe $5.00 for showing up. the average payofffor the one-hour experimental session was$10.03.

IV. Results

Our discussion of the experiment's resultswill be broken into four sections. In the firsttwo sections we will investigate if the impo-sition of a price-preference rule increased thelikelihood that a high-cost firm would win anauction. We will also examine if the imposi-tion of a price-preference rule increased costeffectiveness and which price-preference ruleresulted in the lowest cost of purchasing forthe auctioneer (experimental administrator).In the tinai two sections we will investigatehow well the theory of auctions predicted thebehavior of the subjects.

The descriptive results of the experiment areshown in Table 2. which we will use to discussboth the procurement cost and representationoutcomes of the experiment.

In Table 2 there are two types of entries:those that are simple empirical calculationsand those that are hypothetical-theoretical cal-

culations using either equilibrium or estimatedbid functions and the assumed cost distribu-tions. The theoretical calculations are placedin bold letters to differentiate them.

A. Representation of High-Cost Eirms

Lines 3-6 in Table 2 present the impactof price-preference rules on the representa-tion of high-cost Type A firms amongst theset of winning firms. Note that as the price-preference given to high-cost firms in-creases, the fraction of contracts awarded tothem increases. Line 5 shows, given our ex-perimental parameters, theory predicts thatthe probability that Type A bidders win in-creases steadily from 19.1 percent in the 0-percent preference auction to 36.9 percent inthe 15-percent preference auction. Our ex-perimental results mirror this consistant in-crease in the frequency with which Type Abidders win. going from 12.1 percent in the0-percent or no-price-preference auction to43 percent in the 15-percent preference auc-tion as shown in Line 4. More importantly,it appears that as the price-preference is in-creased, it becomes responsible for more andmore of these wins, as it turns what wouldhave been losing high-cost bidders underlower preference regimes into winners. Forexample, while 10 of 22. or 45.4 percent, ofthe Type A winners in the 5-percent experi-ment won because of the price-preference,61.8 percent. 21 of 34. of the wins for TypeA subjects in the 10-percent experimentwere the result of the preference rule. Thefact that the percentage falls from 61.8 per-cent to 53.4 percent. 23 of 43. in the 15-

VOL. 89 NO. I CORNS AND SCHOTTER: PRICE PREFERENCE AUCTIONS 297

TABLh 2 — D E S C R I C I IVE R L S U I T S <)I PRRh-PREFtRKNCK AUCTIONS"

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Auction type

Winners

A lypesB types

Type A win frequency

Theoretical Type A winprobability

Wins by preference

Winners average cost

A types

B types

Winners average bid

A types

B tyf>es

Highest cost winner

Average profit per unit

A types

B types

Average observed price

Theoretical expectedprice

Naive cost ofpreference

Real cost

0 percent

12''87

0.121

0.191

117.17(5.68)

113.82(12.25)

124.42(4.79)

120.80(10.75)

A-125B-151

7.25(4.60)6.99

(4.75)

121.24(10.22)

134.13

0(0)

0(0)

5 pcrceni

2278

0.220

0.249

10

120.68(11.85)111.44

(9.29)

126.95(11.85)117.13

(9.29)

A-151B-155

6.27(6.66)5.69

(4.11)

119.29(10.66)

133.24

0.39(1.30)

-1.91(4.76)

10 percent

346r

0.354

0.298

21

126.79(14.45)112.81(11.55)

132.56(13.92)117.52(11.38)

A-1600-144

5.76(5.46)4.71

(3.61)

122.84(14.24)

134.50

1.06(2.76)

-0.28(6.63)

15 percent

4357

0.430

0J69

23

123.74(10.14)112.77(10.38)

131.56(11.01)119.02

(9.90)

A-148B-146

5.47(6.44)5.68

(4.80)

124.41(12.07)

136.06

2.04(4.61)

1.06(6.64)

" Standard errors in parentheses.'' One Type A winner dropped due to reporting cost outside of support.' Four Type B winners dropped due to bid less Ihan cost.

percent case is likely the result of the costrealizations occurring in the 15-percent ex-periment where, at least in one experiment,

the cost realizations for the low-cost B typeswere particularly high. Hence there is littledispute that, at least in our laboratory

298 THE AMERICAN ECONOMIC REVIEW MARCH 1999

setting, price-preference rules increase theprobability tbat high-cost (minority) firmswin contracts.

B. Procurement Price Comparisons

Looking at line 14 of Table 2 we see thatthe average prices paid per auction in our fourexperiments were 121.24, 119.29. 122.84, and124.41 for the 0-percent, 5-percent, 10-percent, and 15-percent treatments, respec-tively. Tbese figures imply tbat on tbe basis ofthe average price paid per auction, the 5-percent price-preference rule seems to be thebest, followed by tbe 0-percent auction, andthen tbe 10-percent and 15-percent auctions.

It is bard to rely on tbese findings as a soliddemonstration tbat tbe price of purcbasing islowest wben tbe 5-percent preference is usedsince tbese differences might not reflect a be-bavioral difference in bidding but rather thefact tbat tbe costs drawn in tbe 5-percent pref-erence treatment were lower tban tbose drawnin otbers. When tbis conjecture is tested usinga Kolmogorov-Smimov test we find that nodifference exists between the distribution ofdrawn costs between any two experiments forany type. In other words, statistically tbe costsdrawn for all experiments came from tbe samepopulation.

Kolmogorov-Smimov Tests for Equalityof Cost Distributions

A types

Experiment pair p-value

0 percent vs.0 percent vs.0 percent vs.5 percent vs.5 percent vs.

10 percent vs.

5 percent10 percent15 percent10 percent15 percent15 percent

0.2320.0910.1870.9530.9530.669

B types

Experiment pair0 percent vs. 5 percent0 percent vs. 10 percent0 percent vs. 15 percent5 percent vs, 10 percent5 percent vs. 15 percent

10 percent vs. 15 percent

p-value0.8430.6070.3340.2520-1310.980

Despite these statistical tests, however, it isstill possible tbat tbe price of purchasing dif-

ferences observed were at least in part due tosmall sample biases in the cost realizations ofour four auctions. In order to control for tbesedifferences, we performed a simulation to cal-culate wbat the price of purchasing wouldbave been in our various auctions if bidders inan auction witb an jc-percent (say 5-percent)rule bad received tbe cost realizations of bid-ders in an auction witb a y-percent (say 0-percent) rule and vice versa. To do tbis weestimated a bid function for eacb type of bid-der in eacb auction using pooled data for bid-der types in eacb experiment. (See Section IV,subsection D, for a full description of tbe es-timation procedures used.) Using tbese bidfunctions we were able to simulate tbe bids ofType A and Type B bidders given any sampleof cost realizations by simply plugging tbesecost realizations into our estimated bid func-tions and playing out tbe auction. Tbese sim-ulation results are presented in Table 3.

In Table 3 tbere are two types of entries; tbosewbicb are derived from calculations on actualdata and tbose which are tbe result of tbe sim-ulations just described. Tbe actual average pur-cbasing prices, wbicb are along the diagonal andare the average observed prices reported in line14 of Table 2, are placed in bold type to distin-guisb tbem from tbe simulated calculations. Forexample, tbe top left diagonal element sbowstbat the average price of purcbasing in tbe 0-percent preference experiment was 121.24.Looking across tbe first row to tbe next cell wesee tbat if tbe bidders in tbe 5-percent preferenceauctions bad actually received tbe same cost re-alizations as tbe 0-percent preference bidders,tben, using tbe estimated bid functions for the 5-percent preference auction, we predict an aver-age purcbasing price of only 120.03. Goingfurther across the first row we see that using tbeestimated bid functions from the 10-percent and15-percent preference auctions, again using tbe0-percent preference auction cost data, we wouldexpect purcbasing prices of 120.97 and 124.25,respectively. In other words, if we look acrossrow 1, we find tbat using tbe cost realizations inthe 0-percent auction and tbe estimated bebaviorin otber auctions, tbe government would bavebad an average savings of almost 1 percent,(120.03 - 121.24)/121.24 = -0.00998, if ithad imposed a 5-percent preference on tbesebidders. Likewise, it would bave bad a savings

VOL 89 NO. I CORNS AND SCHOTTER: PRICE PREFERENCE AUCTIONS 299

TABLE 3—AVERAGK PURCHASINC;

Cost realizations

0 percent5 percent

10 percent15 percent

0 percent

121.24121.10123.12123.35

PRICES, ACTUAL (IN

5 percent

120.03119.29121-37121.89

BOLD) AND

10 percent

120.97120.12122.84122.78

SIMULATED

15 percent

124.25123.44125-52124.41

of 0.22 percent had it used a 10-percent prefer-ence rule, but would have incurred an additionalcost of 2.48 percent had it used a 15-percentpreference rule, given the cost draws in the 0-percent treatment.

Looking across the other three rows we seethat this hasic pattern repeats itself. No matterwhat set of cost realizations is used, the 5-percent preference auction behavior is alwaysthe most cost effective. In addition, as Table 2indicates, not only was the 5-percent rule themost cost effective, it also increased the per-centage of contracts going to high-cost(minority) firms from 12.1 percent in the 0-percent preference treatment to 22.0 percentwhen the 5-percent preference was used. In-terestingly, McAfee and McMillan (1989) es-timate that with the parameters used in ourexperiment a 4.1-percent price-preferencewould have been optimal among the class ofpercentage price-preference rules.

The "Real Cost" accounting method dis-cussed above and presented in line 17 of Table2 can be derived from Table 3 as follows: Takeany auction with a nonzero price-preferencerule, say the 15-percent rule, and look alongthe diagonal in Table 3 to find the actual ex-perimental price associated with that prefer-ence rule. In the 15-percent preference case theactual average price of procurement is 124.41,which is at the lower right-hand comer of thetable. Using the 15-percent treatment cost re-alizations, calculate the expected procurementprice associated with them when bidding be-havior is characterized by the bid functions es-timated in the 0-percent auction. This price ispresented in the lower left-hand comer and is123.35. This difference, {124.41 - 123.35 =1.06), is the real cost of the preference rule.

In terms of statistical significance, it is hardfor the differences we observe to pass a signifi-cance test because even equilibrium purchasing

prices are not predicted to be dramatically dif-ferent between the 0-percent and 5-percentprice-preference auctions. Still, when using the5-percent data and comparing purchasing costsin the 5-percent and O-percent auctions, we find,using a Mann-Whitney U-test, that the null hy-pothesis of the equality of the distributions ofthe winning bids is rejected at the 5-percent level(p-value 0.032). However, the reverse, usingthe 0-percent data for comparison, was not sig-nificant at the 5-percent level. A Mann-WhitneyU-test performed on the actual prices formed inthe 0-percent and 5-percent auctions uncondi-tional on cost realizations also did not show asignificant difference at the 5-percent level.

If we look back again at Table 2 and com-pare line 14 (our experimental average pur-chasing prices) to line 15 {the theoreticalexpected prices of purchasing), we see thatour experimental prices are well below thetheoretically predicted prices. To test thesignificance of this apparent underbiddingphenomenon we ran a Kolmogorov-Smimovone-sample test in which we compared the ex-perimental cumulative frequency distributionsof bids for each type with each preferenceagainst the distributions of bids predicted bytheory, given the same cost draws, with thenull hypothesis that the distributions wereequivalent. In each case we strongly rejectedthe hypothesis of equivalence at the 5-percentlevel. The experimental distribution was sig-nificantly below the theoretically predicteddistribution with the greatest points of diver-gence between the distributions occurring inthe lower regions of the range of bids.

C. Experimental Results and the OptimalAuction Mechanism

As we noted in Section II, subsection A,the percentage price-preference auctions we

300 THE AMERICAN ECONOMIC REVIEW MARCH 1999

^ 4—PROCUKE-MENT pRiCh COMPARISONS: OrriMAL MKCHANI.SM VS,RULE.S

Procuremenl price 0 percent 5 percent 10 percent 15 percent

TheoreticalPreference ruleOptimal mechanism

ActualPreference ruleOptimal mechanism

134.13132.19

121.24124.97

133.24132-19

119.29125.53

134.50132.19

122.84126.49

1.̂ 6.06132.19

124.41127.70

ran are not optimal auctions. We investigateprice-preference auctions because they are fre-quently used. Still, one might ask how muchbetter off the govemment might be if it usedthe optimal auction form. The optimal auctionfor bidders who are asymmetric with respectto their cost distributions takes the followingform. First, bidders submit messages repre-senting their supposed true cost of production.The auctioneer takes these costs as truthful andconstructs the following function:

(5)

j = 1 n,;i = A,B

where n, is the number of firms of Type /, / =A, B\ c,j is the cost message of thejth bidderof Type (•; and G, ( ) is the continuously dif-ferentiable cumulative cost distribution ofType / with density g,{)- The contract isawarded to that bidder with the lowest J, {c,,)at a price equal to that cost report that wouldequate the value of his J, to that ofthe secondlowest bidder (see Myerson, 1981; JeremyBulow and John Roberts, 1989; McAfee andMcMillan, 1989).

Table 4 compares how the price-preferenceauctions we ran compare both theoreticallyand empirically to the outcomes predicted bythe optimal auction mechanism. Startingwith the first two rows we see that the opti-mal auction mechanism generates an ex-pected procurement price of 132.19 givenour assumptions on the number of bidders ofeach type and their corresponding cost dis-tributions. The theoretically expected prices

associated with the price-preference auctionvary depending on the degree of preference.with the lowest, 133.24, being associatedwith the 5-percent preference and the high-est, 136.06. with the 15-percent preference.Looking at the last two rows of Table 4, notethat the experimental price-preference auc-tions performed better than the optimalauction mechanism predicts, had it been im-plemented using the actual cost realizationsof our experimental auctions. For example,while the optimal mechanism predicts an ex-pected procurement price of 125.53 for thecost realizations of the 5-percent price-preference groups, when the 5-percent price-preference rule was used in our experimentthe average procurement price was 1 19.29.This "countertheoretical'" result is clearlyattributable to the fact that subjects in ourexperiments tended to bid more aggressivelythan the theory predicts, resulting in betterthan optimal purchasing prices.

D. Estimation of Bidding Behavior

Probably the best way to see how biddingbehavior changes as we change the price-preference rule is to estimate bid functionsusing the pooled data generated by our ex-periment. We estimated equation (6 ) foreach type of bidder in each preferencetreatment

(6)

where b is the observed bid, c is the cost draw,£ is lower bound of the cost distribution, DTis a dummy variable that takes the value 0 if

VOL. «y NO I CORNS AND SCHOTTER: PRICE PREFERENCE AUCTIONS 301

the observation comes from the first ten roundsof ihe experiment and 1 if from the la.st ten.and / is a function of a vector of parameters,p, c - c, and time. By making / a function ofc - c rather than just the cost draw we caninterpret 0,, as the minimum bid for the typegiven the preference rule. The inclusion of adummy variable on time allows us to see ifbidders are altering their strategic behaviorover time due to learning about the situationthey are in.

Because we observe 20 bid-cost pairs fromeach subject, we cannot employ simple ordi-nary least squares (OLS) since that methodrequires independence across observations. In-stead we use a random-effects specification.'"We estimated / a s a cubic polynomial in c -c but linear in DT. Table 5 reports the resultsof the bid-function estimations. We also rantwo regressions, one foreaeh bidder type, thatpooled all observations for that bidder typeover all experiments and that used a more elab-orate set of dunmiy variables to denote treat-ments and included interactions with thosedummy variables and the cost variables. Sincethe results of Ihese regressions were not dif-ferent either qualitatively or quantitatively, weopted to present these disaggregated regres-sion results for simplicity's sake.

The first thing of note when looking at Ta-ble 5 is that even though four of the eightregressions showed significance for quad-ratic and even cuhic terms at the 95-percentlevel, all bid functions were estimated to bevery close to linear. Second, if we look at theparameter estimates on the lime dummy, wesee that all estimates were negative and thatfive of the eight estimates were significantlydifferent than 0. These results are consistentwith those of Reinhart Setten and JoachimBuchta ( 1994) and Timothy Cason andDaniel Friedman (1995), who investigate

'" In our analysis we dropped observations in which thebid was less than the cost draw, the cost draw repiirtcdwas uutsidc the stated cost distnbutiuii, or ihc submittedbid was a "throw-away" bid. Throw-away bids were ex-tremely high bids that a tew .subjects issued when theydrew a cost with which they associated no chance ol' win-ning As some of these bids were one milHon or more,these observations had to be removed frum the sample dueto the inliuence they would have on the estimation.

learning in sealed-bid and single-call marketinstitutions, respectively. They find, test-ing directional and error-based learningmodels, that over lime participants bid moreaggressively.

Theory predicts that as the preference isincreased for the Type A bidders, their bidfunction should shift upward as they usethe opportunity of decreasing competitionto increase iheir bids. Thus, the 0-percentpreference bid function should lie belowthe others, with the 5 percent next, etc. Forthe Type B bidders, the opposite should beIrue as these low-cost bidders should de-crease their bids at each level of cost aspreference increases sinee they face height-ened competition due to the increase inpreference."

From looking at Table 5, except for theintercept terms, it is hard to tell what the re-lationship between ihe estimated bid func-tions is. if we were to plot the bid functionsfor eacb type bidder we would see that forthe Type A experimental bid functions, the5-percent preference bid function lies belowall others for most of the lower part of theircost domains. The 10-percent and 15-percent bid functions do lie above the 5-percent function as theory would predict,with the 15-percent function being above the10-percent function for all but the lowestcost draws. Thus, the relation between thesethree bid functions is in close accord withthe prediction.s of theory. However, ihe 0-pereenl bid function tends to lie above the 5-percent and the 10-percent functions formost of the lower part of Ihe cost support,contrary to theoretical predictions.

Plotting the Type B bid functions, wewould see the 0-percent bid function does lieabove alt others, followed by the 5-percentand 10-percent functions al least initially, astheory would predict. The 15-percent bidfunction lies below the 0-percent function.

" In pustexperimental surveys given subjects. 16 outof 22 B-type subjects who participated in ex peri men ts withpositive preferences indicated that the existence of (heprice-preference rule led them to bid Inwer thun theywould have if no preference existed For A types, three ofnine subjects indicated that the preference caused them toraise their bids.

302

Price preference

0 percent

5 percent

10 percem

15 percent

0 percent

5 percent

10 percent

15 percent

Intercept

122.02*(1.515)

119.86*(1.508)

120.99*(1.660}

120.76*(1.923)

112.88*(0.961)

108.93*(1.220)

108.13*(1.643)

111.74*(L262)

THE AMERICAN ECONOMIC REVIEW

TABLE 5—ESTIMATES FDR EXPKRIMKNTAL BID FUNCTIONS"

(f - ()

0.645*(0.124)0.753*

(0,121)0.706*

(O.tO2)0.872*

(0.104)

0.552*(0.079)0.746*

(0.098)0.930*

10-125)0.565*

(0.078)

Type /

{c - cf

6.8e-3*(2.8e-3)4.1e-3

(2.6e-3)3.6e-3

(2.2e-3)5.le-4

(2.2e-3)

bidders

(c - c)'

-4.Ie-5*(l.8e-5)

-2.2e-5(l.6e-5)

-1.4e-5(l.3e-5)

- l . ! e -6(I.4e-5)

Type B bidders

9.0e-3*(1.9e-3)5.2e-3*

(2.3e-3)1.2e-3

(3.le-3)9.3e-3*

(l.8e-3)

-5.7C-5*(l.3e-5)

-3.2e-5*(1.6e-5)

-7.3e-6(2.1e-5)

-5-7e-5*(l.2e-5)

DT

-0.888(0.841)

-2.079*(0.858)

-0.574(0.684)

-1.508*(0.684)

-1.882*(0.504)

-1.064(0.604)

-2.482*(0.826)

-1.953*(0.454)

Adjusted R'

0.965

0.965

0.974

0.975

0.964

0.953

0.927

0.975

MARCH 1999

Sample pairs

188

197

199

198

398

399

371

400

" Standard errors in parentheses.* Significantly different from 0 at the 5-percent level.

but is initially above the 5- and 10-percentfunctions. Eventually, though, il does tallbelow all other functions. Because of ourtreatment parameters, these bid functionscannot be expected to be dramatically dif-feretit, since these parameters, theoretically,call for differences in behavior by the bid-ders that should not vary by a large amountfrom treatment to treatment.

V. Conclusions

In this paper we have demonstrated thatthe use of affirmative action programs neednot force policy makers to have to choosebetween the benefits of minority represen-tation and cost effectiveness. In certain cir-cumstances, such as the price-preferenceauctions investigated here, both minorityrepresentation and cost effectiveness can beenhanced simultaneously if the proper price-preference rule is used. This result seems ro-bust to learning on the part of bidders in thesense that after subjects have experiencewith bidding in such auctions, the auctions

run using a 5-percent price-preference rulecontinue to outperform those in which nopreference is given. In general, bidders bidmore aggressively, closer to their cost, as theauction progresses.

Our results do raise a note of caution since, ifthe govemment fails to use the optimal price-preference rule, it could increase its averageprice of purchasing and f^l to reap tbe benefitstbat such price-preference rules offer. Further,we can offer little in the way of guidance abouthow to sel tbe optimal preference without havingestimates of the parameters of tbe cost distribu-tions of the bidders. McAfee and McMillan(1989) offer a rough rule of thumb to help de-cision makers choose the correct preference rule.This is to use one-third ofthe percentage differ-ence between the means ofthe cost distrihutionsofthe two types of firms as the price-preference,but tbis rule is predicated on the assumption ofuniform distributions. With our treatment pa-rameters, their rule suggests a 3.3-percent pref-erence, which is closest to the 5-pea'ent rule thatproved to be best among our limited set of fourrules.

VOL 89 NO. I CORNS AND SCHOTTER: PRICE PREFERENCE AUCTIONS 303

APPENDIX: INSTRUCTIONS FOR

10-PERCENT AUCTION

This is an experiment in the economics ofmarket decision-making. Various researchfoundations and agencies have provided fundsfor the conduct of this research. The instruc-tions are simple, and if you follow them care-fully and make good decisions you might earna considerable amount of money which will bepaid to you after the experiment is over.

Experimental Procedures

In this experiment we are going to conducta series of 20 independent auctions run oneafter the other. When you walked into theroom you had the chance to choose a folderwhich contained these instructions along withother forms and pieces of paper. On the upperright-hand comer of your instruction sheet willbe a subject number (a number from 1 to 6).Check to see that you have a work sheet and20 bid slips each with a different round num-ber written on it. By choosing a folder you alsochose which type of bidder you are, TYPE Aor TYPE B. There will be 2 TYPE A biddersand 4 TYPE B bidders. If your subject numberis 1 or 2, you will be a TYPE A bidder whileif it is 3, 4, 5. or 6 you will be a TYPE B. Ineach round of the experiment you will beasked to enter a bid for a fictitious good orservice that you will provide. The cost of pro-viding this good or service will be randomlydetermined separately and independently foreach bidder in each round of the experiment.The costs will be denominated in a fictitiouscurrency called francs. Each franc will be con-veried into dollars at a rate of 1 franc = $0.25.For TYPE A bidders, their costs will be drawnwith equal probability from the integers lyingin the interval U 10, 220], while for TYPE Bbidders their costs will be drawn with equalprobability from the integers lying in the in-terval 1100, 200]. What this means is that ifyou are a TYPE A bidder, any cost in the in-terval [lit). 220] is as likely to be your costas any other. For example, you are as likely toreceive a random cost of 110 as you are a ran-dom cost of 145 as you are a random cost of220, etc. The same is true of TYPE B biddersexcept, of course, for the fact that their costs

come from a different interval, the interval[100, 200]. Still for TYPE B bidders they areas likely to receive a cost of 100 as they areone of 166 as they are one of 200, etc.

The way this random cost will actually begiven to you is by having, at the beginning ofeach round ofthe experiment, an experimentaladministrator walk around the room with oneof two bags filled with chips. If you are ofTYPE A you will be given the TYPE A bag.You will put your hand in the hag and pull outone and only one chip. In the bag will be anumber of chips with a different number writ-ten on them, one for every number in the in-terval tnO, 220]. The chip that is drawn inthis fashion will be your cost for that round ofthe auction, [f you are a bidder of TYPE B youwill do the same from the TYPE B bag. Sincewe want to keep the identify of the biddertypes secret, you will not notice any differencein the bags, but we will bring them to you ac-cording to your type. [We will let you inspectthe contents of these bags at the beginning ofthe experiment so as to verify their contentsand they will remain in full sight during the 20rounds of the experiment so you will be as-sured that they are as we describe them.]

Your random cost for any round will beknown to you and only you. Do not let anyoneelse see it. Once you observe your random costin any round, write it down in Column 1 ofyour work sheet under the heading RANDOMCOST. Knowing your cost you are now tomake a bid to sell the fictitious good or servicebeing sold. To do this, take out one of the bidslips in your folder labelled with the appro-priate round. On this bid slip write down yourbid for this round. In addition, record your bidin Column 2 of your work sheet under theheading BID. These slips will then be col-lected and brought up to the front of the roomwhere they will be compared by the experi-mental administrator sitting at the desk. Hewill then announce both the winning bid andthe type of bidder {TYPE A or TYPE B) whowas the winner.

Round Payoffs

Your payoffs in any round will be deter-mined in a very simple way. Once the bid slipsfor a round are brought up to the front of the

304 THE AMERICAN ECONOMIC REVIEW MARCH 1999

room, they will be opened and compared. Thiswill be done as follows: First, all TYPE B bidswill be increased by 10 percent. Then the ex-fKrimental administrator will look over all thebids and award the contract to sell the ficlitiousgood (o that bidder of any type with the lowestbid. In short, TYPE A bidders who draw theircosts from ihe interval |110. 220] are given apreference in the bidding since, before the bidcomparisons are made, their costs are not in-creased by 10 percent while the bids of TYPEB bidders are. For example, say that the lowestbid made by a bidder of TYPE B is 60 whilethe lowest bid made by a bidder of TYPE Ais 63. In such a case, the hidder of TYPE Awould win the auction since after the 10 per-cent is added on to the bid of the TYPE Bbidder, their bid would be 66 and greater thanthe bid of the lowest TYPE A bidder. If twobidders are tied for the winning bid, a coin willbe flipped to determine the winner.

The payoff to the winner of the auction issimply equal to their bid minus their cost. Forexample, say that a bidder receives a randomcost of 55. submits a bid of 70 and wins. Thentheir payoff in that round of the experimentwill be PAYOFF = 70 - 55 = 15. Note thatthis is the payoff to any winning bidder re-gardless of their type. The 10-percent increasein the bid of TYPE B bidders is done simplyfor comparison purposes to determine the win-ner. If a TYPE B bidder actually wins, theywin at a price equal to the bid they entered nottheir bid +10 percent. If you do not win theauction, your payoff for that round is 0. Besure in Column 3 I labeled WIN (Yes, No) | ofyour work sheet to record if you won or notin this round ofthe experiment and in Column4 (PRICE) to record the price at which youwon if you did. In Column 5 record your pay-off for this round of the experiment which willbe zero if you lost and will be the differencebetween your winning bid minus your cost ifyou won. Note that the only way you can losemoney in this experiment is to bid below yourcost. Hence, in order to avoid a loss never sub-mit a bid below your cost. If a loss occurs, itwill be subtracted trom the $5.00 given to youfor showing up.

Once a round of the experiment is over, thenext round will start in an identical manner.First experimental administrators will walk

around the room with bags generating randomcosts. Next you will bid. and finally you willbe informed of the winning bid and the typeof bidder who won. You will then your payoffson your work sheet.

Final Payoffs

Your final payoff for participating in the ex-periment will be equal to $5.00 plus the .sumof your earnings over the 20 rounds of the ex-periment. To determine this payoff rememberto convert the fictitious francs you earn in eachround into dollars at the rate of 1 franc =$0.25. This payment will be given to you atthe end of the experiment.

REFERENCES

Ayres, Ian and Cramlon., Peler. "PursuingDeficit Reduction Through Diversity:How Affirmative Action at the FCC In-creased Auction Competition." StanfordLaw Review, A u g u s t 1 9 9 6 . 48(4), p p .761-815.

Bulow, Jeremy and Roberts, John. ' The SimpleEconomics of Optimal Auctions." Journalof Political Economw October 1989,97(5). pp. 1060-90.

Cason, Timothy and Friedman, Daniel. "Learn-ing in Laboratory Markets with RandomSupply and Demand." Mimeo. Universityof Southern California, 1995.

Corns, Allan and Schotter, Andrew. "Can Affir-mative Action Be Cost Effective? An Ex-amination of Price-Preference Auctions."C. V. Starr Center Working Paper No. 96-02. New York University. January 1996.

Jordan, Donald E. "In-State Preferences inPubhc Contracting: State's Rights vs. Eco-nomic Sectionalism." University of Colo-rado Law Review, March 1978, 49( 1), pp.205-31.

Maskin, Eric and Riley, John G. "AsymmetricAuctions." Mimeo. UCLA, June 1995.

McAfee, R. Preston and McMillan, John. "Gov-ernment Procurement and InternationalTrade." Journal of International Econom-ics, May 1989. 26(3/4). pp. 291-308.

Myerson, Roger. "Optimal Auction Design."Mathematics of Operations Research, Feb-ruary 1981. 6 ( 1 ) . pp. 5 8 - 7 3 .

VOL 89 NO. I CORNS AND SCHOTTER. PRICE PREFERENCE AUCTIONS 305

National Association of State Purchasing Officials.State and local government purchasing, MhEd.Lexington,KY: National Association ofState Purchasing Officials, 1994.

National Institute of Government Purchasing. Re-suits: 1993 procurement practices. Reston,VA: National Institute of Govemment Pur-chasing, 1994.

Riley, John and Li, Huagang.'Freeware Program to COMPute Equilib-Hum Bids and COMPare Expected Reve-nue." Mimeo. UCLA, 1993.

Seiten, Reinhart and Buchta, Joachim. "FirstPrice Auctions with Directly Observed BidFunctions." Discussion Paper No. B-270,University of Bonn, 1994.