Bidding for Incomplete Contracts: An Empirical Analysis of Adaptation Costs

Transcription

1 Onlne Appendx for Bddng for Incomplete s: An Emprcal Analyss of Adaptaton Costs Patrck Baar Stephane Houghton Steven Tadels Decemer 202 The followng Appendx provdes addtonal detals aout the data and estmaton procedures used n the paper. Tales A-A3 summarze the ddng ehavor of the top 20 frms n our sample, the numer of partcpants n each aucton, and the dstruton of these auctons over tme. The next two tales present nformaton aout our use of nstruments n the reduced form regressons of ds on contract characterstcs and ex post changes. Specfcally, n Tale A4, we present F-statstcs from frst-stage regressons of the nstruments. Tale A5 demonstrates the roustness of our results y comparng model specfcatons that nstrument for dfferent susets of the potentally endogenous varales. A fnal secton descres n detal the procedure used to otan the structural estmates. Ths secton also ncludes Tale A6, whch presents results for alternatve specfcatons of the frst-stage recovery of the d dstrutons usng fxed effects and random effects to control for unoserved aucton heterogenety. Unversty of Mnnesota and NBER Texas A&M Unversty UC Berkeley

2 ID No. of Wns Total Bd for s Awarded Tale A: Bddng Actvtes of Top 20 Frms Fnal Payments No. of Partcpaton Condtonal on Bddng for a on s Bds Rate Average Bd Awarded Entered Average Engneer's Estmate Average Dstance Mles) ,232,998 66,5, % 3,395,548 3,379, ,245, ,245, % 0,607,480 0,894, ,048,703 02,084, % 3,769,467 3,44, ,47,853 94,787, % 3,932,62 3,72, ,495,433 72,25, % 2,20,26 2,377, ,088,982 76,24, % 2,806,625 2,830, ,970,83 62,64, % 3,236,709 3,030, ,666,668 53,890, % 9,007,85 9,037, ,605,745 5,533, %,990,36 2,26, ,852,728 45,655, % 2,609,335 2,688, ,695,376 46,204, % 3,23,777 2,886, ,092,725 36,268,057 0.% 33,092,725 28,8, ,96,930 3,053, % 2,094,049 2,065, ,786,493 26,426,965 9.% 7,283,86 7,406, ,566,823 27,995, %,62,933,630, ,883,692 27,84, % 2,89,430 2,00, ,556,856 25,487, %,358,393,427, ,454,933 23,79, %,597,387,633, ,8,363 25,627, % 4,954,998 4,93, ,904,644 24,262, % 2,644,02 2,55, Tale A2: Bd Concentraton Among s Awarded to Lowest Bdder Numer of Bdders Total s n s n s n s n s n s n Tale A3: Proect Dstruton throughout the Year Month Jan Fe Mar Apr May Jun Jul Aug Sept Oct Nov Dec s n s n s n s n s n s n

3 Tale A4: Frst-Stage Results Testng Instrument Qualty Endogenous Varale Frst Stage F-Stat Postve Adustments Negatve Adustments 9.22 Extra Work 4.79 Deductons 5.53 CCDBOverrun 3.96 Numer of Oservatons 366 The fve categores of ex post changes are each normalzed y a measure of proect act sze, q. These suggest that the resdent engneer s dentty s only strongly correlated wth postve adustments and the dollar overrun on temzed tasks, ut weakly correlated wth extra work and deductons. Tale A5: Bd Functon Regressons Usng Actual Quanttes Instead of Estmates Varale IV. VII. V. VIII. VI. IX. DIST ) 5.85) 5.94) 3.6) 3.6) 3.6) 4.98) 5.32) 5.3) RDIST ) 3.24) 3.43) -0.5) -0.5) -0.5).83).57).69) FRINGE ) 0.02) 0.04) 6.46) 6.46) 6.46) 5.59) 5.32) 5.32) Numer of Bdders ).2).9) 0.47) 0.58) 0.55) -0.80) -0.73) -0.78) NPosAd ) 3.87) 3.92) 5.85) 3.82) 3.89) 6.39) 4.67) 4.76) NNegAd ) -.78) -2.25) -2.24) -.72) -2.27) -2.25) -.62) -2.87) NEX ).64).76).77).66).79).79) 2.49) 3.52) NDED ) -0.99) -.28) -.84) -.30) -.80) -.46) -.58) -.22) NOverrun ) 3.72) 3.79) 5.46) 3.70) 3.78) 5.76) 3.94) 4.04) Constant ) 29.73) 3.30) -.9) -2.7) -2.06) 44.80) 44.59) 46.82) Proect None None None Fxed Fxed Fxed Instruments None Resdent None Resdent None Resdent Engneer Engneer Engneer Resdent Engneer, only for NPosAd, NOverrun Resdent Engneer, only for NPosAd, NOverrun Resdent Engneer, only for NPosAd, NOverrun R Num. of Os Ths tale reproduces sx of the columns from Tale 7 n the ody of the paper. An addtonal column has een added for each of the no/fxed/random effects specfcatons, showng the estmates when we only nstrument for NPosAd and NOverrun where nstrument strength s not an ssue. Note the smlarty n our estmates across specfcatons. As wth Tale 7, the dependent varale for all nne regressons s the vector product of the unt prce ds and the actual quanttes, dvded y a measure of the proect sze q act ). Cluster-roust standard errors are used to compute t-statstcs, shown n parentheses. NOverrun s a measure of the quantty-related overrun on standard contract tems, calculated as the vector product of the CCDB prces where avalale) and the dfference etween actual and estmated quanttes. 3

4 A Detals on the Structural Estmaton Our structural approach uses a two-step semparametrc estmator that ulds on those dscussed n Elyakme, Laffont, Losel, and Vuong 994) and Guerre, Perrgne, and Vuong 2000). In the frst step, we estmate the densty and the CDF of the d dstruton for proect n, denoted y h n) and H n) respectvely. In the second step, we use those estmates n a GMM estmator ased on the frst-order condtons n Equaton 4). Ths allows us to recover the adustment cost coeffcents, τ a+, τ a, τ d, and τ x, along wth a specfc form of the penalty from skewed ddng captured y the parameter σ. Step : Estmatng Bd Dstrutons Because the dder s payoff functon contans expectatons of the proalty that hs d s the lowest, the frst-order condtons wll contan the densty and CDF of the d dstrutons. Specfcally, we are nterested n an estmate for h n) q e,n) ) H n) q e,n) ) for each contract n and each dder. As we note n the paper, we cannot recover fully nonparametrc estmates of these dstrutons whle stll controllng for mportant measures of frm-specfc and aucton-specfc heterogenety. Instead we use the followng semparametrc approach that homogenzes the sumtted ds from all frms and all contracts, and uses the homogenzed ds to consstently estmate the underlyng dstruton of frm valuatons. Frst, we regress the normalzed d on the frm s dstance and a frnge ndcator, allowng for proect-specfc random effects: ) n) q e,n) n) q e = x n) µ + u n) + ε n) where x n) ncludes the dder s dstance to the o ste and an ndcator for whether the dder s a frnge frm wth less than % of the value of contracts awarded). Let ˆε n) denote the ftted resdual from ths regresson: ˆε n) = n) q e,n) n) q e x n) ˆµ û n) Ths approach s detaled n the Athey and Hale 2007) chapter of the Handook of Econometrcs, and smlar versons are appled n Krasnokutskaya 20) and Shneyerov 2006). 4

5 These resduals are assumed to e d wth dstruton G N ), where N ndexes the dstruton y the numer of dders n contract n). We can use the emprcal dstruton of these resduals to recover an estmate for the dstruton of ds, snce as we show n the paper, H n) ) G N ) n) x n) q e,n) µ u n) Specfcally, n order to construct Ĥn) q e,n) ), we frst compute the emprcal CDF of the resduals, Gˆ N ), y poolng all resduals from ds on contracts wth the same numer of dders,n, as n contract n). 2 Then we evaluate ths dstruton at n) q e,n) xn) n) qe,n) ˆµ û n) to determne the proalty that dder s d of n) q e,n), normalzed, would e less than hs rval dder s, normalzed d. Put smply, we count the fracton of the ftted resduals that are less than n) q e,n) xn) n) qe,n) each dder, for each of dder s rvals, ndexed y. ˆµ û n). Ths s done for each contract n and Next, n order to recover the emprcal densty of the ds, Ĥ n) q e,n) ), we need an estmate of the emprcal densty of the resduals, g N ), where agan, N ndexes the densty y the numer of dders n contract n). We use a kernel densty estmator, wth a normal kernel and a andwdth determned y Slverman s rule of thum a value of for our data). 3 Usng a change of varales, we convert ths estmated resdual densty to an estmate of the d densty: ĥ n) ) = ) n) ĝ N q e,n) n) x n) q e,n) ˆµ û n) We use the aove to calculate ĥn) q e,n) ) for each contract n wth numer of dders, N ) and each dder, for each of dder s rvals, ndexed y. Each of the resultng values are then comned wth the estmates of the CDF to form the expresson n. Note that the estmates of oth Ĥn) ) and ĥn) ) make use of dder- and proectspecfc nformaton, as they are evaluated at values that depend on the proect s sze, n) q e,n), rval dder s characterstcs x n), and the unoserved proect heterogenety, û n). Furthermore, a separate dstruton s estmated for each set of N dders to account for the fact that, n equlrum, the dstruton of ds wll e dfferent n a 2-frm aucton 2 We thank an anonymous referee for remndng us to emphasze that n a frst-prce aucton, the dstruton of the mean zero ε n) wll vary y the numer of dders n equlrum. That s, there s a separate emprcal dstruton for contracts where n=2 whch we estmate usng resduals from 266 ds), n=3 estmated usng resduals from 552 ds), n=4 67 ds), n=5 639 ds), n=6 444 ds), n=7 448 ds), n=8 200 ds), n=9 80 ds), n>=0 26 ds). We pool contracts wth over 0 dders as there are a lmted numer of contracts wth such large sets of dders. 3 Varyng ths andwdth slghtly dd not sgnfcantly alter the results. 5

6 as compared to a 5-frm aucton, snce dders know the numer of partcpants at the tme of ddng. These estmated dstrutons are reasonaly precse, drawng upon anywhere from 80 to 67 oserved ds. The Matla code to construct these estmates s avalale as a supplement to ths onlne appendx. Step 2: GMM Estmaton of the Frst-Order Condtons We use the estmates from Step to construct ĥ n) q e,n) ) Ĥn) q e,n) ) ). Ths term s found n the dder s frst-order condton gven n equaton 0) of the paper. Followng that equaton, we can construct the composte error, ẽ n), as: ẽ n) T = n) n) q a,n) q a,n) d ts ) q a,n) ĥ n) q e,n) ) ds t t= Ĥn) q e,n) ) [ + τ a+)a n) n) q a,n) τa )An) + τx)xn) + + τ d )D n)] T P d ) ts ) P ) ĥ n) q e,n) ) n) q a,n) ds t= t Ĥn) q e,n) ) where we parameterze P ) as P ) = σ T t= t t ) 2 q e t q a t q e t We form the moment condton m N σ, τ a+, τ a, τ d, τ x, ĥ, Ĥ) = N ẽ n) σ, τ a+, τ a, τ d, τ x, ĥ, Ĥ)zn) z n) ) n where the nstruments, z n) nclude the engneer s estmate, a full set of dummy varales for the resdent engneer assgned to the proect, and n some specfcatons) month and dstrct dummy varales. We use a non-lnear least squares optmzaton algorthm Matla s lsqnonln) to mnmze the oectve functon m N W m N, where W s a postve sem-defnte weghtng matrx. We frst estmate σ, τ a+, τ a, τ d, τ x ) usng the dentty weghtng matrx, then use those estmates to construct the optmal weghtng matrx as the nverse of the sample varance of m N. 6

7 Tale A6: Structural Estmaton, usng Alternatve Specfcatons for the Frst-Stage Recovery of the Bd Dstrutons I-A I-B II-A II-B III-A III-B IV-A IV-B Impled Margnal Transacton Costs Postve Adustments τ A+ ) ) 0.409) 2.2) 0.373) 4.05) 0.40) 2.3) 0.379) Negatve Adustments τ A+ ) ) 3.56) ) 4.323) ) 3.08) ) 3.05) Extra Work τ X ) * ) 0.52).470) 0.203) 2.708) 0.54).469) 0.98) Deductons τ D ) ) 4.878) ) 3.860) ) 4.844) ) 3.60) Skewng Parameter Penalty σ) E E E E E-05 -.E E E E-05).00E-05) 3.38E-05) 9.0E-06) 5.56E-05) 9.49E-06) 3.3E-05).04E-05) Numer of Os Frst-Stage Bd Dstruton** Fxed Fxed Fxed Fxed Weghtng Matrx*** Identty Optmal Identty Optmal Identty Optmal Identty Optmal Instruments Used n Second Stage GMM Resdent Engneer, Engneer s Estmate 7 Resdent Engneer, Engneer s Estmate, Month and Dstrct Dummes Resdent Engneer, Engneer s Estmate Resdent Engneer, Engneer s Estmate, Month and Dstrct Dummes * These estmates represent an upper ound on transacton costs assocated wth changes n scope. They do not account for margnal costs assocated wth performng the extra work, whch for a reasonale proft margn of 20 percent would lower our estmate y $0.80. ** To recover the d dstruton from whch the moment condtons ased on the frst-order condtons) are formed, we otan resduals from a frst stage regresson of ds on contract and dder characterstcs. Ths homogenzes the data y controllng for contract- and dder-specfc characterstcs. In Columns I-A, I-B, II-A, and II-B, the frst-stage regresson ncludes dder dstance, frnge status, and a contract fxed effect. In Columns III-A, III-B, IV-A, and IV-B, the frst-stage regresson ncludes dder dstance, frnge status, the numer of dders, and a contract random effect the fxed effect approach dd not nclude the numer of dders as t would have een fully asored y the fxed effect. In oth cases, the resduals for all 366 ds 89 contracts) were then pooled n order to recover the ddng dstruton from whch dders would form ther expectatons of wnnng. Ths dffers from the approach n the paper where separate dstrutons are recovered for each set of contracts wth the same numer of dders ut the resultng estmates are very smlar. We prefer the ndexng approach used n the paper, as t trades off a hgher varance fewer oservatons used to construct each dstruton) n favor of unasedness. *** Consstent GMM estmates were computed usng the dentty matrx as the weghtng matrx. In a second step, effcent GMM estmates were computed usng the optmal weghtng matrx derved from the varance of the sample moments n the frst step. Standard errors appear n parentheses.