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Using spatial econometric techniques to detect collusive behavior in procurement auction data
Mats Bergman, Johan Lundberg, Sofia Lundberg, Johan Stake
Summary
โข Test to see if bidding behavior can be captured by spatial econometric techniques due to non-independent bidding between cartel members
โข Use data from known Swedish asphalt cartel during the 1990s
โข Test if bids between lowest bid in cartel and the rest of the cartel bids can be observed econometrically
โข Find significant results of non-independence between cartel members bids using spatial econometrics, which dissapears during the time after the cartel
โข Problems with one specification which returns significant results in the case after the cartel was dissipated
Background
โข Procurement auctions used frequently for public contracts in the EU (1994 directive)
โข First-price sealed bid auctions theoretically assigns to bidder with lowest marginal cost โ assuming there is no collusion!
โข Swedish Competition Authority conducted dawn raids in October 2001 at several asphalt paving companies
โข Trials lasted for over 40 days and in 2007 nine companies were convicted to pay over 1.2 billion dollars in fines
Previous work
โข Jakobsson and Eklรถf (2003) analyzed the same asphalt cartel using a reduced form model describing non-independent bidding
โข Collusion in public contracts has been analyzed in fields such as: โข frozen seafood (Koyak & Werden, 1993) โข school milk (Pesendorfer, 1995; Porter & Zona, 1999) โข highway constructions (Porter & Zona, 1993) โข highway repair (Bajari & Ye, 2003)
โข Detecting collusion difficult โ most papers econometrically confirm the cartel
โข Following Bajari & Ye, non-collusive bidding should fulfill; 1. Conditional independency โ independent bids when controlling for production cost effects 2. Exchangability - bids independent of other bidders
โข We contribute to this literature by using spatial econometric techniques to test for collusive behavior
Econometric setup
โข A specific number of bidders create a cartel with intention to collude in procurement auctions
โข Consider a set of contracts C, for which two types of bidders bid, A and B;
A
B
C
Cartel โ bids are non-independent
No cartel โ bids are independent
Bids between types A and B are independent
Econometric setup
โข So, define bid b for contract c by bidder i belonging to group A; ๐๐,๐๐ด
โข One firm, i, in the cartel (type A) bids a low bid; ๐๐,๐๐ด
โข While the rest of the cartel members, j, bid high; ๐๐,๐๐ด ๐๐๐ ๐ โ ๐
โข With C contracts and on average ๐ด + ๐ต bidders, we define a weight matrix W;
๐ถ ร (๐ด + ๐ต) ร ๐ถ ร ๐ด + ๐ต
with elements such that ๐ค๐๐๐ด,๐๐
๐ด > 0 and; ๐ค๐๐
๐ต,๐๐๐ต = ๐ค๐๐
๐ต,๐๐๐ด = ๐ค๐๐
๐ด,๐๐๐ต = ๐ค๐๐
๐ด,๐๐๐ด = ๐ค๐๐
๐ต,๐๐๐ต = 0
Econometric setup
โข A simple test for collusion among bidders of type A could then be performed;
๐ = ๐๐พ๐ + ๐ฟ๐ท + ๐
๐ = ๐ฃ๐๐๐ก๐๐ ๐๐ ๐๐๐ ๐๐๐๐ ๐ฟ = ๐๐๐ก๐๐๐ฅ ๐๐ ๐๐๐๐๐ฃ๐๐๐ก ๐๐๐ฃ๐๐๐๐๐ก๐๐ ๐ = ๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐ก
โข ๐ and ๐ฝ are the coeffients to be estimated
โข If the bids are non-independent: ๐ โ 0
โข Note also that ๐ < 1 is consistent with a Nash equilibrium
Econometric setup
โข It is not obvious what value we should assign ๐ค๐๐๐ด,๐๐
๐ด. Theory gives no guidance in this matter โ how should we express the degree of dependence between different cartel members?
โข Two approaches of defining the weight matrix are used; โข ๐๐,๐
๐ด is regressed on the sum of cartel members bids (Row standardized)
โข ๐๐,๐๐ด is regressed on the average of cartel members bids (Non-row standardized)
โข We also test to exclude the lowest cartel bid from the regression, which, using both weight matrixes above should produce even stronger effects.
โข Since our regression equation is a spatial lag model which becomes biased and inconsistent with OLS, we apply an IV estimator using ๐พ๐ฟ as instruments for ๐พ๐
โข ๐พ should also preferably be exogenous, which is the case here.
Data
โข Data consists of observations from the Swedish Road Administration, all procurements from 1992 up to and including 2009
โข We gathered data on region, year, procurement procedure, bids, number of bidders, quantity (where applicable)
โข Exclude combinatorial bids, since this might influence bidding behavior
โข Vast majority of procurements use a simplified procurement procedure, since many contracts below the threshold value (5.1 million euros in 2014)
โข Bids are measured as bid per square meter of asphalt
Table 1: Descriptive statistics
Mean Std. dev. Min Max
Whole sample (1992-2009)
Bid per square kilometer ๐ 4.889 23.226 0.013 308.222
Volume ๐๐๐๐ข๐๐๐ 59.546 101.418 0.133 1,397.753
Competition ๐ถ๐๐๐๐ 5.433 1.522 1 10
Population density ๐ท๐๐๐ ๐ 55.871 56.945 3.289 200.471
Number of procurements 568
Observations 2,801
1992 โ 2000
Bid per square kilometer ๐ 5.222 24.918 0.026 308.222
Volume ๐๐๐๐ข๐๐๐ 45.644 57.734 0.133 607.613
Competition ๐ถ๐๐๐๐ 5.691 1.489 1 10
Population density ๐ท๐๐๐ ๐ 67.217 57.690 3.317 195.275
Number of procurements 422
Observations 2,207
2004 โ 2009
Bid per square kilometer ๐ 3.651 15.340 0.013 144.582
Volume ๐๐๐๐ข๐๐๐ 11.120 181.038 0.170 1,397.753
Competition ๐ถ๐๐๐๐ 4.475 1.235 1 7
Population density ๐ท๐๐๐ ๐ 13.716 25.911 3.289 200.471
Number of procurements 146
Observations 594
Empirical model
โข The empirical model for this study is defined as;
๐ = ๐ผ๐ก + ๐๐พ๐ + ๐ ๐ถ๐๐๐, ๐๐๐๐ข๐๐, ๐๐ , ๐ก + ๐
Where,
๐ผ๐ก capture time effects,
๐ถ๐๐๐ measures competition (number of bidders per contract),
๐๐๐๐ข๐๐ is the quantity of the contract, and
๐๐ is a control for regional disparaties (SRAs 7 regions)
Row standardized weights matrix, ๐ 2. Period 1992-2000. Row standardized weights matrix, ๐ 2. Period 2004 โ 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
๐ - - 0,434
(3,67)
0,400
(3,31)
- - 0,630
(0,43)
0,379
(0,50)
๐ (ln) 0,084
(2,65)
0,102
(3,29)
- - -0,253
(-0,83)
-0,135
(-1,52)
- -
๐ฝ๐๐๐๐ - - -4,794
(-0,55)
- - - 5,382
(0,31)
-
๐ฝ๐๐๐๐2 - - 0,570
(0,71)
- - - -0,231
(-0,11)
-
๐ฝln (๐๐๐๐) 1,521
(3,90)
- - - -2,204
(-0,47)
- - -
๐ฝ๐๐๐๐ - - - 2,904
(1,07)
- - - 47,126
(0,55)
๐ฝ๐๐๐๐ 2 - - - -0,008
(-1,13)
- - - -0,565
(0,57)
๐ฝln (๐๐๐๐ ) - -8,979
(-4,94)
- - - -21,497
(-1,92)
- -
๐ฝ๐ ๐๐๐ก - - -0,176
(-6,18)
-0,177
(-6,14)
- - -0,034
(-1,21)
-0,044
(-2,39)
๐ฝ๐ ๐๐๐ก2 - - 0,000
(5,73)
0,000
(5,69)
- - 0,000
(1,27)
0,000
(2,37)
๐ฝln (๐ ๐๐๐ก) -0,861
(-33,86)
-0,817
(-34,95)
- - -0,904
(-6,45)
-0,849
(-18,53)
- -
Results
Non-row standardized weights matrix, ๐๐. Period 1992-2000. Non-row standardized weights matrix,๐๐. Period 2004 โ 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
๐ - - 0,154
(5,64)
0,160
(7,13)
- - 0,204
(0,32)
0,523
(1,48)
๐ (ln) 0,050
(4,92)
0,054
(6,19)
- - -0,101
(-1,19)
-0,070
(-2,42)
- -
๐ฝ๐๐๐๐ - - -8,023
(-0,86)
- - - 0,355
(0,02)
-
๐ฝ๐๐๐๐2 - - 0,606
(0,64)
- - - 0,623
(0,29)
-
๐ฝln (๐๐๐๐) 2,567
(5,83)
- - - -0,550
(-0,39)
- - -
๐ฝ๐๐๐๐ - - - 3,279
(1,36)
- - - 47,405
(0,53)
๐ฝ๐๐๐๐ 2 - - - -0,009
(-1,37)
- - - -0,571
(-0,55)
๐ฝln (๐๐๐๐ ) - -9,160
(-5,18)
- - - -20,118
(-1,80)
- -
๐ฝ๐ ๐๐๐ก - - -0,147
(-5,79)
-0,151
(-7,76)
- - -0,042
(-2,25)
-0,036
(-2,54)
๐ฝ๐ ๐๐๐ก2 - - 0,000
(5,04)
0,000
(6,96)
- - 0,000
(2,37)
0,000
(2,62)
๐ฝln (๐ ๐๐๐ก) -0,838
(-33,77)
-0,782
(-38,88)
- - -0,883
(-10,82)
-0,854
(-23,85)
- -
Results
Row standardized weights matrix, ๐ ๐. Period 1992-2000. Row standardized weights matrix, ๐ ๐. Period 2004 โ 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
๐ - - 0,326
(2,54)
0,341
(2,96)
- - 0,154
(0,12)
0,823
(0,82)
๐ (ln) 0,120
(3,75)
0,088
(3,01)
- - -2,828
(-0,37)
-0,220
(-2,68)
- -
๐ฝ๐๐๐๐ - - -13,111
(-0,89)
- - - 14,804
(0,77)
-
๐ฝ๐๐๐๐2 - - 1,214
(0,88)
- - - -1,165
(-0,50)
-
๐ฝln (๐๐๐๐) 2,134
(4,46)
- - - -21,727
(-0,34)
- - -
๐ฝ๐๐๐๐ - - - 3,442
(1,10)
- - - 49,184
(0,54)
๐ฝ๐๐๐๐ 2 - - - -0,010
(-1,17)
- - - -0,598
(-0,57)
๐ฝln (๐๐๐๐ ) - -9,132
(-4,89)
- - - -21,090
(-1,90)
- -
๐ฝ๐ ๐๐๐ก - - -0,209
(-7,89)
-0,206
(-8,49)
- - -0,043
(-3,55)
-0,047
(-4,18)
๐ฝ๐ ๐๐๐ก2 - - 0,000
(6,54)
0,000
(7,20)
- - 0,000
(3,59)
0,000
(4,00)
๐ฝln (๐ ๐๐๐ก) -0,871
(-44,04)
-0,842
(-45,97)
- - -1,373
(-0,86)
-0,834
(-28,51)
- -
Results โ excluding lowest cartel bid
Non-row standardized weights matrix, ๐ ๐. Period 1992-2000. Non-row standardized weights matrix, ๐ ๐. Period 2004 โ 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
๐ - - 0,165
(3,62)
0,162
(4,86)
- - 0,110
(0,16)
0,381
(0,80)
๐ (ln) 0,062
(4,55)
0,062
(5,22)
- - -0,013
(-0,08)
-0,129
(-3,47)
- -
๐ฝ๐๐๐๐ - - -12,590
(-0,70)
- - - 1,558
(0,06)
-
๐ฝ๐๐๐๐2 - - 0,871
(0,49)
- - - 0,480
(0,16)
-
๐ฝln (๐๐๐๐) 2,649
(6,29)
- - - 1,655
(0,79)
- - -
๐ฝ๐๐๐๐ - - - 4,028
(1,32)
- - - 48,540
(0,56)
๐ฝ๐๐๐๐ 2 - - - -0,011
(-1,36)
- - - -0,589
(-0,59)
๐ฝln (๐๐๐๐ ) - -9,084
(-4,92)
- - - -18,081
(-1,65)
- -
๐ฝ๐ ๐๐๐ก - - -0,185
(-6,78)
-0,199
(-10,07)
- - -0,047
(-3,87)
-0,049
(-4,71)
๐ฝ๐ ๐๐๐ก2 - - 0,000
(5,25)
0,000
(8,13)
- - 0,000
(3,80)
0,000
(4,43)
๐ฝln (๐ ๐๐๐ก) -0,875
(-43,06)
-0,825
(-49,52)
- - -0,795
(-12,68)
-0,836
(-30,55)
- -
Results โ excluding lowest cartel bid
Results
โข Relatively clear and unambigious results โ spatial econometrics show sign of collusion
โข ๐ is significant and therefore implies non-independence in the cartel period, and produces no significant effect in the latter period (using a row standardized weight matrix and all cartel bids included)
โข Other estimation also follow this, but the estimation using log of population density and log of volume consequently implies non-independent bids โข Possible explanations?
โข Opens up for possibilities to use spatial econometrics to scan procurement data by testing different cartel specifications (hopefully!)