- The study uses spatial econometric techniques to test for collusive bidding behavior in Swedish asphalt procurement auctions during the 1990s, when there was a known asphalt cartel. - Significant results showing non-independence between cartel members' bids are found using spatial econometrics when analyzing data from 1992-2000, but these effects disappear in the 2004-2009 period after the cartel was dissolved. - Two approaches are used to define the spatial weights matrix, which models the dependence between bids: regressing the lowest cartel bid on the sum/average of other cartel bids, and excluding the lowest bid.

1. Using spatial econometric techniques to detect
collusive behavior in procurement auction data
Mats Bergman, Johan Lundberg, Sofia Lundberg, Johan Stake

2. Summary
• Test to see if bidding behavior can be captured by spatial econometric techniques
due to non-independent bidding between cartel members
• Use data from known Swedish asphalt cartel during the 1990s
• Test if bids between lowest bid in cartel and the rest of the cartel bids can be
observed econometrically
• Find significant results of non-independence between cartel members bids using
spatial econometrics, which dissapears during the time after the cartel
• Problems with one specification which returns significant results in the case after
the cartel was dissipated

3. Background
• Procurement auctions used frequently for public contracts in the EU (1994
directive)
• First-price sealed bid auctions theoretically assigns to bidder with lowest marginal
cost – assuming there is no collusion!
• Swedish Competition Authority conducted dawn raids in October 2001 at several
asphalt paving companies
• Trials lasted for over 40 days and in 2007 nine companies were convicted to pay
over 1.2 billion dollars in fines

4. Previous work
• Jakobsson and Eklöf (2003) analyzed the same asphalt cartel using a reduced form model
describing non-independent bidding
• Collusion in public contracts has been analyzed in fields such as:
• frozen seafood (Koyak & Werden, 1993)
• school milk (Pesendorfer, 1995; Porter & Zona, 1999)
• highway constructions (Porter & Zona, 1993)
• highway repair (Bajari & Ye, 2003)
• Detecting collusion difficult – most papers econometrically confirm the cartel
• Following Bajari & Ye, non-collusive bidding should fulfill;
1. Conditional independency – independent bids when controlling for production cost effects
2. Exchangability - bids independent of other bidders
• We contribute to this literature by using spatial econometric techniques to test for
collusive behavior

5. Econometric setup
• A specific number of bidders create a cartel with intention to collude in
procurement auctions
• Consider a set of contracts C, for which two types of bidders bid, A and B;
A
B
C
Cartel – bids are non-independent
No cartel – bids are independent
Bids between types A and B
are independent

6. Econometric setup
• So, define bid b for contract c by bidder i belonging to group A; 𝑏𝑖,𝑐
𝐴
• One firm, i, in the cartel (type A) bids a low bid; 𝑏𝑖,𝑐
𝐴
• While the rest of the cartel members, j, bid high; 𝑏𝑗,𝑐
𝐴
𝑓𝑜𝑟 𝑖 ≠ 𝑗
• With C contracts and on average 𝐴 + 𝐵 bidders, we define a weight matrix W;
𝐶 × (𝐴 + 𝐵) × 𝐶 × 𝐴 + 𝐵
with elements such that 𝑤𝑖 𝑐
𝐴,𝑗 𝑐
𝐴 > 0 and;
𝑤𝑖 𝑐
𝐵,𝑗 𝑐
𝐵 = 𝑤𝑖 𝑐
𝐵,𝑗 𝑐
𝐴 = 𝑤𝑖 𝑐
𝐴,𝑗 𝑐
𝐵 = 𝑤𝑖 𝑐
𝐴,𝑖 𝑐
𝐴 = 𝑤𝑖 𝑐
𝐵,𝑖 𝑐
𝐵 = 0

7. Econometric setup
• A simple test for collusion among bidders of type A could then be performed;
𝑏 = 𝜌𝑾𝑏 + 𝑿𝜷 + 𝜀
𝑏 = 𝑣𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑏𝑖𝑑𝑠
𝑿 = 𝑚𝑎𝑡𝑟𝑖𝑥 𝑜𝑓 𝑟𝑒𝑙𝑒𝑣𝑎𝑛𝑡 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑡𝑒𝑠
𝜀 = 𝑒𝑟𝑟𝑜𝑟 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡
• 𝜌 and 𝛽 are the coeffients to be estimated
• If the bids are non-independent: 𝜌 ≠ 0
• Note also that 𝜌 < 1 is consistent with a Nash equilibrium

8. Econometric setup
• It is not obvious what value we should assign 𝑤𝑖 𝑐
𝐴,𝑗 𝑐
𝐴. Theory gives no guidance in
this matter – how should we express the degree of dependence between
different cartel members?
• Two approaches of defining the weight matrix are used;
• 𝑏𝑖,𝑐
𝐴
is regressed on the sum of cartel members bids (Row standardized)
• 𝑏𝑖,𝑐
𝐴
is regressed on the average of cartel members bids (Non-row standardized)
• We also test to exclude the lowest cartel bid from the regression, which, using
both weight matrixes above should produce even stronger effects.
• Since our regression equation is a spatial lag model which becomes biased and
inconsistent with OLS, we apply an IV estimator using 𝑾𝑿 as instruments for 𝑾𝒃
• 𝑾 should also preferably be exogenous, which is the case here.

9. Data
• Data consists of observations from the Swedish Road Administration, all
procurements from 1992 up to and including 2009
• We gathered data on region, year, procurement procedure, bids, number of
bidders, quantity (where applicable)
• Exclude combinatorial bids, since this might influence bidding behavior
• Vast majority of procurements use a simplified procurement procedure, since
many contracts below the threshold value (5.1 million euros in 2014)
• Bids are measured as bid per square meter of asphalt

10. Table 1: Descriptive statistics
Mean Std. dev. Min Max
Whole sample (1992-2009)
Bid per square kilometer 𝑏 4.889 23.226 0.013 308.222
Volume 𝑉𝑜𝑙𝑢𝑚𝑒𝑐 59.546 101.418 0.133 1,397.753
Competition 𝐶𝑜𝑚𝑝𝑐 5.433 1.522 1 10
Population density 𝐷𝑒𝑛𝑠𝑐 55.871 56.945 3.289 200.471
Number of procurements 568
Observations 2,801
1992 – 2000
Bid per square kilometer 𝑏 5.222 24.918 0.026 308.222
Volume 𝑉𝑜𝑙𝑢𝑚𝑒𝑐 45.644 57.734 0.133 607.613
Competition 𝐶𝑜𝑚𝑝𝑐 5.691 1.489 1 10
Population density 𝐷𝑒𝑛𝑠𝑐 67.217 57.690 3.317 195.275
Number of procurements 422
Observations 2,207
2004 – 2009
Bid per square kilometer 𝑏 3.651 15.340 0.013 144.582
Volume 𝑉𝑜𝑙𝑢𝑚𝑒𝑐 11.120 181.038 0.170 1,397.753
Competition 𝐶𝑜𝑚𝑝𝑐 4.475 1.235 1 7
Population density 𝐷𝑒𝑛𝑠𝑐 13.716 25.911 3.289 200.471
Number of procurements 146
Observations 594

11. Empirical model
• The empirical model for this study is defined as;
𝑏 = 𝛼 𝑡 + 𝜌𝑾𝑏 + 𝑓 𝐶𝑜𝑚𝑝, 𝑉𝑜𝑙𝑢𝑚𝑒, 𝑞 𝑟, 𝑡 + 𝜀
Where,
𝛼 𝑡 capture time effects,
𝐶𝑜𝑚𝑝 measures competition (number of bidders per contract),
𝑉𝑜𝑙𝑢𝑚𝑒 is the quantity of the contract, and
𝑞 𝑟 is a control for regional disparaties (SRAs 7 regions)

12. Row standardized weights matrix, 𝐖2. Period 1992-2000. Row standardized weights matrix, 𝐖2. Period 2004 – 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
𝜌 - - 0,434
(3,67)
0,400
(3,31)
- - 0,630
(0,43)
0,379
(0,50)
𝜌 (ln) 0,084
(2,65)
0,102
(3,29)
- - -0,253
(-0,83)
-0,135
(-1,52)
- -
𝛽𝑐𝑜𝑚𝑝 - - -4,794
(-0,55)
- - - 5,382
(0,31)
-
𝛽𝑐𝑜𝑚𝑝2 - - 0,570
(0,71)
- - - -0,231
(-0,11)
-
𝛽ln(𝑐𝑜𝑚𝑝) 1,521
(3,90)
- - - -2,204
(-0,47)
- - -
𝛽 𝑑𝑒𝑛𝑠 - - - 2,904
(1,07)
- - - 47,126
(0,55)
𝛽 𝑑𝑒𝑛𝑠2 - - - -0,008
(-1,13)
- - - -0,565
(0,57)
𝛽ln(𝑑𝑒𝑛𝑠) - -8,979
(-4,94)
- - - -21,497
(-1,92)
- -
𝛽𝑠𝑞𝑟𝑡 - - -0,176
(-6,18)
-0,177
(-6,14)
- - -0,034
(-1,21)
-0,044
(-2,39)
𝛽𝑠𝑞𝑟𝑡2 - - 0,000
(5,73)
0,000
(5,69)
- - 0,000
(1,27)
0,000
(2,37)
𝛽ln(𝑠𝑞𝑟𝑡) -0,861
(-33,86)
-0,817
(-34,95)
- - -0,904
(-6,45)
-0,849
(-18,53)
- -
Results

13. Non-row standardized weights matrix, 𝐖𝟐. Period 1992-2000. Non-row standardized weights matrix,𝐖𝟐. Period 2004 – 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
𝜌 - - 0,154
(5,64)
0,160
(7,13)
- - 0,204
(0,32)
0,523
(1,48)
𝜌 (ln) 0,050
(4,92)
0,054
(6,19)
- - -0,101
(-1,19)
-0,070
(-2,42)
- -
𝛽𝑐𝑜𝑚𝑝 - - -8,023
(-0,86)
- - - 0,355
(0,02)
-
𝛽𝑐𝑜𝑚𝑝2 - - 0,606
(0,64)
- - - 0,623
(0,29)
-
𝛽ln(𝑐𝑜𝑚𝑝) 2,567
(5,83)
- - - -0,550
(-0,39)
- - -
𝛽 𝑑𝑒𝑛𝑠 - - - 3,279
(1,36)
- - - 47,405
(0,53)
𝛽 𝑑𝑒𝑛𝑠2 - - - -0,009
(-1,37)
- - - -0,571
(-0,55)
𝛽ln(𝑑𝑒𝑛𝑠) - -9,160
(-5,18)
- - - -20,118
(-1,80)
- -
𝛽𝑠𝑞𝑟𝑡 - - -0,147
(-5,79)
-0,151
(-7,76)
- - -0,042
(-2,25)
-0,036
(-2,54)
𝛽𝑠𝑞𝑟𝑡2 - - 0,000
(5,04)
0,000
(6,96)
- - 0,000
(2,37)
0,000
(2,62)
𝛽ln(𝑠𝑞𝑟𝑡) -0,838
(-33,77)
-0,782
(-38,88)
- - -0,883
(-10,82)
-0,854
(-23,85)
- -
Results

14. Row standardized weights matrix, 𝐖𝟏. Period 1992-2000. Row standardized weights matrix, 𝐖𝟏. Period 2004 – 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
𝜌 - - 0,326
(2,54)
0,341
(2,96)
- - 0,154
(0,12)
0,823
(0,82)
𝜌 (ln) 0,120
(3,75)
0,088
(3,01)
- - -2,828
(-0,37)
-0,220
(-2,68)
- -
𝛽𝑐𝑜𝑚𝑝 - - -13,111
(-0,89)
- - - 14,804
(0,77)
-
𝛽𝑐𝑜𝑚𝑝2 - - 1,214
(0,88)
- - - -1,165
(-0,50)
-
𝛽ln(𝑐𝑜𝑚𝑝) 2,134
(4,46)
- - - -21,727
(-0,34)
- - -
𝛽 𝑑𝑒𝑛𝑠 - - - 3,442
(1,10)
- - - 49,184
(0,54)
𝛽 𝑑𝑒𝑛𝑠2 - - - -0,010
(-1,17)
- - - -0,598
(-0,57)
𝛽ln(𝑑𝑒𝑛𝑠) - -9,132
(-4,89)
- - - -21,090
(-1,90)
- -
𝛽𝑠𝑞𝑟𝑡 - - -0,209
(-7,89)
-0,206
(-8,49)
- - -0,043
(-3,55)
-0,047
(-4,18)
𝛽𝑠𝑞𝑟𝑡2 - - 0,000
(6,54)
0,000
(7,20)
- - 0,000
(3,59)
0,000
(4,00)
𝛽ln(𝑠𝑞𝑟𝑡) -0,871
(-44,04)
-0,842
(-45,97)
- - -1,373
(-0,86)
-0,834
(-28,51)
- -
Results – excluding lowest cartel bid

15. Non-row standardized weights matrix, 𝐖𝟏. Period 1992-2000. Non-row standardized weights matrix, 𝐖𝟏. Period 2004 – 2009.
(1) (2) (3) (4) (1) (2) (3) (4)
𝜌 - - 0,165
(3,62)
0,162
(4,86)
- - 0,110
(0,16)
0,381
(0,80)
𝜌 (ln) 0,062
(4,55)
0,062
(5,22)
- - -0,013
(-0,08)
-0,129
(-3,47)
- -
𝛽𝑐𝑜𝑚𝑝 - - -12,590
(-0,70)
- - - 1,558
(0,06)
-
𝛽𝑐𝑜𝑚𝑝2 - - 0,871
(0,49)
- - - 0,480
(0,16)
-
𝛽ln(𝑐𝑜𝑚𝑝) 2,649
(6,29)
- - - 1,655
(0,79)
- - -
𝛽 𝑑𝑒𝑛𝑠 - - - 4,028
(1,32)
- - - 48,540
(0,56)
𝛽 𝑑𝑒𝑛𝑠2 - - - -0,011
(-1,36)
- - - -0,589
(-0,59)
𝛽ln(𝑑𝑒𝑛𝑠) - -9,084
(-4,92)
- - - -18,081
(-1,65)
- -
𝛽𝑠𝑞𝑟𝑡 - - -0,185
(-6,78)
-0,199
(-10,07)
- - -0,047
(-3,87)
-0,049
(-4,71)
𝛽𝑠𝑞𝑟𝑡2 - - 0,000
(5,25)
0,000
(8,13)
- - 0,000
(3,80)
0,000
(4,43)
𝛽ln(𝑠𝑞𝑟𝑡) -0,875
(-43,06)
-0,825
(-49,52)
- - -0,795
(-12,68)
-0,836
(-30,55)
- -
Results – excluding lowest cartel bid

16. Results
• Relatively clear and unambigious results – spatial econometrics show sign of
collusion
• 𝜌 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)
• Other estimation also follow this, but the estimation using log of population
density and log of volume consequently implies non-independent bids
• Possible explanations?
• Opens up for possibilities to use spatial econometrics to scan procurement data
by testing different cartel specifications (hopefully!)