bergman lundberg lundberg stake ippc2014

Using spatial econometric techniques to detect collusive behavior in procurement auction data

Mats Bergman, Johan Lundberg, Sofia Lundberg, Johan Stake

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

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

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

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

Econometric setup

• So, define bid b for contract c by bidder i belonging to group A; 𝑏𝑖,𝑐𝐴

• One firm, i, in the cartel (type A) bids a low bid; 𝑏𝑖,𝑐𝐴

• While the rest of the cartel members, j, bid high; 𝑏𝑗,𝑐𝐴 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 𝑤𝑖𝑐𝐴,𝑗𝑐

𝐴 > 0 and; 𝑤𝑖𝑐

𝐵,𝑗𝑐𝐵 = 𝑤𝑖𝑐

𝐵,𝑗𝑐𝐴 = 𝑤𝑖𝑐

𝐴,𝑗𝑐𝐵 = 𝑤𝑖𝑐

𝐴,𝑖𝑐𝐴 = 𝑤𝑖𝑐

𝐵,𝑖𝑐𝐵 = 0

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

Econometric setup

• It is not obvious what value we should assign 𝑤𝑖𝑐𝐴,𝑗𝑐

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,𝑐𝐴 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.

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

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


Volume 𝑉𝑜𝑙𝑢𝑚𝑒𝑐 45.644 57.734 0.133 607.613




Observations 2,207

2004 – 2009


Volume 𝑉𝑜𝑙𝑢𝑚𝑒𝑐 11.120 181.038 0.170 1,397.753




Observations 594

Empirical model

• The empirical model for this study is defined as;

𝑏 = 𝛼𝑡 + 𝜌𝑾𝑏 + 𝑓 𝐶𝑜𝑚𝑝, 𝑉𝑜𝑙𝑢𝑚𝑒, 𝑞𝑟 , 𝑡 + 𝜀

Where,

𝛼𝑡 capture time effects,

𝐶𝑜𝑚𝑝 measures competition (number of bidders per contract),

𝑉𝑜𝑙𝑢𝑚𝑒 is the quantity of the contract, and

𝑞𝑟 is a control for regional disparaties (SRAs 7 regions)

Row standardized weights matrix, 𝐖 2. Period 1992-2000. Row standardized weights matrix, 𝐖 2. 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)

- - -

𝛽𝑑𝑒𝑛𝑠 - - - 2,904

(1,07)

- - - 47,126

(0,55)

𝛽𝑑𝑒𝑛𝑠2 - - - -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

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)

-


(5,83)

- - - -0,550

(-0,39)

- - -

𝛽𝑑𝑒𝑛𝑠 - - - 3,279

(1,36)

- - - 47,405

(0,53)

𝛽𝑑𝑒𝑛𝑠2 - - - -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)


(-33,77)

-0,782

(-38,88)

- - -0,883

(-10,82)

-0,854

(-23,85)

- -

Results

Row standardized weights matrix, 𝐖 𝟏. Period 1992-2000. Row standardized weights matrix, 𝐖 𝟏. 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)

-


(4,46)

- - - -21,727

(-0,34)

- - -

𝛽𝑑𝑒𝑛𝑠 - - - 3,442

(1,10)

- - - 49,184

(0,54)

𝛽𝑑𝑒𝑛𝑠2 - - - -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)


(-44,04)

-0,842

(-45,97)

- - -1,373

(-0,86)

-0,834

(-28,51)

- -

Results – excluding lowest cartel bid

Non-row standardized weights matrix, 𝐖 𝟏. Period 1992-2000. Non-row standardized weights matrix, 𝐖 𝟏. 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)

-


(6,29)

- - - 1,655

(0,79)

- - -

𝛽𝑑𝑒𝑛𝑠 - - - 4,028

(1,32)

- - - 48,540

(0,56)

𝛽𝑑𝑒𝑛𝑠2 - - - -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)


(-43,06)

-0,825

(-49,52)

- - -0,795

(-12,68)

-0,836

(-30,55)

- -

Results – excluding lowest cartel bid

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!)

bergman lundberg lundberg stake ippc2014

Business