essays in industrial organizationfile/dis4811.pdfthe impact weakens with increasing distance within...

ESSAYS IN INDUSTRIAL ORGANIZATION

DISSERTAT ION

of the University of St. Gallen,

School of Management,

Economics, Law, Social Sciences

and International Affairs

to obtain the title of

Doctor of Philosophy in Economics and Finance

submitted by

Nicolas Eschenbaum

from

Germany

Approved on the application of

Prof. Dr. Stefan Bühler

and

Prof. Dr. Christine Zulehner

Prof. Dr. Reto Föllmi

Dissertation no. 4811

Difo-Druck GmbH, Bamberg

The University of St. Gallen, School of Management, Economics, Law, So-

cial Sciences and International Affairs hereby consents to the printing of the

present dissertation, without hereby expressing any opinion on the views

herein expressed.

St. Gallen, June 15, 2018

The President:

Prof. Dr. Thomas Bieger

ACKNOWLEDGEMENTS

I am particularly grateful for the guidance by my supervisor Stefan Bühler

who gave me the opportunity and freedom to pursue this research agenda.

The thesis committee composed of Stefan Bühler, Christine Zulehner, Reto

Föllmi, and Thomas Epper provided further helpful advice and comments. I

am also very thankful for the support and friendship of the many colleagues

and friends in St. Gallen and around the world, whose input played an im-

portant role in shaping this thesis and made working on it so much easier.

Finally, I owe special gratitude to my parents and family; this project would

never have existed without their support and love over the many years.

St. Gallen, July 2018 Nicolas Eschenbaum

iii

CONTENTS

summary vi

zusammenfassung vii

1 escalating fines and prices: the curse of positive selection 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Static Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.1 Skimming Property . . . . . . . . . . . . . . . . . . . . . . 8

1.3.2 Commitment . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3.3 Non-Commitment . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Relation to Monopoly Pricing . . . . . . . . . . . . . . . . . . . . 18

1.4.1 Behavior-Based Pricing . . . . . . . . . . . . . . . . . . . . 19

1.4.2 Pricing with Positive Selection . . . . . . . . . . . . . . . 20

1.5 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.5.1 Heterogeneous Discount Factors . . . . . . . . . . . . . . 21

1.5.2 Changes in the Economic Environment . . . . . . . . . . 23

1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2 geographic market definition in swiss grocery retailing: a non-

parametric approach 31

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3 Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.5 Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

contents v

3 dealing with uncertainty: seller reputation in the online mar-

ket for illegal drugs 71

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2 The Darknet Platforms . . . . . . . . . . . . . . . . . . . . . . . . 75

3.3 Data and Descriptives . . . . . . . . . . . . . . . . . . . . . . . . 77

3.4 Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.4.1 Identification . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.4.2 Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

SUMMARY

This thesis contains three essays in industrial organization.

Chapter 1 studies escalating fines for repeat offenders, that is, fine increases

in the number of previous offenses. We demonstrate that a fine-setting author-

ity does not in fact have an incentive to increase the fine for repeat offenders.

However, if the authority has an interest in redistributing offender gains to

society, escalation does occur and is driven by the incentive to reduce the fine

for low-value offenders in the future in order to redistribute additional pri-

vate gains. The model we develop nests optimal law enforcement with uncer-

tain detection and behavior-based monopoly pricing with imperfect customer

recognition.

Chapter 2 develops a non-parametric approach to empirically determine

the geographic size of a market. I study the impact of a new store entry

on competing stores in an increasing range to the site of entry. I apply the

estimator to the Swiss grocery retail industry and find that markets are highly

localized in a tight four kilometer radius. I further document evidence that

the impact weakens with increasing distance within a local market and that

the local market in which a small grocery retailer competes in is only two

kilometers in size.

Chapter 3 examines the value of seller reputation in the online market for

illegal drugs. In this black market, no legal institutions exist to alleviate un-

certainty and buyers must instead rely solely on seller reputation provided by

a rating system. We identify sellers that were forced to open new accounts in

the market following a sudden exit of a major sales platform, resetting their

reputation in the process. We find that a one-percentage-point increase in

seller rating increases the unit price charged by 2-12$, depending on the drug

type. Our work demonstrates that reputation plays a crucial role in enabling

market transactions when legal institutions are lacking.

ZUSAMMENFASSUNG

Diese Dissertation umfasst drei Kapitel aus dem Forschungsfeld der Indus-

trieökonomik.

Kapitel 1 untersucht eskalierende (monetäre) Bestrafung für Wiederholungs-

täter, sprich, steigende Geldbußen in der Anzahl vergangener Vergehen. Es

wird gezeigt, dass es keinen Anreiz für die Autorität gibt Wiederholungstäter

härter zu bestrafen. Sollte die Autorität aber ein Interesse daran haben, den

bei Tätern entstandenen privaten Nutzen an die Gesellschaft umzuverteilen,

dann führt dies zu Eskalation, indem es fallende Strafen für erstmalige Täter

zur Folge hat. Das entwickelte Modell bildet sowohl die Theorie der optima-

len Strafverfolgung, als auch die monopolistische Preisbildung ab.

Kapitel 2 entwickelt einen nicht-parametrischen Schätzansatz um die geo-

graphische Größe eines Marktes empirisch zu messen. Dazu wird die Auswir-

kung des Eintritts eines neuen Geschäftes auf die lokalen Konkurrenten in

wachsender Distanz gemessen. Die Methode wird auf den Schweizer Lebens-

mitteldetailhandel angewendet und es wird gezeigt, dass dort die Märkte eng

abgegrenzt sind in einem vier Kilometer großen Radius (gemessen in Pend-

lerdistanz).

Kapitel 3 untersucht den Wert von Reputation im Online-Markt für illega-

le Drogen. In einem solchen Schwarzmarkt sind Käufer großer Unsicherheit

ausgesetzt, da keinerlei Institutionen wie das Rechtssystem existieren. Statt-

dessen verlassen sich die Beteiligten auf die Reputation der Verkäufer, ge-

messen mithilfe von Bewertungen auf digitalen Plattformen. Es werden Ver-

käufer identifiziert, die durch einen plötzlichen Marktaustritt einer Plattform

gezwungen waren ein neues Konto zu eröffnen und dadurch ihre Reputation

zu verlieren. Es wird gezeigt, dass ein Prozentpunkt in der Bewertung eines

Verkäufers es ermöglicht den Verkaufspreis um 2-12$ zu erhöhen, je nach Art

der Droge. Die Analyse zeigt, dass Reputation einen besonderen Wert hat, um

Transaktionen zu ermöglichen wenn wichtige Institutionen fehlen.

vii

1ESCALAT ING F INES AND

PR ICES : THE CURSE OF

POS IT IVE SELECT ION

(joint with S. Bühler)

abstract

This paper shows that escalating fines emerge in a generalized version of

the canonical Becker (1968) model if the authority (i) does not fully credit

offender gains to social welfare, and (ii) lacks commitment ability. We demon-

strate that the authority has no incentive to increase the fine for repeat of-

fenders because of their positive selection. Instead, escalation is driven by the

authority’s incentive to reduce the fine for low-value offenders in the future

and redistribute additional offender gains to society. Our analysis nests opti-

mal law enforcement with uncertain detection and behavior-based monopoly

pricing with imperfect customer recognition.

1.1 introduction

Escalating fines for repeat offenders are ubiquitous, but they pose a serious

challenge for the theory of optimal law enforcement. Why should the fine for

a given offense increase with the number of previously detected offenses? Es-

calating pricing schemes for repeat customers (e.g., mobile phone subscribers,

insurance buyers) pose a similar challenge. Why should loyal customers pay

higher prices than new ones? Surprisingly, standard theory struggles with

1

2 escalating fines and prices

answering these questions when the economic environment does not change

over time.

The repeated canonical model of optimal law enforcement (Becker 1968;

Polinsky and Shavell 2007), for instance, cannot explain escalating fines. Var-

ious authors have therefore suggested alternative explanations. For example,

if law enforcement is error-prone, accidental and real offenders are more dis-

tinguishable when the number of offenses increases; it then makes sense to

charge higher fines for repeat offenders (Stigler 1974; Rubinstein 1979; Chu

et al. 2000; Emons 2007). Similarly, if repeat offenders learn how to avoid de-

tection, escalating fines may keep notorious offenders deterred (Baik and Kim

2001; Posner 2007).1 Finally, if conviction carries a negative social stigma, es-

calating fines may be needed to keep up deterrence for previously convicted

offenders (Rasmusen 1996; Funk 2004; Miceli and Bucci 2005).2 Interestingly,

none of these explanations addresses the underlying inter-temporal fine dis-

crimination problem.

In this paper, we view a fine as a price (Gneezy and Rustichini 2000) and

study a generalized offender model that nests the canonical Becker (1968)

model of optimal law enforcement and behavior-based monopoly pricing

(Armstrong 2006; Fudenberg and Villas-Boas 2007) as special cases. We show

that, contrary to what intuition might suggest, escalation is driven by decreas-

ing fines for low-value offenders rather than increasing fines for high-value

offenders. The result arises from the following logic: If the authority (i) does

not fully credit offender gains to welfare, and (ii) lacks commitment ability,

it has an incentive to lower the fine for first-time offenders in the future and

redistribute additional offender gains to society. Consequently, some forward-

looking offenders strategically delay their offense to benefit from lower fines

in the future, which drives a wedge between the optimal fine and the in-

tertemporally indifferent type (cutoff) for first-time offenses. This wedge is

the source of the fine increase for repeat offenders, as the cutoff for repeat

offenders is optimally kept constant because of their positive selection (Tirole

1 Some authors have argued, though, that declining penalty schemes are optimal if law en-forcement becomes more effective in pursuing notorious offenders (e.g. Dana 2001, Mungan2009). Similarly, wealth constraints may make decreasing fines optimal (e.g. Anderson et al.2017), or lead to falling fines for first offenses over time, but constant ones for repeat offenses(Polinsky and Shavell 1998).

2 See Miceli (2013) for a survey of the relevant literature.

1.1 introduction 3

2016). Put differently, escalating fines cannot be explained by an incentive

to ratchet up (Freixas et al. 1985) the fines for repeat offenders. This “curse”

of positive selection is arguably the reason why the theory of optimal law

enforcement has struggled to explain escalating fines.

We develop our line of argument in a simple two-period model. Follow-

ing Polinsky and Shavell (2007), we assume that private offender gains are

continuously distributed and fixed, and we suppose that the authority and

offenders share the same discount factor.3 In period 1, forward-looking of-

fenders self-select into offenders and non-offenders, and both offenders and

non-offenders may commit the offense in period 2. The authority detects

offenses with exogenous probability.4 This implies that, in period 2, the au-

thority can distinguish two groups of offenders: repeat offenders recognized

from detected previous offenses, and non-recognized offenders who either

did not offend in period 1 (‘true’ first-time offenders) or were not detected

as offenders in period 1 (‘false’ first-time offenders). The authority can set

three fines for detected offenders: The fine for first-time offenders in period 1,

the fine for (true and false) first-time offenders in period 2, and the fine for

recognized repeat offenders in period 2.

We derive three key results. First, with commitment the authority can do no

better than set all fines equal to the optimal static fine. The well-known result

that it is optimal not to discriminate prices with commitment (Stokey 1979;

Hart and Tirole 1988; Acquisti and Varian 2005; Fudenberg and Villas-Boas

2007) thus not only extends to settings with imperfect customer recognition,

but also to optimal law enforcement. It is worth noting that setting all fines

equal to the optimal static fine is not uniquely optimal: falling fines for repeat

offenders may also be optimal. Yet, it is never optimal to choose escalating

fines, if the authority has the ability to commit. Second, without commitment

optimal fines for repeat offenses escalate if and only if optimal fines for first-

time offenses decrease. Put differently, escalation (if any) is generated by

decreasing fines for low-value offenders rather than increasing fines for repeat

offenders with identifiable high types. Escalation is thus explained by the

3 We will relax this assumption in subsection 1.5.1.4 That is, law enforcement is uncertain (Polinsky and Shavell 2007), or consumption is subject

to payment evasion (Buehler et al. 2017). Examples for payment evasion include digital piracy,shoplifting, fare dodging, etc.


effect that Coasian dynamics (Coase 1972; Hart and Tirole 1988) have on the

optimal fine for first-time offenses. Third, optimal fines for repeat offenders

do indeed escalate if the authority cannot commit to future fines and gives

less than full weight to offender gains. In contrast, if the authority gives

full weight to offender gains, it maximizes standard social welfare, sets all

expected fines equal to the social cost of the offense, and has no incentive to

lower the fine for first-time offenders.

Our paper makes a twofold contribution. First, we add to the theory of

optimal law enforcement (Polinsky and Shavell 2007) by providing a novel

explanation for escalating fines that builds on behavior-based price discrimi-

nation. We develop our explanation in a generalized version of the canonical

offender model where offender gains are not necessarily fully credited to wel-

fare. The assumption that offender gains are fully credited to welfare has long

been criticized on the grounds that it is difficult to see why illicit individual

offender gains should add to social welfare (Stigler 1974; Lewin and Trumbull

1990). Our analysis relaxes this assumption and shows that it has prevented

the canonical model from addressing escalation in repeated settings, as stan-

dard welfare maximization forces expected fines down to the social cost of an

offense. Our model brings the analysis closer to the distributive view of jus-

tice, which suggests that the optimal punishment “appropriately distributes

pleasure and pain between the offender and victim” (Gruber 2010, p. 5).

Second, we contribute to the literature on behavior-based price discrimi-

nation by adding two new ingredients to the analysis. The first ingredient

is imperfect customer recognition, which allows us to extend the analysis to

settings in which the seller cannot perfectly track the purchase histories of

its customers and is thus unable to distinguish a true from a false first-time

consumer in period 2. The paper closest to ours is Conitzer et al. (2012).

These authors study the extreme cases of either no recognition or full recog-

nition in a two-period model with repeat purchases. We consider a setting in

which customer recognition is imperfect and allow for the full range from no

recognition to full recognition. In a recent paper, Bellefl2016) study imperfect

customer identification in a monopoly setting without repeated purchases.

Our paper is also related to Villas-Boas (2004) who studies a setting in which

1.2 static model 5

an infinitely-lived firm faces overlapping generations of two-period-lived con-

sumers and cannot distinguish ‘young’ from ‘old’ first-time consumers.

The second ingredient that we add is non-profit maximization by the seller.

As discussed above, we find that a welfare-maximizing seller does not want to

discriminate prices, irrespective of commitment. The reason is that payments

amount to costless money transfers if full weight is given to offender gains.

The seller thus cannot do better than setting prices equal to the social cost of

consumption. With less weight given to individual gains, the seller’s profit

motive kicks in, and prices are optimally being discriminated. As one might

expect, prices are highest if no weight is given to individual gains and the

seller acts as a profit-maximizing monopolist.

The remainder of the paper is organized as follows. Section 1.2 introduces

the generalized offender model and derives the optimal static fine. Section

1.3 studies the optimal fines in the two-period version of the generalized of-

fender model, both with and without commitment by the authority. Section

1.4 discusses the relation to behavior-based pricing problems and shows that

the static fine is equivalent to the standard monopoly price if detection is

perfect and zero weight is given to offender gains. We further illustrate the

connection with two examples from dynamic monopoly pricing. Section 1.5

considers various extensions. Section 1.6 offers conclusions and directions for

future research.

1.2 static model

We build on the canonical model of optimal law enforcement pioneered by

Becker (1968) and studied extensively in Polinsky and Shavell (2007). Con-

sider a population of individuals who obtain gain g ≥ 0 from committing an

offense that generates social harm h ≥ 0. Individual gains are private knowl-

edge and drawn independently from a distribution with density function z(g)

and cumulative distribution function Z(g) on [g, g], with g > h > g and

z(g) > 0 for all g, such that neither complete deterrence nor zero deterrence

is optimal from a standard welfare perspective. Individuals who commit the

act are detected with exogenous probability π ∈ (0, 1] and must pay the fine


f ≥ 0. Individuals are risk-neutral, implying that only offenders whose gain

exceeds the expected fine, g ≥ π f , choose to commit the act.

The enforcement authority is assumed to maximize social welfare W, which

is defined as the sum of the gains offenders obtain from committing the harm-

ful act less the harm caused (Polinsky and Shavell 2007, p. 413),

W( f ; h, π) =∫ g

π f(g − h)dZ(g). (1.1)

Note that the fine f imposed on detected offenders is a socially costless trans-

fer of money from offenders to the enforcement authority, as the offenders’

gains are fully credited to social welfare. It is well known that, in this canon-

ical setting, the optimal fine f ∗(h, π) = h/π implements the first-best out-

come (see, e.g., Polinsky 2007): Only individuals whose private gain exceeds

the social harm (‘efficient offenders’) commit the harmful act, while all other

individuals (‘inefficient offenders’) are deterred.

The assumption that ‘illicit’ offender gains are fully credited to welfare has

long been criticized in the literature (Stigler 1974; Lewin and Trumbull 1990;

Polinsky and Shavell 2007). We relax this assumption and let the authority

maximize a weighted sum of surplus, with weight one given to expected

income from fine payments net of social cost, and weight α ∈ [0, 1] given to

offenders gains. The authority’s objective function is then given by

Ω( f ; h, π, α) =∫ g

π f(π f − h)dZ(g) + α

∫ g

π f(g − π f )dZ(g), (1.2)

which is equivalent to (1.1) if the authority gives full weight to offender gains,

α = 1, and thus maximizes standard welfare. For α < 1, offender gains

are not fully credited to social welfare, as the authority gives relatively more

weight to net income from fine payments. When α = 0, the authority focuses

exclusively on net redistribution from offender payments.

Our first result characterizes the optimal static fine for the generalized

canonical offender model.

1.3 dynamic model 7

Proposition 1 (static fine). Suppose the authority’s objective function Ω( f ; h, π, α)

is strictly quasi-concave and offender gains are weighted with α ∈ [0, 1]. Then, the

optimal static fine satisfies

f ∗(h, π, α) =hπ+

(1 − α)[1 − Z(π f ∗)]z(π f ∗)π

, (1.3)

with d f ∗(h, π, α)/dα ≤ 0.

Proof. Using Leibniz’s rule, differentiating Ω( f ; h, π, α) with respect to f yields

the first-order condition

(1 − α)[(1 − Z(π f ∗)]− (π f ∗ − h)z(π f ∗) = 0.

Solving for f ∗ yields the optimal static fine f ∗(h, π, α). The comparative-

statics effect of an increase in α on f ∗(h, π, α) is readily determined by ap-

plying the implicit function theorem to the first-order condition and noting

that the cross-partial derivative satisfies Ω f α = −[1 − Z(π f )] ≤ 0.

Proposition 1 shows the optimal static fine depends on the weight that the

authority gives to offender gains. If offender gains are not fully credited to

welfare (α < 1), the optimal fine exceeds the first-best level h/π, such that

some efficient offenders with types g > h are deterred. The optimal fine now

reflects the enforcement authority’s interest in redistributing illicit offender

gains to society. Note that complete deterrence is not optimal, even if offender

gains are not credited to welfare at all (α = 0). The reason is that the authority

still benefits from the net income from fine payments. Figure 1.1 illustrates

the generalized static offender model with three different values for α. The

shaded area corresponds to the authority’s surplus if α = 12 .

1.3 dynamic model

Let us now consider the repeated version of the generalized offender model

with two periods t = 1, 2. Suppose that the authority and offenders share the


g

g

g

1 − Z(g)1

π f ∗(·, 1) = h

π f ∗(·, 0) = h + 1−Zz

π f ∗(·, 12) = h + 1−Z

2z

Figure 1.1: Static modelNotes: The figure shows the optimal expected fine π f ∗(·, α) in the generalized offender model with a linear demandfor α ∈ {0, 1

2 , 1}. The shaded area indicates the authority’s surplus Ω for α = 12 .

same discount factor δ ∈ (0, 1),5 and assume that the authority can set three

fines f = { f1, f2, f2} that are imposed on detected offenders: f1 for first-time

offenders in period 1, f2 for first-time offenders in period 2, and f2 for repeat

offenders in period 2. Finally, assume that offenders are forward-looking and

cannot commit to future offense decisions.

1.3.1 Skimming Property

Since higher types have higher gains, the skimming property (Fudenberg

et al. 1985, Cabral et al. 1999, Tirole 2016) ensures that higher-type offenders

make their purchases no later than lower-type offenders. Specifically, if a type

g chooses to offend in period t, then so does a higher type g′ > g. To see

how the skimming property works in our setting, consider the gain of an

offender with type g from offending in period 1 and period 2 vs. the gain

5 We will relax this assumption in Section 1.5.1.

1.3 dynamic model 9

from offending in period 2 only. For this individual to offend in period 1, we

must have that the gain from offending in period 1 and period 2,

φ1(g) ≡ g − π f1 + δ[π(g − π f2) + (1 − π)(g − π f2)],

exceeds the gain from offending in period 2 only,

φ2(g) ≡ δ(g − π f2).

It is straightforward to see that

φ1(g′)− φ1(g) > φ2(g′)− φ2(g), for g′ > g,

which implies that there exists a unique cutoff g∗1(f) which splits the type set

into offenders and non-offenders in period 1. Similarly, in period 2 we have

that g′ − π f2 > g − π f2 and g′ − π f2 > g − π f2, so that in each period and

each segment there exists a unique cutoff.

By choosing the menu of fines f, the authority induces individuals to self-

select into different offender segments. In doing so, the authority may or may

not be able to commit to the menu of fines at the beginning of period 1. We

consider each case in turn.

1.3.2 Commitment

Suppose that the authority is able to commit to the full menu of fines f at the

beginning of period 1. In this case, the fines f2 and f2 applied in period 2 are

not conditioned on the offenders’ behavior in period 1. The next proposition

establishes that under commitment it is optimal not to vary the fines in the

generalized offender model. This result is reminiscent of classic findings in

the price discrimination literature, which show that it is optimal not to price

discriminate under commitment if consumer types are fixed and the seller

and individuals share the same discount factor (Stokey 1979, Hart and Tirole

1988, Acquisti and Varian 2005, Fudenberg and Villas-Boas 2007).6

6 We discuss the relation of the generalized offender model to dynamic pricing models insection 1.4.


Proposition 2 (commitment). Suppose the authority can commit to the full menu

of fines at the beginning of period 1. Then, it can do no better than set all fines equal

to the optimal static fine, that is, f ∗1 = f ∗2 = f ∗2 = f ∗(h, π, α).

Proof. Consider high-valuation individuals with g′ ≥ g∗ and low-valuation

individuals with g < g∗, where g∗ is the optimal static cutoff. For all high-

valuation individuals to reveal themselves in period 1, fines must be cho-

sen such that the cutoff in period 1 satisfies g∗1 ≤ g∗. Similarly, for all low-

valuation individuals to reveal themselves, we must have g∗1 ≥ g∗. This im-

mediately implies that g∗1 = g∗. In addition, it cannot be optimal to choose

a cutoff g∗2 �= g∗1 whenever g∗1 = g∗, as the authority could do better by

setting g∗2 = g∗1. Therefore, the unique optimal policy is to set the fines

such that the cutoffs are equal, g∗1 = g∗2 = g∗. By Proposition 1, optimal-

ity requires that g∗2 = π f ∗2 = π f ∗(h, π, α) = g∗1. The indifference condition

φ(g∗1) = φ(g∗2) then simplifies to g∗1 − π f1 + δπ(g∗1 − π f2) = 0, which is satis-

fied for f ∗1 = f ∗2 = f ∗2 = f ∗(h, π, α).

Proposition 2 shows that the authority can do no better than achieve the

optimal static outcome in both periods: With commitment, it is optimal to

set the optimal static fine f ∗ for all offenders and thus abstain from inter-

temporal discrimination ( f1 �= f2) or behavior-based discrimination ( f2 �= f2).

It is worth noting that constant fines are not uniquely optimal. Decreasing

fines for repeat offenders that implement equal cutoffs, g∗1 = g∗2, such that

only detected repeat offenders benefit from the lower fine period 2, whereas

previously non-detected repeat offenders face the optimal static fine in pe-

riod 2, may also be optimal. Yet, the authority cannot do better with decreas-

ing rather than constant fines. Escalating fines, in turn, cannot be optimal,

because individuals cannot be coerced to offend at arbitrary fines.

The result clarifies why the literature on optimal law enforcement has strug-

gled to explain escalating fines in the repeated canonical framework: if the

authority can commit to fines, it is simply not optimal to escalate fines if the

economic environment does not change over time. Next, we consider the case

where the authority lacks commitment ability.

1.3 dynamic model 11

1.3.3 Non-Commitment

Consider a setting in which the authority lacks commitment ability. The

authority will then want to condition the fines in period 2 on the offenders’

observed behavior in period 1 (i.e., whether or not they were previously de-

tected as offenders). As a result, optimal fines in period 2 must account for

both right-truncation for first-time offenders and left-truncation for repeat of-

fenders, as the cutoff in period 1, g∗1, separates the type set into non-offenders

[g, g∗1 ] and offenders [g∗1, g], respectively.

To understand how left- and right-truncation affect the setting of fines, con-

sider the optimal fine f2 for repeat offenders in period 2. Left-truncation at

g∗1 implies that the optimal expected fine for repeat offenders must be at least

as large as the cutoff in period 1, π f ∗2 ≥ g∗1, as all previously detected of-

fenders must have types g ≥ g∗1 (otherwise they would not have offended

in period 1). This immediately implies that it cannot pay off to strategically

offend in period 1: a loss incurred in period 1 cannot be recouped in period 2,

as the optimal fine for repeat offenses cannot fall. Strategic delay is thus the

only way in which individuals may benefit from non-myopic behavior, which

implies that the cutoff in period 1 must satisfy g∗1 ≥ π f ∗1 . Note that right-

truncation at g∗1 does not eliminate all types g ≥ g∗1 from the pool of first-time

offenders in period 2. The reason is that a share (1 − π) of the individuals

with types g ≥ g∗1 who offend in period 1 go undetected.

We now proceed to characterize optimal individual behavior conditional on

types.

Proposition 3 (self-selection). Suppose that the authority lacks commitment ability.

Then, individuals optimally condition their behavior on types as follows:

(i) Types g < min{π f1, π f2} never offend.

(ii) Types g ≥ π f2 always offend.

(iii) For f2 ≥ f1, individuals behave as if they were myopic, such that types g ∈[π f1, π f2) offend in period 1 and types g ∈ [π f2, π f2) offend in period 2 if not

previously detected.


(iv) For f2 < f1, types g ∈ [π f1, g∗1) strategically delay the offense in period 1 and

offend in period 2; types g ∈ [g∗1, π f2) offend in period 1 and offend in period 2

if not previously detected; types g ∈ [π f2, g∗1 ] offend in period 2.

Proof. We consider each statement in turn.

(i) If f1 ≤ f2, offenders act as if they were myopic. For types g < π f1 it is

not profitable to offend in period 1, and at best equally unprofitable in

period 2. If f1 > f2, types g < π f2 do not find it profitable to offend in

period 2, and thus even less so in period 1.

(ii) For types g ≥ π f2 it is always profitable to offend, even at the expected

fine π f2 ≥ g∗1 in period 2, and thus also at the expected fine π f1 ≤ g∗1 in

period 1.

(iii) For f2 ≥ f1, strategy delay is not profitable by assumption, and individ-

uals thus behave as if they were myopic. Therefore, all types g ≥ π f1

offend in period 1, and all types g ≥ π f2 that were not previously de-

tected offend in period 2. The result follows from noting that types

g ≥ π f2 always offend by (ii).

(iv) For f2 < f1, it is profitable for types g ∈ [π f1, g∗1) to strategically delay

offending in period 1 by construction, and to offend in period 2 by as-

sumption. Similarly, it is profitable for g ∈ [g∗1, π f2) to offend in period 1

by construction. In period 2, optimal behavior is myopic, and offending

is profitable only if not previously detected (π f2 < g∗1 ≤ π f2).

Proposition 3 characterizes how individuals optimally self-select based on

their types. Essentially, two cases need to be distinguished. First, if the fine for

first-time offenses increases, f2 ≥ f1, forward-looking offenders cannot gain

from strategic delay and behave as if they were myopic. The cutoff in period 1

is then given by g∗1 = π f1. This case is illustrated in panel a) of Figure 1.2.

Second, if the fine for first-time offenses decreases, f2 < f1, some forward-

looking agents strategically delay the offense to benefit from the lower fine in

period 2. The cutoff in period 1 then exceeds the myopic level, g∗1 > π f1, as

illustrated in panel b) of Figure 1.2.


g gπ f1 = g∗1

non-offenders offenders

(a) f1 ≤ f2: myopic

g gπ f1 g∗1π f2

offendersdelaying typesnon-off.

(b) f1 > f2: strategic delay

Figure 1.2: Self-selection in period 1Notes: The figure illustrates how individuals with different types optimally self-select in period 1. Panel (a) showsthe case of weakly increasing fines for first-time offenses. Panel (b) shows the case of decreasing fines for first-timeoffenses.

Next, we study how the authority optimally chooses fines, accounting for

optimal self-selection by individuals.

Optimal Fines in Period 2

We first consider the optimal fine for repeat offenders in period 2, f ∗2 . This

fine must maximize the authority’s surplus generated by previously detected

repeat offenders with types g ∈ [g∗1, g],

f ∗2 = arg maxf2∈F2

{(π f2 − h)

1 − Z(π f2)

1 − Z(g∗1)+ α(g − π f2)

1 − Z(π f2)

1 − Z(g∗1)

}, (1.4)

where F2 ≡ { f2 : π f2 ≥ g∗1} is the set of fines for which the expected fine for

repeat offenders exceeds the cutoff g∗1. Our next result shows how the optimal

fine is determined.

Proposition 4 (repeat offenders). Suppose that the authority lacks commitment

ability. Then,

(i) if g∗1 < π f ∗(h, π, α), the optimal fine for repeat offenders in period 2 equals the

optimal static fine, f ∗2 = f ∗(h, π, α).

(ii) if g∗1 ≥ π f ∗(h, π, α), the optimal fine for repeat offenders in period 2 keeps the

cutoff constant, π f ∗2 = g∗2 = g∗1 .

Proof. We consider both statements in turn.

(i) For g∗1 < π f ∗(h, π, α), it is optimal for the authority to set f ∗2 = f ∗(h, π, α)

by Proposition 1, as individual behavior is myopic in period 2.


(ii) For g∗1 ≥ π f ∗(h, π, α), the surplus in (1.4) is maximized at the lower

bound after left-truncation, π f ∗2 = g∗2 = g∗1.

Proposition 4 states that the optimal fine for repeat offenders in period 2

equals the optimal static fine if the cutoff in period 1 is below the optimal

static cutoff. The intuition for this result is straightforward: since individuals

are myopic in period 2 and the left-truncation at g∗1 does not prevent the

authority from reaching the static optimum, it is best to choose the optimal

static fine. This finding might suggest that escalation occurs if the initial

cutoff is lower than the static optimum. However, as will become clear below,

it cannot be optimal for the authority to induce a cutoff g∗1 that is below the

static optimum, since this would induce a loss that cannot be recouped in

period 2. Henceforth, we therefore focus on the case where g∗1 exceeds the

optimal static cutoff.7

Proposition 4 further demonstrates that if g∗1 exceeds the optimal static cut-

off, the optimal cutoff for repeat offenders in period 2 must equal the cutoff

from period 1, g∗2 = g∗1. That is, the optimal fine for repeat offenders in pe-

riod 2 does not exclude previous offenders. This result reflects Tirole’s (2016)

insight in the context of dynamic pricing that the set of inframarginal con-

sumers is invariant to left-truncation under positive selection. At first glance,

the result may seem surprising as cutoff invariance obtains even though exit

(i.e., no offense) is not absorbing in our setting. Note, however, that the cutoff

invariance result holds only for repeat offenders with types above the cutoff

level g∗1 who must have committed the offense in period 1 by construction.

Therefore, exit is indeed absorbing for repeat offenders.8 Exit is clearly not

absorbing, though, for offenders with types below the cutoff level g∗1.

The result sheds further light on why the literature on optimal law enforce-

ment has struggled to explain escalating fines: The notion that repeat offend-

ers should pay higher monetary fines in period 2 than first-time offenders in

period 1 because of identifiably higher private gains turns out to be incorrect. In a

7 Mueller and Schmitz (2015) analyze a setting in which the initial fines for first-time offendersare exogenously restricted.

8 Put differently, individuals cannot self-select into the set of repeat offenders after exit inperiod 1.


fixed economic environment with a given type distribution, the authority can

induce the optimal cutoff g∗1 by the appropriate choice of fines right from the

start and does not benefit from the identification of individual offenders over

time.

Next, we determine the optimal fine for offenders in period 2 that were not

previously detected, f ∗2 . This fine maximizes the authority’s surplus gener-

ated by true first-time offenders in period 2 with types g ∈ [π f2, g∗1 ] and false

first-time offenders who are in fact repeat offenders with types g ∈ [g∗1, g] that

were not previously detected,

f ∗2 = arg maxf2

⎧⎨⎩[∫ g∗1

π f2

(π f2 − h)dZ(g) + α∫ g∗1

π f2

(g − π f2)dZ(g)

](1.5)

+ (1 − π)

[∫ g

g∗1(π f2 − h)dZ(g) + α

∫ g

g∗1(g − π f2)dZ(g)

]⎫⎬⎭ .

The next result shows that the optimal fine for first-time offenders in pe-

riod 2 is lower than the optimal static fine if the authority does not maximize

standard welfare.

Proposition 5 (first-time offenders). Suppose that the authority lacks commitment

ability. Then, the optimal fine for first-time offenders in period 2 satisfies

f ∗2 (g∗1; h, π, α) =hπ+

(1 − α)[Z(g∗1)− Z(π f ∗2 ) + (1 − π)[1 − Z(g∗1)]]z(π f ∗2 )π

. (1.6)

If the authority gives less than full weight to offender gains, α < 1, this fine is lower

than the optimal static fine, f ∗2 (g∗1; h, π, α) < f ∗(h, π, α).

Proof. Using Leibniz’s rule, maximizing the surplus in (1.5) with respect to f2

yields f ∗2 in (1.6). For α < 1, we must have f ∗2 (g∗1; h, π, α) ≤ f ∗(h, π, α) by con-

struction. However, f ∗2 (g∗1; h, π, α) = f ∗(h, π, α) requires complete deterrence

(g∗1 = g) in period 1 by Proposition 1, which cannot be optimal because of

h < g by assumption.

Two comments are in order. First, if the authority gives full weight to of-

fender gains (α = 1), the optimal fine for first-time offenders in period 2


equals the standard welfare-maximizing fine, f ∗2 = h/π. This finding is intu-

itive, as standard welfare maximization forces the expected fine down to the

social cost of the offense. Second, if the authority gives less than full weight

to offender gains (α < 1), the optimal fine is strictly smaller than the static

optimal fine. To understand the intuition for this result, consider the extreme

case where the cutoff is at the upper bound of the type set, g∗1 = g, and note

that f ∗2 (g; h, π, α) = f ∗(h, π, α). Next, consider a marginal reduction in the

cutoff value g∗1. This reduction eliminates offenders with types just below the

cutoff level from the pool of true first-time offenders and adds them to the

pool of false first-time offenders, but with probability less than one. For a

cutoff level g∗1 < g, the optimal fine must therefore be lower than the optimal

static fine.

Establishing Escalation

We now establish the conditions under which escalation occurs. To do so,

we determine the cutoff level g∗1(f) in period 1 using the indifference condition

which equates an offender’s utility from consuming in period 1 and period 2

with the utility from consuming in period 2 only. Specifically, the indifferent

type g∗1 must satisfy the condition

g∗1 − π f1 + δ[π(g∗1 − π f2) + (1 − π)(g∗1 − π f2)] = δ(g∗1 − π f2), (1.7)

where the left-hand side accounts for the fact that an offender in period 1 faces

two possible outcomes: with probability π the offense in period 1 is detected,

in which case the repeat offender faces the expected fine π f ∗2 in period 2; with

probability (1 − π) the offense is not detected, and the repeat offender faces

the same expected fine π f2 as a true first-time offender in period 2. Now, since

g∗1 − π f2 ≤ 0 by Proposition 4, a previously detected offender will either not

offend (if g∗1 − π f2 < 0), or get a zero surplus from offending (if g∗1 − π f2 = 0)

in period 2. In both cases, the second term is zero, such that the indifference

condition simplifies to

g∗1 − π f1 = δπ(g∗1 − π f2). (1.8)


We can now derive the following result.

Proposition 6 (escalation). Suppose that the authority lacks commitment ability.

Then, optimal fines for repeat offenders escalate, f ∗2 > f ∗1 , if and only if the optimal

fines for first-time offenders decrease, f ∗2 < f ∗1 .

Proof. Suppose the optimal fines for first-time offenders decrease, f ∗2 < f ∗1 .

Then, using (1.8), we have g∗1( f ∗1 , f ∗2 ) > π f ∗1 . Since g∗1 ≤ π f ∗2 by Proposition 4,

we must have π f ∗2 > π f ∗1 and thus f ∗2 > f ∗1 . This establishes sufficiency.

To establish necessity, assume that f ∗2 > f ∗1 , and thus π f ∗2 > π f ∗1 . Since

the optimal cutoff in period 1 must satisfy g∗1 ≥ π f ∗(h, π, α), we must have

π f ∗2 = g∗2 = g∗1 > π f ∗1 by Proposition 4. The latter inequality requires f ∗2 < f ∗1by (1.8).

Proposition 6 highlights that escalating fines for repeat offenders (if any) fol-

low from decreasing fines for low-value offenders rather than increasing fines

for detected high-value offenders. The prospect of decreasing fines induces

some individuals with types above the expected fine to strategically delay the

offense, which in turn drives a wedge between the expected fine π f ∗1 and the

cutoff g∗1 in period 1. This is illustrated in panel (a) of Figure 1.3. The wedge

these delaying offenders cause gives rise to escalation, f ∗2 > f ∗1 , because by

Proposition 4 the cutoff is invariant from period 1 to period 2, g∗1 = π f ∗2 ,

which is illustrated in panel (b) of Figure 1.3. In contrast, if there is no wedge

between the expected fine and the cutoff, π f ∗1 = g∗1, cutoff invariance yields

constant fines π f ∗1 = π f ∗2 .

The following corollary is an immediate implication.

Corollary 1. Suppose that the authority lacks commitment ability and attaches weight

α < 1 to offenders. Then, optimal fines escalate,

f ∗2 > f ∗1 > f ∗2 . (1.9)

Proof. By Proposition 5, f ∗2 < f ∗(h, π, α) for α < 1. The indifference condition

(1.8) then immediately implies that g∗1 > π f ∗1 > π f ∗2 . Substituting g∗1 = π f ∗2by Proposition 4 yields the result.

The result demonstrates that, without commitment, the authority has an in-

centive to lower the fine for first-time offenses if it gives less than full weight


g

1 − Z(g)

h

π f ∗1

g∗1

first-time offenders

delaying offenders

non-offenders

(a): period 1

g

1 − Z(g)

h

π f ∗2

π f ∗2

repeat offenders

first-time offenders

(b): period 2

Figure 1.3: Dynamic model without commitmentNotes: The figure illustrates the optimal fines and induced inter-temporal cutoff when the authority lacks commit-ment ability. Panel (a) depicts the first period and shows the wedge between cutoff and expected fine that delayingoffenders cause. Panel (b) depicts the second period and shows the resulting escalation in price for repeat offenders.

to offenders gains. The intuition for this result is straightforward: if full

weight is given to offender gains, fine payments are irrelevant for the author-

ity’s surplus, and optimal expected fines must reflect the (fixed) social cost

of the offense. There is thus no incentive to lower the fine for first-time con-

sumption. However, if less than full weight is given to offender gains, the

redistribution motive kicks in, and the authority has an incentive to lower the

fine and redistribute additional fine payments in the next period.

1.4 relation to monopoly pricing

We have noted above that the choice of optimal fines by an authority is

closely related to profit-maximizing monopoly pricing. To clarify this relation,

recall that the authority’s static objective function is given by Ω( f ; h, π, α). The

following corollary is an immediate implication of Proposition 1.

1.4 relation to monopoly pricing 19

Corollary 2 (static monopoly price). Suppose the authority gives zero weight to of-

fender gains and detects offenses with probability one, Ω( f ; h, 1, 0). Then, relabelling

the fine as a price, f ≡ p, the optimal fine is given by the static monopoly price

pm(h, 1, 0) = h +1 − Z(pm)

z(pm). (1.10)

Corollary 2 shows that it is natural to view a fine as a price (Gneezy and

Rustichini 2000): the optimal (surplus-maximizing) fine is exactly equal to the

monopoly price if the authority focuses on maximizing net income from fines

and can perfectly detect offenses.

More generally, the canonical Becker (1968) model and standard monopoly

pricing are nested special cases of the generalized offender model that differ

in (i) the weight given to offender gains (consumer rents, respectively) and (ii)

the probability of detecting an offense (consumption). To illustrate how the

results for the generalized offender model carry over to dynamic monopoly

pricing, we next consider two well-known examples for dynamic monopoly

pricing with α = 0 and π = 1, assuming that individual gains g are uniformly

distributed on [0, 1].

1.4.1 Behavior-Based Pricing

Armstrong (2006, pp. 6) studies behavior-based monopoly pricing in a two-

period model where production is costless, h = 0. This setting is a special

case of the generalized offender model in which prices p = {p1, p2, p2} rather

than fines are chosen so as to maximize intertemporal profits.

With commitment, it is optimal not to discriminate prices and set all prices

equal to the static monopoly price p∗1 = p∗2 = p∗2 = pm = 12 . This result is

a special case of Proposition 2. If the monopolist lacks commitment ability,

prices are chosen so as to maximize intertemporal profits

π1 + δπ2 = p1(1 − g∗1) + δ[ p2(1 − g∗1) + p2(g∗1 − p2)],

where the price for repeat consumers in period 2 is p∗2 = pm = 12 if g∗1 < pm

and p∗2 = g∗1 if g∗1 ≥ pm, which is in line with Proposition 4. The price


for first-time consumers in period 2 must account for right-truncation and is

given by p∗2 = 12 g∗1, which is in line with Proposition 5. Using these prices, it

is straightforward to solve the indifference condition for the cutoff g∗1(p1) =

(2p1)/(2 − δ). Maximizing over p1 then yields the profit-maximizing prices

(Armstrong 2006)

p∗1 =4 − δ2

2(4 + δ); p∗2 =

2 + δ

2(4 + δ); p∗2 =

2 + δ

(4 + δ).

The monopolist thus practices behavior-based price discrimination as ana-

lyzed above: profit-maximizing prices for repeat consumers escalate because

the monopolist cannot resist the temptation to lower the price for low-type

consumers who have not consumed in period 1. The pricing for repeat con-

sumers, in turn, is time-consistent.

1.4.2 Pricing with Positive Selection

Tirole (2016) analyzes dynamic monopoly pricing with positive selection,

assuming that production is costly, h = c, and that consumers can consume in

future periods only if they have consumed in all previous periods (absorbing

exit). Consider the two-period version of this setting. Since types g < g∗1cannot consume in period 2 by assumption, first-time consumption in period 2

is excluded and the monopolist chooses two prices only, p1 and p2. This two-

period example is a special case of the generalized offender model in which

only types above g∗1 stay in the market.

It is shown that, with commitment, it is optimal not to discriminate prices

and set all prices equal to the static monopoly price, which assuming a uni-

form distribution of gains is given by

p∗1 = p∗2 = pm =1 + c

2,

which is in line with Proposition 2. More interestingly, Tirole (2016) shows the

result holds even if the monopolist lacks commitment ability. The intuition

for this result is as follows: Since exit is absorbing by assumption, all types

g < g∗1 below the cutoff are excluded in period 1, such that the monopolist is

1.5 extensions 21

not tempted to lower the price for non-consumers below the static monopoly

price. The profit-maximizing price for the remaining types g ≥ g∗1, in turn, is

the static monopoly price, which is the lower bound after left-truncation. This

is in line with the cutoff invariance result of Proposition 4.

1.5 extensions

We now consider several extensions. First, we allow for heterogenous dis-

count factors in the fixed-environment setting analyzed above. Second, we

discuss changes in the environment that may provide alternative explanations

for escalating pricing schemes.

1.5.1 Heterogeneous Discount Factors

So far we have assumed that all decision makers have the same discount

factor δ. We now consider settings in which the authority and individuals

have different discount factors, δA �= δI . With heterogeneous discount factors,

a given surplus arising in period 2 is valued differently by the authority and

individuals in period 1. This suggests that it may be beneficial for the author-

ity to shift surplus gained by offenders from one period to the other, while

keeping the overall offender surplus constant. For example, if the authority is

more patient than individuals, δA > δI , the authority can offer them a lower

surplus tomorrow in exchange for a higher surplus today by adjusting the

prices accordingly. Specifically, the authority has an incentive to backload the

fines ( f1 < f2) when it is more patient than individuals, δA > δI , and frontload

the fines ( f1 > f2) when it is less patient, δA < δI . The next result estab-

lishes that, although heterogenous discount factors may provide an incentive

to backload fines, they do not provide a new rationale for escalation.

Proposition 7 (heterogeneous discounting). Suppose that the authority and indi-

viduals have unequal discount factors, δA �= δI . Then,

(i) if the authority lacks commitment ability, escalating fines are optimal for α < 1.


(ii) if the authority can commit and is more patient that individuals, δA > δI ,

constant fines are optimal.

(iii) if the authority can commit and is less patient than individuals, δA < δI , opti-

mal fines for repeat offenders are frontloaded and satisfy f ∗1 = f ∗(1 + πδI) >

f ∗2 = 0.

Proof. Consider the three statements in turn.

(i) Propositions 3-5 continue to apply as they are independent of the dis-

count factors (δA, δI). Proposition 6 relies on the individuals’ indiffer-

ence condition, which now reads g∗1 − π f1 = δI(g∗1 − π f2) rather than

(1.8). As before, this implies that g∗1( f ∗1 , f ∗2 ) > π f ∗1 , and since Proposi-

tion 4 continues to hold, the results of Proposition 6 and Corollary 1 still

apply.

(ii) As established in the proof of Proposition 2, with authority commit-

ment the unique optimal policy is to set the fines such that the cut-

offs satisfy g∗1 = g∗2. Since offenders cannot commit, optimality re-

quires that g∗2 = π f ∗2 = π f ∗(h, π, α) = g∗1. The indifference condi-

tion then reads g∗1 − π f1 + δIπ(g∗1 − π f2) = 0, which is satisfied for

f ∗1 = f ∗2 = f ∗2 = f ∗(h, π, α).

(iii) As established in (ii), with authority commitment the cutoffs satisfy

g∗1 = g∗2, and g∗2 = π f ∗2 = π f ∗(h, π, α). If δA < δI , the authority can

strictly gain by transferring its surplus in period 2 to offenders in ex-

change for extracting their surplus in period 1. Optimality requires

that the authority’s period-2 surplus is fully transferred, which imme-

diately implies that π f ∗2 = 0. The indifference condition then reads

g∗1 − π f1 + δIπg∗1 = 0, which yields f ∗1 = f ∗(1 + δIπ).

Proposition 7 shows that heterogeneous discount factors cannot explain

escalating fines. Although the authority has an incentive to backload the

fines when it is more patient than individuals, our previous results continue

to hold regardless of authority commitment. The intuition for this result is

straightforward: Since the authority cannot coerce individuals into offending

1.5 extensions 23

at fines at which they would not voluntarily offend from a myopic perspective

in period 2, it cannot gain from lowering fines in period 1 in exchange for

increasing fines in period 2. Thus, it can never profitably act on its incentive

to backload.

However, heterogeneous discount factors may yield decreasing fines. If

the authority can commit and is less patient than offenders, forward-looking

repeat offenders will accept frontloaded fines that compensate them for a

loss in period-1 surplus with an appropriate gain in period-2 surplus. As

the authority can strictly gain from transferring period-2 surplus to repeat

offenders in exchange for a higher period-1 surplus, it will optimally give

up its total surplus in period 2, so that repeat offenders effectively pay once

for committing the offense twice. As a consequence, the authority charges a

fine in the first period that maximizes the total payment for the two periods

subject to the constraint that the total surplus of repeat offenders is at least as

large as that generated by constant fines.

Finally, note that frontloading is impossible if the authority lacks commit

ability. This follows immediately from the fact that offenders are forward-

looking. Without authority commitment, offenders will not accept frontloaded

fines, as they correctly anticipate that the authority will not want to lower the

fine below the optimal static level in period 2 to compensate for the higher

fine in period 1.

1.5.2 Changes in the Economic Environment

The preceding analysis has focused on a fixed economic environment. How-

ever, there may be scenarios in which optimal fines escalate because of changes

in the economic environment. For instance, a number of authors in the litera-

ture on explaining escalating fines have considered the effect of a lower detec-

tion probability for repeat offenders (e.g. Baik and Kim 2001). In this section,

we consider two exogenous parameter changes that give rise to such changes

in the economic environment: (i) an increase in the social cost of offending,

and (ii) a decrease in the detection probability as a function of the number of

previous offenses.


Increasing Social Cost of Consumption

The next result establishes that an increase in the social cost of offending

may indeed lead to escalating fines. More interestingly, it also shows that an

increase in social cost may eliminate behavior-based discrimination.

Proposition 8 (increasing social cost). Suppose the social cost of offending h is

known to increase over time, so that h2 > h1. Then,

(i) with authority commitment, the authority can do no better than set the fines

equal to the respective optimal static fines, f ∗1 = f ∗(h1, π, α) and f ∗2 = f ∗2 =

f ∗(h2, π, α), and hence f ∗1 < f ∗2 = f ∗2 .

(ii) if the authority lacks commitment ability, the increase in social cost reduces the

incentive to lower the fine for first-time offenders and eliminates behavior-based

discrimination altogether if π f ∗2 (h2, π, α) ≥ g∗1 .

Proof. Consider each statement in turn.

(i) With authority commitment, optimality requires that the authority avoids

strategic delay by offenders and accounts for the increase in the social

cost of offending. By Proposition 1, it is optimal for the authority to

set the fines such that g∗2 = g∗2 = π f2 = π f ∗2 = π f ∗(h2, π, α) and

g∗1 = π f ∗1 = π f ∗(h1, π, α). The result follows from h2 > h1.

(ii) By Proposition 5, f ∗2 (h, π, α) is increasing in the social cost of offending h.

By Proposition 6, behavior-based escalation occurs if and only if f ∗2 < f ∗1 ,

which is not possible when π f ∗2 (h2, π, α) ≥ g∗1.

Proposition 8 shows how an increase in the social cost of offending leads to

escalating fines when the authority can commit. Note, though, that the logic

is very different from that identified above: with commitment, it is optimal

for the authority to charge the optimal static fine in each period. However,

since optimal static fines increase mechanically due to the increase in social

cost, escalating fines emerge even though the authority can commit.

The result also shows that, if the authority lacks commitment ability, an

increase in the social cost may eliminate behavior-based discrimination. If the

1.5 extensions 25

optimal static fine for first-time offenders in period 2 (i.e., after the increase

in social cost) lies at or above the cutoff g∗1, the authority cannot benefit from

lowering the fine. This ensures that individuals behave as if they were myopic,

since they cannot gain from delaying consumption. In this case, the outcome

is the same as under authority commitment: the optimal static fine in period 2

increases mechanically due to h2 > h1.

Decreasing Detection Probability

Finally, we consider a decrease in the detection probability as a function of

the number of detections.

Proposition 9 (decreasing detection probability). Suppose the probability of de-

tection is known to decrease in the number of detections, so that π2 < π1. Then,

(i) with authority commitment, the authority can do no better than set π1 f ∗1 =

π2 f ∗2 and hence f ∗1 < f ∗2 .

(ii) if the authority lacks commitment ability, optimal fines are escalating for α < 1.

Proof. Consider the two statements in turn.

(i) Under authority commitment, it must still be that g∗1 = g∗2 = π1 f2. The

indifference condition then becomes g∗1 − π1 f1 + δπ1(g∗1 − π2 f2) = 0,

which as before is satisfied for π1 f ∗1 = π2 f ∗2 . With π1 > π2, it follows

immediately that f ∗2 > f ∗1 .

(ii) The change in the detection probabilities does not affect the optimal

cutoff values under non-commitment, which give rise to escalating fines

for α < 1 by Corollary 1. Optimal fines must now compensate for the

decrease in the detection probability and thus continue to escalate.

Proposition 9 demonstrates that our analysis generalizes naturally to set-

tings in which offenders become more effective at avoiding detection after

having been fined for an offense. If the authority is able to commit, it still

cannot do better than obtain the optimal static surplus in each period. Yet,

because the detection probability for repeat offenders decreases, the fine for


repeated consumption must increase to compensate. This is directly in line

with the finding in Proposition 8. Similarly, if the authority lacks commitment

ability, optimal fines continue to escalate, as they must implement the same

cutoff values and therefore increase even more than in the standard setting to

compensate for the decrease in the detection probability.

1.6 conclusion

We have studied how escalating fine schemes emerge in a fixed economic

environment in which offender types are private knowledge, the authority

imperfectly recognizes previous offenders, and individual offender gains are

not necessarily fully credited to welfare.

The key insight of our analysis is that escalation is driven by an incentive

to reduce the fine for low-value offenders, rather than an incentive to increase

the fine for high-value repeat offenders. The intuition for this result is as

follows: if the authority cannot commit not to lower the fine in the future,

some forward-looking offenders strategically delay offending to benefit from

lower fines in the future, which drives a wedge between the optimal fine

and the cutoff for first-time offenses. This wedge is the source of the fine

increase for repeat offenders, while the positive selection of repeat offenders

dictates that the optimal fine for repeat offenders keeps the cutoff constant. In

addition, we have illustrated the relations to dynamic monopoly pricing and

considered various extensions, including heterogenous discount factors and

changes in the economic environment.

Our analysis suggests various avenues for future research. First, one could

study how commitment by individuals affects the scope for escalating pricing

schemes. Second, one might examine how competition among sellers affects

the scope for escalating pricing schemes. Third, it would be interesting to pro-

vide systematic empirical evidence on escalating prices. We hope to address

these issue in future research.

references 27

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2

GEOGRAPH IC MARKET

DEF IN IT ION IN SWISS

GROCERY RETA I L ING : A

NON-PARAMETR IC

APPROACH

abstract

This paper develops a non-parametric approach to empirically determine

geographic market size. I provide estimates of local business-stealing effects

across distance by studying the impact of store entry on competitors in an

increasing range to the site of entry. Entropy balancing is employed to control

for systematic differences across local markets. I estimate that markets for

Swiss grocery retailing stores are highly localized in a tight four kilometer

radius. I further document evidence that the impact weakens with increasing

distance and that smaller retailers compete in a more narrow market of only

two kilometers in size.

2.1 introduction

Antitrust law in numerous jurisdictions, including the EU and the US, re-

quires competition authorities to define the relevant market before proceeding

to analyse the case. No matter what is the firm conduct that is to be investi-

gated, market definition is generally considered to be “central to reasonable-

ness analysis” (Baker and Bresnahan 2008, p. 1). The European Commission

for example provided its first notice on merger regulation explicitly on the

issue of market definition (The European Commission 1997), while in the US,

31

32 market size and entry

the 2010 Horizontal Merger Guidelines continue to emphasize the important

role of market definition (Federal Trade Commission and U.S. Department

of Justice 2010). Arguably, “the outcome of more cases has surely turned on

market definition than on any other substantive issue” (Baker 2007, p. 1)

In practice however, empirically determining the relevant market for analy-

sis is challenging and a variety of different methods have been used to delin-

eate markets in antitrust investigations. Some of the more ad-hoc approaches

have been strongly criticized (Katz and Shapiro 2003; Danger and Frech 2001;

Capps et al. 2002) and may compare unfavourably to more structural, empir-

ical antitrust market definitions (Gaynor et al. 2013). But regardless of the

method of choice, the focus of the analysis lies on determining demand sub-

stitution of consumers (Baker and Bresnahan 2008).

This paper develops a different and non-parametric approach to empirically

estimate geographic markets. I examine the business-stealing effect of store

entry and the extent of local geographic markets in the grocery retail industry.

Instead of studying the choices of entering firms, I contrast existing retailers

that experienced entry to those that did not. To isolate the effect, I control for

crucial elements of consumer demand and store competition by exploiting the

unique spatial detail of my dataset covering the entire universe of Swiss retail-

ers and resident population geocoded to their exact location with a precision

of one square meter. This allows me to estimate the causal effect of entry on

the competitive outcome of existing stores that is due to demand substitution

by consumers. Studying the effect across an increasing range of distance to

the site of entry then allows inferring the extent of the geographic market.

Exploiting the competitive impact of store entry to study geographic mar-

ket size has been done before in some antitrust investigations (for example by

the Bundeskartellamt in Germany on the merger of the supermarket chains

Edeka and Tengelmann (Bundeskartellamt 2015)). Similarly, the study of en-

try effects and their propagation across distance has been of interest to pre-

vious researchers (for example on Wal-Mart stores in the US (Ellickson and

Grieco 2013)). Compared to previous approaches, the method developed here

allows for entirely non-parametric, causal estimates of market size which do

not require or presuppose assumptions on market structure or consumer de-

mand that in turn may be relevant for subsequent analysis. In particular, I

2.1 introduction 33

explicitly deal with the challenge of estimating business-stealing effects of in-

dividual entry in the presence of interdependence of observations due to store

competition.

The approach is made possible by the richness and degree of spatial detail

available to me in the application on Swiss grocery retailing. The majority

of work in the literature on grocery retail competition has made use of infor-

mation only available on an administrative level, such as municipalities, and

has been forced to define local markets based on this aggregate level (Aguir-

regabiria and Suzuki 2016). In contrast, my data contains both the individual

retail stores and the individual residents of Switzerland and each of their pre-

cise locations, allowing me to consider the unique characteristics of each store

location.9

I then compare the change in the outcome of treated stores (grocery re-

tailers that experienced entry within a given distance) to the corresponding

change of control stores (grocery retailers that did not experience such en-

try). In order to ensure that the estimated effect is due to the entrant under

consideration, I exclude all retailers that experienced more than one entry

within a radius of 10 kilometers. Because it turns out to be difficult to find

control observations that are sufficiently similar to treated ones, I employ the

recently developed method of ‘entropy balancing’ (Hainmueller 2012).10 En-

tropy balancing constructs weights for the control group so that the weighted

average becomes as similar as possible to the treatment group of stores that

experienced entry.

I find sizeable business-stealing effects due to entry within a highly local-

ized four kilometers radius (measured in routing distance) around an entrant.

The estimates also show a more pronounced impact of entry by a competing

store within the first two kilometers, suggesting that the degree of competi-

tion varies by distance within a local market. I further decompose the effect

of entry and find strong evidence that the extent of a local market is consid-

9 Additionally, I make use of the precise locations of Swiss customs offices and border poststo proxy for competition by stores located in neighboring countries across the border andcalculate all distances as routing distances to account for infrastructure and geography.

10 Entropy balancing has become increasingly popular and already been applied to a variety ofsettings, such as online hiring markets (Stanton and Thomas 2016), subsidized employment(Hetschko et al. 2016), syndicated loans (Amiram et al. 2017), or social capital (Satyanath et al.2017).


erably smaller for small grocery retail stores compared to large ones and is

limited to the first two kilometers only. In addition, the estimates suggest that

small stores are less able to react to increased competition due to entry and

in turn are more likely to exit the market.

This paper contributes to two strands of literature. First, I contribute to

the empirical determination of geographic markets. The standard conceptual

frameworks to define the relevant market in antitrust investigations are the

hypothetical monopolist test (HMT) or the test for a small but significant

non-transitory increase in price (SSNIP).11 In either case, the test iteratively

examines the hypothesis that a firm in a successively expanding product or

geographic market could profitably impose a price increase. If sufficiently

many consumers in response decide to switch to an alternative product or

store, the price rise is unprofitable for the firm and it lacks the necessary

market power. The relevant market is then expanded iteratively until the price

rise becomes profitable. Similarly, the method employed here considers the

competitive outcome of retail stores that are (potentially) impacted by entry in

successively greater distances from the entrant. I contribute a reduced-form

empirical approach that refrains from any structural assumptions and is, to

the best of my knowledge, novel to the literature.

Second, I add to the empirical study of market entry and spatial compe-

tition in the grocery retail industry. Previous research has highlighted the

overall impact of retail chains (in particular Wal-Mart) and their stores on

competitors, consumer welfare or the labour market, among other issues (e.g.

Basker 2007; Jia 2008; Ellickson et al. 2013; Holmes 2011; Neumark et al. 2008;

Matsa 2011; Nishida 2014). The focus of this paper is on identifying the local

effects of store entry and so the econometric approach chosen intentionally

avoids any structural modelling framework of retail chain interaction. My

approach can be viewed as an early step in the analysis of retail chains. The

results of such a non-parametric estimation can be used to directly inform

the correct specification of local markets and the choice set of firms in a sub-

sequent structural framework. My analysis contributes to the literature by

11 For a comprehensive treatment of the tests and applications in EU antitrust investigationssee Motta (2004). Coate and Fischer (2008) in turn provide a detailed study of the applica-tion and prevalence of the tests in 116 market definition decisions by the US Federal TradeCommission.

2.2 data 35

providing evidence on the extent of the geographic local market in this indus-

try and the heterogeneity of business-stealing effects within a local market.

The remainder of this paper is structured as follows. Section 2.2 describes

the database and discusses some descriptive statistics. Section 2.3 sets out

the econometric approach, detailing the estimator and identification, as well

as describing the final dataset in more detail. Section 2.4 presents the esti-

mation results, and Section 2.5 provides some robustness checks. Section 2.6

concludes.

2.2 data

My analysis is based on two main data sources. The first is the Swiss Busi-

ness Census (STATENT), which covers the entire universe of plants in the

manufacturing and services sector registered in Switzerland. The census is

collected on a yearly basis since 2011 by the Swiss Federal Statistical Office

and participation is mandatory for firms. It provides detailed information

on each plant including firm ownership, industry classification, and employ-

ment numbers, as well as each plants exact geographic location precise to one

square meter. However, as is common with census-type data, the STATENT

does not provide information on prices, quantities, or costs of stores. In line

with the existing literature on the grocery retail industry, I focus on the im-

pact of entry on store employment instead. The data is available to me for the

years 2011-2013. The second source is the Swiss Population and Household

Census (STATPOP) for the years 2011-2014, which depicts all persons with

permanent and temporary residence in Switzerland annually since 2010. For

each individual the census includes information such as age, sex, nationality

or marital status, and also the precise geocoordinates for a persons residence

with a precision of one square meter. The STATPOP is also collected by the

Swiss Federal Statistical Office.

I complement this wealth of information with an additional data source: the

locations of all Swiss border posts and customs offices provided to me by the

Swiss Customs Department. Switzerland is a small, landlocked country with

a particularly high price level relative to its neighbours Germany, France, Italy,


and Austria. Consequently, Swiss citizens regularly cross the border in order

to shop at significantly lower prices abroad. For example, the Swiss Federal

Customs Administration reported revenues of 48.32 billion CHF in 2015 that

was due to Swiss citizens shopping tourism (Eidgenössische Zollverwaltung

2016).12 The location of customs offices allows me to proxy for international

competition by foreign stores that I am unable to observe directly in the Swiss

data.

The resulting dataset is unique in its spatial detail, because it covers both

plant placement and the spatial distribution of consumers at a very fine level.

For the remainder of the paper, I focus on plants and firms in the grocery

retail industry exclusively.

Table 2.1 shows some first, basic summary statistics for the retail store

dataset, while Table 2.8 (in the Appendix) shows some comprehensive sum-

mary statistics for the population dataset. The Swiss grocery retail landscape

consists of around 5,000 stores, or approximately one store per 1,600 inhab-

itants. There are over 2,000 firms operating the stores and both the overall

number of stores and firms is decreasing during the time period studied. The

data also suggests that the market is becoming more concentrated with fewer

firms relative to stores over time and the mean number of stores per firm in-

creasing each year. In addition, Table 2.1 shows that entering stores have a

significantly smaller average size than established retail stores as measured

by both full-time equivalent (FTE) and total employment. This indicates that

store size may be important to understand the success of a retailer, or its reac-

tion to experiencing entry. I make use of the industry code classification pro-

vided by the Swiss Federal Office of Statistics, which classifies retailing stores

by sales area measured in square meters (see Table 2.9 in the Appendix). As it

turns out, the variation in size of retailing stores measured both by sales area

or employment numbers is very large.

In particular, looking at both the absolute employment numbers in 2011

of stores of varying sizes, as well as their yearly growth from 2011-2012, in-

dicates two distinct groups of retailing stores: i) smaller supermarkets and

mom-and-pop stores with NOGA codes of 471105, 471104 and 471103, and ii)

12 Buying abroad also allows Swiss shoppers to obtain a refund on the foreign VAT and pay the(generally lower) Swiss VAT rate instead. To do so they must show their wares at the localcustoms office, where the tax income is collected.

2.2 data 37

Table 2.1: Retail data summary table

2011 Entry 11-12 2012 Entry 12-13 2013

# Firms 2,242 286 2,147 228 2,035# Stores 5,105 373 5,036 298 4,894Mean # Stores of Firms 196.3 396 205.6 383.6 214.7Mean Employment

Full-time Equivalent 10.65 3.85 10.27 4.00 10.22Total 13.93 5.48 13.7 5.44 13.67

Notes: The table documents the total number of firms, total number of stores, mean number of stores per firm, andmean employment number at a store (in full-time equivalent and total, respectively) yearly from 2011-2013 for allgrocery retailers, as well as separately for entrants in 2011-2012 and 2012-2013.

large supermarkets and supercenters with NOGA codes 471102 and 471101

(see Table 2.2). The first group is characterized by significantly lower employ-

ment numbers and sales area size, relative to the second, as well as consis-

tently negative yearly growth rates. The bigger stores instead appear to be

expanding and growing. I will henceforth refer to these two groups as small

and large stores, respectively.

Table 2.2: Retailers by store classification

FTE Empl. Total Empl. Fluctuation

Store Classification N Mean Growth Mean Growth Exit Entry

Supercenters 76 95.00 0.02 116.50 0.02 0% 0%Large Supermarkets 356 43.08 0.02 55.00 0.01 3% 1%Small Supermarkets 1302 12.46 -0.05 17.00 -0.06 7% 6%Large Shops 2315 4.12 -0.06 6.00 -0.05 5% 6%Small Shops 1056 0.97 -0.10 1.00 -0.11 20% 14%Notes: The table documents per category of store (classified according to the BfS industry classification index, see

Table 2.9 in the Appendix) in 2011 the total number of stores, mean full-time equivalent (FTE) and total employment,growth in FTE and total employment from 2011 to 2012, as well as the percentage of stores in 2011 exiting and per-centage (in proportion of the 2011 total number of stores) of stores entering within the next year.

In addition, the number of small grocery retail stores is significantly higher

than that of the large supermarkets. It is important to note that because of

the relatively low number of large stores, I observe very little entry and exit

for this group. Instead, it is predominantly the small stores that experience

a high degree of fluctuation with a sizeable number of stores entering and

exiting each year. This finding is in line with a large body of classic research

on firm entry and industry dynamics which demonstrates that the size of


an entrant correlates negatively with the likelihood of survival (Sutton 1997;

Geroski 1995).

Indeed, the smallest category of stores, comprised of tiny retailers with on

average only one full-time employee, experience by far the greatest fluctua-

tion: around 20% of existing stores in 2011 exit over the course of the year

and are replaced by new entrants in numbers that constitute 14% of the total

number of stores in the previous year. This also shows the main source of the

overall decrease in the number of stores documented earlier. However, this

does not appear to be a clear pattern across store size, but rather a specific

attribute of these smallest stores. For example, the second largest store types

experience more exit than entry, while the second smallest show the reverse.

In addition, the net fluctuation experienced within the four larger categories

of stores is small, with the entry and exit rates showing a clear positive corre-

lation. This pattern is well documented in the literature (Geroski 1995). For

small shops though, the difference between the entry and exit rate is more

pronounced.

Table 2.3: Store growth rate and entry by population of area surrounding store loca-tions.

<25th percentile >75th percentile

N Growth Entry N Growth Entry

Small 1227 -0.076 25% 1138 -0.062 33%(0.47) (0.41)

Large 37 0.01 0% 126 0.010 60%(0.05) (0.082)

Notes: Standard deviations in parentheses. N is the number of stores open in 2011. Growth is measuredin full-time equivalent employment 2011-2012, while entry is the percentage of entrants in one of the groups.Percentiles shown are of the total population in a 5km radius around the store location.

Finally, I document whether the population in the local area of a store af-

fects the employment growth rates of small and large retailers differently. Ta-

ble 2.3 shows the average growth rate of full-time equivalent employment

from 2011-2012 for large and small stores respectively by the first and third

quartile of the population density at their location. Small stores which are

located in less densely populated areas fare worse relative to small stores at

more populated locations. In either case, on average small stores reduce their

employment hours, but the degree to which stores shrink is more pronounced

2.3 empirical approach 39

in less populated areas. On the other hand, large stores tend to neither expand

nor shrink when located in locations with very little population, but expand

and grow in densely populated areas. In addition, small stores are spread

relatively evenly across the population distribution, while large stores are pre-

dominantly located in the densely populated areas. Table 2.3 also shows the

proportion of entrants of the small or large group respectively that choose

to locate where many or few people live. It is evident that firms place large

stores predominantly in densely populated areas, while small stores enter

more evenly in both highly and very little populated locations.

Taken together, this indicates that there is sizable heterogeneity across store

types, and that small stores appear to ‘play a different game’ than large stores.

It appears likely that the demand that stores face differs systematically by

store type. The results of the estimations bear this out by clearly indicating

that the local market for a small store is smaller than for a large store and that

small stores are more strongly adversely affected by competition with other

small stores.

2.3 empirical approach

In order to estimate the local effect from entry non-parametrically while

allowing it to vary by distance, I make use of standard matching and propen-

sity score techniques. I compare the outcome of retail stores experiencing

entry within a particular ’bandwidth‘ of distance from the store (the treat-

ment group), to retailers that do not experience such entry within the given

bandwidth (the control group). I consider bandwidths of a range of two kilo-

meters, so that a retail store may experience entry within 0-2 kilometers, 2-4

kilometers and so on. The maximum range I consider is ten kilometers.13

The estimated effect is simply the average mean difference of the outcome

between the two groups.

To account for the fact that assignment into the treatment group may be

non-random (as is clearly the case here), I employ entropy balancing (EB) to

13 I increase this range in a robustness check in Section 2.5 and find that the results continue tohold.


preprocess the data and obtain a causal estimate of the effect. EB is part of

the recent development of synthetic control groups, in which treated units

are not compared to single control units or simple averages of controls, but to

a weighted average instead (Athey and Imbens 2017). EB generates individ-

ual weights for all observations of the control group, such that the statistical

moments of the given sets of observable characteristics, and hence ideally

the propensity to be treated, equalize between the treatment and the control

group (Hainmueller 2012). This avoids the difficulty of the usual propensity

score modeling approach of correctly specifying the propensity score model

in order to obtain satisfactory balance between the two groups. Instead, EB

ensures that the covariate distributions are balanced by construction. Since

balancing the covariate distributions using a propensity score model turns

out to be quite difficult in the setting I consider, EB becomes particularly use-

ful.

Specifically, EB employs a loss function that minimizes the entropy distance

of control group individuals’ base weights, where each observation is given

the same base weight, and EB weights upon the condition that the set of

control group covariate moments are as similar as possible to the treatment

group moments. Zhao and Percival (2017) show that this approach can be

viewed as a propensity score weighting method, where the solution to the

EB maximization problem is the logistic regression model with a different

loss function than is used in maximum likelihood estimations. In fact, EB

implicitly also fits a linear outcome regression model and is ‘doubly robust’

(Zhao and Percival 2017): it is sufficient that only one of the two models

(logistic propensity score model and outcome regression model) is correctly

specified for EB to provide a consistent estimate of the average treatment

effect for the treated (ATT).

It is important to note that in order for the results above to hold and the

estimate to be the causal effect of entry, the following standard assumptions

A1 and A2 must be imposed (Zhao and Percival 2017). In addition, to ensure

that the estimated effect is an individual level treatment effect devoid of any

interference (such as general equilibrium or spillover effects), assumption A3


is needed.14 These are well-established assumptions in the literature since the

seminal work of Rosenbaum and Rubin (1983).

A1. (unconfoundedness). {Y(0), Y(1)}⊥X|ZA2. (overlap). 0 < π(Zi) < 1

A3. (stable unit treatment value). Yi = Xi · Yi(1) + (1 − Xi) · Yi(0)

where Xi ∈ {0, 1} is the treatment of unit i, Yi is the outcome of unit i,

π(Zi) = Pr(X = 1|Z) is the estimated propensity score and Z is the vector of

confounding variables.

The assumption of unconfoundedness (A1) states that whether a retail store

experiences entry in the bandwidth considered is independent of the out-

comes, after conditioning on the confounding variables. Put differently, all

variables that affect both the treatment of observed entry and the outcome

of employment adjustments are measured. This is a fairly strong assump-

tion, however the breadth and fine detail of my dataset allows me to control

much more precisely for confounding factors than in previous studies in the

literature. It should also be noted that A1 is equivalent to the assumption of

exogeneity in the error term used in regressions or structural models and is

simply made explicit in propensity score or matching analysis. I construct my

dataset in order to satisfy A1 as follows.

First, I consider the distances to rival stores from the location of an existing

retail store as possible confounding variables. It seems straightforward to as-

sume that retailers take into account competing stores located in their vicinity.

However, without making any ad-hoc assumptions about the size and extent

of local markets, it is unclear across what distance the rival stores need to be

considered in the analysis, so I attempt to be as generous as possible. I group

rival stores in increasing bandwidths of distance from the retail store under

consideration. To limit the number of variables in the estimation without los-

ing too much information, I group competing stores in bandwidths of one

kilometer.

Second, due to the nature of Swiss geography, controlling for infrastructure

and geography is crucial. A location in Swiss alpine towns may have little

14 For a comprehensive discussion on interference effects in causal analysis see e.g. Huber andSteinmayr (2017).


competition from rival stores, but also has difficult access and high trans-

portation cost. I calculate all distances between competing stores as routing

distances, rather than straight or geodesic, using the Open Source Routing

Machine (OSRM). The OSRM makes use of the OpenStreetMap Project to pro-

vide routing distances in the same manner as e.g. Google Maps. It has the

advantage of being able to run locally, rather than via a server and hence there

are only computational limitations to the number of distances that can be con-

sidered.15 In addition, it ensures that every result is directly reproducible.16

Third, I attempt to control for competition from stores located across the

border from Switzerland. As discussed in section 2.2, due to the higher

price level in Switzerland relative to the nations bordering Switzerland, cross-

border shopping of Swiss consumers is commonplace. These foreign stores

however are by definition not part of my retail dataset. I was provided with

a list of the locations of all Swiss border posts and customs offices by the

Swiss Customs Department and consider the nearest routing distance of a

grocery retail store to any one of the border posts as a confounding factor.

Since the list includes customs offices located inside Switzerland (for example

at the Zurich airport) and many border posts are located very close to each

other, I manually narrow down the list from 152 locations to only 54. These

are border posts at (or in the immediate vicinity of) actual border crossings

and should provide a very close approximation. In addition, I also include a

dummy variable for the particular neighbouring country of each border post

(Germany, France, Austria, Italy and Liechtenstein).

Finally, I consider the resident population at any location as a confound-

ing factor. It seems likely that the number of consumers in close proximity

is the most important driver of demand for grocery retail goods. Previous

work has been forced to use e.g. the population per municipality as a market-

level, control variable. Instead, as before I consider bandwidths around each

15 In the case of GoogleMaps, there are strict limitations on the free use of the GoogleMaps APIfor calculations, making it very expensive for use here.

16 Since both GoogleMaps and OpenStreetMap are constantly updated, running the same dis-tance calculations at different points in time will lead to (slightly) varying results. I run allcalculations locally with the map of Switzerland as it existed on 05.10.2016. Unfortunately,there is no way to consider changes to infrastructure over time, since changes in the mapover time may simply represent users uploading details for the first time that have in realityexisted for much longer, rather than actual infrastructure changes.


location and aggregate the number of residents in each bandwidth. I include

bandwidths of one kilometer width up to a ten kilometer distance from the lo-

cation, in addition to bandwidths of 100 meter width for the first 300 meter.17

Lastly, I also include a dummy variable for the language area of Switzerland

that the store is located in (German, French, Italian, or Romansh).

The assumption of overlap (A2) requires that each store in the dataset has

a non-zero probability of experiencing entry. Jointly with A1, these two as-

sumptions ensure that treatment assignment is ‘strongly ignorable’, that is,

analyses on the correspondingly matched data or weighted original data will

yield an unbiased estimate of the treatment effect.

The assumption of the stable unit treatment value (SUTVA, A3) in turn

states that the outcome of a particular retailer Yi is assumed to only be af-

fected by the treatment assignment of that retailer, but not of any other store,

or Yi(di). In essence, the SUTVA explicitly rules out any general equilibrium,

spill-over, or interaction effects that relate to the treatment assignments of in-

dividual observations. This may be a problematic assumption when applying

it to a setting of competing retail stores. For example, there may be a business-

stealing effect due to entry for one particular store that causes an indirect (or

spillover) effect transmitted via competition to a second store. Then, the po-

tential outcome of that second store would no longer be independent of the

treatment assignment of the first. This implies that there are two issues that

need to be resolved: i) if such interference effects exist, entry may have both a

direct and indirect effect on a treated store, ii) with interference, the treatment

assignment of entry may have a non-zero impact on the potential outcome of

the untreated as well.18 Finally, I also need to deal with the fact that the out-

come of a retailer may be affected by multiple entrants, so that Xi ∈ 0, 1, 2, ...,

rather than the treatment being binary.

17 I also have access to detailed municipal-level statistics on population, population density andtaxable income. When correlating employment outcomes on the municipal-level with thesevariables, it turns out that the population variables captures almost all variation that can beexplained using these factors and other information such as total or average taxable incomedoes not add much explanatory power.

18 The mean difference in the observed outcome would then estimate the difference between thetreatment effect for the treated (composed of the direct and indirect effect) and the treatmenteffect (i.e. spillover effect) for the untreated.


To solve these issues, I take two steps. First, I follow Hong and Rauden-

bush (2013) and assume that a store has a limited set of influence, i.e. it only

competes within its local market. Specifically, each store i has a set of influ-

ence that includes all those competing stores that might affect the outcome of

store i. They are denoted by the set of Di, which contains all stores within

a distance x from store i. This is formalized in assumption A4. It allows me

to limit the (potential) competitors that need to be controlled for in the esti-

mation and avoids having to consider possible entry effects that seem highly

unrealistic (e.g. entry in a different part of the country affecting a stores suc-

cess). Additionally, I introduce assumption A5 which states in its weak form

(a) that for a given local market and store there are no interferences between

different local markets and that local markets are intact, such that stores do

not react by migrating from one local market to another in response to en-

try. In its strong form (b) it essentially reintroduces the SUTVA in the context

of local markets and imposes in addition to (a) that there are no spillovers

between stores within one local market that are due to entry.

A4. (local market). Yi only depends on competitors in Di, where Di is the set

of all stores −i, where the distance between i and −i is smaller or equal

to x.

A5 (a). (weak spillovers). Second-order spillovers across local markets are neg-

ligible and local markets are intact.

A5 (b). (strong spillovers). In addition to (a), second-order spillovers between

firms that share a common market (local markets intersect) are negligi-

ble, so that Yi only depends on the treatment assignment of i.

Consider the implications of assumptions A4 and A5 in turn. Figure 2.1

illustrates the implication of A4. The local market assumption states that each

store 1, 2, 3 has a limited set of influence (the local market) that is indicated by

the circle. It only competes with other stores within this range. The effect of

one store on a competing store is indicated by the arrows. For example, store

1 competes with store 2 only, which in turn competes with both store 1 and

store 3.

A5 in its weak form (a) in turn states that the effect of the treatment assign-

ment of store 3 on store 1 via the effect on store 2 is negligible. Similarly, it


1 2 3

Figure 2.1: Interactions between three stores

Notes: The figure shows the implication of assumption A4 for the case of three firms. The arrows represent theeffect of one competitor on another.

implies that the treatment assignment of store 2, if the entry occurs outside of

the local market of store 1 has only a negligible effect on store 1. In its strong

form (b), assumption A5 additionally imposes that when both store 1 and 2

are affected by an entrant, the effect of the treatment assignment of store 2 on

store 1 is negligible and hence the outcome of store 1 only depends on the

treatment assignment of store 1.

The implication of this assumption can be seen in Figure 2.2. Panel (a)

shows the case of entry occurring (X) within the local market of one of the

stores only, or outside the common market of the two stores. Here, A5 (a)

implies that store 2 is affected by entry, but store 1 is not. Panel (b) in turn

shows the case of a retailer entering (X) within the local market of both store

1 and 2. A5 (b) implies that the entrant may have a direct effect on both

existing stores, but that there is no indirect effect from entry via a competing

store, say from 2 to 1. Note that a violation of the strong form of A5 in the

sense of panel (b) would still allow me to consistently estimate the causal

effect of entry, however the estimate would reflect both the direct and indirect

effect. It is unclear how these two could be disentangled. If instead the weak

form of A5 is violated as depicted in panel (a), the resulting estimates would

be biased. I examine whether the assumption A5 (a) holds in the robustness

checks in section 2.5 and find no evidence of a violation of the weak form of

A5.

The second step I take to resolve the issue and to isolate the effect of entry,

is by only comparing retail stores that experienced one entry within one of

the bandwidths to retailers that did not experience any entry within the max-

imum ten kilometers radius. Hence, I implicitly assume that the local market


1 2

X

(a) Indirect effect outsidecommon market

1 2

X

(b) Indirect effect withincommon market

Figure 2.2: Indirect effects

Notes: The figure shows the implication of assumption A5. Panel (a) shows the indirect effect that may arise whenentry occurs outside of the local market boundary for store 1. Panel (b) shows the indirect effect that may arise whenentry occurs within a common market of stores 1 and 2 (i.e. within both of their respective local markets).

extends over no more than ten kilometers, or x = 10 kilometers. Previous

work for example on Wal-Mart has found that the impact of a store entry is

localized to the first four miles around the entry site (Ellickson and Grieco

2013), indicating that a restriction to ten kilometers is not overly strict. In the

robustness checks I increase this radius to 12 kilometers and find the results

continue to hold. If assumptions A1-A2 and A4-A5(a) hold, the estimates

show the causal effect of store entry on existing retail stores. If A5(b) holds

as well, the estimates show the causal, direct effect of entry. The estimated ef-

fect is then the average difference of the control observations, which receive a

weight according to the EB estimation and the treatment observations, which

receive a weight of one.

Table 2.4 shows some key variables of the dataset and their means for three

different groups: i) the full dataset, ii) the control group (retailers that did not

experience any entry within 10 kilometers), and iii) the first treatment group

(retailers that experienced one entry within 2 kilometers but no further entry

within 10 kilometers). Retailers in the control group appear to be located in

areas with a smaller population in their vicinity, relative to retailers in the first

treatment group. The difference in the first kilometers is particulary visible.

Considering the treatment group concerns entry within the first 2 kilometers,

this seems unsurprising.

In addition, retailers in the control group have less competition from other

existing stores in their neighbourhood and tend to be further away from the


Table 2.4: Dataset excerpt

Statistic All Control Treatment 1

Total rivals per one kilometer0-1 kilometer 3.84 2.23 4.651-2 kilometer 5.33 0.90 4.172-3 kilometer 7.13 1.07 2.323-4 kilometer 7.53 1.22 1.554-5 kilometer 7.24 1.36 1.26

Total population per one kilometer0-1 kilometer 3,203.07 948.43 2,823.341-2 kilometer 1,451.27 236.22 514.842-3 kilometer 888.64 193.12 222.323-4 kilometer 737.95 149.73 151.594-5 kilometer 590.86 160.62 87.25

Mean border distance in kilometers 40.38 48.86 40.15Mean FTE employment 10.85 7.02 12.72Mean Total employment 14.43 9.84 16.87Notes: The table shows for the three groups: all stores, the control group (stores that did not experience any entry

within ten kilometers), and treatment group 1 (stores that experienced one entry within two kilometers, but no otherentry), the total number of competing grocery retail stores and total resident population in one kilometer bandsaround a store, the mean border distance in kilometers, as well as the mean full-time equivalent (FTE) and totalemployment of stores.


border. A likely explanation is that with a larger share of the population

in Switzerland living near the border, rather than in the mountainous geo-

graphical center of the country, retailers in less populated areas correlate with

retailers more distant from the border. Finally, stores that experienced entry

are significantly larger than those that did not, as measured by employment

numbers. The full dataset comprised of all 34 confounding variables shown

separately for each treatment as well as the control group can be found in

Table 2.10 in the appendix.

Figure 2.3: Balancing of EB and PS for entry within two kilometers

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Pop_8kmPop_100m

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Language_RomNcomp_5km

Pop_9kmPop_4km

Language_ItaCountry_Ger

Pop_10kmPop_3km

Language_FreNcomp_10km

Pop_200mCountry_Fra

Pop_300mNcomp_7km

Pop_2kmNcomp_4kmNcomp_6kmNcomp_8kmNcomp_9kmNcomp_3km

Ncomp_500mNcomp_500m−1km

Pop_1kmNcomp_2km

−0.5 0.0 0.5 1.0Mean Differences

Sample

●

Unadjusted

Adjusted Entropy

Adjusted Logit

Notes: The figure shows the mean differences of all confounders for treatment group 1 (one entrant within twokilometers, but no other entry) relative to the control group (no entry within ten kilometers) for three samples: un-adjusted, adjusted entropy (where the control group is weighted using the entropy balancing weights), and adjustedlogit (where the control group is weighted using the propensity score (logit) weights).

Lastly, to demonstrate the usefulness of EB in this setting, Figure 2.3 shows

how well the covariates are balanced for the first estimation (treatment group

1). It depicts the standardized mean difference between the treatment and

control group of each covariate in three samples: (i) the raw, unadjusted data,

(ii) the weighted data using entropy balancing (entropy), and (iii) the weighted

data using a standard logistic regression (without interaction terms) for the

2.4 results 49

propensity score (logit). It is immediately visible that weighting using the

propensity score model does not work well. Only around half of the covariates

can be considered balanced (i.e. within the usually considered threshold of a

standardized mean difference below 0.1 indicated by the dashed lines) and

for some of them, the balancing is in fact better in the unadjusted sample.

EB instead by design balances all covariates almost perfectly. The balancing

as measured by the standardized mean difference is documented for each

estimation using EB separately in the Appendix in figures 2.7 to 2.11, and

in detail in tables 2.11 and 2.12. The next section reports and discusses the

results of the main estimations.

2.4 results

Table 2.5 reports the main estimates of the effect of retail store entry in 2011-

2012 on the growth rate of employment of existing retail stores in 2012-2013.

The second and third columns show the parameters of the impact of entry on

all rival retail stores regardless of store size, measured using full-time equiv-

alent (FTE) and total employment, respectively. I find strong and consistent

evidence for a negative effect on changes in both full-time equivalent and to-

tal employment in the first two bandwidths of 0-2 and 2-4 kilometers. These

results suggest that grocery retail stores in Switzerland compete in a highly lo-

calized radius of up to four kilometers, but not beyond. As one might expect,

the effect in the first bandwidth is significantly stronger than in the second for

FTE employment, indicating that business-stealing effects are heterogeneous

within a local market and decrease with increasing distance. The growth rate

of total employment in turn does not show this pattern, however the statisti-

cal significance decreases across distance. In addition, the effect on full-time

equivalent employment is much stronger. In the first bandwidth, stores react

by reducing their FTE employment hours by 12%, while it is much subdued

in the second and around 7%. This seems to indicate that retail stores tend to

focus on adjusting their employment numbers short-term in response to entry

by lowering the hours their employees work, rather than letting them go.


Table 2.5: Impact of store entry on employment growth rate

All stores Small stores

Distance to entry FTE Total FTE Total

0-2 kilometers −0.122** −0.065** −0.088*** −0.098**(0.058) (0.032) (0.032) (0.031)

2-4 kilometers −0.071** −0.065* −0.129 −0.071*(0.026) (0.038) (0.038) (0.042)

4-6 kilometers 0.011 0.003 −0.011 0.005(0.019) (0.010) (0.010) (0.031)

6-8 kilometers −0.021 0.026 0.026 0.029(0.088) (0.104) (0.104) (0.075)

8-10 kilometers 0.102 0.129 0.110 0.097(0.106) (0.123) (0.123) (0.063)

Notes: *** indicates significance at the 1% significance level, ** at the 5% level, * at the 10% level.Heteroscedasticity-robust standard errors in brackets.

The growth rate takes into account the absolute size of a retail establish-

ment as measured in employment, however as discussed earlier in section 2.2,

the growth rates between small and large retail stores differ significantly. In

addition, the location choices of large and small retail stores appeared to not

be identical. In order to examine the differential effects across store hetero-

geneity, I estimate the effects separately by the store types. Since small stores

consistenly make up over 90% of retail stores across the years and the number

of entries observed by large stores is particularly small, I focus on examining

small stores.

The fourth and fifth column of Table 2.5 report the estimates of entry by

small stores in 2011-2012 on the employment growth rate of small retailers

only in 2012-2013. I find a business-stealing effect of a reduced magnitude for

the growth rate in full-time equivalent and of greater magnitude for total em-

ployment within the first bandwidth, relative to the main results. I do not find

a statistically significant effect in the second bandwidth for FTE employment,

but a reduced and less statistically significant effect for total employment. It

appears that smaller stores react more on the extensive margin of employment

adjustments to entry by similar competitors than on the intensive. In addition

I only find an effect in the 2-4 kilometer range on total employment growth

at the 10% significance level and none for FTE employment, indicating that

2.4 results 51

−0.2

0

0.2

Distance in km

(a) All Stores (FTE)

−0.2

0

0.2

Distance in km

(b) All Stores (Total)

−0.2

0

0.2

Distance in km

(c) Small Stores (FTE)

−0.2

0

0.2

Distance in km

(d) Small Stores (Total)

Figure 2.4: Estimated effects of entry

Notes: The figure shows the point estimates and 90% confidence intervals for the estimation results documented inTable 2.5. Distance is measured from left to right in two kilometer bandwidths. The top panels show the effects forall stores, the bottom panels show the effects for small stores only. The left panels show the impact measured infull-time-equivalent (FTE) employment, the right panels show the impact in total employment.

the local market size varies by store size: small retailers compete within a

shorter distance with other small retailers, than large ones. A likely explana-

tion would be that customers are more willing to travel a longer distance for

sizable grocery stores, where a great amount of shopping can be done quickly,

compared to small grocery retailers.

The main results are illustrated in Figure 2.4. The four panels show the

value of the point estimate and the 90% confidence intervals across the in-

creasing distance from left to right. The top panels show the results for all

retailers, documented in columns two and three in Table 2.5, while the bottom

panels show the results for small retailers only, as documented in columns

four and five in Table 2.5. The panels all illustrate the same pattern: the


impact of store entry falls on competitors in the immediate vicinity and no

statistically significant effect can be observed beyond the four kilometer range.

The business-stealing effect from entry for all stores is more sizable within the

first bandwidth, relative to the second, while for small stores the effect is only

evident within the first bandwidth (for total employment it is marginally sta-

tistically significant at the 90% level).

The specifications so far have focused on the intensive margin of changes in

the number of employees or their work hours. Yet, the data shows that there

is a sizable fluctuation in retail store entry and exit, especially for small re-

tailers (see the discussion in section 2.2). I now turn to examining the impact

that store entry has on employment changes that are due to exit. I incorpo-

rate employment destruction that is due to stores exiting the market in the

growth rate measure. Columns two and three in Table 2.6 show the estimated

impact of retail store entry. I find that the effect of store entry is significantly

more pronounced and that the business-stealing effect is of up to twice the

magnitude compared to the previous estimates. It appears that the bigger

component of the observed decreases is due to contraction or reduced growth

of continuing firms, rather than employment destruction due to exit. This is

particularly visible in the FTE employment measure.

Table 2.6: Impact of store entry on employment growth, including employment de-struction due to exit.

All stores Small stores


0-2 kilometers −0.147*** −0.130*** −0.171** −0.155***(0.056) (0.049) (0.075) (0.065)

2-4 kilometers −0.121** −0.120** −0.187 −0.132(0.072) (0.061) (0.134) (0.081)

4-6 kilometers −0.099 −0.092 −0.094 −0.079(0.084) (0.081) (0.237) (0.103)

6-8 kilometers −0.042 −0.046 −0.049 −0.052(0.242) (0.255) (0.239) (0.256)

8-10 kilometers −0.162 −0.186 −0.174 −0.199(0.225) (0.285) (0.226) (0.286)

Notes: *** indicates significance at the 1% significance level, ** at the 5% level, * at the 10% level. Heteroscedasticity-robust standard errors in brackets.

2.4 results 53

In addition, I find more consistent evidence of the impact being centered in

the first two bandwidths, with the impact being greater in the first bandwidth.

As before, the impact appears to be greater on work hour reduction, rather

than in the number of employees. Taken together with the main estimates, the

results suggests very clearly that the local market in Switzerland is limited to

a radius of around four kilometers for a given retailer and that the degree of

competition decreases with distance. It appears that the greater the overlap of

the catchment area of two stores, the greater the extent to which they compete

and negatively impact each other.

Finally, I also provide estimates that include employment destruction from

exit for small retailers only in columns four and five of Table 2.6. As before,

the effect is greater than for all stores in the first bandwidth, but I find no

evidence of an impact of entry by a small retailer on another small retail

store beyond the range of 2 kilometers. The increased size of the effects also

closely mirrors the relative increase observed when estimating the impact for

all retailers.

The estimates overall suggest that the short-term business-stealing effect

from entry is significant and contained in a tight local market. A competing

store may be forced to reduce the work hours of their employees by up to 12%

and the total number of employees by up to 10% for a small retailer. However,

there exists considerable heterogeneity of the impact across both space and

retail store type. The impact on both the intensive margin of employment

adjustments and on the extensive margin of market exit falls more strongly

on small retailers than large ones. In addition, small stores appear to be less

able to react by lowering work hours for employees.

It should also be noted that the estimates do not account for job creation

due to the entry under consideration. A rough calculation suggests that the

change in aggregate, local employment due to job creation by the average

entrant relative to the job losses experienced at competing stores depends on

the measurement used. Given the average number of competing stores within

2 and within 2-4 kilometers distance of entry sites and the main estimates

provided in Table 2.5, the average full-time equivalent employment loss due

to business-stealing effects from entry is approximately 20% larger than the

job creation. However, the data also shows that the average total employment


of an entrant is much larger than the full-time equivalent. Indeed, the same

calculation in absolute terms (that is, for total employment) suggests more

jobs are created by entry than are lost at competing stores. The difference is

sizable: entrants create approximately 10% more jobs than they destroy in the

short-term at competing stores. One possible explanation might be that there

are setup costs in the size of the workforce required for opening or running

a new store. In the next section, I examine the robustness of the assumptions

introduced in section 2.3.

2.5 robustness checks

The estimator employed to study the impact of grocery retail store entry

provides causal estimates of the effect of entry on the outcome of a store given

assumptions A1-A2 and A4-A5 (a). Since it is generally impossible to test for

the strong ignorability condition stated in A1 and unclear how assumption

A5 (b) could be tested,19 I focus on examining whether assumptions A4 and

A5 (a) hold.

Assumption A4 may be violated if the local market area is larger than the

ten kilometers considered in the estimations. In columns two and three in

Table 2.7, I provide the same estimates as in the main results reported in

Table 2.5 for all stores, except with an increased maximum radius of twelve

kilometers. I find that the business-stealing effect is clearly visible as before

and the estimates confirm that the extent of the local market is limited to

the first four kilometers. In particular, the size and statistical significance of

the effect of entry on total employment are very similar when increasing the

distance by two kilometers, while the size of the impact on full-time equiva-

lent employment changes slightly and becomes smaller in the first range, but

larger in the second.

Next, I examine the robustness of assumption A5 (a). It is violated if there

is evidence of spillovers across the local market boundary of ten kilometers.

In order to determine if the assumption holds, I provide evidence of the size

19 The indirect effect from a competitor that is caused by an entrant within the common marketof the two firms would be indistinguishable from the direct effect of that same entry.

2.5 robustness checks 55

1 2 2

X

Figure 2.5: Robustness check for indirect effects

Notes: The figure illustrates the robustness check for spillovers across market boundaries for two separate band-widths of distance between store 1 and store 2. The farther bandwidth is shown in dashed lines. The indirect(spillover) effect by store entry on store 1 via competition with store 2 is indicated by arrows.

of entry effects that can only occur indirectly, given the local market size,

in increasing distance. Specifically, I estimate the effect of entry that occurs

just outside of the ten kilometer radius of a store, but that is within the ten

kilometer radius of a second store, which shares a common market with the

first. This scenario is illustrated in panel (a) of Figure 2.2.

I proceed to continually move the two retail stores away from each other,

while keeping the distance of the entrant to the competing, ‘spillover’ store

that may transmit the effect constant, so that as the distance between the

competitors increases, the distance between the entrant and spillover store

decreases. The approach is illustrated in Figure 2.5. The figure shows the

possible spillover effect from entry on store 1 transmitted through competi-

tion with store 2. The distance between store 1 and store 2 is successively

increased (illustrated in dashed lines), while entry continues to occur within

10-12 kilometers of distance to store 1. By moving the two stores away from

each other, I am able to check for the existence of spillover effects across the

whole spectrum of possible interference by distance. The distances between

stores are grouped as before in 2 kilometer bandwidths.

The estimated impact is reported in in columns four and five in Table 2.7. I

find no evidence of an indirect effect that is due to the impact of an entrant on

a given retail store for any of the different distances considered. The estimates

strongly suggest that there is no concern of a violation of assumption A5 (a).


Table 2.7: Estimates of the robustness checks

(1) (2)


0-2 kilometers −0.092*** −0.077*** −0.012 −0.016(0.040) (0.026) (0.244) (0.029)

2-4 kilometers −0.113** −0.059* 0.025 −0.040(0.056) (0.031) (0.249) (0.053)

4-6 kilometers 0.006 0.009 0.002 0.013(0.017) (0.063) (0.226) (0.218)

6-8 kilometers −0.027 −0.027 −0.034 −0.047(0.285) (0.264) (0.231) (0.205)

8-10 kilometers −0.110 −0.135 0.024 0.001(0.361) (0.487) (0.261) (0.217)

Notes: *** indicates significance at the 1% significance level, ** at the 5% level, * at the 10% level. Heteroscedasticity-robust standard errors in brackets. (1) reports the estimates of the impact of entry on all stores when extending themaximum range from ten kilometers to twelve. (2) reports the estimates of the indirect effect of entry.

2.6 conclusion

This paper exploits highly detailed spatial data of the grocery retail environ-

ment in Switzerland. The dataset constructed controls in a detailed manner

for important drivers of competition and demand in order to be able to ex-

amine the geographic size of local markets. I study the impact of store entry

on competitors using the entropy balancing estimator. The results show that

entry by a retail store does not negatively impact employment at grocery re-

tailers located more than four kilometers away from the entry site. Within this

range, I find consistent evidence of heterogeneity in entry effects and compe-

tition across both distance and store type. Overall, it appears that differen-

tiation of grocery retail stores by location or type softens competition in the

industry. Inside the narrower range of two kilometers, the business-stealing

effect of entry is significantly more pronounced. In the wider range of two

to four kilometers the effect is much subdued. Moreover, the negative impact

in this wider range is mainly driven by competition between larger supermar-

kets and supercenters. For smaller supermarkets and mom-and-pop stores in

turn the impact falls exclusively on the short range of zero to two kilometers,

as they appear to be unable to convince consumers to travel more than two

kilometers for their goods. The estimates suggest that entry by a new small

2.6 conclusion 57

competitor leads to a reduction in employment (or reduced positive growth)

of up to 10% of similarly sized competing retailers.

The results also indicate that this business-stealing effect forces different re-

actions on the intensive and extensive margin for large or small stores. I find

that the average store reacts to entry by reducing full-time equivalent employ-

ment more than total employment, but that this effect reverses for small stores.

Larger stores with more employees appear to be more able to adjust the work

hours of their workforce, rather than letting them go. Furthermore, while

on average the impact is driven by competitors shrinking their employment

numbers or reducing their positive growth, rather than firms responding by

exiting the market, this does not hold true for small retailers. Instead the

impact on the extensive margin is particularly pronounced for small stores,

which show a significant reaction of employment destruction due to exit.


2.7 appendix

Table 2.8: Population data summary table.

Statistic N Mean St. Dev.

Sex 8,174,154 1.506 0.500Marital Status 8,174,154 1.772 0.876Nationality (State) 8,174,154 8,135.986 131.229Reporting Municipality 8,174,154 2,930.933 2,249.550Type of Residence 8,174,154 1.018 0.140Origin Country ID (CH) 8,174,154 1,050.482 2,766.712Origin Country ID 8,174,154 917.419 2,609.824Population Type 8,174,154 1.044 0.276Age 8,174,154 40.880 22.635Nationality Category 8,174,154 1.234 0.423Residence Permit 8,174,154 -0.808 2.307Population Group 8,174,154 1.978 1.602Locality 8,174,154 522,786.900 278,705.900Locality Size 8,174,154 7.455 3.456

Table 2.9: NOGA classification for retailers.

NOGA Code Original Name Translation Size

471101 Verbrauchermärkte Supercenter >2,500 m2

471102 Grosse Supermärkte Large Supermarkets 1,000-2,499 m2

471103 Kleine Supermärkte Small Supermarkets 400-999 m2

471104 Grosse Geschäfte Large Stores 100-399 m2

471105 Kleine Geschäfte Small Stores <100 m2

2.7 appendix 59

Table 2.10: Treatment and control groups.

Variable 0-2 km 2-4 km 4-6 km 6-8 km 8-10 km Control

Pop_100m 7.53 17.81 23.91 13.66 7.69 9.18Pop_200m 13.76 19.59 11.41 8.22 7.69 5.01Pop_300m 16.15 14.61 11.05 12 10.84 5.32Pop_1km 2, 823.34 2, 357.74 1, 476.55 1, 542.56 1, 346.29 948.43Pop_2km 514.84 870.77 771.11 355.78 311.14 236.22Pop_3km 222.32 400.67 500.53 291 248.90 193.12Pop_4km 151.59 198.59 374.40 261.54 236.92 149.73Pop_5km 87.24 153.70 315.07 297.44 400.54 160.62Pop_6km 98.77 198.73 333.14 440.45 574.29 185.98Pop_7km 142.73 168.38 353.12 355.87 337.59 208.79Pop_8km 173.30 439.38 560.09 160.33 347.02 225.32Pop_9km 255.46 317.75 514.40 322.63 461.94 251.40Pop_10km 202.88 237.41 249.46 280.46 391.12 188.97Ncomp_500m 2.38 1.98 1.91 1.78 1.71 1.62Ncomp_500m-1km 2.27 1.26 0.82 0.87 1.02 0.62Ncomp_2km 4.17 2.78 1.64 1.41 1.08 0.90Ncomp_3km 2.32 3.09 1.52 1.77 1.66 1.07Ncomp_4km 1.55 3.59 2.50 2.11 1.55 1.22Ncomp_5km 1.26 2.11 3.28 2.24 1.95 1.36Ncomp_6km 1.97 1.93 2.82 2.36 2.36 1.37Ncomp_7km 2.03 2.16 2.75 3.22 2.32 1.62Ncomp_8km 2.39 2.15 2.73 3.67 2.68 1.80Ncomp_9km 3.08 2.39 2.71 3.09 3.78 1.94Ncomp_10km 2.51 2.54 2.99 3.09 4.15 2.16Border_Dist 40, 148.24 46, 713.21 47, 636.71 42, 684.13 43, 983.34 48, 864.77Border_Germany 0.28 0.39 0.52 0.50 0.42 0.27Border_France 0.46 0.34 0.20 0.29 0.29 0.24Border_Austria 0.02 0.01 0.02 0.01 0.05 0.07Border_Italy 0.23 0.26 0.22 0.12 0.19 0.35Language_German 0.54 0.53 0.76 0.78 0.75 0.63Language_French 0.38 0.28 0.11 0.15 0.20 0.25Language_Italian 0.08 0.18 0.13 0.06 0.05 0.06Language_Romansh 0.01 0 0 0.005 0 0.06


Figure 2.6: Distribution of Retail Store Types

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Ncomp_9kmNcomp_8kmNcomp_7kmNcomp_6kmNcomp_5km

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Figure 2.7: Balancing for entry within 0-2 kilometersNotes: The figure shows the mean differences of all confounders for treatment group 1 (one entrant within twokilometers, but no other entry) relative to the control group (no entry within ten kilometers) for the unadjusted andadjusted (i.e. weighted using EB) samples.

2.7 appendix 61

Table 2.11: Mean differences all retailers.

0-2km 2-4km 4-6km 6-8km 8-10km

Variable Unadj. Adjusted Unadj. Adjusted Unadj. Adjusted Unadj. Adjusted Unadj. Adjusted

Pop_100m −0.074 −0.001 0.116 0 0.088 0 0.066 0 −0.065 0Pop_200m 0.172 0.007 0.205 0 0.142 0 0.083 0 0.079 0Pop_300m 0.228 0.006 0.157 0 0.134 0 0.153 0 0.118 0Pop_1km 0.756 0.028 0.576 0 0.333 0 0.371 0 0.292 0Pop_2km 0.260 0.010 0.373 0 0.378 0 0.164 0 0.128 0Pop_3km 0.084 0.003 0.333 0 0.314 0 0.208 0 0.130 0Pop_4km 0.016 0.001 0.057 0 0.269 0 0.136 0 0.191 0Pop_5km −0.484 −0.016 −0.063 0 0.273 0 0.179 0 0.298 0Pop_6km −0.317 −0.011 −0.096 0 0.195 0 0.258 0 0.245 0Pop_7km −0.152 −0.007 −0.252 0 0.169 0 0.150 0 0.159 0Pop_8km −0.084 −0.003 0.147 0 0.240 0 −0.198 0 0.110 0Pop_9km −0.014 0.001 −0.009 0 0.222 0 0.098 0 0.217 0Pop_10km 0.055 0.003 0.039 0 0.044 0 0.132 0 0.237 0Ncomp_500m 0.541 0.017 0.302 0 0.216 0 0.188 0 0.068 0Ncomp_500m-1km 0.661 0.026 0.374 0 0.094 0 0.217 0 0.284 0Ncomp_2km 0.768 0.031 0.570 0 0.312 0 0.228 0 0.082 0Ncomp_3km 0.498 0.018 0.783 0 0.295 0 0.263 0 0.243 0Ncomp_4km 0.268 0.008 0.710 0 0.446 0 0.312 0 0.140 0Ncomp_5km −0.021 −0.003 0.313 0 0.617 0 0.381 0 0.254 0Ncomp_6km 0.273 0.012 0.336 0 0.555 0 0.414 0 0.409 0Ncomp_7km 0.236 0.010 0.209 0 0.363 0 0.528 0 0.322 0Ncomp_8km 0.287 0.012 0.188 0 0.359 0 0.630 0 0.314 0Ncomp_9km 0.438 0.019 0.089 0 0.282 0 0.356 0 0.522 0Ncomp_10km 0.171 0.010 0.164 0 0.267 0 0.338 0 0.587 0Border_Dist −0.342 −0.013 −0.093 −0 −0.042 0 −0.161 −0 −0.223 0Germany 0.036 0.002 0.123 −0 0.228 0 0.230 0 0.149 0France 0.216 0.007 0.120 0 −0.053 0 0.043 0 0.037 0Austria −0.055 −0.002 −0.061 0 −0.041 −0 −0.059 −0 −0.006 −0Italy −0.133 −0.005 −0.120 −0 −0.092 −0 −0.225 −0 −0.164 −0Liechtenstein −0.063 −0.002 −0.062 −0 −0.042 −0 0.011 0 −0.016 0German −0.096 −0.002 −0.117 −0 0.109 −0 0.158 0 0.109 0French 0.122 0.003 0.069 0 −0.143 −0 −0.114 0 −0.049 0Italian 0.027 0.001 0.107 0.009 0.092 0.039 0.011 0 −0.002 0.016Romansh −0.052 −0.002 −0.059 −0.009 −0.059 −0.039 −0.054 −0 −0.059 −0.016


Table 2.12: Mean differences small retailers

0-2km 2-4km 4-6km 6-8km 8-10km

Variable Unadj. Adjusted Unadj. Adjusted Unadj. Adjusted Unadj. Adjusted Unadj. Adjusted

Pop_100m −0.039 −0.003 0.106 0.00000 0.098 0 0.046 0 −0.032 0Pop_200m 0.144 0.002 0.227 0.00000 0.162 0 0.072 0 0.057 0Pop_300m 0.236 0.0004 0.160 0.00000 0.119 0 0.123 0 0.128 0Pop_1km 0.742 0.006 0.585 0.00001 0.300 0 0.322 0 0.304 0Pop_2km 0.252 0.002 0.364 0.00000 0.369 0 0.191 0 0.126 0Pop_3km 0.076 −0.0005 0.323 0.00001 0.299 0 0.217 0 0.095 0Pop_4km −0.020 0.002 0.081 0.00000 0.236 0 0.128 0 0.173 0Pop_5km −0.444 −0.002 −0.050 0.00000 0.254 0 0.193 0 0.308 0Pop_6km −0.291 −0.001 −0.110 0.00000 0.174 0 0.228 0 0.249 0Pop_7km −0.178 −0.002 −0.281 0.00000 0.160 0 0.137 0 0.169 0Pop_8km −0.134 −0.0002 0.138 0.00000 0.250 0 −0.184 0 0.095 0Pop_9km −0.059 −0.001 −0.006 0.00000 0.205 0 0.086 0 0.218 0Pop_10km 0.050 0.002 0.060 0.00000 0.066 0 0.097 0 0.242 0Ncomp_500m 0.547 −0.001 0.306 0.00001 0.135 0 0.200 0 0.040 0Ncomp_500m-1km 0.651 0.006 0.409 0.00000 0.091 0 0.184 0 0.277 0Ncomp_2km 0.781 0.009 0.566 0.00001 0.229 0 0.231 0 0.115 0Ncomp_3km 0.504 0.005 0.782 0.00000 0.301 0 0.234 0 0.222 0Ncomp_4km 0.261 0.002 0.704 −0.00000 0.467 0 0.298 0 0.145 0Ncomp_5km 0.002 −0.002 0.328 0.00000 0.630 0 0.350 0 0.248 0Ncomp_6km 0.278 0.004 0.352 0.00000 0.563 0 0.396 0 0.407 0Ncomp_7km 0.254 0.003 0.173 0.00000 0.375 0 0.518 0 0.340 0Ncomp_8km 0.302 0.004 0.207 0.00000 0.329 0 0.627 0 0.312 0Ncomp_9km 0.396 0.003 0.111 0.00001 0.273 0 0.345 0 0.531 0Ncomp_10km 0.177 0.003 0.176 0.00000 0.296 0 0.334 0 0.601 0Border_Dist −0.310 −0.0003 −0.127 −0.00001 0.0001 0 −0.180 −0 −0.220 0Germany 0.037 0.001 0.120 0.00000 0.220 0 0.221 0 0.162 0France 0.198 −0.0004 0.114 0.00000 −0.054 0 0.044 0 0.031 0Austria −0.051 −0.0005 −0.058 0.00000 −0.036 −0 −0.056 −0 −0.009 −0Italy −0.123 0.0003 −0.107 0.00000 −0.086 −0 −0.224 −0 −0.159 −0Liechtenstein −0.060 −0.0003 −0.068 −0.00001 −0.045 −0 0.015 0 −0.025 0German −0.088 0.001 −0.118 −0.00000 0.124 0 0.154 0 0.113 0French 0.112 −0.001 0.063 0.00000 −0.154 −0 −0.109 0 −0.054 0Italian 0.031 −0.007 0.117 0.014 0.092 0.046 0.011 0 0.003 0.016Romansh −0.054 0.008 −0.062 −0.014 −0.062 −0.046 −0.056 −0 −0.062 −0.016

2.7 appendix 63

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2.7 appendix 65

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references 67

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3

DEAL ING WITH

UNCERTA INTY: SELLER

REPUTAT ION IN THE

ONL INE MARKET FOR

I LLEGAL DRUGS

(joint with H. Liebert)

abstract

We analyse the reputational effects arising from information revealed in

platform rating systems in the online market for illegal drugs. In this black

market, no legal institutions exist to alleviate buyer uncertainty. We estimate

the value of seller rating for unit prices charged by exploiting the sudden

market exit of a major platform. We track sellers that were forced to migrate

to the competing platform and make use of their ratings ‘reset’. We find that

on average an increase of one percentage point in the rating results in a unit

price increase of 20% of a standard deviation.

3.1 introduction

The rise of online commerce has given market participants the oppor-

tunity to move many transactions from the real world to the digital. Buyers

benefit from the convenience of observing a large selection of goods and hav-

ing them shipped to their doorstep, while sellers make use of online sales

channels as an effective means to market and sell their goods. Often times on-

line sales platforms are the central actor enabling this exchange. By offering

71

72 seller reputation in the online market for illegal drugs

a marketplace for buyers and sellers to interact, they allow trade to occur that

might otherwise not happen.

However, some of the features of trade in the real world cannot simply be

replicated on an online sales platform. In particular, buyers are unable to in-

spect the goods or verify a seller’s identity due to trader anonymity, so that

both the quality of a product and the reliability of the seller are unknown to

buyers beforehand. The only assurance they have is provided by institutions

that exist in the background, such as the law and its enforcement mechanisms.

The platforms attempt to overcome this difficulty by providing a rating sys-

tem of sellers and thereby creating a reputation mechanism, that is meant

to ensure that honest trade is in the sellers interest. Their undeniable suc-

cess across a wide range of different goods and services, such as used goods

(e.g. eBay), hotel rooms (e.g. Booking), or car transport (e.g. Uber), seems to

demonstrate the effectiveness of such rating systems.

In this paper, we study the reputational effects arising from information re-

vealed in platform rating systems in a market that is characterized by both a

complete lack of ordinarily available institutions and a powerful need for mar-

ket participants to remain anonymous: the online market for illegal drugs. In

the past decade, decentralized marketplaces for illegal goods and services

have emerged and become increasingly popular.20 These platforms are lo-

cated on the Tor (‘the onion router’) network, ensuring anonymous commu-

nication and concealing user’s locations, its market participants communicate

amongst each other using encryption programs, and transactions are con-

ducted exclusively in bitcoin. Since privacy networks such as Tor are com-

monly also referred to as the ‘darknet’, these marketplaces are often called

‘darknet platforms’. It is only at the end of a purchase on such a site that in-

dividuals lose some of their anonymity and interact in the real world: when

the product is shipped by mail to the customer.

20 For example, the 2017 Global Drug Survey documents that in the UK in 2017, around aquarter of survey respondents report purchasing drugs online. The findings of the surveyfrom 2017 can be found on the official website at https://www.globaldrugsurvey.com/wp-content/themes/globaldrugsurvey/results/GDS2017_key-findings-report_final.pdfor in Barratt et al. (2016). Soska and Christin (2015) in turn study the first of these platforms,which was called “Silk Road”, and estimate that the website at its height in 2013 had anannual revenue of more than $100 million.

3.1 introduction 73

The nature of these marketplaces exacerbates the problem that reputational

incentives are meant to overcome. In particular, the absence of any ability of

buyers to enforce a contract suggests that moral hazard problems are severe.

It is easy for a seller to simply ship an empty package to a customer or to

not ship anything at all. To solve this problem, darknet markets offer escrow

services. Instead of transferring payment directly to the seller, a buyer may

pay the platform operator, who holds the money in an escrow account and

only releases it to the seller when the product has been received by the buyer.

However, this in turn provides the platform with the incentive to shut down

and disappear with all money held in escrow at an opportune moment.21

We make use of webscrapes of individual offers on the two most popular

platforms for illegal merchandise at the time covered in our data: “Agora”

and “Evolution”. We further add data provided by API requests of the dark-

net search engine “Grams”. The resulting dataset provides a full overview of

the supply of drugs on the two major platforms and covers the time period

of June 2014 until July 2015. It contains information on the prices and quan-

tities of each offer, the type of drug sold, whether the offer allows use of the

escrow services, the country the good is shipped from, as well as the rating,

size, name and public PGP key of the seller.22

The Agora and Evolution platforms were known during their time of opera-

tion for high stability and professionalism, relative to other, small competitors.

Evolution in particular had little to no issue with uptime and accessibility and

became the largest platform by the end of 2014. However, in mid-March 2015,

the administrators of Evolution executed an exit-scam and absconded with

around $12 million in bitcoins stolen from their traders. Dealers selling ex-

clusively on the Evolution platform were subsequently forced to migrate to a

different platform (in all likelihood Agora) or exit the market altogether.

We exploit our knowledge of sellers’ public PGP keys and names to link

dealer accounts over time and across platforms. This allows us to track dealers

21 This has happened numerous times, for example in 2013 alone, at least 7 darknet platformsended in such exit scams. However, the majority of platforms are very shortlived and do nothave a meaningful market share (see Bhaskar et al. (2017) for a detailed documentation ofplatform turnover and size). Exit-scams by dominant platforms are rare.

22 We also observe the product titles, descriptions and individual reviews. Due to some incom-pleteness of the scrapes for the individual reviews, we choose not to make use of them andinstead focus on the aggregate ratings measure.


that sold on Evolution prior to the exit and migrated to Agora following the

exit. Dealers that ‘switch’ the marketplace reset their rating in the process.

This exogenous shock to switchers’ ratings provides us with an instrument to

study the impact of a sellers’ reputation, measured by the aggregate rating,

on the prices of his/her products.

We estimate a statistically significant, positive and large causal effect of a

sellers’ aggregate rating on the unit price he/she charges. The effect varies

slightly across the different types of drugs we consider. In our main results

we find that the value of a one percentage-point improvement of the average

rating causes up to a 45% of a standard deviation increase in the respective

unit price (45% for Cannabis, 15% for Cocaine, 13% for MDMA and 7% for

Speed). We further provide evidence that as a switchers’ rating recovers fol-

lowing the migration, the effect reduces in size and may even vanish. Finally,

the impact of rating is significantly larger than the impact on prices due to

increased competition or the use of the escrow system.

Our work in this paper makes two contributions to the literature. One,

we study a unique black market that has received little attention so far in

economics, in which legal institutions are replaced by centralized platform

mechanisms to enable trade.23 Traders make use of reputation to police them-

selves in order to overcome the institutional void and lack of legal recourse.

Reputation has been suggested to play a crucial role in replacing governmen-

tal and legal institutions in various environments (e.g. in emerging markets

(Gao et al. 2017), among medieval merchant guilds (Greif et al. 1994), in a

private code of law for merchants in the middle ages (Milgrom et al. 1990),

or in pirate organizations (Leeson 2007)). Our results also document that rep-

utation appears not to be transferable between different online marketplaces,

even when doing so would be in the interest of the seller.

Two, we provide reduced-form estimates of reputation effects on online-

sales platforms using a novel approach that exploits the reputational shock

experienced by dealers following the Evolution exit. A sizable literature has

developed that estimates the returns to reputation for high rated sellers in on-

23 We are aware of two recent papers studying the online market for illicit drugs: Bhaskar etal. (2017) and Janetos and Tilly (2017). However, there exists a larger literature in computerscience and criminology on darknet marketplaces (e.g. Soska and Christin (2015), Aldridgeand Decary-Hetu (2014), and Barratt et al. (2016).)

3.2 the darknet platforms 75

line markets (e.g. Resnick and Zeckhauser (2002), Cabral and Hortacsu (2010),

Cai et al. (2014), and Jolivet et al. (2016), see Tadelis (2016) for a recent sur-

vey). Much of the literature documents a small, but positive and statistically

significant effect of reputation on price. We document effects that are more

pronounced than most of the reputational effects found in previous work on

legal sales platforms, indicating that the value of reputation in the absence of

enforcable contracts and legal certainty increases.

The remainder of this paper is structured as follows. Section 3.2 discusses

the institutional setup of the market and its evolution. Section 3.3 explains

how the data was collected and processed, and establishes important stylized

facts about the nature of seller ratings and the determination of prices. Section

3.4 details the Evolution exit-scam and discusses the identification of the rat-

ings effect. Section 3.5 documents and discusses the results. Finally, Section

3.6 concludes.

3.2 the darknet platforms

The origins of the online black market for illegal drugs lie with the first

major darknet platform, Silk Road, launched in 2011. It grew to an unprece-

dented size, due to its focus on providing trader anonymity. It was shut down

by law enforcement in 2013 and its founder sentenced to life in prison. How-

ever, Silk Road combined a series of techological advances and inovations

that have effectively been copied and developed further since then by every

subsequent platform, including the two studied in this paper.

First, Silk Road was located on the Tor network. Tor makes use of a pri-

vate network that directs an internet users signal across different relays and

encrypted nodes before reaching the intended destination, making it very dif-

ficult to track the site or its users. Second, it enabled and encouraged its users

to communicate using PGP encryption. Sellers were expected to provide their

public key alongside their descriptions and prices of their products. Third,

transactions could only be conducted using the cryptocurrency Bitcoin. Each

seller or buyer could deposit and withdraw bitcoins from their account on the

site in order to make payments. Fourth, a centralized feedback and rating sys-


tem was implemented, in which buyers could leave feedback for sellers they

had bought from. Fifth, Silk Road also provided an escrow system. Dealers

could offer their buyers the use of the system in order to give them security

that they will not be defrauded. Instead of making payment directly to the

dealer, the buyer would send his bitcoins to a wallet of the platform. Then,

the dealer would send the merchandise and after the buyer confirmed its ar-

rival, the platform would transfer payment to the seller.24 Sellers could also

choose to forego this system and require the buyers to finalize the payment

early, meaning to send the funds directly to the seller prior to shipment of

the merchandise. For the use of the platform, sellers would be charged a

percentage-based fee for each transaction.

However, on the surface Silk Road and its successors are structured in a

way familiar to any user of eBay or Amazon (see Figure 3.1 for examples

from the Agora platform). Sellers can open accounts for a fixed refundable

bond and create product listings. Each listing contains a description of the

product on offer and a price set by the seller, as well as information on the

shipping origin of the merchandise and the sellers rating and number of sales

made. Buyers in turn can browse the listings by selecting the relevant category

of products, or using the sites’ search function. In addition, buyers are also

able to observe the profile page of the seller, including his/her PGP key and

history of reviews.

In contrast to most legal markets, there is a great deal of darknet platform

turnover. At any given point in time there are dozens of different market-

places active on the darknet. Bhaskar et al. (2017) document the lifetime of 88

separate platforms from 2011-2015 and demonstrate that the vast majority of

them were (very) small in terms of market size and had a very short lifespan.

The few larger platforms (such as Silk Road, Agora, or Evolution) in turn

dominate the market when active and operate for a significantly longer time

period of at least a year. Platforms exit for multiple reasons, among others

a shutdown by the authorities (e.g. Silk Road), an exit-scam (e.g. Evolution),

24 If the buyer did not signal the shipment to have concluded, the payment would be auto-matically released after a waiting period of a few weeks. In addition, platforms often offermediation services in case of disputes (e.g. Agora). Such a system is not unique to illegalonline markets. Airbnb for example holds a buyers payment until 24 hours after check-in “tomake sure everything is as expected” (Airbnb 2017). See Figure 3.1 in the Appendix for anoverview of the escrow system on Silk Road.

3.3 data and descriptives 77

Figure 3.1: Screenshots from AgoraNotes: The figure shows two screenshots of the darknet platform Agora as it appears to buyers browsing.

or voluntarily due to for example security concerns (e.g. Agora). During the

time frame studied in this paper, the Agora and Evolution platforms were the

dominant players in the market. Following the Evolution exit-scam in March

2015, Agora continued to be the largest platform until its voluntary exit in

August 2015.

3.3 data and descriptives

We make use of semi-daily webscrape data from the two darknet platforms

Agora and Evolution, as well as from daily API requests of the darknet search

engine Grams (see Figure 3.2 in the Appendix for a screenshot of the website).

Our data covers the time period of July 2014 to July 2015. The Grams data

allows us to obtain information on the supply of goods on the two platforms.

Illegal drugs account for the largest share of merchandise on offer.25 For

each item on offer we observe the title, price, product category, and shipping

origin, as well as the dealers name and public PGP key. We add to this

25 Drugs and electronic goods (such as eBooks or credentials for hacked Netflix accounts) areby far the two largest categories, making up around 99% of the market.


wealth of information the dealers rating, reviews, and total sales, as well as

the item description from the platform scrapes. The resulting dataset provides

a unique overview of the black market for illegal drugs over the course of a

year.

Items advertised on the darknet platforms are placed in separate product

categories, allowing us to distinguish different types of drugs. However, no

further information on the product is directly provided. Instead, the title and

description of an item contain important information for buyers such as the

quantity of the drug that is sold. We focus on homogeneous goods within

each drug type and extract from the item titles and descriptions information

on the quantity being sold and the size of the batch. Figure 3.2 shows an ex-

ample of an offer for MDMA. In this instance, we determine that the quantity

sold in the offer is 1 gram.

Figure 3.2: Screenshot of Evolution itemNotes: The figure shows a screenshot of an example of an item being sold on the darknet platform Evolution.

We focus on eight product categories for illegal drugs, namely cannabis,

MDMA, cocaine, speed, methamphetamine, heroin, LSD, and ketamine, and

observe a total of 37,057 unique offers of drugs made by 3,005 separate dealers.

Table 3.1 reports the summary statistics for all eight categories. It shows the

average unit price (i.e. the price per consumption unit in USD), the number

of dealers and offers, and the median quantity sold. Cannabis is the cheap-

est type of drug on offer (at around 11 dollars per gram), while meth and

heroin are the most expensive (at over 150 dollars per gram). Cannabis is also

the most popular drug type sold with the most unique offers. The median

quantity advertised for the cheapest drugs cannabis (14g) and speed (20g) is

significantly larger than for the expensive drugs.26

26 Detailed information on the distribution of price and quantity can be found in the Appendixin Figures 3.3 and 3.4.


Table 3.1: Summary statistics

Category Mean unit price # Dealers # Offers Median quantity

Cannabis 11.0 per 1g 1, 415 18, 331 14 gMDMA 44.2 per 1g 779 5, 067 10 gCocaine 112.8 per 1g 741 4, 603 3.5 gSpeed 15.7 per 1g 344 2, 248 20 gMeth 158.5 per 1g 319 1, 889 3.5 gHeroin 154.0 per 1g 271 1, 841 1 gLSD 48.0 per 10×100μg 241 2, 374 100 × 100μgKetamine 58.4 per 1g 137 698 5 g

Notes: The table reports summary statistics for the eight product categories considered. Prices are reported in USD.The Bitcoin exchange rate used corresponds to the day on which the item price was observed. Unit price refers tothe price per consumption unit, defined as 1 gram for all categories except LSD, where it is 100 μg.

The average price however hides two important sources of price variation:

country differences and vendor discounts. The price for the same type of

drug, in the same quantity, often shows stark differences by the shipping ori-

gin of the product. To illustrate this, Table 3.1 in the Appendix documents the

price variation for cocaine across the ten largest countries for the drug, mea-

sured by the total number of unique offers. The average price of one gram of

cocaine ranges from 267.47 USD in Australia to 79.95 USD in the United States.

A likely explanation is that because cocaine must be brought into the country

first to be sold from there, differences in the ease of smuggling the merchan-

dise through customs produce very large differences in the cost to obtain the

drug.27 Similarly, proximity between producer and consumer country may be

an important factor in the cost as well. Table 3.1 also illustrates that the largest

share of dealers active ship their goods from the western world. Figure 3.5

in the Appendix depicts the total number of items observed by the country

shipping origin. The largest source of items is the United States at over 10,000

distinct offers, while other countries with a lot of activity in the market are

for example the United Kingdom (around 4,600 items), or Germany (around

5,100 items).

The second source of large price variations are quantity and finalize early

discounts. Dealers offer their potential customers significantly reduced prices

27 Cocaine is obtained from the coca plant which requires high moisture and low atmosphericpressure to grow. These conditions are difficult to find or reproduce outside of South Amer-ica.


Table 3.2: Quantity and finalize early discounts

Unit price (single unit) Discounts

Category All Escrow Finalize early × 5 × 10 × 50 × 100

Cannabis 17.57 17.62 0.98 0.77 0.68 0.50 0.43MDMA 65.47 64.42 1.09 0.62 0.49 0.33 0.27Cocaine 130.19 132.23 0.94 0.71 0.62 0.56 0.50Heroin 151.98 153.69 0.96 0.66 0.54 0.27 0.22Speed 43.16 37.25 1.84 0.35 0.24 0.14 0.10Meth 177.56 174.94 1.07 0.58 0.42 0.23 0.17LSD 54.13 55.22 0.91 0.78 0.73 0.57 0.51Ketamine 78.89 80.07 0.94 0.58 0.54 0.43 0.37

Notes: The table reports the discount rates for the eight product categories by quantity and by finalizing earlyinstead of using the escrow service. Prices are reported in USD. The Bitcoin exchange rate used corresponds to theday on which the item price was observed. Unit price refers to the price per consumption unit, defined as 1 gramfor all categories except LSD, where it is 100 μg.

for larger quantities in particular. Table 3.2 documents the extent of the dis-

counts on offer. Across all categories, sellers continually demand a lower unit

price as the quantity bought increases. In the most extreme case, buying 100

grams of speed costs on average only 10% of the unit price of 1 gram of speed.

Table 3.2 also shows that the discount for sending the payment directly to

the seller (‘finalize early’) instead of using the escrow system is much smaller

than the documented quantity discounts. In some cases, the average price

even increases. This appears to be driven by differences in offer composition.

Reputable high quality or large volume sellers tend to offer only finalize early

in order to minimize their risk. We account for both aspects of country differ-

ences and quantity discounts in our estimations by including fixed effects for

the shipping origin and for the quantity offered of a product. We also include

use of the escrow service as an explanatory variable.

Figure 3.3 plots the number of unique dealers (vendor accounts) on the two

platforms over time. The size of the platforms increased over the latter half

of 2014, stabilizing around October for Agora and in December for Evolu-

tion. Following the Evolution exit (indicated in grey), the number of dealers

on Agora increased as sellers previously present on Evolution sought to con-

tinue their business on the only large platform left in the market. However,

the limited size of the increase in dealer accounts indicates that in all likeli-

hood not every Evolution seller switched the platform following the exit. As


we will show in Section 3.4.2, the vast majority of sellers in the market are

single-platform sellers and of those on Evolution around ten percent move

their business onto the other platform. In addition, note that Agora had pre-

viously experienced technical difficulties and had more downtime and a re-

duced speed in accessing the site relative to Evolution. Due to the increased

traffic on its site following the exit, the accessibility of the platform suffered

further resulting in larger fluctuations of dealers observed in our scrapes. Fig-

ure 3.6 in the Appendix documents the share uptime and speed in accessing

the two sites in detail.

400

600

800

Jul 2014 Okt 2014 Jan 2015 Apr 2015 Jul 2015

Agora Vendors Evolution Vendors

Figure 3.3: Platform sizeNotes: The figure shows the number of unique dealers (vendor accounts) active on the two platforms. The Evolutionexit is indicated in grey. The flat lines in early 2015 are due to missing data.

For our estimations in Section 3.5 we restrict the analysis to the following

five categories of cannabis, cocaine, MDMA, heroin, and speed, since the re-

maining categories do not contain a sufficient number of sellers that switch.

To focus on a set of homogeneous offers, we limit the sample to a time pe-

riod around the Evolution exit date from mid February to mid March, two

weeks after the Evolution exit. Moreover, we only include product offers from

countries where we observe switching dealers.

Finally, before proceeding to the analysis, we examine the rating of deal-

ers in more detail. Previous work on reputational effects on legal sales plat-


forms has regularly documented that the average rating of a seller tends to be

very high (for example in Cabral and Hortacsu (2010)).28 Because conducting

transactions in this market requires buyers to reveal their physical address

to dealers, this may be further exacerbated due to fears of retaliation. Fig-

ure 3.7 in the Appendix shows the distribution of rating across sellers. As

expected, the distribution is extremely skewed towards the top on both plat-

forms and exhibits the well-documented ‘J-shape’, indicating that the varia-

tion in seller rating between (relatively) highly-rated sellers and (relatively)

lowly-rated sellers may be quite small in absolute numbers. It appears that

when buyers leave a review, most of the time they will tend to leave a perfect

or very good review, sometimes a very bad one, but rarely a mediocre one.

This pattern is well documented for legal markets (Tadelis 2016).

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Figure 3.4: Dealer lifecycleNotes: The figure shows the average rating in the top plot and the number of unique vendor accounts in the bottomplot observed by the number of days passed since the vendor entered the market. Rating is measured on a scaleof 0 to 100 with higher numbers indicating better rating. Entry is defined as the first date of observation for theaccount. We exlude accounts of sellers that have already made sales before the first time they are observed. The 95%confidence band of the average rating is shown in grey.

Figure 3.4 plots the average rating of a dealer over his/her lifecycle. We

track accounts that have been opened on one of the platforms from the day of

entry over time. Entry is defined as the date on which the seller is observed

28 Similar results have also been found for the darknet black market in Bhaskar et al. (2017).


for the first time.29 As sellers mature, the average rating improves and the

variation in rating decreases significantly. The improvement in rating becomes

increasingly less volatile over the first 80 days. Within 100 days of activity it

appears that sellers on average have matured. The difference in the average

rating between a new entrant and a mature seller is very small in absolute

numbers and around 3 (percentage) points. Figure 3.4 also indicates that as

the average rating improves within the first 3 months, a sizable fraction of

new entrants drop out of the market. The remaining share however continues

to trade and its number is stable for a longer time. This suggests that ‘good’

sellers stay in the market long-term, while ‘bad’ types drop out early on. Since

our dataset covers a time period of one year, the number of observations starts

to become small and the ratings information very volatile as we track the

average entrant for more than 200 days.

3.4 empirical approach

In subsection 3.4.1, we present the econometric model used for analysis

and discuss how we tackle the identification of the ratings effect. Subsection

3.4.2 then explains the instrument used and examines the Evolution exit-scam

in detail.

3.4.1 Identification

Our aim is to estimate the impact of a sellers rating on the prices charged

for his/her products on offer. We define an individual item that is sold as the

unique offer observed on one of the platforms, sold by one specific seller, be-

longing to one drug category, of a given quantity, and shipped from a specific

country. We denote the individual items by the index i. We further define

the product market that a given item i is associated with and competes in as

29 We also require that the seller has not made any sales yet, since it is possible for a dealer tobe missed in previous scrapes due to technical difficulties. We further exclude the first fewscrapes in our dataset when many sellers are observed for the first time.


the category of drug and the country of origin of item i, denoted by k and c

respectively. We consider the following pricing equation:

Pricet,i = β1Ratingt,j + β2Nsellerst,k,c + Escrowi + μi + Montht + εt,i, (3.1)

where Pricet,i denotes an item i’s unit price at time t and Ratingt,j denotes the

seller j of item i’s aggregate rating at time t. The variable μi represents the

item-specific fixed effects of seller × category × quantity × country. We in-

clude a monthly time-fixed-effect denoted by Montht. In addition, Nsellerst,k,c

denotes the total number of sellers selling an item in the same product mar-

ket, i.e. in the same category k from the same country c, as the item i at time t,

while Escrowi indicates whether an item i requires using the escrow services

for payment. Finally, εt,i is a scalar unobserved dealer/item-specific shock at

time t that is assumed to be mean-independent of the remaining right-hand

side variables. Note that by including the interacted fixed effects term for

quantity, we explicitly allow for non-linear pricing of products and for the

pricing structure to vary across categories (and countries). We documented

previously in Section 3.3 that quantity discounts are commonplace.

To estimate the above equation, we need to deal with two possible concerns

of endogeneity in the ratings variable. The first is unobserved seller hetero-

geneity. This has been noted before in the literature several times (e.g. in

Resnick and Zeckhauser (2002)) and it has been argued that it may explain

the often puzzlingly small effect that ratings appears to have on price on le-

gal sales platforms (e.g. in Cabral and Hortacsu (2010)). Due to the required

anonymity in the market that we study however, all information available to

buyers is available to us as well. There is no offline presence for dealers or

information on the darknet platforms that we do not observe which may pro-

vide buyers with additional information about sellers. The second concern

however is more severe. Since the ratings information is a summary measure

of past buyers feedback, it is likely to be a function of past prices. Buyers who

purchase an expensive product will have a correspondingly higher expecta-

tion of its quality which will impact the rating they leave for the seller. Then

the aggregate ratings variable in Equation 3.1 is likely to be correlated with

past realizations of ε. We tackle this issue by making use of an instrument


for rating available to us, in order to obtain a clean estimate of the value of

reputation. We discuss the instrument in detail in the following subsection

3.4.2.

Before we proceed, note that while our approach here is reduced-form in

nature and not guided by a structural model, the pricing equation we consider

is consistent with commonly used frameworks in the theoretical literature.30

The most important assumption underlying our statistical model is that the

current rating and the number of competitors are the only relevant endoge-

nous state variables that sellers condition their strategies on. We can describe

a basic theoretic setting that yields our specification as follows. Consider a

model in which each seller is characterized by a type that is known to the

seller, but unknown to buyers. They in turn are able to observe the charac-

teristics and prices of all items on offer, but the final quality of the item and

hence the type of the seller is only observed upon consumption. All buyers

can also observe a public signal, the rating, of the satisfaction of past buyers.31

A pricing equation that depends on the aggregate ratings measure as in

equation 3.1 is then consistent with the equilibrium concept of a Perfect

Markov equilibrium. This is a common solution concept in the theoretical

literature on reputation (Bar-Isaac and Tadelis 2008). Buyers update their

beliefs from the previous period about the distribution of product quality ac-

cording to Bayes’ rule, incorporating all public information available to them.

Given common prior beliefs, all buyers will hold the same beliefs regarding

the distribution of quality at any given point in time. Then the choice to

purchase only depends on the current public information, characteristics, and

beliefs. Consequently, for a given transaction the strategy of the seller (i.e. the

price) will only depend on the current public information, characteristics, and

quality, as in equation 3.1.

However, sellers face competition to a varying degree in our setting, so we

also account for the intensity of competition by including Nsellers in our es-

timation. Standard models of imperfect competition in the style of Ericson

30 See Bar-Isaac and Tadelis (2008) for a survey on models of seller reputation.31 In reality, this signal arises from the set of reviews that buyers have left by choice, which is

generally not modelled in the literature. As far as we are aware, the first paper to endog-enize the decision by buyers to leave a review and explicitly investigate the implications isAcemoglu et al. (2017). However, these authors abstract from the supply side of the marketand focuse on buyer choices.


and Pakes (1995) require the sellers strategy to condition on rival prices in

the Perfect Markov equilibrium. For simplicity we abstract from the addi-

tional complication of strategic interaction and only consider the aggregate

state variable Nsellers, however our pricing equation 3.1 continues to be con-

sistent with a model of imperfect competition and the concept of an oblivious

equilibrium introduced in Weintraub et al. (2008).32 In this equilibrium con-

cept, sellers do not take into account the state variables of every other seller in

the market, but instead consider a long-run stationary aggregate choice. The

authors show that as the number of competitors in an imperfectly competi-

tive market grows large enough, the oblivious equilibrium approximates the

Perfect Markov equilibrium.

3.4.2 Instrument

As outlined in the previous section, the ratings measure is a potentially

endogenous variable. We make use of two crucial features of darknet plat-

forms that allow us to conduct an instrumental variable regression of equation

(3.1): the publication of sellers public PGP keys and the ability of platforms

to perform so-called exit-scams. Consider the two characteristics in turn.

The first aspect we exploit is the nature of encrypted communication on

darknet platforms. These illegal marketplaces highly encourage buyers and

sellers to encrypt their communication. When consumers choose to make a

purchase, they must provide the seller with an address for the shipping of

the merchandise. Doing so in the clear given the illegal nature of the trade

poses an additional risk for buyers. Consequently, dealers are required to

provide their public PGP key for buyers to use in their advertisements on the

platform, so that each vendor account on a platform is linked to a specific

public PGP key. PGP (‘pretty good privacy’) is a popular encryption program

that makes use of public-key cryptography. Each user of PGP has two keys,

one private and one public. Communication with a user can be conducted

by encrypting the information prior to sending with the public key of the

32 Our pricing equation could then be born out of a model of imperfect competition in the styleof Ericson and Pakes (1995), given simplifying assumptions that multi-good sellers do notaccount for their other products and prices when determining the price of one product anddo not vary their set of products on offer.


receiver. Decrypting the message can then only be done by using the private

key which is only known to the receiver.33 Private and public keys are unique

and highly complex. Figure 3.8 in the Appendix shows an example of a public

PGP key.

We exploit our knowledge of sellers’ account names and public PGP keys

to link all dealer accounts across both time and platforms. Previous work on

darknet marketplaces suggests that only a small fraction of dealers operate

across platforms. For example, Soska and Christin (2015) measure the number

of unique ‘aliases’ (account and marketplace pair) a seller uses and show that

more than 75% of sellers only use one. Similarly, Buskirk et al. (2014) suggest

that more than 78% of sellers are only present on a single platform as of

September 2014.

Table 3.3: Unique sellers in the market

Unique sellers

accounts total one account two accounts three accounts four accounts

N 3,005 2,344 1,718 620 23 3

Notes: The table shows the number of vendor accounts and the number of unique sellers in total and by thenumber of accounts sellers use present on the two platforms. There are no sellers active on only one platform withmultiple accounts.

Table 3.3 shows the number of vendor accounts and of operating unique

sellers on the two platforms, as well as the number of accounts unique sellers

use. There are significantly fewer actual unique sellers in the market than

the number of vendor accounts on the two platforms. Of the 2,344 unique

sellers active, around 73% use only one account. This is in line with the

previously documented estimates. Table 3.3 also shows how many accounts

a seller that is active on both platforms uses. Almost all sellers use only

one account on both platforms respectively, while only 23 sellers use three

accounts spread across the two platforms, and three sellers operate with four

33 Technically, it is only computationally infeasible to decrypt without knowledge of the privatekey. Public key cryptographic systems rely on mathematical problems that make it easy togenerate a private and public key pair, but very difficult to re-engineer the private key basedon the public key. This allows the public key to be broadcast and communication remainssecure as long as the private key is secret. The great advantage is that no key must be secretlyexchanged prior to communication commencing. Almost all secure communication (such asonline banking) makes use of a public key cryptography system.


separate accounts. There are no sellers that only sell on one of the platforms,

but use multiple accounts to do so.

The second aspect we exploit is the Evolution exit-scam. When traders con-

duct their business on the darknet platform, they place their bitcoins on their

platform account in order to then make transactions. Furthermore, when mak-

ing use of the escrow system, they place the payment temporarily on a wallet

of the platform operator. In either case, the funds are nominally controlled

by the platform operators as soon as they are transferred to the site accounts.

Even though users can exercise control over the funds in their accounts, this

is at the operators’ discretion. This gives an incentive to the platform adminis-

trators to shut down the site unexpectedly and abscond with all the money in

platform accounts. In mid-March of 2015, Evolution began to disallow with-

drawals of bitcoins from wallets and accounts on the platform, citing technical

difficulties. Escrow accounts were similarly frozen and inaccessible. Within a

week the site went offline. Estimates suggest that the site administrators stole

around 40,000 bitcoins from their users, worth at the time approximately 12

million USD. The exit was highly unexpected, since Evolution was the largest

platform in the market and was known for stability and professionalism. Cur-

sory examination of discussion forums on darknet platforms at the time sug-

gests that it took 2-3 days for traders to start to become aware of the scam

occurring.

However, the market is generally very dynamic with platforms entering

and exiting regularly, so buyers quickly migrated to other platforms to con-

tinue purchasing. Similarly, dealers wishing to continue their business were

forced to migrate to a different platform. At the time, Agora was the only

remaining large and dominant marketplace and saw a sudden increase in

sellers following the Evolution exit (see Figure 3.3). Dealers forced to ‘switch’

the marketplace had to create a new account and hence lost their reputation in

the process.34 We exploit this ratings ‘reset’ of ‘switchers’ to estimate the effect

of ratings on price and we track dealers switching by linking their accounts

34 Agora and Evolution operated in the exact same way and offered the same services to theirusers. They also had the same fee structure for operating a seller account. Figure 3.10 inthe Appendix documents the average price difference between the two platforms over time,showing that there is no sizable or consistent difference that would indicate variation in howthe two platforms operated in the market.


as described before. Hence, we augment equation (3.1) with the following

first-stage regression,

Ratingt,i = δ1Switcht,j × {t ≥ Exit}t + ηi + Montht + ξt,i, (3.2)

to isolate the effect of rating on price, where ηi represents the item-specific

fixed effects and ξt,i the error term.

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les

Agora Dealers Switchers

Figure 3.5: Ratings shock for switchersNotes: The figure shows the mean aggregate rating and mean total sales of switchers (dealers that sold exclusivelyon Evolution before the exit and migrated to Agora following the exit) and dealers present on Agora both beforeand after the exit. The Evolution exit period is highlighted in grey.

Figure 3.5 shows the impact of the exit-scam and subsequent forced move

to Agora on the aggregate rating and sales of switchers and of dealers selling

on Agora both before and after the exit-scam. The Evolution exit period is

indicated in grey. On average, switchers tended to have a higher rating than

dealers selling on Agora prior to the exit. The forced migration in March 2015

caused a ratings shock and lowered the average rating for switchers by around

3 percentage points. Recall from Section 3.3 that a three-point-difference in

the rating was generally found when comparing the average entrant to the


average mature dealer. The rating of the continuously present Agora dealers

instead shows no reaction to the exit. Similarly, the average aggregate sales

of switchers were slightly below those of Agora dealers, but dropped to ap-

proximately zero in the wake of the Evolution exit-scam. Following the exit,

sales began to grow at a very similar rate to the Agora dealer sales, which

again were unaffected by the exit. The average rating of switchers appears

to recover within the three months following the exit, which is also in line

with the approximately 100 days it appears to take for the average dealer to

mature.

Table 3.4: Switchers immediately before and after the exit

Average # offers Median quantity Mean unit price change

Category Before After Before After Absolute Percentage Market

Cannabis 4.96 4.00 7 7 −1.34 −12% +4%MDMA 5.17 3.42 20 5 −10.72 −24% +9%Cocaine 4.08 3.55 2 2 −14.86 −13% +7%Speed 4.25 5.00 17 25 −1.21 −6% +5%Heroin 3.86 5.60 1 1 −36.11 −22% +6%LSD 4.88 4.33 27 23 −0.99 −21% +12%Meth 10.00 10.00 1 1 −37.88 −23% +5%Ketamine 6.00 5.00 1 3 −28.03 −45% +11%

Notes: The table contrasts switchers seven days prior to the exit and two days after the exit. It shows acrosscategories i) the average number of offers per dealer at the two dates, ii) the median quantity of offers at the twodates, iii) the absolute average change in prices charged and percentage change relative to the market price sevendays prior to exit, as well as the overall market price increase in percentage. The price changes shown for switchersare averages of country differences. Only one switcher is observed for Ketamine. Prices are reported in USD. TheBitcoin exchange rate used corresponds to the day on which the item price was observed. Unit price refers to theprice per consumption unit, defined as 1 gram for all categories except LSD, where it is 100 μg.

Table 3.4 documents how switchers price their products seven days before

and two days after the exit. It shows that the average unit price of switch-

ers between the two dates strongly decreased across all categories of drugs,

indicating a clear and immediate adjustment to the large reputational loss

suffered. Taking into account the market price one week prior to the exit,

the percentage change of prices is significant for all drugs and is above 20%

for most categories. The largest change we document occurs for Ketamine,

however we only observe a single switcher in this category. The market price

on the other hand increased across all categories between the week prior and

two days after the exit, further reinforcing that switching has had a powerful,

negative effect on the prices a dealer may charge. The table also provides


information on the average number of offers for products made by switchers

and the median quantity of the offers. It demonstrates that there is little varia-

tion in product offerings before and after the exit by switchers, indicating that

there is no reaction to the exit by adjusting the product portfolio.

Lastly, to gain a better understanding of switchers, Table 3.5 contrasts them

to all other dealers present on Evolution a week prior to the exit. It shows

the proportion of dealers across the different categories of drugs, the aver-

age number of items on offer per seller, and the price differences between

switchers and other Evolution dealers. Switchers are representative for the

average Evolution dealer prior to exit and found in almost identical propor-

tion across the different categories to the average dealer. Once adjusting for

country differences, the average price differences between switchers and other

dealers are quite small. In addition, they tend to offer fewer different prod-

ucts on average than other Evolution dealers across most categories, but this

is not universally the case. In Table 3.2 in the Appendix, we provide a similar

comparison of switchers to Agora dealers one week after the exit. As before,

switchers are found in similar proportions across the categories as all other

Agora dealers, while the price differences become more pronounced.

Table 3.5: Sellers on Evolution seven days prior to the exit

Proportion of sellers Average # offers

Category Switchers Evo dealers Switchers Evo dealers Price difference

Cannabis 0.44 0.46 5.12 10.46 1.09MDMA 0.28 0.29 5.56 5.86 -3.67Cocaine 0.21 0.25 4.33 6.17 -4.25Speed 0.14 0.14 4.25 5.43 -0.15Heroin 0.11 0.10 4.16 7.32 0.61LSD 0.11 0.09 4.83 7.82 -0.19Meth 0.04 0.09 10.00 4.68 4.53Ketamine 0.02 0.02 6.00 2.67 5.76

Notes: The table contrasts switchers to all other Evolution dealers one week before the exit. It shows the proportionof the two groups in each category of drug and the average number of offers. The price difference displayed is theaverage of the difference of the mean price of the two groups by country in each category.

However, we also observe that switchers tend to have a higher average

rating (99.2) the week prior to the exit, compared to all other Evolution dealers

(97.9). It appears that ‘better’, more mature sellers that tend to have a more

narrow offering of products of likely high quality stay in the market and


switch platforms in response to the exit. It is not surprising then that the

average rating for this group of dealers recovers within the 100 days range

after switching.

3.5 results

Table 3.6 presents the main estimation results, corresponding to the model

outlined in section 3.4. We consistently find that a better rating is associated

with a higher price. A one percentage point increase in rating increases the

price for all drugs except Heroin by a substantial and statistically significant

amount. The associated price premium is about $2 for Cannabis, $12 for Co-

caine, $6 for MDMA and $3 for Speed. These results are also economically

significant in their relative magnitude—a one percentage point increase in

rating in the respective estimation sample is associated with up to a 45% of

a standard deviation increase in the respective unit price (45% for Cannabis,

15% for Cocaine, 13% for MDMA and 7% for Speed). The insignificant re-

sult for Heroin should be interpreted with caution, as we only observe six

switching vendors for Heroin.

Table 3.6: Results

Cannabis Cocaine Heroin MDMA Speed

Rating 1.87*** 11.63*** 0.19 6.42*** 2.90***(0.45) (1.89) (0.14) (0.85) (0.69)

Nr. of competitors −0.02*** 0.02 −4.38*** −0.19*** −0.48***(0.00) (0.06) (0.24) (0.03) (0.05)

Escrow 0.27*** 6.45*** 20.89*** 2.59*** 0.49***(0.03) (0.89) (1.86) (0.50) (0.06)

Country × Vendor × Quant FE � � � � �Month FE � � � � �N 113,198 36,613 11,573 38,942 14,653

Notes: Results based on a linear model as specified in section 3.4. The sample is restricted to countries withswitching vendors and a time period around the evolution exit, from one month prior to the exit until two weeksafterwards. Heterocedasticity-robust standard errors given in parentheses. *, ** and *** denote p<0.1, p<0.05 andp<0.01, respectively.

The coefficients for the other variables show the expected sign. An increase

in competition as measured by the number of competitors has a negative

3.5 results 93

Table 3.7: Results with extended post-exit sample


Rating −0.39 8.71*** 0.36** 3.38*** 2.20**(0.40) (2.42) (0.16) (0.64) (0.92)

Nr. of competitors −0.01*** 0.03 −5.43*** −0.07*** −0.15**(0.00) (0.06) (0.26) (0.02) (0.07)

Escrow 0.02 3.85*** 5.32*** 1.21*** −0.23*(0.03) (0.78) (1.39) (0.24) (0.13)

Country x Vendor x Quantity FE � � � � �Month FE � � � � �N 131,419 42,265 13,417 45,205 16,967

Notes: Results based on a linear model as specified in section 3.4. The sample is restricted to countries withswitching vendors and a time period around the evolution exit, from one month prior to the exit until three weeksafterwards. Heterocedasticity-robust standard errors given in parentheses. *, ** and *** denote p<0.1, p<0.05 andp<0.01, respectively.

effect on the asking price of sellers, while use of the escrow service increases

the unit price of the item on offer. The size of the parameters emphasizes

the special role reputation plays in this black market: a one percentage point

increase in rating consistently yields a greater price premium than offering

escrow and more than offsets an increase in competitors (with the exception

of Heroin).

As previously documented, ratings for switching vendors recover quickly.

This implies that the ratings effect should disappear over time. Indeed, the

more we extend the post-exit sample observation period, the more the effect

weakens. The results in Table 3.7 are based on a sample in which the post-

exit cutoff was extended by a week. All coefficients are consistently smaller.

The estimate for Cannabis is indistinguishable from zero, while for Cocaine,

MDMA, and Speed, we observe reductions in parameter size between 25%

and 48%. The exception is the estimate for Heroin which is now marginally

significant and slightly larger, but still negligible in economic terms.

As a robustness check, we perform a placebo test. We assume a pseudo-exit

to occur on 23.02.2015 (before the actual exit) and use similar time restrictions

as previously. The results are given in Table 3.4 in the Appendix. We find

that the coefficients are always insignificant, with the exception of Speed, for

which we find a very small positive effect. However, the estimates are very


noisy. We are confident that our main results identify the effect of rating on

price induced by the platform exit for switching vendors.

The results from our preferred models in Table 3.6 are based on a flexible

within-item specification, including fixed effects based on the intersection be-

tween country, vendor and item quantity. We also report results in Table 3.3 in

the Appendix that rely on a model including country, vendor, item quantity

and month specific effects. The choice of specification and the level of fixed

effects does not influence the results.

3.6 conclusion

In this paper we examine the role that seller reputation plays in the online

market for illegal drugs. We make use of a novel dataset of webscrape infor-

mation of offers on the two dominant sales platforms during 2014/15. Similar

to legal online marketplaces, these ‘darknet platforms’ offer a ratings system

for sellers operating in the market. The institutional void and strong need for

traders to remain anonymous in this black market suggests that reputation is

a driving force to facilitate trade among market participants. The descriptive

analysis highlights that (i) a higher rating is associated with a higher price,

(ii) the ratings distribution exhibits the commonly observed ‘J-shape’, and (iii)

sellers offer large quantity discounts for bulk offers.

In our analysis, we exploit the fact that one of the two platforms suddenly

disappeared in March of 2015 and track sellers that are forced to migrate

to the remaining marketplace in the aftermath. By necessity, these sellers

must register a new account and therefore experience a ratings reset. Using

this exogenous variation in ratings allows us to identify the effect of rating

on the unit price a seller may charge. We consistently find a large, positive

effect of rating on price across drug categories. We find a price premium of

2$ for Cannabis, 12$ for Cocaine, 6$ for MDMA, and 3$ for Speed for each

percentage point increase in rating. On average, this effect corresponds to an

increase of about 20% of a standard deviation of the respective unit price. As

the ratings shock subsides over time, the effect decreases.

3.6 conclusion 95

Our work in this paper demonstrates that rating has a large influence on

price in the absence of legal institutions. A sellers rating appears to be the key

determinant of prices. This corroborates previous literature which suggests

reputation may play a crucial role in facilitating trade when governmental or

legal institutions are lacking. Our results further document that it is difficult

to transfer reputation across different online marketplaces, even when doing

so would be to the sellers’ advantage. Studying the dynamics of reputation

in more detail in such an institutional void is a promising pursuit for future

research.


3.7 appendix

Figure 3.1: Silk Roads payment system

Notes: The figure shows the payment system originated by Silk Road. Using the escrow system of the platform,buyers may transfer payment onto the escrow account instead of sending directly to the seller. Finalizing the orderrefers to buyers signalling receipt of the goods.

3.7 appendix 97

Figure 3.2: Screenshot of the Grams search engine website

Table 3.1: Country differences for cocaine

MedianShipping origin country Mean unit price # Offers # Vendors quantity

United States 79.95 1, 177 200 3.50gUnited Kingdom 105.57 776 120 2gNetherlands 86.05 733 101 3gAustralia 267.47 507 84 2gGermany 92.86 466 62 5gCanada 93.69 265 44 3.50gFrance 107.18 106 18 1gSweden 124.52 73 14 2gBelgium 84.63 62 10 5gItaly 97.21 42 6 5g

Notes: The table reports summary statistics for cocaine for the ten largest countries of origin as measured by thenumber of vendors active, sorted by size. Prices are reported in USD. The Bitcoin exchange rate used correspondsto the day on which the item price was observed. Unit price refers to the price per 1 gram.


Figure 3.3: Distribution of the unit price demanded for all eight categories of drugs

0e+00

1e+05

2e+05

3e+05

0 10 20 30 40 50Cannabis

coun

t

0

25000

50000

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125000

0 50 100 150 200MDMA

coun

t

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0 100 200 300 400Cocaine

coun

t

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0 200 400Meth

coun

t

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30000

0 200 400Heroin

coun

t

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coun

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0 5 10LSD

coun

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0 50 100 150Speed

coun

t

Notes: The figure shows the distributions of the unit price of the eight drugs considered. Prices are reported in USD.The Bitcoin exchange rate used corresponds to the day on which the item price was observed. Unit price refers tothe price per consumption unit, defined as 1 gram for all categories except LSD, where it is 100 μg.

3.7 appendix 99

Figure 3.4: Distribution of the quantity offered for all eight categories of drugs

0e+00

2e+05

4e+05

6e+05

0 100 200 300 400 500Cannabis

coun

t

0e+00

1e+05

2e+05

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coun

t

0e+00

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coun

t

0

30000

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0 50 100 150 200 250Meth

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0 20 40 60Heroin

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coun

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0e+00

5e+04

1e+05

0 500 1000 1500 2000Speed

coun

t

Note: The figure shows the distributions of the quantity of the eight drugs considered. The unit used is grams,except for LSD, where it is micrograms.


Figure 3.5: Number of unique offers for illegal drugs by shipping origin

Notes: The figure shows the total number of unique items shipped from each country on both platforms. The largestmarket is the United States. Most of the offers originate in North America, (Western) Europe, and Australasia.

Figure 3.6: Platform uptimeAgora Evolution

Jul 2014 Oct 2014 Jan 2015 Apr 2015 Jul 2015 Jul 2014 Oct 2014 Jan 2015 Apr 2015 Jul 2015

0.00

0.25

0.50

0.75

1.00

Shar

e U

ptim

e

0

500

1000

1500

Speed (ms)

Notes: The figure shows the percentage share of uptime for each of the two platforms. The speed of accessing thesite is indicated by the shading. The Evolution exit is indicated in grey.

3.7 appendix 101

Figure 3.7: Distribution of seller rating

0

500000

1000000

1500000

0 25 50 75 100Agora

coun

t

0

250000

500000

750000

25 50 75 100Evolution

coun

t

Notes: The figure shows the distribution of ratings of the individual vendor accounts. The rating is scaled for bothplatforms from 0 to 100, where a higher number indicates a better rating.

Table 3.2: Sellers seven days after the exit

Proportion of sellers Mean unit price

Category Switchers Ago dealers Switchers Ago dealers Price difference

Cannabis 0.40 0.52 11.64 10.48 -0.62MDMA 0.25 0.29 34.67 44.32 -6.17Cocaine 0.15 0.26 106.55 111.65 10.12Speed 0.12 0.12 6.18 21.16 -1.77Heroin 0.10 0.10 142.77 169.05 21.23LSD 0.06 0.08 3.67 4.66 1.39Ketamine 0.04 0.04 47.91 54.15 6.91Meth 0.04 0.11 274.20 147.96 -27.04

Notes: The table contrasts switchers to all other Agora dealers one week after the exit. It shows the proportion ofthe two groups in each category of drug and the average unit price. The price difference displayed is the average ofthe difference of the mean price of the two groups by country in each category.


Figure 3.8: An example of a PGP key

Notes: The figure shows an example of a public PGP key block. The key can be used to encrypt information sentto the owner of the private PGP key. These PGP key blocks are provided by the sellers on their account informationand directly visible to buyers.

3.7 appendix 103

Figure 3.9: The bitcoin exchange rate

200

300

400

500

600


0

2000

4000

6000

2012 2014 2016 2018

Exch

ange

Rat

e BT

C−U

SD

Note: The figure depicts the bitcoin-USD exchange rate from 2011 to November 2017. The highlighted segmentshows the exchange rate in the timeframe studied in this paper. The Evolution exit is indicated by the vertical line.

Figure 3.10: Price difference between the platforms

−20

−10

0

10

20

Jul Okt Jan Apr

Mea

n U

nit P

rice

Diff

eren

ce A

gora

−Evo

lutio

n

Notes: The figure depicts the mean unit price differences between the two platforms. Prices are reported in USD.The Bitcoin exchange rate used corresponds to the day on which the item price was observed. Unit price refers tothe price per consumption unit, defined as 1 gram for all categories except LSD, where it is 100 μg.


Table 3.3: Results for alternative specification


Rating 2.03*** 12.50*** 0.20 5.64*** 4.67***(0.48) (2.34) (0.18) (0.95) (1.26)

Nr. of competitors −0.02*** 0.00 −5.78*** −0.16*** −0.39***(0.00) (0.07) (0.26) (0.03) (0.08)

Escrow 0.03 4.81*** 7.39*** 0.94*** −0.25*(0.04) (0.86) (1.43) (0.33) (0.14)

Country x Vendor x Quantity FE � � � � �Month FE � � � � �N 113219 36636 11578 38973 14671

Notes: Results based on a linear model as specified in section 3.4. The sample is restricted to countries withswitching vendors and a time period around the evolution exit, from one month prior to the exit until two weeksafterwards. Heterocedasticity-robust standard errors given in parentheses. *, ** and *** denote p<0.1, p<0.05 andp<0.01, respectively.

Table 3.4: Results for placebo


Rating 3.60 −95.45 −8.64 16.40 0.28***(5.41) (143.48) (7.25) (18.69) (0.08)

Nr. of competitors 0.02 −0.30 −2.22** −0.92 −0.16***(0.05) (0.85) (1.07) (1.07) (0.03)

Escrow −0.12 −5.74 24.46*** 3.34*** 0.58***(0.57) (13.06) (2.33) (0.85) (0.06)

Country x Vendor x Quantity FE � � � � �Month FE � � � � �N 77163 23541 7767 25226 9953

Notes: Results based on a linear model as specified in section 3.4. The sample is restricted to countries with switch-ing vendors and a time period around a placebo evolution exit on 23.02.2015. Heterocedasticity-robust standarderrors given in parentheses. *, ** and *** denote p<0.1, p<0.05 and p<0.01, respectively.

references 105

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STATUTORY DECLARAT ION

Hereby I declare,

• that I wrote this dissertation without any illicit assistance and without

using any other aids than stated and that this dissertation was neither

presented in equal nor in similar form at any other university;

• that I cited all references that were used respecting current academic

rules.

Place and date of issue:

St. Gallen, July 2018

Signature:

(Nicolas Eschenbaum)

CURR ICULUM V ITAE

education

2013–2018 PhD in Economics and Finance

University of St. Gallen, Switzerland

Thesis supervisor: Prof. Dr. Stefan Bühler

2011–2012 M.Sc. in Economics

University of Edinburgh, United Kingdom

2008–2011 B.Sc. in Economics

University of Maastricht, Netherlands

professional experience

2018–now Postdoctoral Researcher, Institute of Economics (FGN)


2012–2018 Research Assistant, Institute of Economics (FGN)


St. Gallen, July 2018

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