Payment Evasion: Payment Evasion

TL;DR: In this article, the authors show that a firm can use the purchase price and the fine imposed on detected payment evaders to discriminate between unobservable consumer types, and they illustrate with data from fare dodging on public transportation.

Abstract: This paper shows that a firm can use the purchase price and the fine imposed on detected payment evaders to discriminate between unobservable consumer types. Assuming that consumers self‐select into regular buyers and payment evaders, we show that the firm typically engages in second‐degree price discrimination in which the purchase price exceeds the expected fine. In addition, we find that higher fines do not necessarily reduce payment evasion. We illustrate with data from fare dodging on public transportation.

Summary

1 Introduction

• Payment evasion—fraudulent consumption by nonpaying consumers—is a serious issue for firms in different industries.
• The implicit assumption is, of course, that the consumers’ co t associated with payment evasion are high enough for them to refrain from fraudulent consumption.
• Yet, since the enforcement by public agencies is sketchy and varies acrossjuri dictions, firms undertake substantial private investments in technologies to detectand punish payment evasion.
• 3Retailers, for instance, regularly impose in-store penalties for shoplifting.
• Using data on the universe of detected payment evaders, the authors find the following main results.

2 The Model

• The authors first introduce the decision makers in their model: the firm and the consumers.
• Next, the authors derive the demand of paying consumers and the demand for payment evasion and study how the demand functions depend on the price and the fine, as well as the cost of evading payment.

2.1 Firm

• The fixed cost of providing the product isF > 0 5Rational consumer choices also give rise to payment evasionunder pay-as-you-wish pricing (Chen et al. 2013).
• The key difference is that, under such a pricing scheme, payment evasion is tolerated and not subject to a fine.
• The authors let(π ,Fπ) denote the detection technology that allows the firm to detect payment evasion with probabilityπ ∈ [0,1] after investingFπ >.
• Forπ < 1, detection is uncertain and assumed equally likely for all consumers (Polinsky and Shavell 2000).
• If no such technology were available, the firm could not recoup the unit cost with the highest possible expected fine, which in turn implies that payment evasion cannot be an additional source of profit.

2.2 Consumers

• The authors consider a market with a mass ofN potential consumers who observe the pricep and the finef before making a choice.
• Assumption 1 assures that consumers self-select into one ofthree segments.
• Notice that Assumption1 implies that the consumers who evade payment suffer from a perceived qualitydegradation (Yaniv 2009, Belleflamme and Peitz 2012).
• This definition implies that a higher price increases payment evasion (∂E/∂ p > 0), mirroring the associated reduction in demand (∂D/∂ p < 0).
• In effect, payment evasion allows the firm to sells two versions of the same product at different prices to consumers with different valuations of these versions.

3 Managing Payment Evasion

• This section derives the optimal price and fine in the presence of payment evasion and provides the relevant comparative statics.
• In addition, weconsider two extensions where the firm has additional tools to deal with payment evasion.
• First, the authors allow the firm to choose the effectiveness of its enforcement technology through costly effort.
• To simplify exposition, the authors suppress the dependence on the model parameters wherever possible.

3.1 Optimal Price and Fine

• In the presence of payment evasion, the firm can generate profit from two consumer segments: paying consumers and payment evaders.
• The reason for the cost-reducing effect is that some payment evaders are deterred and leave the market.
• The maximum admissible fine and the evasion cost clearly affect th firm’s choice of the optimal price.
• In addition, Proposition 2 shows that higher evasion costs go along with a higher price.
• 12This result is reminiscent of multiproduct monopoly pricing with interdependent demands when the products are substitutes (Tirole 1988, p. 69).

3.2 Endogenous Detection Probability

• To endogenize the choice of the detection technology, the authors nowassume that the firm can influence both the detection probability and the cost of the det ction technology through its choice of costly effort.
• To this end, the authors extend their model to a setting where the firm makes sequential decisions.
• Specifically, the authors consider the following two-stage game:.
• This timeline captures a business environment in which the control effort can be varied in the short run, whereas the price and the fine are chosen in the long run.13 0.
• In addition, Proposition 5 shows that the comparative statics with respect to f̄ are similar to the predictions in the law and economics literature:.

3.3 Endogenous Technological Protection

• The authors now assume that the firm can invest in technical protectionto raise the evasion cost borne by consumers before it chooses the price and the fine.
• 14Examples include the installment of anti-shoplifting devices or the use of digital rights management systems.
• Clearly, the optimal choice of technical protection depends on the functional form of the cost functionFk(k).
• Now, if the solution to problem (8), denoted ask∗, exceeds̄k, a level ofk so high that evading payment is “too costly,” payment evasion is prevented endogenously by means of technical protection.
• Fork∗ < k̄, there remains some level of payment evasion, which is detected with probabilityπ .

4 Illustrative Example

• The authors now illustrate their above analysis with an example where the consumers’ indirect utility functions are explicitly specified.
• For simplicity, the authors setN equal to unity and assume that consumer typesθ are drawn independently from a uniform distribution over the interval[0,1].
• In addition, the authors assume that consumers have rational expectations about the actual detection probability and setφ = π .
• In addition, notice that the demand for the outside option does not dependon the pricep.
• The next result illustrates the key results derived in Propositions1 to 4.

5 Empirical Evidence

• The authors examine payment evasion on theZurich Transport Network(ZVV), where evading payment is equivalent to fare dodging.
• In contrast to the extensive literature on the impact of public enforcement on unlawful behavior (see, e.g., Levitt 1997, DiTella and Schargrodsky 2004, DeAngelo 15Waldfogel (2012b) provides a comprehensive survey on the empirics of digital piracy.
• 14 and Hansen 2014), the authors focus on the private enforcement by the ZVV, exploiting passengerlevel data over a period of four years, extending from June 1,2009 to May 31, 2013.
• Then, the authors compare the characteristics of all passengers who use public transportation with those of payment evaders, using census data and individual-level data from the ZVV.
• Next, the authors estimate the amount of payment evasion on the transport network.

5.1 Transportation Company

• The ZVV is a public transportation company that coordinatesmore than 50 operators and offers railroad, bus, tram, and boat services in Zurich and its surrounding regions.
• Specifically, the ZVV chooses the following fines: Passengers who fail to present a valid ticket are required toprove their identity and to pay CHF 80 (about $85) in the case of a first offense.
• In the case of a thirdoffense (or more than three offenses), the fine increases to CHF 150 (about $160), but there are no criminal charges pressed.
• The personal information collected from payment evaders isstored in a data pool operated by the ZVV.
• 17Additional charges apply for noncooperative behavior in ticket inspections, giving incorrect personal information, and for forging tickets (which may lead to criminal prosecution).

5.2 Passengers

• The characteristics of passengers who use the ZVV transportnetwork are obtained from a sample constructed from 2010 census data on transportationand mobility.
• 18 This indirect approach using census data is necessary to construct a reference group, since the ZVV solely collects data on detected payment evaders.
• The characteristics of payment evaders are obtained from a sample constructed from data provided by the ZVV which covers the time span June 1, 2009 to May 31, 2013.19.
• A unique feature of the data is that it includes all passengers who have been detected as payment evaders during the sample period.
• Second, roughly 20% of the payment evaders are caught repeatedly.

5.3 Payment Evasion

• Tickets inspections on the ZVV network are unannounced and co ucted by plain-clothes agents.
• Next, the authors usêπ and the number of detected payment evadersẼ to estimate the total amount of payment evasion asÊ = Ẽ/π̂, which is the empirical counterpart of payment evasionE in the theoretical model (see Definition 1).
• Table 3 summarizes these estimates and provides the relevant deterrence levels for first-time and repeat offenses.
• It is worth noting that even the lowest available ticket price is higher than any of the expected fines, a necessary condition for payment evasion to occur (consistent with Proposition 1).
• Second, further increasing the detection probability through higher effort is too costly.

5.4 Increase in Maximum Admissible Fines

• The industry association for public transportation allowed its members to charge higher maximum fines for payment evasion starting from June 1, 2011.
• Some high-type evaders are induced to pay the price, while some l w-type evaders are induced to refrain from consumption, as illustrated in Figure 2.
• Reweighting is 20 performed such that the distribution of all offenders is taken as the reference distribution, and the individuals in the different offense groups are reweight d accordingly.
• Accounting for the change in the control effort does not qualitatively affect the results.
• Table 3 suggests that the detection probability was indeed reduceda cordingly.

6 Conclusion

• This paper has examined endogenous payment evasion in a model where the firm can charge a price to paying consumers and levy a fine on consumerswho are detected as payment evaders.
• In addition, the authors have provided empirical evidence on payment evasion on theZurich Transport Network, where evading payment is equivalent to fare dodging.
• In the theoretical part, the authors have derived three key results.
• Specifically, the presence of payment evaders leads to a peculiar form of price discrimination where the regular price exceeds the expected fine.
• The authors havconstructed the empirical counterparts of the relevant quantities in the theoreticalmodel, and they have found that the exogenous increase in the maximum admissible fines did not have a significant effect on payment evasion.

Figures

Figure 1: Cut-Off Values and Consumer Decisions.

Table 3: Quantifying Payment Evasion and Deterrence.

Figure 2: Deterrence Effect of a Higher Fine.

Figure 3: Number of Detected Payment Evaders, Total and by Gender.

Table 1: Fines for Traveling Without a Valid Ticket.

Figure 4: Normalized Number of Detected Payment Evaders by Subgroup.

Table 2: Descriptive Statistics for the Different Groups.

Full text

School of Economics and Political Science,
Department of Economics
University of St.Gallen
Payment Evasion
Stefan Buehler, Daniel Halbheer, Michael Lechner
November 2014 Discussion Paper no. 2014-35

Editor:
Martina Flockerzi
University of St.Gallen
School of Economics and Political Science
Department of Economics
Bodanstrasse 8
CH-9000 St. Gallen
Phone +41 71 224 23 25
Fax +41 71 224 31 35
Email seps@unisg.ch
Publisher:
Electronic Publication:
School of Economics and Political Science
Department of Economics
University of St.Gallen
Bodanstrasse 8
CH-9000 St. Gallen
Phone +41 71 224 23 25
Fax +41 71 224 31 35
http://www.seps.unisg.ch

Payment Evasion
1
Stefan Buehler, Daniel Halbheer, Michael Lechner
Author’s address:
Prof. Stefan Buehler
FGN-HSG
Varnbüelstrasse 19
CH-9000 St. Gallen
Phone +41 71 224 23 03
Fax +41 71 224 28 74
Email stefan.buehler@unisg.ch
Website www.fgn.unisg.ch
Associate Prof. Daniel Halbheer
HEC Paris
Department of Marketing
1, rue de la Libération
78351 Jouy-en-Josas Cedex
France
Email halbheer@hec.fr
Prof. Michael Lechner
SEW-HSG
Varnbüelstrasse 14
CH-9000 St. Gallen
Phone +41 71 224 28 14
Fax +41 71 224 23 02
Email michael.lechner@unisg.ch
Website www.sew.unisg.ch
1
The authors thank the Zurich Transport Network ZVV, Hofwiesenstrasse 370, 8090 Zurich, and in particular Peter
Nordenson, for providing the data, as well as Berno B¨uchel, Aaron Edlin, Preyas Desai, Markus Reisinger, and seminar
participants at the University of Hamburg, the University of Lausanne, and the University of Nuremberg for helpful
comments and suggestions.

Abstract
This paper models payment evasion as a source of profit by letting the firm choose the price
charged to paying consumers and the fine collected from detected payment evaders. The
consumers choose whether to purchase, evade payment, or refrain from consumption. We
show that payment evasion allows the firm to charge a higher price to paying consumers and
to generate a higher profit. We also show that higher fines do not necessarily reduce
payment evasion. Finally, we provide empirical evidence which is consistent with our
theoretical analysis, using comprehensive micro data on fare dodging on the Zurich
Transport Network.
Keywords
Payment Evasion, Pricing, Fine, Self-Selection.

1 Introduction
Payment evasion—fraudulent consumption by nonpaying consumers—is a serious issue
for firms in different industries. There are various ways in which consumers might obtain
a product or service without payment, including shoplifting (Yaniv 2009, Perlman and
Ozinci 2014), wardrobing (Timoumi and Coughlan 2014), and digital piracy (Chellappa
and Shivendu 2005, Vernik et al. 2011).
1
Another classic example for payment evasion
is fare dodging on public transportation (Boyd et al. 1989, Kooreman 1993).
2
Standard price theory abstracts from payment evasion and posits the excludability
of nonpaying consumers based on pricing alone. Or, as Hirshleifer et al. (2005, p. 19)
put it: “To acquire a commodity buyers must be willing to pay the market price [...].”
The implicit assumption is, of course, that the consumers’ cost associated with payment
evasion are high enough for them to refrain from fraudulent consumption. It is well
known, though, that many products exhibit some degree of nonexcludability (Novos and
Waldman 1984). Several legal instruments have been designed to enforce the exclusion
of nonpaying consumers, including patents, copyrights, and trade marks. Yet, since the
enforcement by public agencies is sketchy and varies across jurisdictions, firms undertake
substantial private investments in technologies to detect and punish payment evasion.
Antitheft devices, video-surveillance cameras, and digital rights management systems all
serve this purpose. It is fair to say that firms spend great effort on managing payment
evasion, but they rarely eliminate it.
In line with this observation, this paper models payment evasion as a source of profit
for the firm. Our focus is therefore on the management of payment evasion, rather than
its elimination. Key to our analysis is the firm’s ability to collect fines—albeit limited up
to a maximum admissible level mandated by law—from consumers detected as payment
evaders.
3
In such a setting, there are two sources of revenue: paying consumers and
payment evaders. We develop a model in which the firm chooses both the price charged
to paying consumers and the fine faced by payment evaders in order to maximize its
expected profit. An important feature is that the demands from paying consumers and
payment evaders are interdependent. Observing the price and the fine, consumers can
1
Belleflamme and Peitz (2012, 2014) provide a comprehensivesurvey and a recent update on the theory
of digital piracy.
2
Recent evidence from the US shows that shoplifters steal more than $13 billion worth of goods from
retailers every year (National Association for Shoplifting Prevention 2014); return fraud costed retailers
more than $9 billion in 2013 (National Retail Federation 2014); the consumption of digitally pirated music
in 2008 is estimated to be between $7 and $20 billion (Frontier Economics 2012).
3
Retailers, for instance, regularly impose in-store penalties for shoplifting. Under New York’s state law,
retailers may collect a penalty “not to exceed the greater of five times the retail price of the merchandise”
(N.Y. GOB. LAW §11-105).
2

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Payment evasion" ?

This paper models payment evasion as a source of profit by letting the firm choose the price charged to paying consumers and the fine collected from detected payment evaders. The authors show that payment evasion allows the firm to charge a higher price to paying consumers and to generate a higher profit. The authors also show that higher fines do not necessarily reduce payment evasion. Finally, the authors provide empirical evidence which is consistent with their theoretical analysis, using comprehensive micro data on fare dodging on the Zurich Transport Network. 

Q2. What are the future works mentioned in the paper "Payment evasion" ?

Their analysis suggests several avenues for future research. Second, one could extend the analysis to allow for competition among firms to study the role of payment evasion as a particular form of non-price competition. The authors hope to address these issues in future research.