n?u=RePEc:tut:cccrwp:2016-03-ccr&r=hpe

WORKING PAPER 2016-03-ccr

Preliminary version: December 2016

**Cheat** or **Perish**? A **Theory** of **Scientific**

**Customs**

Benoît LE MAUX

CREM-CNRS and Condorcet Center, University of Rennes 1,

France

Sarah NECKER

University of Freiburg, Walter-Eucken Institute, Deutschland

Yvon ROCABOY

CREM-CNRS and Condorcet Center, University of Rennes 1,

France

CONDORCET CENTER FOR POLITICAL ECONOMY

UNIVERSITY OF RENNES 1 – CREM-CNRS

www.condorcet-center.fr

**Cheat** or **Perish**? A **Theory** of **Scientific** **Customs** ∗

Benoît LE MAUX

benoit.le-maux@univ-rennes1.fr

University of Rennes 1, CREM-CNRS, Condorcet Center

Sarah NECKER

necker@eucken.de

University of Freiburg, Walter-Eucken Institute

Yvon ROCABOY

yvon.rocaboy@univ-rennes1.fr

University of Rennes 1, CREM-CNRS, Condorcet Center

December 1, 2016

Abstract

We develop a theory of the evolution of scientific misbehavior. Our empirical analysis of a

survey of scientific misbehavior in economics suggests that researchers’ disutility from cheating

varies with the expected fraction of colleagues who cheat. This observation is central to our

theory. We develop a one-principal multi-agent framework in which a research institution aims to

reward scientific productivity at minimum cost. As the social norm is determined endogenously,

performance-related pay may not only increase cheating in the short run but can also make cheating

increasingly attractive in the long run. The optimal contract thus depends on the dynamics of

scientific norms. The premium on scientific productivity should be higher when the transmission

of scientific norms across generations is lower (low marginal peer pressure) or the principal cares

little about the future (has a high discount rate). Under certain conditions, a greater probability of

detection also increases the optimal productivity premium.

JEL-Classification: A11, A13, K42.

Keywords: Economics of Science, Contract **Theory**, **Scientific** Misbehavior, Social Norms.

∗ The authors thank Roland Kirstein, David Masclet and Fabien Moizeau for helpful suggestions. Earlier

versions of this paper were presented at the University of Magdeburg, 2014; the European Public Choice Society

Meeting, Groningen, 2015; the Max Planck Institute Bonn, 2015; The Spring Meeting of Young Economists,

Ghent, 2015; the Beyond Basic Questions Workshop, Hannover, 2015, the University of Lisboa, 2015; the

University of Minho, 2015; and the University of Hamburg, 2016.

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1. Introduction

**Scientific** misbehavior imposes high costs on society. It has been estimated that every

paper retracted due to scientific misbehavior costs almost $400,000 in funds from the US

National Institutes of Health, for a total of $58 million between 1992 and 2012 (Stern et al.,

2014). These investments are at best wasted; misbehavior also misleads and delays scientific

progress. To minimize scientific misbehavior and the resulting costs, it is fundamental

to understand to what extent scientific misbehavior results from the rewards proposed to

researchers, and in particular the incentives to publish. Can rewards increase misbehavior?

Do rewards imply not only a short-run rise but also an increasing level of misbehavior over

time, by changing the social norms guiding research misbehavior? What is the best policy

of research institutions if their rewards induce misbehavior? These are the questions that we

address in this paper.

While incentives to publish have a long history in the US and Canada, they have become

increasingly important in other countries over the last two decades. Research evaluation

agencies have been established (e.g., in the UK and France), bibliometric indicators have

been included in the formulae used to allocate research funds (e.g., in Belgium, Denmark,

and Portugal), researchers’ salaries have been linked to performance (e.g., in Germany, Spain,

adn China), and researchers’ contract duration has been modified (e.g., in Finland and Italy).

The aim of these reforms was to improve the efficiency of public research by increasing the

quantity and quality of research output while taking the public budget constraint into account.

Franzoni et al. (2011) show that country incentives to publish are indeed positively related to

its scientists’ (successful) submissions to the journal Science.

Unfortunately, these reforms have also been cited as an explanation for the increasing

prevalence of unethical behavior in academia, such as the disproportionately high number of

positive findings (Fanelli, 2010) and statistically-significant results (Brodeur et al., 2016),

and articles being retracted due to fraud (Fang et al., 2012). 1 The idea is analogous

to the traditional economic model of crime, in which unethical behavior rises with the

associated monetary benefit (Becker, 1968). More specifically, a growing body of literature

has shown that competitive pressure is positively related to cheating (e.g., Schwieren and

Weichselbaumer, 2010, Gilpatric, 2011, Cartwright and Menezes, 2014). Necker (2014)

provides evidence for the same link in academia.

However, the previous literature is static in nature, and does not investigate the dynamics

of scientific cheating. As such it may miss important incentive effects. Recent research has

suggested that moral costs (the costs arising from the desire to do the right thing) are at least

as important for honest behavior as financial incentives (e.g., Mazar et al., 2008a; Gneezy

et al., 2013). As in the theory of social customs, a deviation from a social norm by a few

people can produce the erosion of the norm in the long run (e.g., Akerlof 1980, Corneo 1995,

Lindbeck et al. 1999, Fischer and Huddart 2008). This idea is central to our work here. If

rewards influence the perception of what is morally acceptable in the scientific community,

1 We define unethical behavior as actions that are “either illegal or morally unacceptable to the larger

community” (Jones, 1991, p. 367).

2

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misbehavior may increase over time.

To our knowledge, the existing literature has not looked at the extent to which

remuneration policies influence social customs, and how contracts should be designed to steer

the social custom towards honest behavior. An exception is Fischer and Huddart (2008), but

their analysis does not consider the evolution of the optimal contract over time. We fill this

gap by proposing a dynamic principal multi-agent model of scientific misbehavior. Academia

is a particularly interesting example for analyzing the link between rewards, norms, and

misbehavior. Although employers (government, universities or research centers) can provide

incentives for performance, they cannot directly control monitoring. The design of the reward

policy is therefore fundamental.

In our model, researchers (the agents) are heterogeneous in terms of labor productivity.

The research institution (the principal) aims to reward performance at the lowest possible

cost. The principal, however, cannot observe researchers’ productivity. For less-productive

researchers, this asymmetric information creates incentives to cheat in order to obtain the

same rewards as more-productive researchers. Following theories of social customs, a central

assumption of our model is that the researcher’s decision to cheat depends on the fraction of

colleagues who cheat. We back this assumption up with evidence from a survey of economists.

Our empirical analysis suggests that cheating is negatively related to utility; however, the

disutility of cheating falls with beliefs over the fraction of colleagues who cheat.

Our theoretical model reveals that the introduction of a premium on research

productivity (performance-related pay) not only leads to fraudulent behavior in the short run,

but may also change the norms of the scientific community in the long run (towards a “cheat or

perish” culture). Research institutions have to bear this in mind when introducing productivity

premia. The optimal contract depends on the dynamics of scientific norms (fraud). The

optimal scientific productivity premium is higher when there is less transmission of scientific

norms across generations (lower marginal peer pressure) or the principal cares little about the

future (has a high discount rate). Under certain conditions, a higher detection probability

(so that the expected reward from fraud is lower) also increases the optimal productivity

premium. We emphasize that a productivity premium, by fostering scientific fraud, may

produce negative externalities on scientific journals and their editors, while more effective peer

review creates positive externalities for the principal. The two actors should hence cooperate.

Our work contributes to the economics literature in a number of ways. First, we

contribute to the literature on the evolution of social customs. To our knowledge, we are

the first to model the principal-agent relationship in a dynamic setting in which behavior is

contagious. We not only investigate the long-run equilibrium, as do, e.g., Akerlof (1980),

Corneo (1995) and more recently Fischer and Huddart (2008), but also the convergence

process during which agents modify their decision to obey the code of good conduct. Second,

only a few pieces of work have theoretically analyzed researcher misbehavior. None of those

considers the principal-agent relationship or the moral costs of cheating. 2 Third, in contrast to

2 The economic theory of scientific fraud in Wible 1998 assumes that researchers optimally split their time

between fraudulent and legitimate activities. Hoover (2006) uses a game-theoretic model to show that it is

rational to engage in academic plagiarism if the probability of prosecution is low. Lacetera and Zirulia (2009)

study malfeasance in the research and publication process through a dynamic game of incomplete information.

3

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much of the related literature on rank-order tournaments (see e.g. Gilpatric, 2011), we allow

for agent heterogeneity.

The remainder of the paper is organized as follows. Section 2 discusses the literature

emphasizing the importance of the internal costs of cheating, and presents our empirical

results. Section 3 develops the theoretical framework and Section 4 simulates the model.

Last, Section 5 concludes.

2. The moral costs of cheating

2.1. Traditional theory in the light of recent evidence

The traditional economic theory of crime (proposed by Becker, 1968) focuses on individuals’

extrinsic motivations to cheat. **Cheat**ing results from a purely rational cost-benefit analysis of

the associated expected external rewards and costs. In a tournament, the benefits from cheating

increase with the intensity of competition (Gilpatric, 2011). However, recent findings from

psychology and behavioral economics indicate that rewards, monitoring, and sanctions have a

less clear-cut influence than that assumed in traditional theory (e.g., Rosenbaum et al., 2014).

A number of contributions have shown that individuals cheat much less than predicted (e.g.,

Gneezy, 2005; Mazar et al., 2008b; Gneezy et al., 2013; Abeler et al., 2014). A few people

cheat as much as they can, a few people are completely honest, and most people cheat a little.

Conrads et al. (2014) find such heterogeneous reactions to competitive incentives. There then

seems to be some variation in moral costs, i.e. the costs that arise from the desire to do the

right thing.

In line with the theory of social customs, the extent to which others follow (or are

believed to follow) the social norm has been shown to play a role. A classic example is given

in Cialdini et al. (1990), where individuals’ littering in public places depends crucially on

the littering behavior of other people. Experimental participants steal more from each other

according to others’ stealing (Falk and Fischbacher, 2002). Gino et al. (2009) show that

observing a confederate cheating is contagious. Abeler et al. (2014) find that participants who

believe that others cheat are also more likely to cheat themselves. Bailey et al. (2001) and

Necker (2014) provide evidence that economists’ beliefs about others’ behavior are related to

their own admitted misbehavior. The social context is therefore essential for misbehaviour, as

stressed in the theory of crime in Funk (2005).

2.2. Evidence on researchers’ moral costs

The above literature review suggests that individuals experience moral costs from cheating

that vary with the belief about or observation of what others are doing. We here consider

whether this also applies to researchers by using a unique survey of economists. In 2010

and 2011, an anonymous online survey was conducted among the members of the European

Economic Association (EEA), the German Economic Association, and the mailing lists from

Last, Kiri et al. (2014) show that increasing the benefit from confirmatory results is a way of improving the

reliability of scientific research.

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Table 1. List of questions/practices

1 Have you ever copied parts from work of others without citing?

2 Have you ever copied from your own previous work without citing?

3 Have you ever refrained from citing results or opinions that are not in line with your own analysis?

4 Have you ever refrained from checking the contents of the works cited?

5 Have you ever suffered from incorrectly being excluded as co-author?

6 Have you ever cited strategically to raise publication prospects (e.g. to please editors or possible referees)?

7 Have you ever refrained from citing work in lower ranked journals, which in a ranking from A+ to C rank

lower than A?

8 Have you ever refrained from citing work from other disciplines?

9 Have you ever maximized the number of publications by dividing the work to the smallest publishable unit,

meaning several individual articles covering similar topics and differing from each other only slightly?

10 Have you ever complied with suggestions by referees or editors when you thought that they are wrong?

11 Have you ever defined the research question according to data availability?

12 Have you ever excluded part of the data (e.g. outliers) without reporting this?

13 Have you ever corrected data to fit the theory?

14 Have you ever fabricated some data?

15 Have you ever presented empirical findings selectively so that they confirm one’s argument

16 Have you ever used tricks to increase t-value, R2, or other statistics?

17 Have you ever searched for control variables until you got the desired results?

18 Have you ever stopped statistical analysis when you had a desired result?

the French Economic Association and the Journées de Microéconomie Appliquée. The survey

requested information on economists’ norms, (mis-)behavior, professional situation, and life

satisfaction. A summary of the responses can be found in Necker (2014). Feld et al. (2014)

use the survey to show that the professional situation helps determine economists’ satisfaction.

This information allows us to see whether reported misbehavior and satisfaction are related,

and whether the link depends on beliefs over peer behaviour.

One concern regarding self-reports is that they underestimate the true frequency of

misbehavior. However, John et al. (2012) find that the bias seems to be smaller with regard

to questionable research practices, and the survey focuses on these kinds of practices. The

sample has been shown to be representative of the population. 3 We include all respondents

for whom information is available (n = 934). To account for item-non response, missing

values were replaced via multiple imputation. 4 At the minimum, this survey yields suggestive

evidence on researchers’ moral costs from misbehavior.

The survey asked economists to assess the justifiability of 18 research practices on a

6-point Likert scale, and to report their own engagement in these practices (see Table 1).

We create a misbehavior index M i based on the answers. We first calculate the average

justifiability of each practice. Second, for each respondent, we sum the average justifiability

3 The response rate was 17% in the first wave (EEA) and 11% in the second (German) and third (French)

waves. Survey participants are representative of members of the association in terms of gender and location of

workplace. The comparison of responses from early and late respondents, and from participants who continued

until the last page and those that dropped out, do not indicate unit-non response bias. A detailed description of

the methodology, the representativeness analysis, and the multiple imputation can be found in Necker (2014).

4 The data are imputed using multiple imputation using chained equations. The methodology is described,

e.g., in Cameron and Trivedi (2005).

5

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Table 2. Misbehavior, beliefs and satisfaction a

(1) (2) (3) (4)

Own misbehavior M i -0.296*** -0.448* -0.264** -0.445*

(0.106) (0.235) (0.108) (0.239)

Belief B i -0.029*** -0.037** -0.027*** -0.037**

(0.007) (0.016) (0.008) (0.016)

M i ∗ B i 0.013 0.015

(0.020) (0.020)

Other controls NO NO YES YES

F 13.7 9.5 3.2 3.2

R2 0.03 0.03 0.12 0.12

N 934 934 934 934

a These are OLS coefficients. Standard errors between brackets. All

five imputations are used, with the results combined using Rubin’s rule.

Hypothesis tests are based on robust standard errors. The measures of fit are

the lowest statistic among results from the five imputations. Significance

levels: ∗ = 10% ∗∗ = 5% ∗ ∗ ∗ = 1%.

of the practices that he or she admits to having employed and divide this by the total number

of practices. 5 A higher index value indicates that the respondent admits to having employed a

greater number of practices or of less well-accepted practices.

Economists’ beliefs regarding others’ behavior are captured by responses to the question

on what fraction of research in the top journals the respondent believes to be affected by four

categories of misbehavior (e.g., “incorrect application of empirical methods”). Respondents

answered on a 10-point scale from “up to 10%” to “up to 100%.” We calculate a variable B i as

the sum of these four responses (which we treat as continuous): a higher value of B i implies a

greater perceived prevalence of misbehavior. The satisfaction question is “Generally speaking,

how satisfied are you with the life you lead?” Responses were given on a 6-point Likert scale

(“highly dissatisfied” to “highly satisfied”). In line with the literature, reported satisfaction is

employed as a measure of utility U i (e.g., Layard et al. (2008)).

To see whether researchers’ utility U i is affected by misbehavior M i , and whether this

link depends on the fraction of researchers who are believed to cheat B i , we estimate the

following ordinary least squares (OLS) equation. Much of the happiness literature treats the

dependent variable as cardinal and uses OLS (Ferrer-i Carbonell and Frijters, 2004).

U i = γ 0 + γ 1 M i + γ 2 B i + γ 3 M i × B i + x i γ 4 + ε i . (1)

The interaction M i × B i captures whether the effect of misbehavior on satisfaction is lower

when others are believed to misbehave more. We include gender, year of birth, citizenship,

academic position, and whether the respondent has tenure or not in the controls, x i . We

estimate the model with and without the interaction M i ×B i and with and without the controls.

Table 2 shows the regression results. Own misbehavior M i is negatively correlated

with satisfaction. A one standard-deviation (SD) rise in this index reduces satisfaction by

1/10 of a SD (column (1)). This effect is largely unchanged when control variables are

included (column (3)). Although these results cannot prove causality, they are consistent

5 The summary statistics of the variables used appear in Necker (2014).

6

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Figure 1. The marginal effect of the interaction effect

Note: The figures are calculated from the regression shown in column (4). These are

average marginal effects ∂U i

∂M = γ

i

1 +γ 3 B i with 95%-confidence intervals at different values

of B i .

with individuals facing moral costs from cheating. While the relationship seems small in size,

we should remember that participants report their overall satisfaction with life. The belief that

misbehavior is widespread is also negatively related to satisfaction. A rise in this belief by

one SD implies a fall in satisfaction of 1/7 of a SD.

The second and fourth columns present the estimates including the interaction term

M i × B i . The coefficient on this interaction is insignificant. However, Brambor et al. (2006)

stress that the standard error of interest is not the standard error of γ 3 but that on the value

of ∂U i

∂M i

= γ 1 + γ 3 B i . We thus calculate the derivative and its standard error at different levels

of B i : the results are shown in Figure 1. These indicate that, for instance, respondents who

believe that on average up to 10% of the research in journals is subject to misbehavior (B i = 4)

experience a utility loss of 0.4. By way of contrast, respondents who believe that on average up

to 30% of the research in journals is subject to misbehavior (B i = 12) experience a utility loss

of 0.3. The effect of M i on U i is insignificant, i.e., no significant utility loss, for economists

who believe that there is a high prevalence of misbehavior (B i ≥ 15). The results are consistent

with the notion that researchers’ moral costs of cheating vary with their beliefs about what

their peers do.

3. A dynamic theory of optimal scientific misconduct

A fundamental goal in the reward structure of science is to establish priority of discovery

by being the first to communicate an advance in knowledge. Publication is a necessary step

in establishing this priority and gaining recognition from the scientific community (Stephan,

1996). The number of published articles and the ranking of the journals in which articles

are published are thus outcomes of interest for the researcher. The central question here is

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whether these articles will be produced in a fraudulent way. The considerations in Section 2

emphasize the importance of including three different types of motivations in our theoretical

model.

1. Extrinsic motivation. In our setting, this corresponds to the contracts offered to

researchers. In line with Becker (1968), promotion, tenure, and compensation based

on publication are assumed to provide incentives to misbehave.

2. Unconditional (intrinsic) commitment to honesty. We assume that agents are

heterogeneous in the utility loss they experience from dishonestly reporting research.

A similar assumption is made by Funk (2005) in her theory of crime and by Fischer and

Huddart (2008) in their theory of optimal contracting.

3. Conditional (norm-based) commitment to honesty. We assume that individuals’ utility is

affected by others’ obedience to a code of good conduct (Akerlof, 1980, Corneo, 1995).

As a result of this conditional honesty, performance incentives may have multiplier

effects.

3.1. The dynamics of scientific cheating

Consider a scientific community in which an infinite number of researchers (the agents in our

model) are divided up into identical non-overlapping generations, each living for one period t.

The agents are heterogeneous in their job performance θ (see also Lacetera and Zirulia, 2012),

having either low θ L (“normal researchers”) or high θ H (“leading researchers”) scientific

productivity, with θ L < θ H . These differences may reflect multiple factors: ability, teaching

and administrative duties, research budgets, spillover effects due to the presence of colleagues

who are specialized in the field, or family life. The distribution of θ is characterized by:

p = P(θ = θ L ) ∈ (0,1) and 1 − p = P(θ = θ H ), (2)

Researchers are hired by a single principal, e.g. the government, a university, or a

research institute. 6 The principal aims to reward productivity by paying researchers with

low productivity yt L and researchers with high productivity yt H , with y H > y L . High-type

researchers receive higher remuneration, which can take the form of a higher salary or of

rewards, prizes, and other monetary compensations. The core of the problem here is that

the principal cannot observe agents’ productivity θ, although it is common knowledge that θ

takes the value of θ L with probability p. In other words, the principal only observes output

(e.g., publications) without knowing whether these were produced unethically.

We distinguish between researcher utility functions u L and u H . However, these functions

are similar, depending only on lifetime income y t and being concave (so that individuals are

risk-averse). We assume that u(0) = 0. The agents will accept a contract offer only if their

utility there is greater than their reservation utility, denoted by u L min and uH min

. Researchers with

6 One justification for the focus on one principal is that it reflects a national government’s choice of policies

that provide incentives for researchers to publish, as described in the introduction or in Franzoni et al. (2011).

These incentives affect every researcher in the country in a similar way.

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a contract offer that produces utility lower than the reservation level will leave the scientific

community (the participation constraint). We have u L min < uH min and we let yk min , k = L,H,

denote the reservation income such that u k (y k min ) = uk min .

We assume that there is a code of good conduct in the scientific community. High-type

researchers reach high levels of output, earning yt H , without having to infringe this code. In

contrast, due to information asymmetries, low-type researchers can improve their publication

record by not obeying the code. Since our interest is in cheating, which is by assumption only

carried out by low-type researchers, we focus on them in the following. 7

Low-type researchers choose an action a ∈ A = {Obey,Disobey}. If they obey the code,

they receive yt L . If they disobey, it is impossible for the principal to distinguish low-type from

high-type agents. The agent receives yt H . We assume that the growing demand for publication

slots is satisfied by a growing supply of publication slots/journals. 8

All researchers are audited with certainty but this auditing process is imperfect, with a

probability π of being detected when cheating. If a low-type researcher obeys the code, he/she

is not punished and receives yt L . If a low-type disobeys and is not detected, he/she obtains the

salary of the high-type researcher yt

H without being punished. However, if the misbehavior is

detected, he/she is punished by a sanction s t , which reduces his/her lifetime income.

Researchers face moral costs. These vary by the individual’s commitment to honesty

(integrity), denoted by α i hereafter, which is independent of what others are doing and is

private information. This has a continuous uniform distribution on the unit interval I, i.e.

F(α) = α. In other words, α percent of researchers have an integrity coefficient less than or

equal to α.

Moral costs are also conditional on peer behavior. Past behaviors, whether they are

observed or not, create a working atmosphere in which agents form certain attitudes of

approval or disapproval, affecting the disutility of cheating agents. The fraction of lowproductivity

researchers who cheated in the past period is denoted by β t−1 . The peer-pressure

function v translates past cheating β t−1 into peer pressure: v(β t−1 ). We assume v > 0 and

v ′ = −µ with µ ≥ 0, i.e. peer pressure is a constantly decreasing function of the share of

past cheaters. The moral costs of cheating then fall with the fraction of cheaters in the past

period. A higher value of the scalar µ (the marginal peer pressure) implies that v decreases

more steeply with β t−1 , which increases the utility from cheating more.

Agent i will not cheat if the utility from choosing a = Obey (the left-hand side of

equation 3) is larger than the expected utility from choosing a = Disobey weighted by the

7 Schwieren and Weichselbaumer (2010) show experimentally that less-able individuals cheat more. Charness

et al. (2013) find that experimental participants who have lower rank in the performance distribution cheat more.

8 Although acceptance rates are falling at the top journals, the number of available publication slots has

increased extensively. Between 1997 and 2006, the number of journal articles covered by the Science Citation

Index (SCI) increased by 2.2% per year. The number of journals covered in the extended SCI increased from

5,467 in 1998 to 8,060 in 2009 (from 600 in 1964). The increase in the number of journals may even be

underestimated, as the SCI covers a falling proportion of the traditional scientific literature (Larsen and Von Ins,

2010).

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unconditional (α) and conditional (β) commitment to honesty (the right-hand side) 9 :

u L (y L t ) ≥ (1 − αi )

v(β t−1 ) × [ πu L (y L t − s t ) + (1 − π)u L (y H t ) ] , (3)

Equation (3) shows the incentive-compatibility constraint, in which peer pressure and

the unconditional commitment to honesty (α i ) interact. Since low-type agents vary only with

respect to the integrity coefficient, α will separate those who misbehave from those who do

not. Equation (3) can be rewritten as:

α i ≥ 1 −

u L (y L t )v(β t−1 )

πu L (y L t − s t ) + (1 − π)u L (y H t ) , (4)

The researchers who refrain from cheating are those with a higher value of the integrity

coefficient, as illustrated in Figure 2(a). As researchers are distributed on the unit interval,

the share of dishonest scientists among the low-types (β t ) in the short-run is directly given by

Equation (4). We have:

β t = 1 −

u L (y L t )v(β t−1 )

πu L (y L t − s t ) + (1 − π)u L (y H t ) . (5)

The fraction of cheaters will fall with y L t , π and s t , but rise with y H t , as stated in Proposition

1. These are the predictions of the traditional economic model of crime. The condition v ′ ≤ 0

implies that β t rises with β t−1 .

Proposition 1. The model leads to the following comparative-static derivatives:

∂β t

∂β t−1

≥ 0,

∂β t

∂y L t

≤ 0,

∂β t

∂y H t

≥ 0,

∂β t

∂π ≤ 0,

∂β t

∂s t

≤ 0.

The influence of β t−1 on β t is central in our theory, as it determines the extent to which

the t − 1 generation affects that at period t. One important result is that the marginal impact

of β t−1 depends on the contract, as shown in the following equation:

∂β t

∂β t−1

=

u L (y L t )

πu L (y L t − s t ) + (1 − π)u L (y H t ) × −v′ (β t−1 ) (6)

Past social customs will matter more for current social customs as (1) marginal peer pressure

is higher and (2) current incentives to cheat are lower. The higher the utility from honesty,

u L (yt L ), or the lower the expected utility from cheating, πu L (yt

H − s t ) + (1 − π)u L (yt H ), the

9 It is possible that researchers derive disutility from others’ cheating even if they do not cheat themselves,

as suggested by our empirical results. If we consider that the norm (1 − β t ) is a public good from which

agents derive utility, β t would appear on both sides of the equation in the multiplicative utility function, thereby

canceling each other out. Another possibility is to assume that disutility falls with the share of deviators in

the case of an additively-separable utility function (as in Lindbeck et al., 1999). We consider a multiplicative

function for the main reason that it allows us to assume that even the most amoral researcher (with α = 0) is

affected by peer pressure. This implies that β t = 0 is a potential long-run equilibrium (if peer pressure is strong).

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(a) Period 1: initial setting

Dishonest low-types

Honest low-types

(b) Period : short-run impact of external factors

(c) Period 1: contagion effects

Figure 2. The link between the contract, individual morality and the social norm.

greater is the impact of β t−1 on β t . One possible interpretation is that people pay more (less)

attention to norms when current incentives encourage (discourage) honesty.

A key feature of the model is that a change in any of the variables yt L , yt

H and s t or the

parameter π affects not only β t but also β t+1 , i.e. the level of future fraud:

∂β t+1

∂(.) = ∂β t

∂(.)

}{{}

initial

× ∂β t+1

∂β t

} {{ }

contagion

(7)

Equation (7) shows that the derivative consists of an initial and a contagion effect, as illustrated

in Figures 2(b) and 2(c). Greater publication incentives not only encourage fraud at t but also

reduce the conditional commitment to honesty at t + 1. The latter effect can be interpreted as

the “crowding out” of social norms by external incentives. As we will see below, performancerelated

pay can have multiplier effects. Publication pressure not only leads to fraudulent

behavior in the short run but can also make cheating increasingly attractive in the long run.

3.2. The optimal remuneration of researchers in the short run

We describe the contracts by adopting the following time line within each period: (1) β t−1

is known; (2) researchers learn their type (productivity θ and integrity α); (3) the principal

designs the salary policy; (4) each researcher accepts or rejects a contract (i.e. decides to

fraud or not); and (5) researchers who reject both contracts receive their reservation utility.

We assume that in each period the principal cannot withdraw the offer once it is accepted.

Any withdrawal would destroy the reputation for honouring agreements.

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Table 3. Components of the Principal’s cost function

Percentage of

Percentage of

low-type researchers: p high-type researchers: (1 − p)

Percentage of Percentage of

dishonest researchers: honest researchers:

β t (1 − β t )

Probability of

being discovered: π yt H − s t yt L yt

H

Probability of

not being discovered: (1 − π) yt H yt L yt

H

The principal aims to identify the remuneration policy or remuneration contracts

(yt

L∗ ,yt

H∗ ,st ∗ ) that reward differences in productivity at the lowest possible expected cost

per capita (denoted ec t ), given the incentive-compatibility and participation constraints. 10

Expected costs per capita are given by the following expression:

ec t = π p [ β t × (yt H − s t ) + (1 − β t ) × yt

L ]

+(1 − π)p [ β t × yt H + (1 − β t ) × yt

L ]

+ (1 − p) × y

H

t (8)

Table 3 sets out the components of the principal’s cost function. The principal bears costs

of (yt

H − s t ) if the researcher is a cheating low-type and the misconduct is detected, i.e. with

a probability of [π × p × β t ]. The costs are yt

H in the case of a non-detected cheating lowtype,

with a probability of [(1 − π) × p × β t ], or in the case of a high-type researcher, with a

probability of [1 − p]. The costs are yt L in the other states of nature.

The decision to pay based on publication implies that the principal cares about

performance. The principal cares about fraud if it affects costs, but not about fraud per se.

This assumption is motivated by the observation that universities and research centers take

the credit for publications, but are generally not held liable for inaccuracies in the results.

Moreover, better performance may allow the principal to obtain a higher operating budget.

Performance and the related budget are thus a realistic objective for the principal.

A central assumption is that the probability of detecting misconduct cannot be controlled

by the principal, i.e., it is exogenous. In academia, quality control is exercised by peer

review. An important aim of peer review is to discourage and detect fraud (Stephan, 2012).

The principal can send scientific work to qualified peers to assess whether the work is nonfraudulent.

However, the reliability of the peer review process cannot be controlled by the

principal. The optimal remuneration policy is thus given by:

min

{y L t ,y H t ,s t}

ec t = ec t (y L t ,y H t ,s t )

s.t. u L (y L t ) ≥ u L min ,

u H (y H t ) ≥ y H min , (9)

Disobedience can be eliminated by setting yt L = yt

H = ỹ, i.e. a contract without any

performance-based incentives. However, if ỹ is too low, high-type researchers will leave the

10 Note that, by construction, we focus on expected cost per capita due to the infinite number of agents.

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Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

scientific community. This is a standard adverse-selection problem. On the other hand, if ỹ

is set such that u H (ỹ) ≥ u H min

, i.e. such that high-types accept the contract, the remuneration

scheme will be costly to the principal. Were information about researcher type to be perfectly

known by the principal, she/he would give y H min to the high-types and yL min

to the low-types.

However, information is asymmetric.

An important feature of the model is the nonlinear relationship between low-type

income (yt L ) and expected costs per capita (ec t ). At low values of yt L , the incentives to cheat

are high for low-types, which implies that the principal has to pay yt

H to many researchers,

producing high ec t . If the principal increases yt L , disobedience is reduced. However, ec t

increases due to the increase in yt L . Hence, there exists an optimal level of remuneration (of

fraud) at which the differences in productivity are rewarded at minimum cost.

To solve the optimization problem, the principal first chooses the lowest value of yt

H such

that the participation constraint of the high-types is satisfied, i.e., yt

H∗ = y H min

. Second, given

that punishment is free, the sanction must be as high as possible. By assumption, therefore,

st ∗ = y H t , which is the well-known penalty “à la Becker.” The optimization problem for an

interior solution thus becomes:

min

{y L t }

ec t = [p(1 − β t )] × y L t + [p(1 − π)β t (y L t ) + (1 − p)] × y H min

where β t = 1 − v(β t−1)u L (yt L )

.

(1−π)u H min

The optimal income of low-types (yt

L∗ ) is determined by substituting β t (yt L ) into the

expected-cost function ec t and solving the following first-order condition:

u L (y L∗

t

(10)

) − u L′ (yt

L∗ )((1 − π)y H min − yL∗ t ) = 0. (11)

Interestingly, the probability of being detected, π, and the reservation income of the hightypes,

y H min

, are the only variables which affect short-run optimal income. Using the implicitfunction

theorem, we have:

∂y L∗

t

∂π < 0,

∂yt

L∗

∂y H > 0. (12)

min

First, there exists a tradeoff between the probability of detection and the optimal value of yt L∗ .

Second, the higher is the (reservation) income of the high-types, the greater are the incentives

to cheat, and the higher should be low-type income.

Once the optimal value of yt

L∗ is determined, we can calculate the optimal level of fraud

βt

∗ (from equation (5)) and optimal expected costs ect ∗ (from equation (8)). This allows us to

determine the sign of the derivative of ect ∗ with respect to β t−1 :

Proposition 2. From the optimal value of ec ∗ t in the short run, we have ∂ec∗ t

∂β t−1

≥ 0.

A rise in the share of past cheaters, β t−1 , will reduce moral costs, v(β t−1 ), increasing the

incentive to cheat. As stated previously, in the short run the optimal value of yt

L∗ is independent

13

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

of β t−1 . From Proposition 1, a rise in β t−1 will produce higher β t and, from equation (8),

greater expected costs ec ∗ t . This yields Proposition 2.

3.3. The optimal remuneration of researchers in the long-run

A change in remuneration may not only affect short-run expected costs but, due to the effect on

moral costs, those in the long run as well. Figure 3 provides an illustration of this phenomenon

in a two-period setting. As shown in panel a, the principal chooses the optimal contract at

point A to minimize expected costs ec t (equation (11)). This yields the level of fraud in t

(equation (5)), as shown in panel b. The level of fraud determines future costs ec t+1 , as shown

in panel c, given the remuneration policy at t + 1 (Proposition 2). In contrast, if the principal

chooses contract B, the expected costs in t are higher than the optimal level, as shown in panel

a. However, the level of fraud is lower (panel b), which reduces future expected costs (panel

c). There is thus a tradeoff between present and future expected costs (panel d). In the longrun,

it might be optimal to pay a higher wage to low-types, and thus reduce fraud, in order to

minimize total expected costs.

The aim of this section is to determine the optimal contract that minimizes total expected

cost in a T -period setting. We consider two types of long-run contracts: the first-best and the

second-best. In both cases, the principal wishes to identify the optimal remuneration policy

(y L t ,y H t ,s t ,∀t = 1...T ) that minimizes the present value of expected costs (PEC, hereafter).

Following the discussion above, the principal sets y H t to y H min and s t to y L t in both types of

contracts.

First-best optimal contract. Under this contract the incomes of low-type researchers across

all periods minimize the present value of the expected cost of the remuneration policy. Unlike

in Section 3.2, the principal takes into account that today’s salary has an effect on the future

fraction of cheaters, via the social norm. The principal is assumed to be non-myopic and can

set a different salary in each t. From equation (10), the expected cost ec t at period t can be

written as a function of yt L and β t−1 . The optimization problem is

min

{y L 1 ,yL 2 ,...,yL T} PEC = ∑T ec t (yt L ,β t (yt L ,β t−1 ))

t=1 δ t−1

where β t (yt L ,β t−1 ) = 1 − v(β t−1)u L (yt L )

, t = 1...T,

(1−π)u H min

(13)

and δ ≥ 1 is the discount factor. In this setting, the principal chooses at t = 1 the contract

menu for all periods. The problem is convex. The levels of y L t , t = 1,...,T , are given by the

following first-order conditions:

∂PEC

∂y L t

= 1 ( ∂ect

δ t−1 ∂yt

L + ∂ec )

t ∂β t

∂β t ∂yt

L +

T

∑

k=t+1

1

δ k−1 ∂ec k

∂β k

∂β k

∂y L t

= 0, t = 1...T. (14)

Equation 14 shows that yt

L has two effects on the present value of the expected costs. The

first term represents the effect of yt

L on present expected cost (via the direct change in the

14

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

(d) The principal’s tradeoff

Expected costs

in period t

(a) The optimal contract

B

B

A

∗

A

Expected costs

in period t+1

∗

A

B

∗

∗

A

B

Income y

in period t

(c) Future expected costs

Fraud in

Period t

(b) The level of fraud

Figure 3. Optimal contract, misbehavior and consequences for the future

remuneration cost, and the indirect effect via the present population of cheaters). The second

term corresponds to the impact of yt

L on the expected costs over future periods through the

change in social customs. The effect of yt L on β k in equation (14) can be expressed as:

∂β k

∂y L t

=

[ ∂βk

× ∂β k−1

× ... ∂β ]

t+1 ∂βt

∂β k−1 ∂β k−2 ∂β t ∂yt

L

=

k

∏

m=t+1

∂β m ∂β t

∂β m−1 ∂yt

L , (15)

i.e., the income yt L chosen in period t will affect the level of fraud β t , which in turn will affect

the level of fraud in t + 1 and so on. The term ∏ k ∂β m

m=t+1 ∂β

is a multiplier:

m−1

k

∏

m=t+1

∂β m

∂β m−1

=

k

∏

m=t+1

µu L (y L m)

(1 − π)u H . (16)

min

This multiplier rises with marginal peer pressure µ, future incomes y L m, and the probability of

detection π. While the principal takes µ and π to be exogenous, contagion can be influenced

by the choice of y L m. The multiplier is directly connected to the contagion effects in equation

(7), i.e. the extent to which past generations influence future generations. Equation (14) can

15

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

now be rewritten as:

[

]

0 = u L (yt L ) − ((1 − π)y H min − yL t ) × u L′ (yt L ) −

T

∑

k=t+1

1 (

(1 − π)y

H

δ k−t min − y L ) k

k ∏

m=t+1

µu L (y L m)

(1 − π)u H u L′ (yt L ), t = 1...T. (17)

min

The first term is equivalent to the first-order condition for the short-run equilibrium (equation

(11)). The second term represents the impact of y L on the principal’s costs in future periods

(the contagion effects). The first-best optimal salary is higher than the short-run optimal salary

in all periods except for the last, as it brings about lower future costs. If the parameters of the

model do not change, the optimal salary falls over time and, in the last period, the optimal

salary is set at its short-run optimal level.

Second-best optimal contract. A policy under which income falls over time (at least up to

the last period, as in the first-best optimal contract) may not be socially acceptable. We now

consider that the principal is not totally free to set the optimal income in each period, and thus

has to design a second-best optimal policy. We suppose that the non-myopic principal knows

that remuneration affects the future size of the population of cheaters. However, the principal

is restricted in designing the policy, since income cannot change over time. The optimization

problem is

min

{y L }

PEC = ∑ T t=1

ec t (y L ,β t (y L ,β t−1 ))

δ t−1

where β t (y L ,β t−1 ) = 1 − v(β t−1)u L (y L )

, t = 1...T.

(1−π)u H min

(18)

The first-order condition is:

dPEC

dy L =

T

∑

t=1

which can be rewritten as:

0 =

T

∑

t=1

T −1

∑

t=1

(

1 ∂ect

δ t−1 ∂y L + ∂ec )

t ∂β t

∂β t ∂y L

+

T

∑

t=2

t−1

1 ∂ec t ∂β

δ t−1 ∂β t

∑

k

k=1

t−1

∂y ∏ L

m=k

1

[

]

δ t−1 v(β t−1) u L (y L ) − ((1 − π)y H min − yL ) × u L′ (y L ) −

[ µu L (y L )

1

δ t

t

∑

k=1

(1 − π)u H min

∂β m+1

∂β m

= 0, (19)

] k ]

v(β t−k )[

((1 − π)y H min − yL ) × u L′ (y L ) . (20)

As in the first-best case, the second-best optimal salary is higher than the short-run optimal

salary as the principal takes into account that a higher low-type salary reduces the future

population of cheaters, and so future costs. However, remuneration does not change over

time, implying higher costs for the principal.

Let yt

First and yt

Second denote the optimal incomes of low-type researchers in the first- and

second-best contracts respectively. As can be seen from equations (17) and (20), marginal

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Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

peer pressure, the discount factor and the probability of detection determine the principal’s

efficient choice under both contracts. Using the implicit-function theorem to calculate the

partial derivatives yields the following proposition:

Proposition 3. The first-best and second-best optimal contracts have the following

comparative-static derivatives:

∂y First

t

∂ µ > 0, ∂yt

Second

> 0,

∂ µ

∂y First

t

∂δ

< 0,

∂y Second

t

∂δ

< 0,

∂y First

t

∂π ≶ 0, ∂yt

Second

< 0.

∂π

From Proposition 3, the lower is µ or the higher is δ, the closer the optimal incomes

are to that under the short-run contract (until we have yt

First = yt

Second = yt

L∗ ). On the other

hand, as these variables fall the principal has to increase the low-type salary above the level

in the short-run contract. We call this a prevention policy that aims to reduce fraud in future

periods. This is a central finding of our analysis. If µ = 0, the actions of others do not

affect the individual decision to cheat. Contagion effects are then absent (the multiplier is

zero). Any prevention policy is cost-ineffective since it cannot influence the social norm and

implies high remuneration costs. On the other hand, when µ > 0, a change in yt L also affects

future researchers, making a prevention policy more cost-effective. The higher is µ, the lower

the optimal performance premium. The optimal incomes yt

First and yt

Second also fall with the

principal’s patience. When δ = 0, the principal does not care about about future expected

costs and so does not implement a prevention policy. For the second-best optimal contract,

there exists a tradeoff between the probability of detection and the optimal value of the lowtype

salary. However, for the first-best optimal contract, the sign of the derivative with respect

to π is ambiguous. Section 4 offers a more detailed analysis of these relationships.

4. The main characteristics of optimal policies

This section identifies the main characteristics of optimal policies (short-run vs. long-run,

and first-best vs. second-best) by using simulation results. In contrast to the conventional

literature on social norms (e.g., Akerlof 1980 and Corneo 1995), we are not only interested in

the long-run equilibrium (Section 4.1) but also, and more importantly, in how fraud evolves

over time (Sections 4.2 and 4.3). The dynamics of social norms are important as they affect

the principal’s expected costs and the choice of the optimal contract.

4.1. The long-run equilibrium level of fraud

Which fraud equilibrium will prevail in the long run when the low-type salary does not change

over time, i.e. in the case of the short-run second-best contract? We analyze this question

by appealing to the concept of “stationary points” that we define as an equilibrium which

continues to hold in each period (see, e.g., Corneo, 1995). Assuming that y H t = y H min , s t = y H min ,

and v(β t−1 ) = k − µβ t−1 , i.e. constant marginal peer pressure, equation (5) can be rewritten

17

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

as:

β t = 1 −

ku L (yt L )

(1 − π)u L (y H min ) + µu L (yt L )

(1 − π)u L (y H min )β t−1, (21)

which is the equation of a line with positive slope.

The interior stationary value of β is attained when β t = β t−1 = β, that is when:

β =

1 − uL (y L t )

(1−π)u L (y H min )k

1 − uL (y L t )

(1−π)u L (y H min )µ . (22)

By definition, an interior stationary point β is stable if the absolute value of the derivative

of β t with respect to β t−1 in equation (21) is strictly less than 1, and unstable if it is strictly

greater than 1. This derivative is the slope of the line. Hence, the equilibrium is stable if

µ < (1 − π)uL (y H min )

u L (y L t )

= k 0 (23)

In addition, note that, since β ∈ [0,1], two corner stationary equilibria may exist:

β = 0 if k > (1 − π)uL (y H min )

u L (y L t )

= k 0 and β = 1 if k > µ. (24)

Figure 4 shows the possible sets of equilibria for different values of the peer-pressure

function k and µ. Equation (21) is depicted by the black lines. On these equilibrium curves, β t

is only a function of β t−1 , and all other variables are held constant. The model parameters were

chosen for graphical convenience: y H min = 100, yL t = 37.5, u(y) = y 0.6 , π = 0.05, and p = 0.5.

The intersections with the 45-degree line indicate the interior stationary point (equation (22)).

If µ = 0, or equivalently v(β t−1 ) = k, the moral costs of cheating are independent of past

cheating. The slope is zero and the equilibrium level of fraud is reached immediately. This

is shown in Figure 4a. From equation (21), fraud is equal to 1 − ku L (y L t )/[(1 − π)u L (y H min )].

Fraud is then zero only if k exceeds the following value:

k 0 = (1 − π)uL (y H min )

u L (y L t )

(25)

For instance, in Figure 4a, β = 0 holds for k 0 = 1.7. When k is lower, the moral costs

exogenously fall for the whole scientific community and the level of fraud becomes non-zero.

When 0 < µ < k 0 the slope of the line is less than one. If µ < k < k 0 (Figure 4b), there

is a unique stable interior solution at the intersection of the 45-degree line and the equilibrium

curve. From equation (24), the conditions that µ < k and k < k 0 imply that the stationary point

is less than 1 and greater than 0, respectively, i.e. we obtain an interior solution. On the other

hand, if k > k 0 (Figure 4c), the unique stable equilibrium is zero.

Last, if 0 < k 0 < µ the slope of the line is over one. Two corner equilibria coexist (see

18

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

(a) Nonsocial preferences (µ=0)

(b) One stable interior equilibrium (0

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

Income and Misbehavior

(a) First-best optimal contract

50

45

yL

40 β

35

Optimal stationary percentage of cheaters PEC → 1997.12

0 10 20 30 40

Income and Misbehavior

(b) Second-best optimal contract

50

45

yL

40 β

35 Optimal salary → 43.7165 Optimal stationary percentage of cheaters → 43.3057

PEC → 1997.2

0 10 20 30 40

Income and Misbehavior

(c) Short-run optimal contract

50

45 β

40

yL

35 Optimal salary → 37.3125 Optimal stationary percentage of cheaters → 49.9167

PEC → 2002.35

0 10 20 30 40

Figure 5. Optimal policy with low marginal peer pressure.

of cheaters and future expected costs. As shown in Figure 6, the differences between the three

optimal contracts are much more pronounced with higher peer pressure (µ=1.007). This latter

implies that the social norm is more sensitive to changes in remuneration.

Figure 7 shows the difference between the short-run and second-best optimal salaries,

and illustrates two situations with different values of marginal peer pressure µ. The income

of low-type researchers is on the horizontal axis and the present value of expected cost on

the vertical axis. The present value of expected cost is seen to be minimized when income

is at its second-best optimal level. Income here is higher than at the short-run optimal level.

The gap between the two optimal income levels depends on v(β t ). When µ is high, the

share of cheaters is more sensitive to income. The principal then sets the income of low-type

researchers at a higher level. It should be noted that the first-best optimal contract cannot be

shown in this figure as optimal remuneration differs in each period.

4.3. The probability of detection as a positive externality for the principal

The disclosure of scientific misconduct may affect the reputation of journals in which the

falsified research appeared. The implementation of a performance-based remuneration policy

that fosters scientific fraud may thus produce negative externalities for journals. Reciprocally,

the peer-review process organized by editors may yield a positive externality for the principal

if it deters researchers from cheating.

Positive externalities arise if, by increasing the probability of being detected, peer review

20

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

Income and Misbehavior

(a) First-best optimal contract

100

80 yL

60

40

β

20

0

Optimal stationary percentage of cheaters PEC → 2205.08

0 10 20 30 40

Income and Misbehavior

(b) Second-best optimal contract

100

80 yL

60

40

β

20

0

Optimal salary → 77.3784 Optimal stationary percentage of cheaters → 39.42

PEC → 2209.61

0 10 20 30 40

Income and Misbehavior

(c) Short-run optimal contract

100

80

60

β

40 yL

20

0

Optimal salary → 37.3125 Optimal stationary percentage of cheaters → 88.2379

PEC → 2265.56

0 10 20 30 40

Figure 6. Optimal policy with high marginal peer pressure.

T → 40 ; δ → 1.1 ; π → 0.05 ; p → 0.5

k → 1.1 and μ → 1.007

Short-run opt. contract: yL → 35.625 and PEC → 989.286

Second-best opt. contract: yL → 68.0962 and PEC → 967.655

1050

Present Value of the Expected Cost

1000

950

Short-run

opti. contract

Second-best

opti. contract

900

Short-run

opti. contract

Second-best

opti. contract

k → 1.1 and → μ → 0.4

Short-run opt. contract: yL → 35.625 and PEC → 883.414

Second-best opt. contract: yL → 41.4597 and PEC → 881.328

0 20 40 60 80 100

Income

Figure 7. Short-run and second-best optimal contracts for two different specifications of v(β t−1 ).

21

Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

80

(a) First-best optimal contract after a shock in π from → 0.01 to → 0.15 at period → 10

Income and Misbehavior

yL

60

40

β

20

PEC without shock → 984.64

PEC with shock → 950.94

0

0 10 20 30 40

80

(b) Second-best optimal contract after a shock in π from → 0.01 to → 0.15 at period → 10

Income and Misbehavior

yL

60

40

β

20

PEC without shock → 984.734 PEC with shock → 951.459

0

0 10 20 30 40

100

(c) Short-run optimal contract after a shock in π from → 0.01 to → 0.15 at period → 10

Income and Misbehavior

80

60

β

40

yL

20

PEC without shock → 1002.71 PEC with shock → 972.318

0

0 10 20 30 40

Figure 8. A positive shock to the probability of detection.

80

(a) First-best optimal contract after a shock in π from → 0.15 to → 0.01 at period → 10

Income and Misbehavior

yL

60

40

β

20

PEC without shock → 901.298 PEC with shock → 935.598

0

0 10 20 30 40

80

(b) Second-best optimal contract after a shock in π from → 0.15 to → 0.01 at period → 10

Income and Misbehavior

yL

60

40

β

20

PEC without shock → 901.607 PEC with shock → 935.793

0

0 10 20 30 40

100

(c) Short-run optimal contract after a shock in π from → 0.15 to → 0.01 at period → 10

Income and Misbehavior

80

60

β

40

yL

20

PEC without shock → 929.257 PEC with shock → 959.639

0

0 10 20 30 40

Figure 9. A negative shock to the probability of detection.

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Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

reduces the expected benefit of fraud, thereby reducing the share β of cheaters (equation (5)).

Ceteris paribus there will be fewer low-type researchers to whom the principal pays y H and

the salary of honest low-types will be lower (equation (8)).

The prospect of a rise in π in the future may also affect the optimal contract, as shown

in Figure 8. This shows what happens if the probability of detection exogenously rises from

1% to 15% in period 10. The dashed lines show the optimal values of y L and β in the absence

of a π shock, whereas the solid lines show these values with this shock (which is common

knowledge and taken into account by the principal). In the latter case, y L in the first-best

optimal contract (panel a) rises until one period before the change in π. This is followed by

the usual pattern of a decreasing y L over time. Setting a high value of y L t in the periods prior

to the shock increases the shock’s negative impact on the percentage of cheaters. Formally,

the reduction in the percentage of cheaters β following the rise in π depends on the value of

y L when the shock occurs. The change in β following a change in π is

∂β t

∂π = −v(β t−1)ut L (yt L )

(1 − π) 2 u H < 0 (26)

min

The impact of y L t here depends on the sign of the cross-partial derivative.

∂ 2 β t

∂π∂y L t

= − v(β t−1)ut L′ (yt L )

(1 − π) 2 u H < 0 (27)

min

The higher is yt

L when the jump in π occurs, the lower is β afterwards. In other words, it

is worth increasing the salary of low-type researchers prior to the shock as this increases the

reduction in the percentage of cheaters after the shock.

Figure 8a shows that the first-best salary after the positive shock is lower than that in

the absence of the shock (the dashed line). Mathematically, this can easily be explained. The

short-run optimal salary yt

L∗ is a lower bound of the first-best salary yt

First . Since a rise in π

produces lower yt

L∗ (see equation (12)), yt

First will fall accordingly. In the second-best optimal

contract, the prospect of a future rise in π slightly reduces low-type salaries over the whole

period. In contrast, the increase in π reduces salaries only after the shock for the short-run

optimal contract. Figure 9 depicts the symmetric case in which there is a fall in π from 15%

to 1%. Compared to the no-shock situation, the first-best salary resulting from the shock is

lower before the shock and greater afterwards. A low probability of detection thus forces the

principal to reward scientific productivity after the shock.

5. Conclusion

The decision to misbehave in our theory is determined by three types of motivation: an

unconditional commitment to honesty, a commitment to honesty which is conditional on what

others are doing, and extrinsic incentives. The novelty of the model is that each motivation

interacts with the others and plays a role in the decision to cheat. If some researchers are

attracted by the pecuniary gain from breaking the code of good conduct, this can affect the

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Filename: scientificmisbehavior-proofreading-dbspaceAC2.pdf December 1, 2016

perception of what is good behavior and in turn generate more disobedience.

The main purpose of our theory is to show which contract the principal (the government,

a university, or a research institute) will choose if the aim is to reward differences in

productivity at the lowest possible expected cost per capita. If the information about the

researcher type was perfectly known, the principal would remunerate the less productive

researchers at the lowest possible salary. However, if this information is unknown, lowproductivity

types may cheat: the larger the difference in salary, the greater the incentives

to fraud. Moreover, the principal has to consider that the performance-related pay not only

encourages fraud at t but also lowers the conditional commitment to honesty at t + 1. Due to

the rising share of cheaters, the expected costs of the salary policy rise over time. The principal

thus faces a tradeoff between higher expected costs today (by reducing the productivity

premium) and in the future (by increasing the share of futur cheaters). We investigate this

tradeoff and show that, inter alia, the size of the productivity premium depends on three of our

model parameters: the discount rate, marginal peer pressure and the probability of detection.

Table 4 provides a summary of these results.

Our policy implications are threefold. First, in a time in which most researchers’ salaries

and funds are related to performance, we show that a slight reduction in the performance

premium may actually be efficient. This may not only reduce scientific fraud in the shortrun,

and thereby improve the quality of scientific production, but also change the social norm

guiding research misbehavior in the long run. This policy can also reduce the size of the

negative externality on scientific journals caused by the performance premium.

Second, our analysis stresses the role of marginal peer pressure for the adverse effects of

performance-based pay. Greater marginal peer pressure increases the importance of offering

a lower productivity premium. A principal who wants to offer a high premium to remunerate

performance should first make sure that social norms (i.e. fraud behaviors) are only weakly

transmitted. Moreover, moral reminders that increase the unconditional commitment to

honesty may prove to be useful.

Third, it is well known that the likelihood that scientific misconduct be detected is low.

An example is Alan Sokal’s fake submission that was accepted for publication in a journal.

Our model shows that the dynamics of fraud and its cost to the principal strongly depend on

the detection probability. Since employers in academia cannot directly control monitoring, a

low-premium policy is fundamental unless the probability of detection exogenously increases

as editors try to save the reputation of their journals.

Although academia is a particularly interesting example for the analysis of the

link between rewards, norms, and misbehavior, our theoretical framework also has other

applications. This is the case when the principal is interested in performance but less in

how performance is achieved. An example is given by the banking industry, and in particular

the case of Jerome Kerviel, a French trader who was convicted for breach of trust, forgery

and unauthorized use of bank computers. His type of trading behavior was widespread in

the profession, and also highly profitable. When the principal does not care about fraud but

remunerates performance, the consequences for agents’ behavior may be devastating in the

long run.

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Table 4. Summary of the theoretical results

Variable Definition Low value High value

Marginal peer Extent to which When µ is low, agents have nonsocial When µ is high, behaviors, whether they

pressure µ present behaviors preferences. An increase in y L will not are good or bad are passed on to the next

influence future ones. change the norm much. A prevention generations. An increase in y L will change

policy is inefficient.

the norm. A prevention policy is efficient.

Probability of Probability of being When π is low, cheating is attractive. The When π is high, the expected benefit of

detection π detected when cheating,

leading to punishment

principal has to increase the income of

low-types, thereby reducing the productivity

premium.

fraud is low. The principal has a greater

incentive to reward performance.

fac-

Discount

tor δ

Extent to which the

principal cares about

future costs.

If δ is low, the principal cares a lot

about future costs. A prevention policy is

efficient.

If δ is high, the principal cares less

about future costs. The principal has less

incentive to increase the income of lowtypes,

which yields a higher level of fraud.

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