Content uploaded by Aldo Rustichini
Author content
All content in this area was uploaded by Aldo Rustichini on Sep 22, 2014
Content may be subject to copyright.
1
A Fine is a Price
*
Uri Gneezy** and Aldo Rustichini***
Preliminary draft, October 5, 1998
Abstract
The deterrence hypothesis predicts that the introduction of a penalty for a
specific behavior, which leaves everything else unchanged, will reduce the occurrence
of that behavior. We present here the result of a field study of this hypothesis,
conducted in a group of day-care centers in Israel.
In these day-care centers, parents sometimes arrive late to collect their children,
forcing a teacher to stay after the official closing time. We study the behavior of the
parents over three periods. In the first four weeks period we simply record the number
of late-coming parents. In the second period, twelve weeks long, we introduce a
monetary fine for late-coming parents. As a result the number of late-coming parents
increased significantly. In the last period of four weeks we observed the effect of
cancellation of the fine. Here the result was that the number of late-coming parents
remained stable at the level prevailing in the second period, hence higher than it was in
the first period, before the introduction of the fine.
Our results are not immediately evidence against the deterrence hypothesis.
Rather we argue that penalties, (just as rewards), are usually introduced into an
incomplete contract, social or private. These penalties may change the information or
the perception that agents have of the outcome in the states where the contract is
silent, and therefore the effect on behavior may opposite than expected. If this is true,
the deterrence hypothesis loses great part of its predictive strength, since the clause
``everything else is left unchanged’’ might be hard to satisfy or verify.
* We thank David Easley, Patrick Francois, Edward Glaeser, David Levine, Ellen Nyhus, Tom
Palfrey, Luca Rigotti, Jose Scheinkman, Peyton Young, Paul Webley for very useful
conversations on the interpretation of the results of our experiment.
** University of Haifa, Israel. Email: gneezy@econ.haifa.ac.il
*** CentER for Economic Research, Tilburg University, The Netherlands. Email: aldo@kub.nl
2
Introduction
Suppose you are a manager of a day-care center for little children. The day-
care is scheduled to operate every day until 16:00, when the parents of the children are
supposed to come and collect them. However, quite frequently parents arrive late to
collect their child, forcing you to stay for some extra time in the day-care after working
hours. You are considering few alternatives in order to reduce the frequency of parents
coming late. A natural option, which is commonly used in other situations, is to
introduce a fine: every time a parent will come late, (s)he will have to pay a fine. Will
that reduce the number of parents coming late?
This prediction seems extremely plausible. It is also commonly made in two
distinct fields of research: the legal and criminal studies, on the one hand, and
psychological studies on the other. In our field study, this prediction is violated: the
observed relationship is significant and positive.
In particular, we study the effect of fines on the frequency with which parents
arrive late to collect their child. Our data includes observations of 11 day-care centers
over a period of 20 weeks. In the first 4 weeks we simply observed the number of
parents that arrive late every week. At the beginning of the fifth week, a small fine was
introduced in 7 out of the 11 day-care centers. In the other 4 day-care centers no fine
was introduced, and they serve as a control group. The fine was imposed on parents
3
coming late 10 minutes or more. The result of introducing the fine was a sharp and
significant increase in the number of parents coming late. This increase was more or
less stable over the 12 weeks period in which the fine was imposed.
At the beginning of the 17th week, the fine was removed. For the remaining 4
weeks we observed the removal of the fine had no effect on the number of parents
coming late. This number remained on the same level as it was when the fine was
active and higher than in the initial 4 weeks.
We do not claim that every time a fine is introduced the effect is similar. It is
easy to speculate that with a very large fine that no parent would have come late. What
this field study teaches us, we believe, is that introducing fines changes the perception
of people regarding the environment in which they operate. In particular we argue that,
like in many real-life situations, the environment in our study is defined by an
incomplete contract. In the specific situation we are considering, the exact
consequence of the behavior of the parents was not specified in all detail. For instance,
there was no precise set of clauses specifying what would be the consequence of one,
two or several occurrences of a delay. Parents could form a belief on that, as they
probably did, and act accordingly.
The introduction of the fine into this incomplete contract reshaped the
perception of the parents regarding this environment. The precise form and way in
which this change takes place is only beginning to be understood: this field study is a
step in this direction.
4
2. Related literature
To contrast this result with the literature we have just mentioned, we proceed
first with a discussion of theories and evidence in two different fields of research: legal
studies and psychology. We do this for two reasons. First, we think that the evidence
we present sheds some light on the relative merits of two main competing
explanations. Second, we suggest that the explanation we present for the seemingly
paradoxical behavior of the parents is new.
2.1 Crime and punishment
Two main theories are used in the field of legal studies to justify punishment.
The first is the deterrence theory, which justify punishment as deterrent of future
crimes, and is grounded on the assumption that a higher expected punishment produces
lower criminal behavior. The second motivation for justification for punishment is
retribution for the past crime. Unlike the retribution theories, the deterrence theory can
be phrased as an empirical hypothesis. One can test whether prediction that more
severe, faster, and more certain punishment produces a decrease in the level of crime.
The literature presenting the deterrence argument goes back at least to Beccaria,
Bentham, but also Blackstone (1765-1769: see in particular volume 4, commentary 11-
12). This hypothesis has received new strength from major contribution from law and
economics. Some of the fundamental papers are Becker (1968), Stigler (1970), Ehrlich
(1973), Harris (1970). The literature elaborating on these initial contributions is very
5
large: a review has been given recently by Ehrlich (1996). It is important to recall that
the economic analysis of the effect of a punishment on behavior is not direct, and
requires instead a complete specification of the market forces. The equilibrium level of
crime is determined by the intersection of a supply and demand curve, and the effects
of punishment are determined in the general equilibrium. A change in one of the
parameters, like the level of punishment, changes the decision problem of the single
agent (and this fact would tend to reduce his preferred level of crime). But it also
changes the problem of the others, and their reactions, and therefore again the problem
of the single decision-maker. The overall result might not be the reduction one might
have anticipated by considering the problem of the agent in isolation. For example,
this reduction might be smaller because some have withdrawn from criminal activity,
and the returns of crime for you have gone up.
A similar point, in a game theoretic model, has been recently raised by Tsebelis
in a sequence of papers: see Tsebelis (1989), (1990a), (1990b) and (1990c). It may be
useful to recall here the main idea in a simple model. Tsebelis considers a game
between the police and the public. The public may or may not violate a speed limit and
the police may or may not enforce the laws against speeding. If the police do not
enforce, the public will violate the speed limit. If the police do enforce, then the public
will not commit violations: so the game has no pure strategy Nash equilibrium. It has
mixed-strategy equilibrium. The probability that the public will commit violation is
given by the condition that the police are indifferent between enforcing or not. This
6
condition insures that this probability only depends on the payoff of the police. In
particular it will not change if, for instance by introducing punishments, the payoff of
the public changes. Hence the conclusion of Tsabelis is that “Penalty has no impact on
1
If we turn to empirical analysis, a systematic study of the effect of punishment
on crime was developed in the seventies (for a review of this earlier work see Cook
(1980), Gibbs, (1975), Zimrig and Hawkins (1973)), and is still in progress. It has
reached levels of passion in the debate on the effectiveness of the death penalty, as in
the exchange around the 1978 report of the National Academy of Sciences: see
Blumstein, A. Cohen, J. and Nagin, D. (1978), and the comments in Ehrlich and Mark
(1977).
Evidence has piled up on the side of those denying and those asserting the
deterrence effect. See as examples of the second Ehrlich (1973), (1975), Carr-Hill and
Stern (1973), Phillips and Votey (1975), Wolpin (1978a), (1978b), Yu, J. and Liska,
A., (1993), Yu (1994), Imrohoroglu, Merlo and Rupert (1997). As examples of the
first, see the evidence presented in Blumstein, A. Cohen, J. and Nagin, D. (1978), Avio
(1979), Hoenack and Weiler (1987), as well as the evaluation in McManus (1985). A
survey of this literature is given in Liska (1987). Few would claim however that
deterrence has no effect, in all cases. The disagreement is on how large the effect is,
and what form is more or less effective. For the purpose of the discussion of our
1
The conclusion has been analyzed and challenged in several papers: see Bianco (1990), Hirschleifer
7
results, it suffices to note here that none of these important refinements of the
deterrence idea explains, or even considers, the possibility that a penalty might produce
an increase in the behavior that is penalized.
2.2 Behavior and punishment
The literature in psychology on this topic is also very large, and is textbook
material (for a clear exposition, see Bandura (1969), or more recently Schwartz
(1984)). The first to study systematically the connection is Thorndyke (1931), (1932).
In his early work punishment represents one half of the Law of Effect: punishment
decreases the likelihood of the behavior that produces it, just as a reward increases the
likelihood of an action that produces it. Later Thorndyke himself put into doubt the
punishment side of the Law of effect. A first test of these conflicting views was given
in Estes (1944): his experiments showed that while punishment depressed behavior, it
only did it in a temporary way. In addition, this depression was taking place
independently of the behavior of the animal (the subjects in his experiments). A host of
studies followed, and the conclusion is still controversial.
2
This large body of literature agrees on few general findings. When negative
consequences are imposed on a behavior, they will produce a reduction or a cessation
of that particular response. When those negative consequences are removed, the
and Rasmussen (1991), Ordeshook (1990), Rapoport (1990), Tullock (1991).
2
Detailed studies of the different effect of intensity, duration, frequency and conditions of negative
consequences are in Azrin (1956, 1959, 1960), Azrin and Holz (1966), Chapman (1962), Church
(1963), Powell and Azrin (1968), Rotemberg (1959), Solomon (1964).
8
behavior that has been discontinued will tend to reappear. In some conditions,
however, the modification of behavior may become permanent. The changes induced
by the punishment may be enduring changes or not, according to several factors. It
may change depending on the severity of the punishment, on whether it is associated
with the stimulus or only with the actual behavior, and so on. A punishment is most
effective in reducing a behavior when it is certain, and it follows immediately that
behavior. Finally, adaptation tends to develop to the punishment itself. So if the
severity and other parameters of the punishment are left unchanged, its effectiveness
tends to decrease over time.
A direct comparison of the results of this evidence with our particular
experiment would be misleading. That literature deals with the behavior modification
following the introduction of some punishment, as a long lasting effect. In addition, the
effect is rarely considered as mediated by foresight of the subject (an exception is the
work of Bandura (1969) and in general the Social Learning Theorists.
Some of the experiments arising from the cognitive dissonance and in general
the cognitive approach are more directly relevant. For instance the studies of Aronson
and Carlsmith (1963) and Freedman (1965) try to determine the difference in the effect
of punishments of different sizes. In the Aronson and Carlsmith study children were
forbidden to play with a specific toy, under the threat of a mild or more severe
punishment, and their liking of the toy was then tested. The hypothesis these
experiments are testing, and partly support, is that a mild punishment may have longer
9
and more lasting effects. The reason for this: the incongruous behavior (of not playing
with a toy under a mild threat) induces, to eliminate the cognitive dissonance, the
children to think that the desired object is not so worthwhile after all.
Finally, the issue of the effect of punishment on motivation and behavior is of
course related to the parallel one of the effect of rewards on motivation and
performance. Suppose that in a contractual relationship you introduce a reward, which
is conditional on performance. Even if the reward is small but leaves unchanged all the
remaining terms of the contract, it should produce an increase in performance. The
literature here is also very large (see Cameron and Pierce (1994), and Eisenberger and
Cameron (1996) for recent review and evaluations of the experimental evidence). The
conclusions in this direction are even less firm than in the case of punishments.
We may now turn to the report of our study and of the results.
3. Procedure
3.1 Background
There are two types of day-care centers for children in Israel: private and
public. This study was conducted in 11 private day-care centers in the city of Haifa,
from January to June 1998. All centers are in the same part of town, with no distinct
features that we are aware of between them. In these day-care centers the owner is
also the principal. A diploma, which is achieved after two years of studies, is needed in
order to be a principal. In all the day-care centers studied the manager stays in the day-
10
care until 13:00. After that time the assistants are in charge. During the day children
are organized into groups according to the age, from one to four years old. The
maximum number of children allowed in each daycare is 35, with some exceptions of
additional few more children. The fee for each child in the center is NIS 1,400 per
month (about $380 at the time of the study).
In the contract signed at the beginning of the year it is written that the day-care
operates between 7:30 to 16:00. There is no mentioning of what happens if parents
come late. In particular, before the beginning of the study there was no fine for coming
late. When parents did come late, one of the teachers had to stay and wait for them
with the child(ren). Teachers would rotate on the task. The task of taking care of
children when the parents were coming late to pick them up is considered part of the
job of a teacher, and this fact is clearly explained to them at the moment of hiring.
3.2 Organization of the study
At the beginning of the study research assistants went to the day-care centers
and asked the principals to participate in an academic study about the influence of
fines. It was promised to each manager that at the end of the study she
3
will receive
coupons for buying books with a value of NIS 500. The principals were given a
telephone number at the university were they could call and verify the details (none of
the principals actually did that).
3
All the managers in the study (and as far as we know in Israel) are females.
11
The overall period of the study was 20 weeks.
4
In the first four weeks we
simply recorded the number of parents coming late in each week. At the beginning of
the fourth week, a fine was introduced in 7 out of the 11 day-care centers.
5
The
decision in which day-care to introduce the fine was done randomly. The
announcement about the fine was made with a note posted in the announcement board
of the day-care center. Parents read the announcement on this board everyday, since
important announcements are posted there (such as what to bring on the next
morning). The announcement specified that the fine will be of NIS 10 paid for a delay
of ten minutes or more. A translation from Hebrew is presented in Appendix 1A. Very
rarely parents came after 16:30. The fine was per child; if for example parents had two
children in the day-care, and they came late, they had to pay NIS 20. Payment was
done at the end of the month, to the principal of the day-care. There are special
payments made during the year, which are paid on a monthly basis to the owner, and
the fines were added to these payments. The money was paid to the owner, and the
teacher who was staying was not getting any additional money. The teachers were of
course informed about the fine, but they were not informed about the study.
Registering the names of parents coming late was anyway a common practice.
After the 16
th
week the fine was removed with no explanation. The cancellation
was done with a note on the board with an announcement similar to the first one. If
4
actually it was 21 weeks, with a break of 1 week because of a holiday after week XX. Moreover,
week number XXX included only XXX days of study, so the number in that week is calculated as
5/XXX times XXXX.
12
parents asked why the fines were removed, the principals were directed to reply that
the fine had been a trial for a limited time, and that now the results of this trial were
being evaluated.
3.3 Comparison with other payment and fines in Israel
A fine of NIS 10 in Israel today is relatively small, but not insignificant. For
comparison, the fine for illegal parking is NIS 75; the fine for passing with a red light is
NIS 1000 plus penalties; the fine for not collecting the droppings of the dogs is NIS
360. For many of these violations the detection and enforcement rate is however small
or even zero, as in the case of the last. On the specific topic of fines for failing to
collect dog droppings, see the interesting paper by Webley, Siviter, Payne and Scott
(1998). For a different comparison, a baby sitter earns between NIS 15 to NIS 20 per
hour. The average gross salary per month in Israel at the time of the study was NIS
5,595.
4. Results
We start by presenting the raw data in Table 1. The first column reports the
number of the day-care center in our study, such that the first 7 are the day-care
centers in which a fine was introduced and last 4 are the control group. The second
column reports the total number of children in the corresponding day-care. The other
5
At the beginning there were actually 12 day-care centers, but the recording from one day-care were
incomplete and so after the 4
th
we decided not to continue the study in this day-care.
13
columns reports the number of times per week that parents came late (each occurrence
of a delay is a separate item). For example, in week 5, in day-care number 4, we see
that 7 times parents came late to collect their child.
---------------------Insert Table 1--------------
As a first indicator for the effect of the fine, we compare in Figure 1 the
average number of parents who came late per week in all 7 day-care centers in which
the fine was introduced, with the corresponding average in the 4 centers of the control
group. This figure seems to indicate a rather dramatic impact.
14
Figure 1: Comparison of the averages of the two groups
0
5
10
15
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
week number
#of parents
with fine control
In the group with the fine the number of occurrences of a delay increased
steadily in the first three-four weeks after the introduction of the fine, to finally settle at
a level higher than the initial one. In the control group, on the other hand, no
noticeable change takes place after week 4. The number of late arrivals seems to
remain steady after the fine is removed. The rest of the discussion in this section is
devoted to test this first informal impression.
Table 2 reports the average number of late-coming parents in the different day-
care centers, according to 4 stages in the study (the stage with the fine, weeks 4-17 is
divided into two parts).
15
Table 2: Average number of late-coming parents, according to 4 periods: Before the fine (weeks 1-4);
The first four weeks with the fine (weeks 5-8); The entire period with the fine (weeks 5-16); The post
fine period (weeks 17-2).
Center # # of
Children
week
1-4
week
5-8
Week
5-16
Week
17-20
1 37 7.25 9.5 12.5 15.25
2 35 5.25 9 12.2 13.25
3 35 8.5 10.25 16.8 22
4 35 6.25 5.75 6.3 5
5 34 9 15 19.1 20.25
6 33 11.75 20 24.6 29.5
7 28 6.25 10 13.1 12
8 35 8.75 8 7.2 6.75
9 34 13.25 10.5 10.9 9.25
10 34 4.75 5.5 5.5 4.75
11 32 13.25 12.25 13.1 12.25
The first statistical test we report (in Table A.1 in the Appendix) tests the
hypothesis that the increase in the number of parents coming late is simply a time
trend, independent of the fact that a fine was introduced. To test this we check
whether a time trend exists in the control group. This might happen if, for instance,
parents acquire overtime more familiarity with the teachers of the day-care and so feel
more justified in stretching the rules a little. The regression shows that we can reject
this hypothesis: we found no time trend in the data.
16
The second regression, presented in Table A.2 of the Appendix, is a linear
regression of the number of late parents on the dummy variables for three possible
states. The first is the state where no fine is present, the second where a fine has been
introduced, and the third is the state where the fine has been introduced and later
removed. As can be seen from the table, the effect of the fine is significant, that is, after
the fine was introduced significantly more parents came late than before the fine was
introduced. This is true also for the last period. That is, after the fine was canceled
significantly more parents came late than before it was introduced. The coefficient in
the state where the fine has been removed is greater than when the fine was
introduced, but this difference is not significant.
A direct test of the hypotheses regarding the distribution of the random
variable “number of parents coming late” is provided by the non-parametric Mann-
Whitney U test. First, we find that the number of late-coming parents in the test group
and in the control group, before the introduction of the fine (weeks 1-4), is not
statistically different; (z=1.802, p<.072). Now we state our two main results.
Result 1: The effect of introducing the fine was a significant increase in the
number of late-coming parents. Two tests support this conclusion. First, the number of
late-coming parents in the period of the fine (weeks 5-16) in the test group and in the
control group is significantly different. In particular, more parents came late in the
centers in which the fine was introduced. [This difference is statistically significant
17
(z=4.460, p<.000).] Second, the number of late-coming parents before the fine is
introduced (weeks 1-4) and when the fine is imposed (weeks 5-16) in the test group is
significantly different (z=-6.086, p<.000).
Result 2: Removing the fine did not effect the number of late-coming parents
relative to the time of the fine. In particular this number remained higher in the test
group than in the control group. Two tests support this conclusion. First, the number
of late-coming parents in the period when the fine is imposed (weeks 4-16) and when
the fine is removed (weeks 16-20) in the test group is not significantly different
(z=0.676, p<.499). Second, the number of late-coming parents in the period after the
fine was canceled (weeks 16-20) in the test group and in the control group is
significantly different. In particular, more parents came late in the centers in which the
fine was introduced. [This difference is statistically significant : z=3.628, p<.000.]
5. Interpretation of the results
Any model, or explanation, of these results has to provide two specific
predictions: first, the fact that the rate of delay increases after the introduction of a
fine; and, second, the fact that this rate is stable after the fine is removed.
The literature we have reviewed in section 2 does not seem to provide a
satisfactory explanation for both these results. In particular, the controversial issue in
the literature was whether punishment induces reduction in the relevant behavior or
18
not. From either the theoretical or empirical point of view the possibility of an increase
in the behavior which is being punished was not even considered.
The models investigated in the literature have at least three properties which
are different from the environment of our study. First, the “crime” in our study is very
mild, and so are the punishments.
Second, no uncertainty of punishment exist since parents are sure of being
detected and fined. And the third difference is that there are no “general equilibrium
effects” in our study simply because no other price changed after the introduction of the
fine.
The model we suggest is different from all these models in one central
assumption: we assume that the fine changes the perception of the agents about the
social situation in which they are involved. We present here a few possible explanations
of the data, mainly based on this assumption. Later we will discuss their relative merits.
5.1 The differential information-incomplete contract model
In the initial period parents that are not facing a fine can only refer to a partially
specified contract to anticipate the consequences of a delay. During the initial
operating weeks of the day-care, parents probably acquire some additional information.
For instance, they learn that for the mild level of occurrences of late arrivals that
actually take place the penalty is not severe. This is of course not sufficient to know
that the same would hold for worse behavior on their part. The implicit contract that
19
the day-care center is presenting to the parents might for example be perceived as
follows: “We are going to take care of your children after the closing time when you
come late. We are not going to put a price schedule for this extra service, which will be
therefore performed for free. Of course this is supposed to be an exceptional case, and
you should come late only if it is strictly necessary. If you come late too often, we
might do something about it.” In order to avoid this unspecified and uncertain, but
possibly more serious consequence, parents refrain from “too many” delays.
The introduction of the fine makes the sure consequence of a delay worse
(because, on top of the above, parents have to pay for each delay), but provides
information. Note that none of the explicit terms of the contract has changed, neither
any of the relevant laws or the widely accepted social norms. The new information is
relevant if we consider the incomplete contract between the owner and the parents.
The contract is incomplete since the exact terms of payment for coming late are not
specified.
6
The behavior in the first three-four weeks is also consistent with this
explanation: parents are slowly testing the reaction of the day-care centers to higher
levels of delays. As they see no reaction over and above the fine, they continue to
increase their delay. In the final period, after the fine is removed, the information that
6
It is essential for this explanation that the contract will be incomplete. The alternative is that the
contract was complete before and after the introduction of the fine, and simply changed from one to
the other as the result of the unilateral decision of the owners of the day-care center. This argument
however does not give us any way to explain why parents increase the number of delays when the
price has risen.
20
the delay is not too bad of course persists. Parents keep coming late because they have
learned this fact. If they slightly increase the number of times they come late it is
because now the cost of doing so is even smaller than in the second period.
5.2 A simple formal model
We now outline, in an informal way, an explicit game to capture the importance
of this new information. The players in the game are the day-care owner and a finite
group of parents. For simplicity, the game goes on for an infinite number of periods,
and players discount their utility of every period. Players play sequentially in each
period. First the owner chooses an amount of fine out of a feasible set of fines. If the
fine is non zero then she has to pay for the first period a fixed implementation cost. If
the fine is zero she pays nothing. After that, each of the parents chooses simultaneously
an amount of delay, out of a fixed interval. The payoff for the owner is the fee for that
period, minus the cost, call it c, of the delay to her, all multiplied by the total delay.
The payoff to each parent is the value v of the delay (getting late to the day-care center
has a value for him, say because it gives him some flexibility) minus the fee, all
multiplied by the amount of the delay. The maximum amount of fee that the owner
may charge is randomly determined. It is chosen at the beginning of the game and
communicated to the owner only. To fix the ideas, we assume that it is either a large
value A with probability p or a small value a, with A>v >c> a >0. This is the type of
the owner. All the rest is known to every player.
21
We are going to describe an equilibrium of the game. It is convenient to begin
the description from the strategy of the parents. They choose an amount of delay d
which is just enough to make the owner indifferent between paying the cost of
introducing the fee and charging zero fee, facing the delay d each time in the future.
Parents keep doing this until some of the parents have chosen a higher delay in the
past, or the owner has charged a positive fine. After that, they simply choose in each
period the delay that maximizes the payoff for that period.
The owner charges zero fee in each period, until all parents have chosen the
delay d in each of the previous periods, and the owner herself has chosen a zero fine. If
any of the players, including her, has deviated in the previous periods, she chooses the
maximum feasible fine for all the future periods, irrespective of the action of the other
players, including her, in the past periods. Of course, given the strategy, the choice of
fine reveals completely her type.
For some p large enough this is an equilibrium. Again let us begin from the
parents. Each of them does not choose a delay larger than d, because in the event of an
owner with A as a maximum fee his value in future periods will be zero. For large p,
sticking to the equilibrium is better than any one-period gain. After the deviation of
some player, including himself, the best one period choice is the best choice, given that
he will face in any case the maximum fine according to the owner’s type.
22
The owner is indifferent, if her type is A, between charging a fine or not (her
future payoff is zero in both cases). If she is of type a she strictly prefers not to charge
a fine.
This equilibrium is inefficient. Moreover, the following two facts are easy to
see:
1. Suppose that, off the equilibrium path, a type a owner charges a fine a. In the
equilibrium for that subgame parents now choose an amount of delay larger than d.
In fact, since v > a, they choose the maximum delay possible. This is now an
efficient equilibrium.
2. Suppose that, in this subgame, the owner cancels the fine. Now the parents know
that the owner type is a, and they choose the maximum delay possible.
Both facts, 1 and 2 above, match our data: in the first three-four weeks after
the introduction of the fine the level of delay by the parents increased, and then it
stayed constant after the fine was withdrawn. It is an off-the-equilibrium path, but in
our study the introduction of the fine was not decided by the owner, but by us.
5.3 Rationalizations
A slightly different interpretation of the results may be the following. The
parents may have thought that the fines were being paid, at least in part, to the
teachers. This may have induced some of them to put less care in the time of arrival to
23
the daycare center, because what earlier was a nuisance imposed on the teachers, could
now look like a service against payment, although indirect. The parents knew that the
payment of the fine was due at the end of the month, to the owner. They were never
told that the teachers were being paid extra, and in fact if they asked, they were told
that that the teachers will not be paid more than before the fine was introduced.
In any case, this reason is not very convincing. Usually a relationship between
worker and employee is a relatively formal contract, with a well specified payment
schedule, that is not likely to be altered as a consequence of changes in the policy of
the firm towards the customers. In addition this explanation is particularly hard to
believe in light of the results in the third phase. After the fine is removed, it is hard to
believe that payments were still being made to teachers
5.4 The cognitive psychology explanation
A different interpretation of the results is possible. The introduction of the fine
may change the perception of coming late and of taking care of the children after
closure. According to this interpretation (that we may loosely call “cognitive
psychology”), in the first period the action of the teachers is interpreted by the parents
as a generous, non-market activity. They might think as follows: “The contract with the
day-care only covers the period until 4pm in the afternoon. After that, a teacher is just
a nice person who is generous. I should therefore not abuse of his patience.”
24
The introduction of the fine changes this perception into the following: “The
teacher is taking care of the child as much as she does earlier in the day. In fact this
activity has a price (which is called “fine”). I will therefore buy of this service as much as
needed.” In the third period, the reasoning just above does not change. Simply, the price
of a service has gone down.
5.5 Comparison with the IQ experiments
The explanation we have just suggested may seem more convincing in the light
of a different but related experiment of the same authors, that we briefly describe here.
The experiments reported in Gneezy and Rustichini (1998) study the effect of rewards
on performance. In one of them for instance we asked different groups of students to
solve an IQ test. To one group we promised NIS 0.1 per question they answered
correctly, to a second group we promised NIS 1, and to a third group NIS 3. Finally,
we did not mention money to a fourth group. The first group had the worst
performance, even worse than the last group to which no compensation was offered.
We seem to observe the same general regularity as in the current study: a price
of zero is very different from not mentioning a price. In particular, a price of zero is
not just a very low price.
6. Conclusions: Incomplete contracts and incentives
25
There seems to be little doubt on the fact that in our group of day-care centers
the introduction of a fine increased the behavior that was fined, and that the behavior
did not increase significantly when the fine was removed. These are the facts that we
have to explain. These facts might be, in themselves, little more than a curious finding.
It is clear first of all that a large fee would eventually reduce that behavior. For
instance, in many day care centers in the USA the fee for coming late is clearly
announced at the start of the year, and is linear in the time of delay. Due to this
proportionality, the resulting penalty is also more severe for the average delay than the
one we introduce in our experiment, even after we adjust for the difference in prices
and incomes in the two countries. We have not carefully examined if the average delay
is different, but this would be an interesting research.
Second, a contract where the amount paid is proportional or monotonically
increasing in the amount of the delay is likely to be closer to an efficient contract than
the lump sum fine we introduced in the experiment.
Finally, the method of analytical economics applied to the theory of optimal
fines (as summarized in Ehrlich (1996)) reminds us that the relationship between fines
and externality is not going to be a mechanical, direct implication of a smaller
externality following from a higher penalty. This effect is going to be mediated by
general equilibrium effects, that might weaken or even nullify the direct effect. Still we
have tried to argue that the evidence we have, and in particular the paradoxical positive
relationship in the second period cannot be explained in this usual way.
26
Fines, as well as rewards, are decided in a larger context, that we may define,
for convenience, a game. Many of the games we face in real life are not completely and
precisely defined. This is the case even when their description is reasonably accurate,
as is, after all, a contract for child-care in a private day-care center. People facing this
game do not come to it with simply their preferences and beliefs, but rather with a
perception of the strategic situation they are facing. The contract that is presented to
them may changes this perception. The evidence we have seen suggests that
introducing a fine may also change this perception of the game, and of the equilibrium.
This change of perception may be a simple acquisition of information (as it is in the
simple model we have proposed above), or it may be a more dramatic shift of
perception, as we have tried to discussed above.
A final comment: there is no reason to believe that this effect is limited to
minor faults, like a delay in the time of picking up one’s child. For instance, the
statement of a government that tax evasion is going to be more severely pursued may
be interpreted in different ways.
27
Appendix A1
Announcement: A fine for coming late
As you all know, the official time at which the day-care ends every day is
16:00. Since some parents are coming late we (with the approval of “Authority for
Private Day-Care Centers in Israel”) have decided to impose a fine on parents coming
late.
As of Sunday (January XX), a fine of NIS 10 will be charged for every time a
child will be collected after 16:10. This fine will be calculated monthly and will be paid
together with the regular monthly payment.
Sincerely,
The manager of the day-care
28
Table A. 1: time trends in the data.
a) Regression with time for the control group.
Source | SS df MS Number of obs = 80
---------+------------------------------ F( 1, 78) = 0.56
Model | 9.92716165 1 9.92716165 Prob > F = 0.4555
Residual | 1376.26034 78 17.6443633 R-squared = 0.0072
---------+------------------------------ Adj R-squared = -0.0056
Total | 1386.1875 79 17.5466772 Root MSE = 4.2005
------------------------------------------------------------------------------
w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
week | -.0610902 .0814446 -0.750 0.455 -.2232339 .1010535
_cons | 9.828947 .9756367 10.074 0.000 7.886604 11.77129
------------------------------------------------------------------------------
b) Regression with time for the test group.
Source | SS df MS Number of obs = 140
---------+------------------------------ F( 1, 138) = 38.27
Model | 1741.22642 1 1741.22642 Prob > F = 0.0000
Residual | 6279.37358 138 45.5027071 R-squared = 0.2171
---------+------------------------------ Adj R-squared = 0.2114
Total | 8020.60 139 57.7021583 Root MSE = 6.7456
------------------------------------------------------------------------------
w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
week | .6116004 .0988687 6.186 0.000 .416107 .8070938
_cons | 7.478195 1.184363 6.314 0.000 5.136351 9.82004
------------------------------------------------------------------------------
Table A.2:
Effects of the fees. The dummy variables are ``nf’’ (there is no fee),
``f’’ (there is a fee), ``wf’’(a fee was introduced and later removed).
reg w nf f wf
Source | SS df MS Number of obs = 220
---------+------------------------------ F( 3, 216) = 22.62
Model | 2518.67159 3 839.557197 Prob > F = 0.0000
Residual | 8018.6875 216 37.1235532 R-squared = 0.2390
---------+------------------------------ Adj R-squared = 0.2285
Total | 10537.3591 219 48.1157949 Root MSE = 6.0929
29
------------------------------------------------------------------------------
w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
nf | -1.4375 1.337866 -1.074 0.284 -4.074444 1.199444
f | 5.8125 .9518358 6.107 0.000 3.936424 7.688576
wf | 7.5625 1.337866 5.653 0.000 4.925556 10.19944
_cons | 9.1875 .6812081 13.487 0.000 7.844834 10.53017
------------------------------------------------------------------------------
Table A.3 Effects of the fees. The dummy variables are ``nf’’ (there is no fee),
``f’’ (there is a fee), ``wf’’(a fee was introduced and later removed). In addition,
a time trend variable (``w’’) is introduced.
. reg w nf f wf week
Source | SS df MS Number of obs = 220
---------+------------------------------ F( 4, 215) = 17.95
Model | 2638.44973 4 659.612433 Prob > F = 0.0000
Residual | 7898.90936 215 36.7391133 R-squared = 0.2504
---------+------------------------------ Adj R-squared = 0.2364
Total | 10537.3591 219 48.1157949 Root MSE = 6.0613
------------------------------------------------------------------------------
w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
nf | -.0041041 1.549696 -0.003 0.998 -3.058646 3.050438
f | 5.8125 .9468946 6.138 0.000 3.946115 7.678885
wf | 6.129104 1.549696 3.955 0.000 3.074562 9.183646
week | .1791745 .099232 1.806 0.072 -.0164176 .3747666
_cons | 7.306168 1.242928 5.878 0.000 4.856284 9.756052
------------------------------------------------------------------------------
30
References
Avio, K., (1979), ``Capital Punishment in Canada: A Time-Series Analysis of the
Deterrence Hypothesis’’, Canadian Journal of Economics, 12, 4, 647-676.
Azrin, N. H., (1956), ``Some effects of two intermittent schedules of immediate and
non-immediate punishment’’, Journal of Psychology, 42, 3-21.
Azrin, N. H., (1959), ``Punishment and recovery during fixed-ratio performance’’,
Journal of the Experimental Analysis of Behavior, 2, 302-305.
Azrin, N. H., (1960), ``Effects of punishment intensity during variable-interval
reinforcement’’ Journal of the Experimental Analysis of Behavior, 3, 123-142.
Azrin, N. H. and Holz, W.C., (1966), ``Punishment’’, In Honig, W. K. (Ed), Operant
Behavior, New York, Appleton-Century-Crofts.
Bandura, A., (1969), Principles of Behavior Modification, Holt, Rinehart and
Winston,
Beccaria, C., (1774), ``An Essay on Crimes and Punishment’’. Trad. H. Paolucci,
Indianapolis, Indiana.
Becker, G. B., (1968), ``Crime and Punishment: An Economic Approach’’,
Journal of Political Economy, 169.
Bentham, J., (1789), An Introduction to the Principles of Morals and Legislation,
London, Pickering.
Bianco, W. T., (1990), ``Crime and Punishment’’, American Political Science Review,
84, 569-573
Blackstone, W. (1979), Commentaries on the Laws of England, A Facsimile Edition
of the First Edition of 1765-1769, University of Chicago Press.
Blumstein, A., Cohen, J. and Nagin, D., (1978), Deterrence and Incapacitation:
Estimating the Effect of Criminal Sanctions on Crime Rates, Washington, D.C.,
National Academy of Sciences.
Brumm H. J. and Cloninger, D. O., (1996), ``Perceived risk of punishment and the
commission of homicides: A covariance structure analysis’’, Journal of Economic
Behavior and Organization, 31, 1-11.
31
Cameron J. and Pierce, W. D., (1994), Reinforcement, Reward, and Intrinsic
Motivation: a Meta-Analysis, Review of Educational Research, 64, 363-423.
Car-Hill R. A. and Stern, N., (1973), ``An Econometric Model of Supply and
Recorded Offences in England and Wales’’, Journal of Public Economics, 2, 289-
318
Chapman, R. W., (1962), ``School Suspension as Therapy’’, Personnel and Guidance
Journal, 40, 731-732
Church, R. M., (1963), ``The varied effect of punishment on behavior’’, Psychological
Review, 60, 369-402
Cook, P. J., (1980), `` Research in Criminal Deterrence: Laying the groundwork for
the second decade’’, in Crime and Justice: An annual review of research, volume
2, Chicago, University of Chicago Press.
Deci, E. L., (1971), ``Effects of externally mediated rewards on intrinsic motivation’’,
Journal of Personality and Social Psychology, 22, 113-120.
Ehrlich, I., (1973), ``Participation in Illegitimate Activities: A Theoretical and
Empirical Investigation’’, Journal of Political Economy, 81, 521-565.
Ehrlich, I., (1975), ``The Deterrent Effect of Capital Punishment: A Question of Life
and Death’’, American Economic Review, 65, 3, 397-417.
Ehrlich, I. And Mark, R., (1977), ``Fear of Deterrence: a Critical Evaluation of the
`Report of the Panel on Research on Deterrent and Incapacitation Effects’’’,
Journal of Legal Studies, 6, 2, 293-316.
Ehrlich, I., (1996), Crime, Punishment, and the Market for Offences, Journal of
Economic Perspectives, 10, 1, 43-67.
Eisenberger, R. and Cameron, J., (1996), ``Detrimental Effect of Reward. Reality or
Myth?’’ American Psychologist, 51, 11, 1153-1166.
Estes, W. K., (1944), ``An Experimental Study of Punishment’’, Psychological
Monographs, 3, 263.
Gibbs, J. (1975), Crime, Punishment and Deterrence, New York, Elsevier.
32
Gneezy U., and Rustichini, A. (1998), ``Pay enough, or Don’t Pay at All’’, CentER
Discussion Paper, Tilburg University.
Harris, J. R., (1970), ``On the Economics of Law and Order’’, Journal of Political
Economy, 78, 165-174
Hirschleifer, J. and Rasmussen, E., (1991) ``Are Equilibrium Strategies Unaffected by
Incentives? The Police Game’’, UCLA Discussion paper.
Hoenack , S. and Weiler, W. (1980), ``A Structural Model of Murder Behavior and the
Criminal Justice System’’, American Economic Review, 70, 3, 327-341.
Imrohoroglu, A., Merlo, A. and Rupert, P., (1997), ``On the Political Economy of
Redistribution and Crime’’, Federal Reserve Bank of Minneapolis DP.
Liska, A. E., (1987), Perspectives on Deviance, Englewood Cliffs, NJ, Prentice Hall
Phillips, L. and Votey, H., (1975), ``Crime Control in California’’, Journal of Legal
Studies’’, 4, 2, 327-349.
McManus, W., (1985), ``Estimates of the Deterrence Effect of Capital Punishment: the
Importance of the Researcher’s Prior Belief’’, Journal of Political Economy, 93,
417-425.
Ordeshook, P. C., (1990), ``Crime and Punishment’’, American Political Science
Review, 84, 573-575.
Powell J. and Azrin, N. (1968) The Effect of shock as a punisher for cigarette
smoking, Journal of Applied Behavior Analysis, 1, 63-71.
Pyle, D. J., (1984), The Economics of Crime and Law Enforcement, St. martin’s Press,
New York.
Rapoport, A. (1990) ``Comments on Tsebelis’’, Rationality and Society, 2, 508-511
Rotenberg, I. C., (1959), Effect of Schedule and Severity of Punishment on Verbal
Behavior, Journal of Experimental Psychology, 57, 193-200.
Solomon, R. L., (1964), Punishment, American Psychologist, 19, 239-253.
Schwartz, B., (1984), Psychology of Learning and Behavior, W.W. Norton and Co.
33
Stigler, G. J., (1970), ``The Optimum Enforcement of Laws’’, Journal of Political
Economy, 169.
Thorndyke, E. L., (1931), Human Learning, New York, Appleton-Century-Crofts.
Thorndyke, E. L., (1932), Fundamentals of Learning, New York: Teachers College,
Columbia University.
Tittle, C.R and Rowe, A. R., (1974), ``Certainty of arrest and Crime rates: A further
test of the deterrence hypothesis’’, Social Forces, 52, 455-462.
Tsebelis, G., (1989), ``The Abuse of Probability in Political Analysis: The Robinson
Crusoe Fallacy’’, American Political Science Review, 83, 77-92.
Tsebelis, G., (1990a), ``Crime and Punishment’’, American Political Science Review,
84, 576-586.
Tsebelis, G., (1990b), ``Are sanctions effective? A game theoretic analysis’’, Journal of
Conflict Resolution, 34, 3-28.
Tsebelis, G., (1990c), ``Penalty has no impact on Crime: A game theoretic analysis’’,
Rationality and Society, 2, 255-286.
Tullock, G., (1991), ``The Effect of Fines on Regulated Industries’’, Journal of
Theoretical Politics, 3, 81-101.
Wolpin, K., (1978a), ``An Economic Analysis of Crime and Punishment in England
and Wales’’, Journal of Political Economy, 86, 5, 815-840.
Wolpin, K., (1978b), ``Capital Punishment and Homicide in England: A Summary of
results’’, American Economic Review, 68, 2, 422-427.
Webley, P. Siviter, C., Payne M. and Scott, P. (1998) ``Why do some owners allow
their dogs to foul the pavement? The social psychology of a minor infraction’’,
Department of Psychology, University of Exeter.
Yu, J. and Liska, A., (1993), ``The Certainty of Punishment: A Reference group
Effect and its Functional Form, Criminology, 31, 3, 447-464.
Yu, J., (1994), ``Punishment Celerity and Severity: Testing a Specific Deterrence
Model of Drunk Driving Recidivism’’, Journal of Criminal Justice, 22, 4, 355-
366.
34
Zimrig F.E. and Hawkins, G.J., (1973), Deterrence, Chicago, University of Chicago
Press.
