%Paper: ewp-le/9506001
%From: Eric Rasmusen <erasmuse@rasmusen.bus.indiana.edu>
%Date: Wed, 14 Jun 95 13:37:34 -0500

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                   \begin{center}
\begin{large}
 {\bf Stigma and Self-Fulfilling Expectations of Criminality }\\
  \end{large}
         \vspace*{20pt}
       February 7, 1995  \\
        \bigskip
 Eric Rasmusen \\
 

 

        {\it Abstract} 

        \end{center}
      A convicted criminal suffers not only from public penalties,
but from stigma, the reluctance of others to interact with him
economically and socially. Conviction can convey useful information 
about a person, which makes
stigmatization an important and legitimate function of the criminal
justice system,  quite apart from moral considerations. Whether 
stigma will operate in this way depends on expectations and the crime 
rate, however,  which can lead   to multiple, pareto-ranked
equilibria with different amounts of crime and stigma. 




             \vspace* {.3in}
\begin{small}
          \noindent 

\hspace*{20pt}	  	  Indiana University
School of Business, Rm. 456, 

  10th Street  and Fee Lane,
  Bloomington, Indiana, 47405.
  Office: (812) 855-9219.   Fax: 812-855-3354. Internet: 
Erasmuse@.indiana.edu.\\ 

%  Draft: 7.5.  %(Draft 1.1, January 1990).
 

\vspace* {.2in}
 I thank  James Coleman,
Jeffrey Grogger,   John Lott, A. Mitchell Polinsky,
Peter Siegelman, Gary Schwartz,  the editors and referees of this 
journal, and participants in workshops at the
University of Chicago,   the University of Illinois,
and UCLA  for helpful comments. 



\end{small}

  %---------------------------------------------------------------
       \newpage

\begin{center} 

   {  I. 	INTRODUCTION}
     \end{center}
 

   The economic approach to crime   accepts that internal motivations 
such as conscience
are important in determining whether someone commits a crime, but
focuses on more easily measured and manipulated external incentives
such as criminal penalties.  This approach is theoretically
attractive, consistent with common sense, and has had  some degree of 
success in
explaining  empirical variation in crime 
rates.\footnote{\label{ehrlich} The seminal theoretical article is: 
Gary Becker, Crime and Punishment: An
Economic Approach, 76  Journal of Political Economy 

  169   (1968). Empirical studies range   from the seminal article by 
Isaac Ehrlich, Participation in
Illegitimate Activities: A Theoretical and Empirical Investigation, 
81
  Journal of Political Economy  521 (1973); to the recent article by 

Helen Tauchen, Ann Witte, \& Harriet Griesinger, Criminal Deterrence:
Revisiting the Issue with a Birth Cohort, 126  Review of Economics
and Statistics     399 (1994).} At first glance, the    pattern of 
crime in the United States  supports the importance of external 
penalties.     From 1960 to 1980, the number of prisoners per crime 
fell by 58\%
and the number of crimes per youth rose by 51\%, as data in Section
IV of this article will  show.  By 1990, however, the number of 
prisoners per
crime had returned to almost its 1960 level, but the number of crimes
per youth was 166\% higher.  This does not imply that penalties did 
not deter crime  in 1990, but it does  seem  that something happened
to make the  penalties a less powerful disincentive. 


        The economic model of crime has been elaborated  over the 
years, but we still do not have a satisfactory explanation for the 
decreased impact of criminal penalties.  A number
of articles have explored variants on what I will call the ``overload
theory'':  that when crime increases, law enforcement funding does 
not
increase enough to prevent the expected penalty from declining, which
increases crime  still further.\footnote{The idea of the overload 
theory is
mentioned as early as Ehrlich, {\it supra} note \ref{ehrlich}, and
can be found formalized in Francis Lui, A Dynamic Model of Corruption
Deterrence, 32 Journal of Public Economics   215  (1986); Jens
Andvig \& Karl Moene, How Corruption May Corrupt, 

 13  Journal of Economic Behavior and Organization   63  (1990);
Scott Freeman, Jeffrey Grogger \& Jon Sonstelie, The Spatial
Concentration of Crime, Working paper, Dept of Economics, University
of California, Santa Barbara, July 1989;  Raj Sah,   Social Osmosis 
and Patterns of Crime, 99 Journal
of Political Economy    1272 (1991);  and Joel Schrag  \& Suzanne
Scotchmer, The Self-Reinforcing Nature of Crime, Working paper,
Graduate School of Public Policy, University of California, Berkeley,
May 1994.}
 The overload theory can explain  how  a society might move from an 
equilibrium with low crime to one with high crime, but  the 

    amount of crime is still mediated by   the expected
penalty, so it cannot explain the U. S. pattern. 

 

 


Over a period as long as thirty years, it may be that social
influences  are more important determinants of changes in crime rates 
than are the incentives traditionally studied by
economists.  Some social influences, such as the present-orientedness 
or the effect of conscience, are the kinds of tastes that economists 
take as given in their models. Stigma, the  social influence to be 
studied  in this article, is not. 

Stigma refers to  the reluctance  of  people   to interact with  a 
person who has a criminal record.    For the   criminal, stigma
is an external incentive, like a jail term, not an internal
motivation, like conscience.  Standard economic modelling can be used
to ask how the criminal will respond to stigma and why people 

find it in their self-interest to treat criminals differently from
noncriminals. 


 

Stigma  can  be  either economic    (a lower wage)  or social 
(difficulty finding a spouse).   Economic stigma is the easier of 
these to
measure, and a number of scholars have tried  to estimate its
impact.\footnote{ \label{lott} This literature includes: 

  John Lott, The Effect of Conviction on the Legitimate Income of
Criminals,  34  Economics Letters  381 (1990); Freeman, Richard,
Crime and the Employment of Disadvantaged Youth, in Adele Harrell and
George Peterson, eds., Drugs, Crime and Social Isolation: Barriers to
Urban Opportunity, Washington: Urban Institute Press, 1992; John
Lott, An Attempt at Measuring the Total Monetary Penalty from Drug
Convictions: The Importance of an Individual's Reputation, 21 
Journal of
Legal Studies  159  (1992);   Jonathan Karpoff \& John
Lott, The Reputational Penalty Firms Bear from Committing Criminal
Fraud, 36 Journal of Law and Economics   757 (1993); and
Joel Waldfogel, The Effect of Criminal Conviction on Income and the
Trust `Reposed in the Workmen',  29 Journal of Human Resources 

 62 (1994). } Whether stigma is found to be important seems to
depend on the context.  Lott, for example, finds a short-run income
reduction of 39\% from bank embezzlement and 41\% from bank
larceny,\footnote{\label{lott2} John Lott, Do We Punish High-Income
Criminals Too Heavily?,  30 Economic Inquiry  583 (1992).}
and Grogger finds that arrests can explain about two-thirds of the
black/white youth employment differential in his
sample.\footnote{   Jeffrey Grogger, Arrests, Persistent Youth
Joblessness, and Black-White Employment Differentials, 74  Review of
Economics and Statistics   100 (1992).} In two other
studies,   Grogger finds only a short-lived effect of arrests
on youth earnings.\footnote{\label{grogger} Jeffrey Grogger, The 
Effect of Arrest on
the Employment and Earnings of Young Men, Quarterly Journal of
Economics, forthcoming; Jeffrey Grogger, Criminal Opportunities,
Youth Crime, and Young Men's Labor Supply, working paper, Dept. of
Economics, University of California, Santa Barbara, California,
February 1994.} 

 

These  articles   sought to measure the amount of stigma, rather than 
to explain its presence or absence. One approach to modelling stigma 
would be to use the theory of repeated games. 

   If a prisoner's dilemma is repeated  an infinite number of times 
with sufficiently little discounting,  then the two players may each 
choose  to cooperate for fear that a betrayal would lead to a 
cessation of cooperation by the other player.  The reputation model 
of Klein and Leffler relies on essentially the same reasoning:  a 
firm produces high-quality products because if it ever betrays 
consumers with a low-quality product, they will cease 
buying.\footnote{ Benjamin Klein  \& Keith Leffler,   The Role of 
Market Forces
in Assuring Contractual Performance,  89  Journal of Political
Economy  615 (1981).}    David Hirshleifer and myself have shown how 
a model of this kind can support costly ostracism:  members of a 
group can be given the incentive to expel an offending  member  even 
if his presence would add to the group's wealth.\footnote{David 
Hirshleifer  \& Eric Rasmusen, Cooperation in a
Repeated Prisoner's Dilemma with Ostracism, 12  Journal of
Economic Behavior and Organization   87  (1989).} This distrust of a 
player who has deviated from cooperation    seems especially apt for 
situations where a criminal has offended against the person who 
stigmatizes him----stealing from his employer, for example, who 
thereupon fires him. 

  The present article will take a different approach, more suitable 
for  modelling the reluctance of an outsider who is unaffected by the 
particular crime to interact with the criminal.  In such a  case, it 
would seem that stigma is   an informational phenomenon, based on 
public disclose of the character of the stigmatized person. 
Section II  of the article  constructs two   formal models of the
interaction between the decisions of potential criminals to commit
crime and of employers to stigmatize detected criminals.  Both models
show how    multiple equilibria could exist, so that in some cases 
stigma is 

present and crime is low  and in   other  cases stigma is absent and 
crime is high.
Section III explores the implications of stigma for public policy on 
enforcement, punishment, and disclosure.  Section IV  examines the 
empirical  plausibility  of the model,  and  applies  it to  the 
increase in crime since
1960.  Section V concludes. 



 %---------------------------------------------------------------
 \begin{center}
  { II.  MODELLING STIGMA }
 \end{center}

The idea to be modelled is that a public declaration of a person's
criminality  makes other people
reluctant to interact with him.  For modelling purposes, this 
reluctance will take the form of   employers paying  lower wages to 
those  convicted of  crimes.\footnote{The same model could be used 
for
social stigma with appropriate changes in interpretation, e.g.,
friends do fewer favors for  those convicted   of  crimes, because 
they are  revealed as less likely to reciprocate.  } 


  Two models will be developed, both based on the idea that 
conviction
conveys information about criminality and that employers prefer not
to hire criminals  but do not have a direct taste for
stigma.\footnote{ The most obvious link between crime and
productivity is employee theft and the precautions needed to avoid
it.  Dickens, Katz, Lang and Summers cite studies claiming that
employee theft costs American business between 15 and 56 billion
dollars per year, accounts for between 5 and 30 percent of business
failures, and induces spending of 12 billion dollars per year on
prevention. See William Dickens, Lawrence Katz, Kevin Lang, \&
Lawrence Summers,
 Employee Crime and the Monitoring Puzzle, 7 Journal of Labor
Economics,   331 (1989) at 332, 335.} In the moral hazard
model, all workers begin with equal marginal products, but any worker 
who
engages in crime becomes less productive.  In the adverse selection
model, crime has no effect on productivity, but some workers begin
with lower marginal products regardless of whether they commit
crimes, and these workers  have a greater tendency to commit crimes. 

 

 



\begin{center}{\it  A.  The Moral Hazard Model}
 \end{center}
 

    The decisionmakers in the model are risk-neutral workers and
risk-neutral employers. The workers must decide whether to commit
crimes, unobserved by employers unless they are caught and convicted,
and the employers must decide how much to pay convicted and
unconvicted workers. 

 


  If a worker decides to engage in crime, he is caught and convicted 
with
exogenous probability $\alpha \in (0,1)$.  The direct reward from
crime is $V$ and the public penalty from being convicted is
$P$.\footnote{The exogeneity of  $\alpha$,  $V$
and $P$ is a simplifying assumption made to highlight the effect of 
stigma. Quite plausibly,    the reward for crime 

falls as the amount of crime rises,  because of competition for 
criminal opportunities. The public
penalty might either rise (from growing public concern over crime) or
fall (the ``overload theory'' of Section I).   These effects are 
ruled out
in  the present model.  Note also that  in this model courts do not 
use character evidence to stigmatize defendants,  the idea behind 
multiple equilibria in  Joel Schrag \&
Suzanne Scotchmer, Crime and Prejudice: The Use of Character in
Evidence in Criminal Trials, 10 Journal of Law, Economics, and
Organization  319  (1994).} There is a continuum of workers, so 
$\theta \in
[0,1]$, the proportion that choose crime, is unaffected by any
individual's decision.  Workers are identical except for a
heterogeneity parameter $u$ with cumulative distribution $F(u)$
across the population, where a positive $u$ denotes an individual
whose aversion to crime is greater for unmodelled reasons such as
moral scruples, lack of skill, or poor criminal
opportunities.\footnote{Heterogeneity is imposed so that statements
can be made about how the amount of crime changes with the
parameters, since if individuals are identical either all are
criminal or all are noncriminal. The conclusion found below that
multiple equilibria can exist would remain valid even if all
individuals were identical.} Let $F'(u)>0$ for any $u$, which implies
that some people will choose crime no matter how high the penalties
and some people will refrain from crime no matter how low the
penalties. 

 

  Whether a worker has  been convicted or not, he offers himself for
employment.  Crime hurts net productivity. In legitimate employment, 
the
criminal's marginal product is $m$ and the noncriminal's is $m+y>m$.
This may be  so for a variety of reasons, including  employee theft,
resistance to authority,   and lack of attention to acquiring 
legitimate skills.
  Employers compete with each
other for workers, but all they  observe are convictions, not
criminality or marginal product.

 In equilibrium, a convicted worker will earn his marginal product of
$m$. A worker whose innocence  was known would receive $m+y$, but
the category of unconvicted workers pools  noncriminals with
unconvicted criminals, so the wage for an unconvicted worker, $w$,
will lie in the interval $[m, m+y]$ and depend on the proportion of
unconvicted workers believed to be criminals.  Fraction $\alpha$ of
the $\theta$ criminal workers are convicted, leaving proportion $(1-
\alpha \theta)$ of the population unconvicted, which is the
denominator for the expected-value expression (1) below. Of the
unconvicted $(1- \alpha \theta)$, amount $(1-\theta)$ are noncriminal
and have marginal product $m+y$, while amount $\theta (1-\alpha)$ are
unconvicted criminals with marginal product $m$. Hence, the average
marginal product in the unconvicted population is
  \begin{equation} \label{e1}
 \begin{array}{ll}
 w &= \left( \frac{1-\theta}{1-\alpha\theta} \right) \left(m+y 
\right)
+ \left( \frac{\theta(1-\alpha)}{1-\alpha\theta} \right) m\\
 & \\
  & = m + \frac{1-\theta}{1-\alpha \theta}y.\\
 \end{array} 

  \end{equation}
 It can immediately be seen that the wage of the unconvicted worker
falls with the amount of crime:
  \begin{equation} \label{e2}
  \frac{\partial w}{\partial \theta} = -\left( \frac{1 - \alpha}
{(1-\alpha\theta)^2} \right)y < 0.
  \end{equation}

 Depending on whether he is  criminal or  noncriminal, the
worker's expected payoff is
   \begin{equation} \label{e3}
 \pi_c=  (V - \alpha P) + (1-\alpha)w + \alpha m-u
 \end{equation}
 or
   \begin{equation} \label{e4}
 \pi_{nc}=w.
 \end{equation}
 The worker will choose to be criminal if $A$, the
attractiveness of crime, is positive.  Using (1), (3), and (4), its 
value is 

 \begin{eqnarray} \label{e4a}
   A &\equiv &\pi_c - \pi_{nc} \\ 

 & = &V - \alpha P + (1-\alpha)w + \alpha m-u  - w \nonumber\\
 & = &\left( V - \alpha P \right) - \alpha \left(
\frac{1-\theta}{1-\alpha\theta} \right)y - u.
 \end{eqnarray}
 

\noindent
{\it  PROPOSITION 1:   The attractiveness of crime is:
(a)
  increasing in  the  direct reward to   crime, $V$;
 (b)
 decreasing in the personal  disutility of crime, $u$; 

 (c) decreasing in  the criminal penalty, $P$;
 (d)
  decreasing in  the productivity damage, $y$;  (e) decreasing in the 
probability $\alpha$ of conviction,  even  if $P=0$; and 

  (f) increasing in the aggregate crime rate, $\theta$.} 


\begin{small}
{\it Proof}: Points (a) through (d) are obvious from inspection of
equation (\ref{e4a}). Regarding point (e):
  \begin{equation} \label{e7}
 \frac{ \partial A}{\partial \alpha } = -P - \left(
\frac{1-\theta}{(1-\alpha\theta)^2} \right)y. 

  \end{equation}
 This expression is negative.     Regarding
point (f):
  \begin{equation} \label{e8}
 \begin{array}{ll} 

 \frac{\partial A}{\partial \theta} & = \frac{\alpha y}{1-\alpha 
\theta }
-\frac{\alpha^2 (1-\theta) y}{(1-\alpha \theta)^2}\\
 & \\
  & =\alpha y  \left( \frac{1-\alpha }
{(1-\alpha \theta)^2} \right).\\
\end{array}
  \end{equation}
 This expression is positive under our assumption that
$0 < \alpha <1$.   Q.E.D.
 \end{small}

Increasing the  probability and amount of punishment  reduce the
attractiveness of crime, but the effects of $\alpha$ (the probability
of conviction) and $P$ (the penalty) diverge. $P$ exerts a negative
effect only once in equation (6), when it is multiplied by $\alpha$
in the official punishment. $\alpha$ exerts two additional
negative effects. If the probability of conviction is high, then (i)
the probability of being convicted and stigmatized is higher and (ii)
the amount of stigma is greater. Contrary to simpler models of crime,
enforcement has more impact than punishment: holding the expected
penalty $\alpha P$ constant at 2, a value of $P=20$ combined with
$\alpha=.1$ would not deter crime as strongly as $P=4$ and $\alpha =
0.5$. Even if $P=0$,    the threat of stigma might be sufficient to
deter crime by itself.

 The variable $\theta$, representing the proportion of criminals, is
endogenous; it determines the individual worker's decision, but
itself is determined by the decisions of all workers.  When $\theta$
rises, the wage loss from conviction falls. The payoffs of  both
criminal and noncriminal workers decline, but the payoff of
noncriminal workers declines more. From  equations (3) and (4) it can
be seen that $\frac{\partial \pi_{nc}} {\partial \theta} =
  \frac{\partial w}{\partial \theta},
 $
 and
  $
 \frac{\partial \pi_c}{\partial \theta} = - 

  (1-\alpha)(
  \frac{d w}{d \theta} )$.
 Since $ \frac{\partial \pi_c}{\partial \theta} =-(1-\alpha)
\frac{\partial \pi_{nc} }{\partial \theta}$, a high crime rate hurts
the noncriminal more than the criminal.
 


There exist cutoff levels of $u$ such that individuals with
heterogeneity parameters in the interval $ [-\infty, \underline{u}]$
will always engage in crime, those in the interval $
(\underline{u},\overline{u})$ will decide based on $\theta$, and
those in the interval $ [\overline{u}, +\infty]$ will always refrain
from crime.\footnote{The values of $u$ that bound the intervals can
be found by setting $A=0$ and $\theta$ equal to zero or to one in
equation (6), giving $\underline{u}=(V - \alpha P) -
\frac{\alpha}{1-\alpha} y$ and $\overline{u}=(V-\alpha P)$. } In this
interval, let $\tilde{\theta}(u)$ be the crime level at which an
individual of type $u$ is indifferent between crime and noncrime. For
$\theta> \tilde{\theta}(u)$ he will choose crime, and for smaller
$\theta$ he will not. $\tilde{\theta}(u)$ is increasing in $u$, and
this implies that if $\theta= \tilde{\theta}(u)$, all individuals in
the interval $[-\infty, u]$ will choose crime.
 Figure 1 puts $F(u)$ and $\tilde{\theta}(u)$ on the same diagram.
Any intersection $(u^*,\theta^*)$ between the curves
$\tilde{\theta}(u)$ and $F(u)$ will be an equilibrium. At $\theta^*$,
the marginal criminal, with utility parameter $u^*$, will be
indifferent about choosing crime because $A(u^*,\theta^*)=0$, while
the $F(u^*)$ individuals with lower levels of $u$ will choose crime
and the $(1-F(u^*))$ with higher levels will refrain from crime.

 

  \bigskip
\epsfysize=2in

\epsffile{/Users/erasmuse/@Papers/stigma/Figures/Figure_1.eps}
 

 

 

{\it PROPOSITION 2: Depending on  the distribution of the
taste for crime, $F(u)$, there may exist multiple equilibria.  If 
there are
three equilibria, with crime levels $\theta^-<\theta^{*}<\theta^+$,
then the two outer equilibria are stable and the middle one is
unstable.  The equilibria can be pareto-ranked, with lower crime 
levels being superior.}

\begin{small}
{\it Proof.} {\it (i) Existence.}
 An equilibrium is at an intersection of $\tilde{\theta}(u)$ and 
$F(u)$. 

 $\tilde{\theta}(\underline{u})=0$ and
$\tilde{\theta}(\overline{u})=1$ by definition of $\underline{u}$ and
$\overline{u}$.  That $\tilde{\theta}(u)$ is increasing and
continuous can be seen as follows.  $\tilde{\theta}$ is found by
setting $A$ equal to zero and solving for $\theta$ in equation (6): 

 \begin{equation} \label{e10}
 V-\alpha P - \frac{ 1-\theta}{1-\alpha \theta} \alpha y -u=0,
 \end{equation}
 which implies that
 \begin{equation} \label{e11}
 \tilde{\theta} = \frac{V-\alpha P - \alpha y- u}{\alpha (V -\alpha P
- y - u)}.
 \end{equation}
 The derivative of (10) with respect to $u$ exists and is
 \begin{equation} \label{e12}
 \frac{\partial \tilde{\theta}}{\partial u} = \frac{-1}{\alpha 
(V-\alpha
P - y - u)} + \frac{\alpha (V-\alpha P - \alpha y -u) }{\alpha^2
((V-\alpha P) - y - u)^2} = \frac{y (1-\alpha) }{\alpha (V-\alpha P
-y - u)^2},
 \end{equation}
 which is positive because $\alpha \in (0,1)$.

Because $\tilde{\theta}(u)$ is continuous, increasing, and takes
every value between 0 and 1, and F is nondecreasing,
continuous, and restricted to values between 0 and 1, there
must be some $u^*$ at which $F(u^*) = \tilde{\theta}(u^*)$.  Thus, an
equilibrium exists. The curve $F$ might intersect $\tilde{\theta}(u)$
at more than one point, generating the multiple equilibria of Figure 

1, or it might intersect just once.

{\it (ii) Stability.} An equilibrium $\theta$ is stable with respect
to a dynamic process if for arbitrarily small $\epsilon$ and an
initial state $ (\theta+ \epsilon)$ or $(\theta - \epsilon)$, the
limit of the dynamic process is $\theta$. The simplest dynamic
process is myopic: ``In period $t$, individuals make their decisions
as if they believe that $\theta_t$ will equal $\theta_{t-1}$,'' but
any equilibrium stable with respect to myopic dynamics will also be
stable with respect to a rational-expectations dynamics in which the
equilibrium jumps instantly to the value to which myopic dynamics
would converge slowly.

 An equilibrium's stability depends on whether $F$ cuts
$\tilde{\theta}(u)$ from above or below.  If $F$ cuts
$\tilde{\theta}(u)$ from above (that is, if $F(u^*-\epsilon) >
\tilde{\theta}(u^*-\epsilon)$ and $F(u^*+\epsilon) <
\tilde{\theta}(u^*+\epsilon)$), then the equilibrium is stable.
Suppose that these inequalities are true and the system starts at
$\theta' < \theta^*$ where $u=u^*-\epsilon$. The amount of crime will
increase, because $F(u)=\theta'$, which  is greater  than
$\tilde{\theta}(u)$,the amount of crime that induces individual $u$
to undertake crimes. If $F$ intersects $\tilde{\theta}(u)$ from 
above,
then $F$ must have a gentler slope than $\tilde{\theta}(u)$ at
$u^*-\epsilon$, so the increase in crime will not overshoot $u^*$,
and myopic dynamics will converge at $u^*$.

 If $F$ does not cut $\tilde{\theta}(u)$, but rather intersects it at
the extreme value of $\overline{u}$ or $\underline{u}$, then the
equilibrium is still stable. The previous paragraph's argument still
applies to dynamics starting from values of $u$ nearer 0 than $u^*$,
and if the system starts at a more extreme value of $u$, even myopic
dynamics instantly lead back  to $u^*$.  If there is a single
equilibrium, then $F(u)$ either intersects $\tilde{\theta}(u)$ at an
extreme value, in which case the same argument shows it is stable, or
$F(\underline{u}) >0$ and $F(\overline{u}) < 1$. But if this is the
case and $F$ is continuous, then $F$, starting greater than
$\tilde{\theta}(u)$ and ending smaller than $\tilde{\theta}(u)$, must
cut $\tilde{\theta}(u)$ from above, and the equilibrium is stable.
If there are three equilibria, then any equilibrium at
$\underline{u}$ or $\overline{u}$ is an outer equilibrium, and is
stable by the same argument. That argument also shows that the
smallest equilibrium  must either be  at $\underline{u}$
or (given that $\tilde{\theta}(u)$ is upward sloping) at a point
where $F(u)$ cuts $\tilde{\theta}(u)$ from above. But if $F$ cuts
$\tilde{\theta}(u)$ from above at the first equilibrium, then it must
cut from below at the middle equilibrium, $u^*$.  And if it cuts from
below at $u^*$, then for slightly larger $u$, $F(u)$ lies above
$\tilde{\theta}(u)$, and it must cut $\tilde{\theta}(u)$ from above
at the final equilibrium. Hence the two outer equilibria are stable,
and the middle equilibrium is not.

{\it (iii) Optimality.} Even from the point of view of the potential 
criminals, the  high-crime equilibrium is
dominated by the low-crime equilibrium.  Inequality (2) shows that 
$w$ falls in $\theta$, and equations (3)
and (4) show that $w$ is a component of the payoffs of both the
criminal and the noncriminal, so the high-crime equilibrium has lower
payoffs for all.  Q.E.D.
 \end{small}

 Proposition 2 establishes the possibility of multiple,
pareto-ranked, stable equilibria. Every individual, whether his
particular tastes lead  him to be criminal or noncriminal,  prefers
the low-crime equilibrium, in which stigma has a strong effect and
convicted criminals receive large cuts in their wages. This is less
paradoxical when it is rephrased: every individual prefers the
equilibrium in which lack of a criminal record is rewarded by a wage
premium. The punishment of   stigma and the reward of a
 wage  premium for a clean record are   equivalent; what matters is 
that
  a wedge between the wages of the convicted and the   unconvicted 
deter crime.

 


\begin{center} {\it B. An Adverse Selection Model of Stigma}
 \end{center}

    The moral hazard model captures  the channels in which stigma 
operates when crime reduces productivity.    Stigma can be effective, 
however, even when crime does not reduce  productivity.  In that 
case, whether an employee committed crimes in the
past would not affect  his wage in a world of perfect
information, but under imperfect information, employers  might  use
criminality as a proxy for low productivity. 


 To model this, let   $m$ be the marginal product of the low-ability 
workers, who always commit crimes
and  who form proportion $\overline{\theta}$ of the
population.  Let $m+y$ be the marginal product of high-ability
workers, who choose whether or not to commit crimes and  who form 
proportion
$1-\overline{\theta}$ of the population.  The total proportion of
criminal workers is $\theta> \overline{\theta}$.  A criminal is
caught and convicted with probability $\alpha$, and crime has no
effect on   productivity.  Let us assume,
for simplicity, that there is no other worker heterogeneity of the 
kind 

  $F(u)$ represented  in the moral hazard model. 


 In equilibrium, the wage for a convicted worker is not necessarily
$m$, as in the moral hazard model, because high-ability workers might
be convicted too.  Low and high-ability workers are convicted at the
same rate, so all that matters is the relative proportion in the
criminal population. The   wage for the convicted is
  \begin{equation} \label{e21}
 w_c =\left( \frac{\overline{\theta}}{\theta} \right) m + \left(
\frac{\theta - \overline{\theta}}{\theta} \right) (m+y),
  \end{equation}
 which equals $m$ only if $\theta = \overline{\theta}$. 


The unconvicted population is composed of unconvicted criminals with
low ability (proportion $\overline{\theta} (1-\alpha)$), unconvicted
criminals with high ability ($(\theta -\overline{\theta})
(1-\alpha)$), and noncriminals with high ability $(1-\theta)$, a
total probability mass of $1-\alpha \theta$.  The unconvicted wage is
therefore
  \begin{equation} \label{e22}
 w = \left( \frac{\overline{\theta} (1-\alpha)}{1-\alpha\theta} 
\right)
m
 + \left( \frac{1-\overline{\theta} - \alpha
(\theta-\overline{\theta})}{1-\alpha\theta} \right) \left(m+y 
\right). 

  \end{equation}

 The adverse selection model has  two equilibrial: a
pooling, high-crime equilibrium in which the high-ability workers
  choose crime and the unconvicted wage equals the convicted wage;
and a separating, low-crime equilibrium in which the high-ability
workers refrain from crime and conviction carries stigma. 

 In the low-crime equilibrium, only low-ability workers commit
crimes, and convicts are paid the low-ability wage.  High-ability
people refrain from crime, because they do not want to risk being
pooled with the low-ability convicts. The unconvicted are paid a wage
between the low- and high-ability wages, because low-ability
criminals who are not caught are indistinguishable from high-ability
workers. In the high-crime equilibrium, everyone  commits crimes, and 
the
wage for  the convicted and the unconvicted  is the same. 


 

 Formally, in the low-crime equilibrium, none of the high-ability
workers choose crime. This means that $\theta = \overline{\theta}$,
  \begin{equation} \label{e23}
 w_c = m,
  \end{equation}
 and 

  \begin{equation} \label{e24}
 w = \left( \frac{\overline{\theta} (1-\alpha)}{1-\alpha
\overline{\theta}} \right) m
 + \left( \frac{1-\overline{\theta} }{1-\alpha \overline{\theta}}
\right) \left(m+y \right). 

  \end{equation}

In the high-crime equilibrium, all of the high-ability workers choose
crime. This means that $\theta = 1$,
  \begin{equation} \label{e25}
 w_c = \overline{\theta} m + (1 - \overline{\theta}) (m+y),
  \end{equation}
 and
  \begin{equation} \label{e26}
 \begin{array}{ll}
 w &= \left( \frac{\overline{\theta} (1-\alpha)}{1-\alpha} \right)
m
 + \left( \frac{1-\overline{\theta} - \alpha
(1-\overline{\theta})}{1-\alpha} \right) \left(m+y \right)  \\
 & \\
 & = \overline{\theta} m + (1 - \overline{\theta}) (m+y). 

 \end{array}
  \end{equation}
 The wage is the same for both convicted and unconvicted workers in
the high-crime equilibrium.  Neither equilibrium is Pareto-dominant,
in contrast to the moral hazard model.  The low-ability workers
prefer the high-crime equilibrium, but the high-ability workers
prefer the low-crime equilibrium.


The moral hazard and adverse selection models make similar
predictions, except that a move from low to high crime leaves the
  wage for the convicted unchanged in the moral hazard model and
raises it in the adverse selection model.  This is because in the
adverse selection model, the average wage is independent of the
number of criminals. As criminality increases, the wage of the
unconvicted falls but the wage of the convicted rises.  The biggest
difference is perhaps in the welfare implications, since in the
adverse selection model the cost of high crime is limited to the
crime itself rather than to ill effects on worker productivity. 

 


%---------------------------------------------------------------

 

\begin{center}
   {  III.    STIGMA AND PUBLIC  POLICY}
 \end{center}
 

 

\begin{center} {\it  A.   The Government's Choice of the Probability 
of Conviction   }
 \end{center}
 

   In the standard  economic model of crime,   only the expected
penalty   matters for deterrence, and the division between
punishment and probability of conviction is important only to  the
government's expense of punishment. In the stigma model,  the 
probability of conviction, $\alpha$, has a double deterrent
effect, operating via not only the public punishment $P$ but  private 
stigma.  Even if $P=0$, if stigma is sufficiently great,
crime is deterred.\footnote{In many cases, $P=0$ is a reasonable
approximation.  The stigma arises from arrest, even if no trial
follows, or conviction is followed by probation instead of
imprisonment.  Only 51\% of federal and an estimated 46\% of state
felony convictions were followed by incarceration in a typical year
(Federal: from 1 July 1985 to 30 June 1986, \label{(BJS-1988c)}
Bureau of Justice Statistics, U.S. Dept of Justice,  Technical
Appendix, Report to the Nation on Crime and Justice, Second Edition 

(1988) at   54. State: 1986 data, Bureau of Justice
Statistics, U.S. Dept of Justice, Sourcebook of Criminal Justice
Statistics, 1988, Table 5.31.} 


Paradoxically, the productivity loss from crime can be beneficial to 
the potential criminal and to society, because 

it permits  a low-crime equilibrium  to exist even  when official 
penalties are low.  The productivity loss  helps to explain the lower 
crime rates of the affluent, since
for many well-paying jobs a large productivity loss is plausible. 

Lott has shown empirically that a larger portion of the punishment
for a wealthier person is indeed in the form of wage
loss.\footnote{Lott, 1992, {\it supra} note \ref{lott}.} Facing a
heavier penalty, he is more strongly deterred. Stigma 

may also 

  help explain why crime rates are so high among the young. For
reasons unrelated to crime, young people are less likely to be
employed, and therefore less likely to suffer immediate economic
stigma if caught. Although the participation rate for males aged
18-19 is only 68.1\%, it rises to 94.3\% for males aged 25 to
34.\footnote{\label{Handbook} This is 1988 data, from: Bureau of
Labor Statistics, U.S. Dept of Labor, Handbook of Labor Statistics,
1989, pp. 26, 137.  Unemployment rates were 14.6\% for age 18-19,
5.3\% for 25-34.  The corresponding figures for black males alone
are: participation for ages 18-19, 56.0\%; participation for ages
25-34, 89.3\%; unemployment for ages 18-19, 31.7\%; unemployment for
ages 25-34, 11.0\%. } The  situation is self-reinforcing, since
employers are more relucant to hire the young if they are
disproportionately criminal. 


  The probability of conviction is thus a more powerful policy tool
than the official penalty   when stigma is 

effective.  What conviction probability is optimal?  That depends on
the relative costs of enforcement and crime,   which equilibrium is
in effect, and   the likelihood of random shocks to individual
tastes for crime. 


    Figure 1 showed $F(u)$, the distribution of individual aversions
to crime, and $\tilde{\theta}(u)$, the critical levels of crime that
induce different individuals to engage in crime.  In Figure 2, a
reduction in enforcement (the probability $\alpha$ or the size $P$ of
punishment) shifts down $\tilde{\theta}(u)$ from
$\tilde{\theta_0}(u)$ to $\tilde{\theta_1}(u)$ If the system begins
at $E_0$, then whether enforcement should be increased or reduced
depends on their costs compared to the costs of crime--- productivity
loss, victim precautions, and so forth. If crime is costly compared
to enforcement, then $\tilde{\theta}(u)$ should be shifted up by
increasing the amount of enforcement.  If enforcement is more costly,
then $\tilde{\theta}(u)$ should be shifted down. Figure 2 shows the
effect of reduced enforcement: $\tilde{\theta}(u)$ shifts to
$\tilde{\theta}_1(u)$ and the equilibrium moves smoothly from $E_0$
to   higher crime at $E_1$. 


 

 \bigskip
\epsfysize=2in

\epsffile{/Users/erasmuse/@Papers/stigma/Figures/Figure_2:_Reducing_Pe 
nalties.eps}
 

 $E_1$ will be the optimal equilibrium from the point of view of the
government for a wide range of costs of enforcement.  If enforcement
is reduced any further, then $\tilde{\theta}(u)$ shifts to
$\tilde{\theta}_2(u)$ and the equilibrium shifts discontinuously to
much higher crime at $E_2$.  $E_1$ is the equilibrium with the lowest
level of enforcement that still enables private stigma to effectively
supplement public punishment.
 

 Equilibrium $E_1$, however, is not robust to small shocks in
$\alpha$, $P$, and $F(u)$. If enforcement dips slightly, or
individuals become less averse to crime, then the low-crime
equilibrium disappears, and crime increases discontinuously. A small
shock can be drastically multiplied. Since the expectations that
maintain the low-crime equilibrium are a form of valuable social
capital, the presence of random shocks would make a higher level of
enforcement optimal than would otherwise be the case, and the optimal
expected amount of crime would be less than $\tilde{\theta}(u)$. 


 The optimal level of enforcement also depends on which equilibrium
is in effect. Suppose that enforcement has  fallen  enough  that 
$E_2$
is the equilibrium.  If enforcement increases, the
$\tilde{\theta}(u)$ curve returns to $\tilde{\theta}_1(u)$, but the
equilibrium does not return to drastically lower crime at $E_1$, but
to slightly lower crime at $E_3$.  Thus, although enforcement levels
resulting in $\tilde{\theta}_1(u)$ may be optimal starting from
$\tilde{\theta}_0(u)$ or $\tilde{\theta}_1(u)$, if the system begins
at $\tilde{\theta}_2(u)$ a lower level of enforcement may be optimal.
If crime is low, long jail sentences may be optimal to maintain
stigma, but if crime is high, and stigma has ceased to work, the
authorities should give up and become more lenient. The optimal
enforcement effort can actually fall as crime increases.  The stigma 
model  also  suggests   that a ``big push'' would
be the most effective way to reduce crime. It may be worth
investing resources to push the system back to the low-crime
equilibrium,  even if  it is not worthwhile trying to ameliorate the
high-crime equilibrium. 

 

\begin{center} {\it  B. The  Advantages of Stigma as a Punishment}
 \end{center}
 

 One of the oldest issues in the economics of crime is how society
can deter crime efficiently. Imprisonment is   costly,  and   Becker 
has suggested that fines be
used wherever possible  because they are transfers rather than social
costs.\footnote{Becker, {\it supra}, note \ref{ehrlich}.} If the fine
is large and the probability of detection small, the expected penalty
can  be  large enough to yield deterrence at a low social cost.  This
policy has well-known practical problems, of which the most important
is the inability of   criminals to pay substantial fines.  High fines 
also raise the concern that the government may be tempted to
prosecute the innocent for the sake of   revenue.
 

Stigma avoids these problems.  Although many people have little
liquid wealth, the market value of most people's future labor rents
is substantial. Stigma is like a fine drawn on those future rents, a
fine which can be collected regardless of the criminal's present
wealth.   Since it is the private sector that imposes the
punishment, stigma is neither costly to the government, like
imprisonment, nor revenue-raising, like fines, so neither concern
will distort the government's decision. 

 

  At the same time, stigma retains the advantage of fines in
deterring the criminal without creating real costs, because it
transfers wealth from the criminal to the rest of society. Stigma
actually increases efficiency, because allocative efficiency
increases as information is disclosed.  The stigma from automobile
speeding, for example, is that the offender will pay more for
automobile insurance after being identified as a fast driver with a
disdain for regulations.  This comes closer to matching the social
cost of the offender's driving with the private cost to himself, and
in some cases he will quit driving.  The effect in the labor market
is similar. 

     Prior to his conviction, the criminal's labor is overvalued in
the market. His loss of income after stigmatization is a gain for
noncriminal workers who would otherwise be pooled with him and paid
less than their marginal products so he could be paid
more.\footnote{Posner   mentions that stigma can supplement
official punishment for white-collar crime, but he misses this point,
claiming instead that ``The economic objection to relying on stigma
for deterrence is that, like imprisonment, it is more costly to
society than the pure fine (or civil penalty) because it does not
yield any revenue'' (Richard Posner, Optimal Sentences for
White--Collar Criminals, 

 17 American Criminal Law Review   409 (1980)  at  416).} 

 

 This benefit of stigma is different from the conventional functions
of punishment---- deterrence, incapacitation, rehabilitation, and
retribution.  Stigma has advantages as a deterrent, and may even
serve to incapacitate the criminal by removing him from jobs that
would give him opportunities for crime, but in disclosing information
it serves a distinctly different function.  Even if stigma had no
effect on the amount of crime, it would improve efficiency. 


 



\begin{center} {\it C. Publicizing  Government Records }
  \end{center}
 

 Because stigmatization is distinct from deterrence, courts need to
convey accurate information to the public, rather than just
inflicting the appropriate penalty. For deterrence, it may not matter
if the court declares someone guilty of counterfeiting  rather than 
their actual crime of burglary, so long as the penalty is appropriate
for burglary. For stigmatization, however, the exact charge is
important, because different kinds of people commit these crimes. 


 This has implications for plea bargaining.  In a plea bargain, the
accused often  pleads guilty to a crime milder than that for which 
the
prosecutor has good evidence. From the point of view of
stigmatization, it would be much better for the plea bargain to take
the form of a guilty plea to the original crime, but with a 
recommendation of a reduced sentence.  The public penalty would be 
the same, but stigma could be more accurately applied. 


         The social utility of stigma is also relevant to the
question of whether criminal records should be open to the public.
Court dockets are open as a matter of constitutional right, and daily
police arrest blotters are traditionally open, but the availability
of records filed by name varies state by state.\footnote{There seems 
no constitutional objection to disclosure.  In 1976, the U.S. 
Supreme Court  established that a police
department could even circulate  the names of those
arrested for  shoplifting (even though not convicted)  to  local 
merchants ({\it
Paul v. Davis}, 424 U.S.  693 (1976)).  The discussion in this 
paragraph and
the next is from \label{(BJS-1988d)} Bureau of Justice Statistics,
U.S. Dept of Justice, Public Access to Criminal History Record
Information  (1988): blotters, p. 2; dockets,
p. 3; Florida, p. 19; Illinois, p. 25; and Bureau of Justice 
Statistics,
U.S. Dept of Justice,    Use and Management of Criminal History 
Record Information: A Comprehensive Report (1993). }  State 
legislatures
have passed a wide variety of statutes ranging from Florida's
completely open records to Illinois' restriction of access to
providers of child care, volunteer organizations associated with
children, detective agencies, security-guard organizations, schools,
and liquor-license holders. Moreover, juvenile records are often kept
secret even when adult records are not. 


The argument for keeping criminal records secret is that by
preventing discrimination against workers with criminal pasts it
gives them higher wages in legitimate employment and greater
motivation for a fresh start. 

 This is sometimes joined to the argument that employers are 
unreasonably prejudiced against workers with criminal records, 
because criminality   is not associated with  productivity. This 
argument is weak because it depends on outside observers knowing 
workers' productivity better than employers 
do.\footnote{Discrimination against criminals
is generally legal, but it has become entangled in racial
discrimination suits. In one case,  a   plaintiff was refused
employment because of his 14 arrests. Judge Hill said: ``There is no
evidence to support a claim that persons who have suffered no
criminal convictions but have been arrested on a number of occasions
can be expected, when employed, to perform less efficiently or less
honestly than other employees. In fact, the evidence in the case was
overwhelmingly to the contrary.  Thus, information concerning a
prospective employee's record of arrests without convictions is
irrelevant to his suitability or qualification for employment.'' {\it
Gregory v.  Litton Systems, Inc.}, 316 F. Supp. 401, 2 FEP 842 (C.D.
Cal 1970), affirmed 472 F 2.d 631, 5 FEP 267 (9th Cir. 1972).} Even 
if  the argument  were valid, however, and stigma were based on 
mistaken beliefs about productivity,  it would not be   conclusive, 
because stigma would still be useful as a punishment.   Stigma based 
on mistaken beliefs   would be a costly punishment because of its 
effect on the labor market, more like imprisonment than fines,  but 
it might still be an optimal part of punishment. 



   A stronger  argument against stigma is based on  an externality 
from employing criminals. 

 If employers were forbidden access to criminal records, they  would 
overestimate
the convicted criminal's productivity and pay him a higher wage.  The
direct effect would be to  hurt  allocative efficiency, since 
employers  would pay a uniform wage which would exceed the criminal 
workers' 

 marginal product  and be less than the  noncriminal workers' 
marginal products. At the higher wage, however, more criminals would 
choose to be employed in legitimate jobs, and  this would raise the 
opportunity cost of crime.\footnote{Note, however, that the 
opportunity cost of crime would fall for workers who had not been 
criminal in the past, since they would receive the same pooled wage 
as the criminal workers. } This social benefit does not figure in the
employer's calculations, so it may be socially beneficial to keep 

criminal records  secret.\footnote{ A subtly different argument with 
similar 

implications is that by raising the criminal's income, legitimate 
employment  reduces his marginal utility of income and his
temptation to commit property crimes.  See Eric Rasmusen, An
Income-Satiation Model of Efficiency Wages, 30
 Economic Inquiry  467 (1992).       }    The tradeoff is between the 
beneficial effect of secrecy on recidivism and the harmful effects on 
deterrence of  first crimes and on allocative efficiency. 


 

 

  Against this benefit must be set the disadvantage that lack of
stigma increases the incentive for crime in the first place.  No
policy that tries to induce the convicted criminal to refrain from
crime by increasing the benefits of legitimate work can escape this
incentive problem, but not all policies create the allocative
distortions of secret records.  Those distortions could be avoided by
tackling the externality problem directly, by keeping records open
but subsidizing the wage of ex-criminals. Such a subsidy would weaken
the deterrence effect of stigma, but it would not distort the labor
market. 


 


 

%---------------------------------------------------------------
\newpage
\begin{center}
   {  IV.  EMPIRICAL APPLICATION OF THE  STIGMA MODEL }
 \end{center}
 

 

    Even during the 1950s, crime in the United States was increasing
at a slow but steady rate, but it then accelerated, increasing by 139
percent during th 1960's.  As Table 1 shows, crime continued to
increase since then, though at a slower rate and with occasional
dips, of which the most notable was a decline in the early 1980's. 

 Part of the increase was due to the baby boom, which increased the
population of young males starting in the 1960's.  Crime increased
faster, however, as the trends for crime per youth in Table 1 and
Figure 3 show, and since 1981 the number of youths has actually
declined. 



\bigskip
\epsfysize=3in

\epsffile{/Users/erasmuse/@Papers/stigma/Figures/Figure_4:_Crime_Rates 
.eps}
  % This is now figure 3

 

 %---------------------------------------------------------------
 

  Decline in punishment is an obvious   explanation  for  the 
increase  in crime.      The criminal justice system became 
strikingly
lenient in the 1960s.     Serious (``index'') crimes   rose
from 3.4 million to 8.1 million crimes per year during the 60's,  and 
arrests
for index property crimes per 100,000 population rose from 570 to
840,  but the   number of people entering prison fell
from 88,575 to 79,351.\footnote{ \label{(FBI)} Arrest rates are from: 
Federal Bureau of Investigation, U.S. Dept of Justice, 

Crime in the United States, annual,  1960, p. 16 and  1970, p.  23.
Crimes and prison entrants are from Table 1.}  Not only did 
imprisonment fail to keep up with the amount of crime, it fell in 
{\it absolute} terms . 


 The problem with this  explanation is that when prison
populations increased  in the 1970s and 1980s,  the crime rate did
not fall correspondingly. Crime per youth   increased by 

59\%  from 1965 to 1975, a time when prisoners per crime fell from
0.018 to 0.011, but crime per youth did not fall correspondingly
from 1981 to 1991, when prisoners per crime actually rose 92\%,  from 
0.012 to 0.023.  By 1991, prisoners per crime was back to the 1963 
level,
but crime per youth was almost twice as large. The seeming
ineffectiveness of punishment is surprising given the cross-sectional 
estimates of
the elasticity of crime with respect to expected punishment,  such as 
the elasticity of $-1.14$ that Ehrlich 

found using 1960 data comparing different states.\footnote{Ehrlich, 
{\it supra} note \ref{ehrlich}.} 

 

  At  least  part  of the answer may lie  in a failure of    stigma. 
The theoretical model has shown that multiple equilibria
are possible, and that changes in the probability of punishment have
asymmetric effects depending on whether the changes are increases or
decreases.      A large enough increase in the crime rate is
self-sustaining, because it reduces stigma enough to make crime
profitable for a much larger group of young people.
 

  The  stigma model suggests the following story.  In 1960, the 
United States
was at a low-crime equilibrium, in which a combination of public
punishment and private stigma deterred crime.    In the 1960s, a 
number
of things happened to make crime more attractive, including possibly
a general decline in morality (a shift rightwards of $F(u)$ in Figure
2) and certainly a lenient government  policy (a decline in $P$ and
$\alpha$).  This shifted the $F(u)$ curve of Figure 2 to the right
and the $\tilde{\theta}(u)$ curve downwards. Eventually there existed
just one equilibrium, with high crime, and the value of
$\theta$ started to move towards it as expectations changed. 


  By 1970 it was clear that the punishment rate was too low, and
 the number of people imprisoned began to rise sharply.  According to
the stigma model, increasing the punishment rate would shift
$\tilde{\theta}(u)$ up again, reducing the amount of crime slightly,
but if the crime rate in 1970 were greater than the middle, unstable,
equilibrium, then the adjustment process would shortly continue to
push the crime rate up to the high-crime equilibrium.  Thus, the
1970-73 crackdown reduced crime per youth slightly, but crime soon
rose again, albeit more slowly, until  1981. The increase in
punishment had only a temporary effect, and did not reduce crime to
its original level.  Although arrest rates did not increase much
during the 1980s (from 1,056 per 100,000 in 1980 to 1,124 in
1988)\footnote{  Crime in the United States, {\it supra},  note
\ref{(FBI)}, 1980-25 and 1988-25.}, imprisonment rates rose sharply,
which caused a decline in crime in the early 1980s. The decline was
small compared to the increase in the 1960s, because the tough policy
of the 1980s was not tough enough to restore stigma.  In the late 
1980's, crime  began to increase again, for   reasons   outside the 
model (e.g. crack cocaine). 



 Support for the stigma explanation is   provided by changes in  the 
pattern of 

arrest rates by  age categories, shown  in Table 2. 

Young people  have become more
criminal  and old people   less criminal.  This is  curious because 
the 35-year-old of 1985, whose arrest rate was
lower than the 1961 35-year-old's, is the same person as the
21-year-old of 1971 whose arrest rate was so much higher than the 
1960
21-year-old's.\footnote{The relevant numbers are underlined in Table
2.} The explanation may be that stigma can decline for a 
subpopulation such as    young  men   even if it retains its strength 
for the middle-aged. The young  have not yet established a reputation 
for productivity in the labor market and their employers are at more 
of an informational disadvantage.   As a result, the decline in 
stigma may have  had a
disproportionate effect on youth crime.\footnote{The effect on
black males, a subpopulation easily identified by employers, may have
been especially strong.  The percentage of black males aged 20-24 not
participating in the labor force rose from 10.2\% in 1965 to 18.5\%
in 1971 and 21.1\% in 1980. For white males, the figures are 14.7\%,
16.8\%, and 12.9\% (from Table 8 of Murray, {\it supra}, Table 1 of 
this paper ).} The increase in official
punishment since 1971, on the other hand, has affected both young and 
old, so
that arrests of older people increased less, or even declined. 
Grogger  notes that between 1973 and 1988, real wages paid to young 
men who worked full-time fell 23\%,  which would more than explain 
the increase in youth arrest rates over that period, according to the 
elasticity of crime with respect to wages that he 
estimates.\footnote{See Grogger, {\it supra}, note \ref{grogger}.} 
The stigma model   suggests that   causality went both ways, and 
real wages fell because crime increased. 

 


  If  the increase in crime   is to be largely  explained by a 
reduction    in stigma,   it must  also   be true that 

 a significant proportion of the population---or at least    of 
subpopulations such as young males---  has become criminal.    The 
shift in the proportion of criminals need not be from
0\% to 100\%, but if the change is merely from 1\% to 5\% the effect
on   average productivity  and thus on stigma will be small.
 

      Criminality is indeed very common  among young males, as 
various studies have shown.\footnote{These studies are summarized in 
Christy Visher  \& Jeffrey Roth, Participation in Criminal
Careers,   in  Alfred Blumstein, Jacqueline Cohen,  Jeffrey Roth, \& 
Christy  Visher,  editors,   Criminal Careers and ``Career
Criminals'', Volume 1,   (1986).
} Ball, Ross and Simpson
 found that as early as 1960, 20.7\% of the boys
and 5.3\% of the girls in Lexington, Kentucky had appeared in
juvenile court.\footnote{John Ball,  Alan Ross,  \& Alice Simpson, 
Incidence and Estimated Prevalance of Recorded Delinquency in a 
Metropolitan Area,  29 American Sociological Review    90  (1964).} 
Tillman  examined a comprehensive set of
arrest records to discover the probability of being arrested for 
Californians who were 18 in 1974.\footnote{\label{tillman} Robert 
Tillman,  The Size of the `Criminal Population': The
Prevalence and Incidence of Adult Arrest,  25 Criminology 

 561 (1987).}  His results are summarized in Table 3:   34\% of the 
white males and 66\% of the black
males were arrested (41\% of the black males   for a
felony). 

  Simply comparing arrests with population is
instructive. In  1987, 543,000 arrests (132,000 for index offenses)
were made out of a population of 1,889,000 18-year-old 
males.\footnote{\label{adjustment} Of 420,950 arrests of males aged 
18 , 102,000 were for index offenses, in the reporting population of
188,928,000. (Crime in the United States, {\it supra},  note
\ref{(FBI)},  1988, Table 34).      The total U.S.  resident 
population was 243,400,000 in
1987 (SA-89-2).  Scaling up the number of arrests by 1.29 and 
rounding
gives 543,000 and 132,000.  The figure of 1,889,000 males of age 18
in 1987 is found by dividing the population aged 15-19 by 5
(SA-89-13).}   More broadly, the Department of Justice estimates that 
40
million Americans have an arrest record for a non-traffic
offense,\footnote{\label{report} Bureau of Justice Statistics, U.S. 
Dept of Justice, Report to the Nation on Crime and Justice, Second 
Edition,
NCJ-105506, March 1988, p. 40.} an especially shocking figure since 
the number of arrests is lower than the  number of crimes 
committed.\footnote{ In 1988, there
were an estimated 2,888,600 arrests for index crimes (out of a total
of 13,812,300 arrests).  13,923,086 index crimes were reported, and
since an estimated 36.9\% of index-crime victimizations were
reported, the total number of index crimes was about
37,731,940.  (Crime in the United States, {\it supra}, 

note \ref{(FBI)}, 1988, Tables 2 and 24,  and  Sourcebook, {\it 
supra}, 

note  \ref{(BJS-1988c)}, Table 3.4.  See {\it supra},  note 
\ref{adjustment} for how
these figures were adjusted for the size of the reporting population.
} Enough people have engaged in crime that if crime and
productivity are linked,  average productivity could be seriously
affected. 


 


%---------------------------------------------------------------
 \begin{center}
V.  CONCLUDING REMARKS
  \end{center}
 

  Since Becker's seminal   article in 1968, economists  studying 
crime have focussed on how 

the probability and severity of punishment  deters a
potential criminal bent on maximizing his utility.  This approach 
emphasizes  the criminal justice system,  not the moral disapproval 
of the 

society in which the system operates.   Reversing the usual pattern, 
economists   stress  the role of the  government   and non-economists 
the private sector  in  preventing crime.
 

   The private sector, however,  unofficially punishes known 
criminals by stigmatizing them. Once  the criminal's behavior becomes 
known,  many other  individuals become more reluctant to interact 
with him. This private reluctance may be as powerful    a 
disincentive to  crime    as   public punishment.   The model  above 
described  economic
stigma, a reduction in the wage   employers are willing to pay 
someone with  a criminal record either because engaging in crime 
reduces productivity (the moral hazard model) or because it 
correlated with low productivity for other reasons (the adverse 
selection model).  Social stigma could be modelled similarly, as  a 
reduction in the
concessions that potential friends or spouses are willing to make to
a convicted individual for the privilege of social interaction with
him.     Whatever its nature, the stigma of a criminal record depends 
on
the informativeness of that record, and thus on the likelihood that
someone without a  conviction  is nonetheless criminal.  It was shown 
that this 

generates multiple equilibria, because if crime is sufficiently 
prevalent, a criminal record loses its informativeness and  thus its 
stigmatizing effect. 


 Stigma makes the  private sector   an important part of criminal 
deterrence,   but the government remains  useful  as a source of
detection and publicity for criminality.    The government also 
influences which of the multiple equilibria is in effect, since a 
reduction in the public penalty  increases the amount of crime, which 
in turn reduces the effectiveness of stigma.  This may help explain 
the asymmetry of the American experience with crime over the past 
three decades, when the initial decrease in public penalties seems to 
have encouraged crime   more than  the later increase discouraged it. 


%---------------------------------------------------------------
\newpage

\begin{small}
 

 \begin{center} {\bf Table 1}\\
  { \bf Crime Trends in the United States }\\ 

 (columns (a), (b) and (c) are in 1000's)\\

   \begin{tabular}{l|ccccc}
  &   &           &  &   & \\
\hline
\hline
 Year     & Index Crimes& Youths    &Prisoners received& Crimes/ &
 Prisoners/\\ 

 & reported & aged 16-24  & from courts & Youth &Crime \\
        & (a) & (b)  &  (c) & (a)/(b) & (c)/(a) \\
  &   &           &  &   & \\
   1960  & 3,397  & 9,642 &  89 & .35 &  .026 \\
  1961  & 3,488  & 9,956 &  94 & .35 &  .027\\
  1962  & 3,752   &10,075 &  89  & .37  & .024\\
  1963  & 4,110  &10,736 &  88 & .38  & .021 \\
  1964  & 4,565  &11,386 &  88 & .40  & .019 \\
  &   &           &  &   & \\
  1965  & 4,740 & 12,019 &  88 & .39  & .018 \\
  1966  & 5,224 & 12,321 &  78 & .42  & .015\\
  1967  & 5,903  & 12,514 &  78 & .47  & .013 \\
  1968  & 6,720  & 12,810 &  72  & .52  & .011\\
  1969  & 8,073  & 13,307 &  75  & .61 & .009  \\
  &   &           &  &   & \\
  1970  & 8,127  & 14,006 &  79  & .58  & .010\\
  1971  & 8,614 & 14,941 &  97  & .58 & .011 \\
  1972  & 8,291 & 15,766 & 117 & .53 & .014 \\
  1973  & 8,781 & 16,284 & 124  & .54 & .014 \\
  1974  &10,348 & 16,612 & 104 & .62  & .010 \\
  &   &           &  &   & \\
 1975  &11,380  & 17,084 & 130 & .67 & .011 \\
  1976  &11,458 & 17,481 & 129  & .66 & .011 \\
  1977  &11,109 & 17,765 & 128  & .63 & .012\\
  1978  &11,348 & 18,002 & 126  & .63  & .011 \\
  1979  &12,400 & 18,183 & 131  & .68  & .011\\
   &   &            &  &   & \\
\hline
\hline
\end{tabular}

\end{center}

\newpage

  \begin{center} {Table 1 (continued)}\\
  { \bf Crime Trends in the United States}\\ 


  \begin{tabular}{l|cc ccc}
  &   &           &  &   & \\
\hline
\hline
Year  & Index Crimes& Youths    &Prisoners received& Crimes/ &
 Prisoners/\\ 

 & reported & aged 16-24  & from courts  & Youth &Crime \\
        & (a) & (b)  &  (c) & (a)/(b) & (c)/(a) \\
  \hline
  &   &           &  &   & \\
   1980  &13,408 & 18,283 & 142  & .73  & .011\\
  1981  &13,452  & 18,208 & 160  & .74 & .012\\
  1982  &13,001  & 18,015 & 177  & .72  & .014\\
  1983  &12,124  & 17,799 & 187  & .68  & .015 \\
  1984  &11,897  & 17,494 & 180  & .68  & .015 \\
   &   &           &  &   & \\
  1985  &12,431  & 17,021 & 198  & .73  & .016\\
  1986  &13,212  & 16,773 & 219  & .79 & .017\\
  1987&  13,509&  16,530  & 242 & .82 &   .018\\
  1988 &  13,923  &   16,249         & 261  &  .86  &.019 \\
 1989 &   14,251 &    15,854       & 316  & .90  &.022\\
  &   &           &  &   & \\
 1990 & 14,476   &  15,602     &  343    & .93  &.024 \\
 1991 & 14,873  &    15,443        & 337 &  .96  &.023 \\
  &   &           &  &   & \\
\hline
  \hline
\end{tabular}
\end{center}
 

 

NOTES.---   (a) ``Index crimes'' do not include arson.
 (b) ``Youths'' are  civilian noninstitutional males.
  (c) ``Prisoners'' refers to persons with at least a one-year
sentence in state and federal prisons.\\

SOURCE.--- (a) 1960-80:  Charles Murray,     Losing Ground: American 
Social Policy
1950-1980 (1984) 

Table 18.  1981-87: SA-89-277, 1988-91: 

SA-93-300.
  Murray's figures, taken from unpublished FBI data, are
more accurate than those in the {\it Statistical Abstract}. He gives
crime rates, not total crime, and the figures here are his 

crime rates  multiplied by  the total resident population,  from 
SA-89-2. 

 (b)  1960-87:    Handbook of
Labor Statistics, 1989,   {\it supra},  note \ref{Handbook},  pp. 
13-14. 1989-91: p. 9 of  August issues of   Employment and Earnings, 
U.S. Department of Labor, Bureau of Labor Statistics.    (c) 1950-54: 
SA-57-186. 1955-70: {\it Historical Statistics}, H1138.
1971-73: SA-75-290.  1974: SA-76-291.  1975: SA-77-315.  1976-78:
SA-80-342.  1979: SA-81-330.  1980-82: SA-84-325.  1983-86: 
SA-89-318. 1987-91: 

SA-93-343.  The 1990-91 figures are the levels for state prisons 
multiplied by    1.062, one plus the 1989 ratio of federal to state 
prisoners. 


\end{small}

\newpage

\begin{center}
  {\bf Table 2}\\
 { \bf Arrest Rates per 100,000 Population}\\

\begin{tabular}{l|rrr rrr rrr  |r}
  \multicolumn{11}{c}{  }   \\
\hline
\hline
 & Under 18 & 18-20 & 21-24 & 25-29 & 30-34 &35-39 &40-44 & 45-49 & 
50+ & All ages \\
  \hline
   &  \multicolumn{9}{|c|}{  } &  \\
   1961 & 1,586& 8,183 & \underline{ 8,167} & 6,859 & 
6,473&\underline{6,321} &5,921 & 5,384 &2,594 &  3,877 \\
 1966  & 2,485 & 8,614 &7,425 &6,057&5,689&5,413 &5,161 &4,850 
&2,298& 3,908\\
 1971 &3,609&11,979 &\underline{ 9,664} & 6,980&6,016 
&5,759&5,271&4,546 &2,011& 4,717 \\
 1976& 3,930&13,057 &10,446 & 7,180&5,656&5,205 &4,621 &3,824&1,515& 
4,804\\ 

 1981& 3,631 &15,069 & 11,949&8,663&6,163 &5,006&4,176& 3,380 &1,253& 
5,033\\
 1985& 3,335& 15,049 & 13,054 & 9,847&7,181 &\underline{5,313}&4,103& 
3,155&1,088 & 5,113 \\
 & \multicolumn{9}{|c|}{  } &  \\
 \hline
 \multicolumn{11}{l}{ \hspace*{12pt} NOTE.--- Over 50\% of arrests
are for ``public order'' offenses (e.g. drunk}\\
 \multicolumn{11}{l}{driving, prostitution), especially for older
people. The underlined entries}\\
 \multicolumn{11}{l}{are mentioned in the text.}\\
 \multicolumn{11}{l}{ \hspace*{12pt}SOURCE.---     Technical 
Appendix, {\it supra}, note \ref{(BJS-1988c)},    pp.
26-27.}\\ 

     \end{tabular}
 \end{center}
 



 \begin{center} {\bf Table 3}\\
  {\bf The Probability of an Individual Being Arrested  Between 1974 
and 1985}\\

\begin{tabular}{l|cc|cc}
 \multicolumn{5}{c}{  }\\
\hline
\hline
 & \multicolumn{2}{c|}{All Offenses} &\multicolumn{2}{|c}{Felony
Index Offenses}\\
      & Male & Female  & Male & Female\\ 

 \hline
 % & \multicolumn{2}{|c|}{  } & \multicolumn{2}{|c }{  }\\
  Black & 66 & 30 & 41&14\\
White & 34 & 10 & 15& 3\\
Total & 35 & 11 & 17 &4 \\
% & \multicolumn{2}{|c|}{  } & \multicolumn{2}{|c }{  }\\ 

 \hline
%\multicolumn{5}{l}{  }\\
 \multicolumn{5}{l}{\hspace*{18pt}  NOTES.-- Californians aged 18
in 1974. ``All Offenses'' excludes drunk}\\
 \multicolumn{5}{l}{ driving, public drunkenness, and possession of
less than 28.5 grams of }\\
 \multicolumn{5}{l}{marijuana.  ``Felony index offenses'' is a
narrower category than ``FBI index offenses''.  }\\
 \multicolumn{5}{l}{ \hspace*{18pt} SOURCE.-- Tillman , {\it supra}, 
note \ref{tillman}. }\\ 

   \end{tabular}
 \end{center}
 

 



\newpage
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%---------------------------------------------------------------
 

 

 

\end{document} 

