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 {  An Income-Satiation Model of Efficiency Wages}\\    
  
           
         
        \bigskip    
 Eric Rasmusen$^*$ \\   
 \bigskip
  RRH: RASMUSEN:   EFFICIENCY WAGES
  
  \titlepage
    
    
   
\begin{flushright}
   AEA categories: J41, J31, D82.
    \end{flushright}
    
   
 {  An Income-Satiation Model of Efficiency Wages}\\    
 
         


Published:{\it  Economic Inquiry }  (July 1992) 30: 467-478. \\


        {\it Abstract}\\    
        \end{center}    
        \par\noindent     
 Efficiency wages are wages that exceed a worker's reservation wage.  
A standard explanation for such  wages is  ``bonding'': by  
increasing the worker's fear of discharge,  high wages increase  the worker's cost
from punishment.
 A neglected alternative  is ``satiation'':   by  
decreasing the worker's marginal utility of income, the high wage decreases the
benefit from misbehavior.  Satiation, unlike bonding, applies even in a one-period
model, but it relies on the misbehavior having a monetary benefit and  on at least
part of the punishment being nonmonetary.

  
      \begin{small}
               \noindent 
\hspace*{20pt} 2000: Eric Rasmusen, 	Professor of Business Economics and Public
Policy and Sanjay Subhedar Faculty Fellow,   Indiana University,
Kelley School of Business, BU 456,   
  1309 E 10th Street,
  Bloomington, Indiana, 47405-1701.
  Office: (812) 855-9219.   Fax: 812-855-3354. Erasmuse@indiana.edu.
Php.indiana.edu/$\sim$erasmuse.
 \end{small}

   %---------------------------------------------------------------    
       \newpage    
    
 \begin{center}    
 {  I. INTRODUCTION}
  \end{center}  

 

 In efficiency wage models, self-interested employers pay workers
more than their reservation wages despite the pressure of a
competitive labor market. The idea has been traced back to Adam
Smith, who said:

 
 \begin{small}    
 \begin{quotation}  
  
 

    ... Fourthly, the wages of labour vary accordingly to the small or    
great trust which must be reposed in the workmen.
\vspace{8pt} 
   
\hspace{12pt} The wages of goldsmiths and jewellers are everywhere 
superior to those of many other workmen, not only of equal, but of 
much superior ingenuity, on account of the precious materials with 
which they are intrusted.   
  \vspace{8pt}  
    
 \hspace{12pt}We trust our health to the physician: our fortune and 
sometimes our life and reputation to the lawyer and attorney.  Such 
confidence could not safely be reposed in people of a very mean or 
low condition. Their reward must be such, therefore, as may give them 
that rank in society which so important a trust requires.$^1$
 \end{quotation}  
  \end{small}  
      
 

 The idea turns up today not only in the academic literature of
efficiency wages, but in the advice of 
management consultants such as Mark Lipman:
  
 
 \begin{small}    
  \begin{quotation}  
 
  
  Of course,  there are employees you could pay three times as much    
and they'd still steal; but generally speaking less stealing goes on    
in plants where people are overpaid than in plants where they are    
underpaid. You've got to make an employee feel that this job is worth    
keeping, that he can't earn more elsewhere.    
  \vspace{8pt}   
 
 \hspace{12pt} So control number one, I tell my clients, is to pay a 
good wage. I make a lot of clients angry by saying this, and some 
tell me to my face that they prefer to accept the existing rate of 
theft, that they will simply make up the loss out of employee 
paychecks; for as long as the stealing goes on, nobody gets a 
raise.$^2$

 \end{quotation}    
   \end{small}  
     
 

  
    Why would a high wage make workers more obedient? Numerous
explanations have been put forward based on such things as moral
hazard, labor turnover, adverse selection, fairness, and even
nutrition; a useful collection of these can be found in the volume
edited by Akerlof and Yellen (1986).  Perhaps the best known
explanation is the bonding model found in, for example, Becker \&
Stigler (1974) and  Lazear \& Moore (1984), in which the employer pays a
high wage so that the worker's loss from being fired deters
misbehavior.
 The present article proposes a different explanation, 
which has so far gone unmentioned in the literature:  that the 
worker who is paid more desires additional income less, and is less 
tempted to acquire it by illegitimate means such as stealing from his 
employer. This, the ``satiation'' model, differs from the bonding 
model because higher pay reduces the benefit from misbehavior rather 
than increasing the cost.   
    
    
 The satiation model relies on a feature common to many agency
problems: at least part of the misbehavior's reward is monetary and
at least part of its punishment is not.
Agency models are
usually constructed in terms of worker effort, a nonmonetary argument of worker
utility, but  the  passage above from Adam Smith, quoted so often
by economists in the agency literature, focusses on trust, not effort.
 Theft from employers, theft from customers, and bribe-taking are
important problems, and if  stealing cannot be
prevented the agent may become unemployable even at a zero wage, since
his marginal product can easily be negative.  

 Employee theft is important because
criminality is not confined to a few anti-social individuals.  Tillman (1987)
finds that 34\% of white males and
66\% of black males who turned 18 in 1974 in California were arrested
within the next eleven years, not including arrests for drunk
driving, public drunkenness, and possession of small amounts of
marijuana.  Large numbers of petty criminals  enter the
workforce, and there is much evidence that employee theft is a major
concern for employers. 
 Dickens, Katz, Lang \& Summers (1989, pp. 332, 335) refer to various
sources that claim employee theft costs American business between
\$15 and \$56 billion per year and induces spending of \$12 billion
per year on prevention.  Lipman \& McGraw (1988) report that in 1984
bank employees stole \$382 million, nine times more than bank
robbers, that insider theft is a factor in one-third of bank
failures, and that employee theft causes 5 to 30 percent of business
failures in general. 
 Clark and Hollinger (1985) interviewed employees in several cities 
and asked them about various forms of misbehavior, a  survey which gives some
indication of what agency problems are
important. As Table 1 shows, many agency problems  add to the worker's 
wealth, not to his leisure.   
   
TABLE 1 GOES HERE
  
   The model of this paper will show how the special properties of 
employee theft make high wages a potential solution to this agency 
problem.  Section 1 will lay out a one-period model based on decreasing
marginal utility of income---the satiation model. Section 2 will
extend the model to two periods and compare it with the standard
bonding model.  Section 3 discusses the  model's
implications, and Section 4 concludes.  
 
%---------------------------------------------------------------    
\pagebreak    
\bigskip    
\begin{center}    
  { II. THE ONE-PERIOD SATIATION MODEL}    
 \end{center}    

  An employer in a competitive labor market offers wage $w$ to a
worker who chooses whether to steal or not steal an amount $v$.  The
employer detects the theft with probability $\alpha$, in which case
the worker retains the wage and the theft amount but incurs a utility
cost $p$ consisting of criminal penalties.  If the worker is fired or
chooses not to work, he earns the reservation wage $w_0$.  The
worker's payoff is his utility $U(x)$ from wage and theft income $x$,
minus the disutility of detection, $\alpha p$. The function $U(x)$ is
assumed to be such that the worker's marginal utility of income is
diminishing and he strongly wishes to avoid zero income: $U' >0$,
$U''<0$, and $\stackrel{lim}{x \rightarrow \infty} U'(x) = 0.$ The
employer's payoff is the worker's output minus the wage and the cost
of theft, $c(v)$.  Assume that the punishment is not enough to deter
theft if the wage equals the reservation wage: 
  \begin{equation} \label{e40}     
  U(w_0+v) - \alpha p > U(w_0).    
 \end{equation}    
  
 
 
 {\bf Proposition 1:} {\it The employer can deter theft by paying a
wage $w^*$ that sufficiently exceeds the reservation wage.  $w^*$
increases with the amount that might be stolen, $v$, and decreases in
the probability and magnitude of punishment, $\alpha$ and $p$.}


 
{\it Proof:} Viewed at the start of the game, the worker's
alternative expected payoffs are 
 \begin{equation} \label{e41}     
  EU(theft) = U(w+v)  - \alpha p    
 \end{equation}   
 and 
  \begin{equation} \label{e42}     
 EU(honesty) =  U(w),    
\end{equation}    
 or $  EU(unemployment) = U(w_0)$, if the worker chooses to be unemployed. 
 To deter theft, equations (\ref{e41}) and (\ref{e42}),    
the payoffs from theft and honesty,    
must be equal:    
 \begin{equation} \label{e43}     
 U(w+v) - \alpha p = U(w),     
 \end{equation}    
 which gives    
 \begin{equation} \label{e45}     
D= U(w+v) - U (w) - \alpha p= 0.    
 \end{equation}    
 Since $U''<0$, the expression $[U(w+v) - U (w)]$ is diminishing    
in $w$, and since $\stackrel{lim}{x \rightarrow \infty} U'(x) = 0,$    
theft can indeed be deterred for a big enough $w$. Moreover, the    
participation constraint is not binding, because, comparing    
(\ref{e40}) and (\ref{e45}), the facts that $U''<0$, and that    
(\ref{e45}) is an equation rather than an inequality, mean that     
 $  w^* > w_0$,    
 in which case the honest worker receives more than the reservation  
utility.

  Differentiating (\ref{e45}) gives $ dD/dw^*= U'(w+v)-U'(w)<0$,
since $U''<0$. 
 The comparative statics results in the proposition follow from implicit
differentation, since   $ dD/dv=U'(w+v)>0$,  $ dD/d\alpha=-p <0$, and  $ dD/dp= -p
<0$.
\\   
 Q.E.D.    
  \bigskip    

  Proposition 1 seems quite straightforward, but its assumptions are
not so simple as they seem. The key assumption is that the marginal
utility of income is decreasing in income but the marginal
disutility of punishment is not.  This assumption is plausible for
punishments such as criminal penalties or social stigma: it says that
the disutility is the same or greater, not less, for a rich worker.  In
the model above, the assumption took the form of a utility function
concave in income and separable in income and punishment, where rich
and poor suffer the same disutility from a given jail term.

Grossman and Hart (1983) point out that if money and effort are not
separable in an agency model, the participation constraint may not be
binding. If effort's disutility falls with income, the principal may
wish to pay the worker a higher wage.
The two inputs into utility in the satiation model, money and
punishment, are separable, but one might imagine instead that higher
income increased the disutility of punishment, which would provide a
separate reason for efficiency wages, one operative even  if utility
were to be linear in money. 
One could also interpret the satiation model as a
Grossman-Hart model in which the utility function is not separable in
money and the effort of refraining from theft.
If we let $q$ represent the probability of refraining from theft, the
worker's expected utility can be rewritten as $EU(q,w) = qU(w) +
(1-q)[U(w+v)-\alpha p]$, which has the non-zero cross-partial
derivative $\partial^2 U/(\partial q \partial w) = U'(w)
-U'(w+v)$. In this interpretation, a higher wage reduces the marginal
disutility of refraining from theft.


If the punishment were monetary---a criminal fine, or the loss of
wages that the employer had contracted to pay the worker--- the
assumption would generally be false, because the rich man would be
more willing to incur the punishment.$^3$
 The satiation model fails under some, but
not all, risk-averse utility functions when punishments are
monetary.
The model's conclusions would continue to hold even when the punishment is
monetary if  risk aversion increased fast enough in wealth, so  the
higher wage reduces the marginal utility of theft income more than it
reduces the marginal disutility from the criminal fine. If the
utility function is concave enough, the worker, on being paid 100
dollars extra wages, becomes more reluctant to risk a 500-dollar fine
to steal 1,000 dollars.  Ito \& Takatoshi (unpublished) note
something similar in a different context: if researchers have {\it
declining} absolute risk aversion, then increasing their salaries can
be desirable because it makes them more willing to take risks in
their research.\footnote{Another  explanation for why the poor commit more crimes
is given by Lott (1990): they are liquidity constrained, so if they have some
immediate desire to spend, they may resort to theft. Even if the penalty is
monetary, if it comes later in time, it may be viewed as the repayment of an
involuntary loan.}

 The term $\alpha p$ represents the nonmonetary punishment. Its most
straightforward interpretation is as the expected disutility of a
prison sentence, but fear of imprisonment is not the only deterrent
to crime.  $\alpha p$ could also represent the expected value of the
stigma and shame that follows wrongdoing when it is discovered, or
the guilt that follows even when it remains concealed.  The admission
that ethical principles affect behavior does not exclude the
usefulness of economic analysis, because  economics is about tradeoffs, and
the fact that an employee feels guilty when he steals does not imply
he will not steal, only that the amount must be large enough to
justify the emotional cost. The satiation model points out that if
the emotional cost is independent of income, the richer worker will
steal less.   

Indeed, if there is an emotional cost to theft, 
employers would take advantage of it by hiring workers with higher costs
and attempting to increase them after hiring takes place. 
Chapter 3 of Frank (1988) points out that the acquisition of a
conscience can be viewed as a way to make wrongdoing more costly;
employers vulnerable to theft would tend to hire workers who give
external signs of possessing consciences.  Akerlof (1983) similarly
points out that parents improve the financial prospects of their
children by instilling them with moral principles.  Once a worker has
a conscience, external incentives such as monitoring or efficiency
wages become more effective. Indeed, the fact that a criminal record
evinces lack of  conscience makes criminal stigma 
 a powerful non-government deterrent to crime. Coleman (1990) notes that even   if
workers lack   consciences when they enter the
firm, the firm has an incentive to provides consciences along with
other  forms of training.  Socialization consists of internalizing norms,
providing the individual with an internal sanctioning system which
provides punishment when he carries out an action proscribed by the
norm. As Coleman puts it, ``Deciding whether internalization of a
norm in another actor is rational must involve balancing the cost of
bringing about the internalization to a given degree of effectiveness
against the discounted future cost of policing to bring about the
same degree of compliance'' (Coleman, 1990, pp. 159, 294). The rational employer
will equate the returns at the margin from socializing his workers
and from paying them efficiency wages.

   Proposition 1 says that a high wage can deter theft, but whether  it is
profitable to do so is  a separate question. Recall that in the passage quoted
earlier, some of  Mr. Lipman's customers ``prefer to accept the existing rate of
theft'' when he tells them ``to pay a good wage.'' The employer will  deter theft
only if the cost of the theft is greater than the wage premium; that is, if
 \begin{equation} \label{e46a}     
  c(v)  \geq w^* - \underline{w},     
 \end{equation}  
 where  $\underline{w}$, the ``theft-tolerating wage,'' satisfies the
participation constraint
 \begin{equation} \label{e46b}     
  U(\underline{w}+v) - \alpha p = U(w_0).   
 \end{equation} 
   The theft-tolerating wage is less than the reservation wage,
because the job provides not only the legitimate wage
$\underline{w}$, but the opportunity to steal $v$.
   
   One might think that paying a wage premium to deter theft could be
attractive for the employer only if the theft is not a pure
transfer--- that the theft must cost the employer more than it
benefits the employee.$^4$ 
This intuition has considerable truth to it, because if the employer cost
$c(v)$ increases, inequality (\ref{e46a}) is more likely to apply.
But it can also apply even if $c(v) \leq v$,
because the theft creates the additional cost of $\alpha p$. The
employer cannot lower the wage by the full amount $v$ unless this
additional cost is eliminated by blocking governmental punishment and
assuring the workers  they need feel no guilt over their
actions.$^5$
If this is done, then ``theft'' is the wrong word to describe the
worker's behavior, just as ``shirking'' is the wrong word to apply to
the lunch breaks of   workers paid annual salaries.  
  
  A numerical example may help to clarify the relationship between
$v$ and $c(v)$. Let the utility of income be $U(x) =1 -e^{- x}$, the
value of theft be $v=1$, the cost to the employer be $c(v)=v=1$ (a
simple transfer), the probability of detection be $\alpha =0.4$, the
punishment be $p=.5$, and the reservation wage be
$w_0=1$.$^6$ This will not deter
theft, because $1-e^{- (w_0+v)} -\alpha p > 1-e^{-w_0}$, ($.66 >
.63$). The employer  has two choices: to pay a low wage and
endure theft, or to pay a high wage and deter it. If he chooses to
endure theft, the wage can be lower than $w_0=1$, because the worker
also has theft income; it solves $1-e^{- (\underline{w}+v)} -\alpha p
= 1-e^{-w_0}$ and equals $\underline{w}= .78$. If the employer wishes
to deter theft, the wage must solve 
  $1-e^{- (w^*+v)}  -\alpha p = 1-e^{-w^*}$, which gives     
  $w^*=1.15$.  Since a wage increase of  .37  deters a theft of 1, the employer
will choose to pay the  efficiency wage.
Note that $w_0$ is uninvolved in the calculation of the efficiency wage, and $w^*
> w_0 > \underline{w}$.
   
 
 %---------------------------------------------------------------    
 \bigskip 
 \begin{center}
{  III. THE TWO-PERIOD SATIATION MODEL  }    
 \end{center}    

 The satiation model does not require more than a single period, but
it is useful to examine what happens with two periods.  This
inevitably brings in the bonding effect, since workers who are
paid more than the reservation wage in the second period to deter stealing in that
period will be
reluctant to risk their job by stealing earlier.
 Assume  that there are 
 two periods of work, in each of which theft might occur and be
 detected. Assume also that there is no discounting, no commitments
can be made by the worker or the employer, and the worker cannot
borrow to smooth his consumption.  
    
    
    
{\bf Proposition 3:} {\it In the two-period satiation model, there is
no stealing in either period, the second-period wage is higher than
the first-period wage and the reservation wage, and the average
lifetime wage exceeds the reservation wage: $w_0 <\frac{w_1^* +
w_2^*}{2} < w_2^*$. } 
    
{\it Proof:}
 Section  1 showed what would happen in the second period,      
since the subgame consisting of the second period is equivalent to the one-period
model.
 Proposition 1 implies that $w_2^*$ equals the $w^*$ that
solves equation (\ref{e45}), that $w_2^* > w_0$, and that stealing does not occur
in the second period.   
 Viewed from the start of the game, the lifetime expected payoff from    
stealing in the first and not the second period is    
 \begin{equation} \label{e61}     
[U(w_1+v)  - \alpha p] + [(1-\alpha) U(w_2^*) + \alpha U(w_0)],     
 \end{equation}    
 and the expected payoff from  not stealing in either period is    
 \begin{equation} \label{e62}     
 U(w_1) + U(w_2^*).    
 \end{equation}    
  If theft is to be deterred in the first period, the payoffs from equations
(\ref{e61}) and (\ref{e62}) must be
equal, so    
 \begin{equation} \label{e63}     
 U(w_1+v) - \alpha p + (1-\alpha) U(w_2^*) + \alpha U(w_0) = U(w_1) +    
U(w_2^*),    
  \end{equation}     
 which gives    
 \begin{equation} \label{e64}     
  U(w_1+v) - U(w_1) - \alpha p - \alpha  [U(w_2^*) - U(w_0)] = 0.    
 \end{equation}    
 Given the assumptions on $U(x)$, by choosing $w_1$ large enough
equation (\ref{e64}) can be satisfied, and theft can indeed be
deterred in the first period.  
    
 Equation (\ref{e64}) combines with (\ref{e45}) to give    
  \begin{equation} \label{e65}     
  [U(w_1+v) - U(w_1)] - [U(w_2^*+v) - U (w_2^*)] = \alpha [U(w_2^*) -    
U(w_0)].     
 \end{equation}    
 Since $w_2^*> w_0$, the right-hand side of (\ref{e65}) is positive.    
This implies that the left-hand side is positive, which implies,    
since $U''<0$, that $ w_1^* < w_2^*$, which implies that $\frac{w_1^*    
+ w_2^*}{2} < w_2^*$.    
     If $w_1 + w_2 = 2w_0$, then the worker would receive a fluctuating    
income stream with an average of $w_0$ per period.  The participation    
constraint requires the worker to receive an income stream with    
utility at least equal to  that of a steady $w_0$ per period. Because    
the utility function is concave, the fluctuating income stream's mean      
must therefore exceed $w_0$; and $\frac{w_1^* +    
w_2^*}{2} > w_0$.\\    
  Q.E.D.    
    
    
 The numerical example of the previous section can be carried over
into the two-period model. The second-period of the two-period model
is equivalent to the one-period model, so $w_2^* = 1.15$.  From
equation (\ref{e64}), the condition for deterring theft in the first
period is 
 \begin{equation} \label{e73}     
 (1-e^{-(w_1+v)}) - (1-e^{-w_1}) -\alpha p - \alpha (    
(1-e^{-w_2^*}) - (1-e^{- w_0})) = 0.    
 \end{equation}    
 This equation yields $w_1^* = 1.05$, which, as Proposition 2
predicts, is less than $w_2^*$. (In this example, $w_1^* >
w_0$, but that is not necessarily the case.) The payoffs in both periods exceed
the reservation wage, and the participation constraint is not
binding.  The employer could have paid $\underline{w}=.78$ in each period and
tolerated theft, but by paying .64 (=(.22+.05) + (.22 + .15)) in wage
premiums  he avoids a theft loss of 2.  Even though theft is
not dissipative (because $c(v)=v$), the employer can profit by using
efficiency wages.  
   
   
    With a few changes in assumptions, the two-period model can be
transformed into a version of the well-known bonding model.  The two
changes are to assume that: (a) the marginal utility of
income is constant instead of diminishing, so $U(x)=x$; and (b) the
employer can commit to the wage $w_2$ and to firing the worker if and
only if he is caught stealing.
In  the bonding model, stealing will occur in
the second period no matter how dissipative it might be, because the  worker
faces no punishment except   $\alpha p$, which by assumption (1) is
too small to  deter. Stealing can be prevented
in the first period, however, by giving the worker an upward-sloping
wage path. In the extreme, the worker is paid zero (or even a
negative amount) in the first period, and  more than the
reservation wage in the second period. This is efficient, because  a worker with
linear utility  cares only about the
average wage and does not mind having low first-period consumption.
The employer can reduce the average wage to where it equals the
reservation wage minus a discount for  the worker's second-period
theft income. The  worker will accept the job  and    refrain from
first-period theft to avoid losing the high second-period wage.


The satiation and bonding models differ in a number of ways, showing
that the claim that  linear utility is a simplifying
and not substantive assumption  (see  Murphy and Topel, 1990, and Shapiro
and Stiglitz, 1984) is more appropriate when  the agency problem is    effort
rather than theft. First, there is no one-period bonding model; unlike
satiation, bonding absolutely requires that the worker  loses wages
if  caught stealing. Second, preventing the worker from smoothing his consumption
over time  is less costly when   utility is linear;
with
concave utility,  the average wage must rise to compensate for an
uneven wage path.  Third, the bonding model requires the employer to
commit to a policy in advance. If the employer could commit to   wages
but not  tenure, he would fire every worker at the
end of the first period to save paying the high second-period wages.
If he could not commit to  wages,  he would retain the
workers but not pay them the high wage. 
In the satiation model, on the other hand, precommitment is superfluous,
because the employer pays a high second-period wage to deter stealing
in the second period, and only incidentally does that help deter
stealing in the first period.$^7$

 The two models' conclusions also differ.
The bonding model implies that older workers steal, and the satiation
model does not; and  in   the bonding model   the worker  receives exactly his
reservation utility over his lifetime, so
there is no queuing for such jobs. The bonding model describes a
sophisticated form of piece-rate, in which accounts are squared at the end of
the working lifetime instead of the end of the day.
  Eaton and White (1982) and Carmichael (1989) note that even in more
complicated versions of the model, the employer would use entrance
fees to extract all surplus from the workers, but we do not commonly
observe such fees. In the satiation model, on the other hand, the
average lifetime wage exceeds the reservation wage and the job can
attract queuing. The employer is unwilling to use entrance fees to
extract the worker's surplus, because the whole point of the wage
premium is to reduce the worker's marginal utility of income. An
entrance fee would avoid doing this only if the reduction in the
worker's wealth at the time he paid the fee did not affect his wealth
at the time he is employed.$^8$

 The satiation and bonding models represent two ways of deterring
theft with high  wages. In the one-period satiation model, high
wages reduce the benefit of theft by making the worker value
additional income less than avoidance of non-monetary punishment,
and in the two-period bonding model, high wages increase the cost
of theft by giving the worker a stream of future income that can be
confiscated by the employer.  The two-period satiation model combines
these two effects, and that is why its wage path, like the bonding
model's, is upward-sloping. It preserves the essential intuition of
the bonding model while eliminating the conclusions that old workers
steal and that the participation constraint  necessarily is binding.
  
%---------------------------------------------------------------    
    
    
 \bigskip    
  \begin{center}    
  {  IV. IMPLICATIONS}    
   \end{center}    
    
The  
 satiation model is most likely to apply if two conditions hold: (1) the
principal's loss from theft is high relative to the agent's gain, and (2)
the agent's marginal utility of income is sharply diminishing. The
first condition might well apply to elected officials. The wedge
 between the high cost to the public of corruption and the low
benefit to the politician is striking, as  
Tullock (1980) points out, and monitor  works less well than in
the private sector because of the multiplicity of voter-principals.  Rather than
rely on ethics committees, it might
be more cost-effective to pay a legislator an extra \$100,000 per year to
prevent him from granting million-dollar favors to lobbyists in
exchange for \$3,000 vacations. No less an authority than the senior
Mayor Daley suggested this to the press   when Chicago aldermen's salaries were
raised from \$8,000 to \$15,000 per year: ``Surely you can't keep a
fella honest--- you fellas   couldn't be paid \$8,000 a
year and be honest in your job.''$^9$
 
  The politician's job is an example of one in which great trust
might justify large wage premiums, but the   model also applies if the
stakes are small and so is the required wage premium. If 
reservation wages are near subsistence, as in much of the
present-day Third World or the West before the Industrial Revolution,
theft is tempting  because the
marginal utility of income is   high relative to the disutility of criminal
punishment. The marginal utility of income is also more sharply diminishing,
however, which reduces the wage premium necessary to deter theft.
 Unfortunately, the satiation model
would be difficult to distinguish from the bonding model in such 
contexts, since the absence of  entrance fees  can
be explained by the worker's lack of initial wealth.  
  
     
   The satiation model also applies to the principal-agent relationship between
government and potential criminals.
Rossi, Berk \& Lenihan (1980) describe two experiments that sought to determine
whether ex-convicts who were paid a form of unemployment insurance upon release
would commit fewer crimes.   In the first, the Baltimore LIFE experiment of 1971,
released convicts were paid \$60 per week until they found a job or \$780    
was paid out. All subjects had less than \$400 in savings, and   arrest did not
remove eligibility for
the payments, but imprisonment did. If one did    
find a job, his payment was reduced, but he continued to receive it    
until the \$780 was exhausted. The results were that the payments    
reduced arrests on theft charges by 8\% in the year after release    
(which was statistically significant), while leaving arrests on other    
charges unaffected, and the payments did not discourage employment    
significantly. This encouraging result supports the satiation model, since it
seems that the incentive to steal declined.
 The second experiment, the TARP experiment in Georgia and Texas, was    
somewhat different because it imposed a stiff tax on the transfers if    
the recipient became employed. The result was that recipients did not    
have significantly different arrest rates than non-recipients, but    
they had much more unemployment. The payments had a desirable direct    
effect on arrests, presumably due to  the  satiation effect, but an undesirable
and
equally strong indirect effect due to reduced employment and the    
consequent increase in the time available for       
crime. Both of these experiments lend support to the importance of satiation when
incomes are very low.
 
The model predicts queuing for jobs, but only for jobs
requiring trust and in which the marginal utility of workers is
sufficiently decreasing.$^{10}$ Across
occupations  requiring similar skills, wages will vary
according to the opportunities for theft, $v$, theft's dissipative cost,
 $c(v)$, and the expected punishment, $\alpha p$. Queuing should be
observed for jobs for relatively unskilled workers who lack outside
wealth---jobs with low wages, not  high wages.  
 The satiation model also predicts that misbehavior    rises when
total income falls for exogenous reasons. In recessions, attorneys
would cheat their clients more as the number of clients dropped, and
production workers would pilfer more as their opportunities for
overtime  diminished.  At the same time, the effort these agents
put forth might well increase, since the reduced hours of work would
 reduce the disutility of effort. 

The satiation model also implies wage stickiness. If the reservation
wage $w_0$ is determined by conditions in industries that do not pay
efficiency wages, then  it will rise and fall with the business
cycle.  But the equilibrium efficiency wage $w^*$ does not depend on
$w_0$. Even if a recession reduces the reservation wage and  the price of the
industry's output, the wage necessary to deter stealing remains
constant, so  employers cannot reduce costs in response to
reduced prices; they must reduce output and employment instead. It is
too dangerous to reduce the wages of workers accustomed to high
consumption; instead, the firm will  discharge some workers and maintain the pay
of
the rest. 
   
 Finally, employers would 
 prefer rich workers to poor workers, since someone with substantial
outside wealth is less tempted to steal.  A worker with more wealth
than talent would be attractive quite independently of his social
graces or family connections.$^{11}$ If effort is important, however,
the advantage of the rich worker is less clear; the same satiation
effect which makes stealing less tempting also reduces the
effectiveness of monetary incentives for effort.$^{12}$
 The advantages and disadvantages of rich workers  have    
implications for the desired age of workers. If liquidity constraints prevent
workers from smoothing their consumption over their lifetime, wealth effects can
make  old workers  less willing than young workers to trade off current wages
against the risk of punishment.
If wages rise with    
age this is obvious: older workers earn more. If wages are flat,    
this may still be true, because the older worker has been able to    
accumulate more precautionary savings and pension wealth.      
It may be  harder to induce the old worker to exert effort, but    
easier to prevent him from stealing, in contrast to the    
bonding model.  It is not that the older man  fears to lose his pension, but that
his pension  reduces his temptation to steal.
    
   
%---------------------------------------------------------------    
\bigskip    
    
\begin{center}    
 {V. CONCLUDING REMARKS}    
 \end{center}    
    
Readers may decry the addition of   yet another efficiency wage    
model to the literature, but the satiation model has the virtues of simplicity,  a
distinctive channel of operation, and different empirical
implications. It implies that misbehavior will not be any more common    
in old  workers than in young, that the worker's average wage over  his      
career   will be  greater than the reservation wage,  and that queuing will  occur
when trust is
needed and worker wealth is low. The model can make such predictions    
precisely because it is particular enough not to apply to    
the typical modern job: it applies when the misbehavior adds to    
income, when a nonmonetary punishment exists, and when the marginal    
utility of income is  significantly diminishing relative to the loss    
from employee theft. Employers pay high wages not to increase the worker's loss
from firing, but to change his marginal rate of substitution between income and
punishment, making theft a less attractive option. The high wage is neither carrot
nor stick, but a way to reduce the worker's temptation.
  
 %---------------------------------------------------------------    
    
\newpage    
    
\begin{center}    
 {  REFERENCES}    
  \end{center}    
    
  Akerlof, George.  ``Loyalty Filters.'' {\it American Economic  
Review},   March 1983,  54-63.  
 
 Akerlof, George and Janet Yellen, eds.
 {\it Efficiency Wage Models of the Labor Market.} Cambridge:
Cambridge University Press, 1986.

 
  Becker, Gary and George Stigler. ``Law Enforcement, Malfeasance, and
Compensation of Enforcers,'' {\it Journal of Legal Studies}, January 1974, 1-18.
    
 (BLS) Bureau of Labor Statistics, U.S. Dept of Labor, {\it Handbook    
of Labor Statistics,}  Bulletin 2340, August 1989.     
  
 Carmichael, H. Lorne. ``Self-Enforcing Contracts, Shirking,    
and Life Cycle Incentives.'' {\it Journal of Economic Perspectives},    
 Fall 1989, 65-84.    
    
Clark, John and Richard Hollinger. {\it Theft by Employees},    
Lexington, Mass.: D.C. Heath and Company, 1983.    
  
Coleman, James.  {\it Foundations of Social Theory}, Cambridge,  
Mass: Harvard University Press, 1990.   
    
 Dickens, William, Lawrence Katz, Kevin Lang, and Lawrence Summers.   
 ``Employee Crime and the Monitoring Puzzle.'' {\it Journal of    
Labor Economics},  July 1989, 331-347.    
    
    
 Eaton, B. Curtis and William White. ``Agent Compensation and    
the Limits of Bonding.'' {\it Economic Inquiry}, 20 1982, 330-343.    
      
 Frank, Robert. {\it Passions Within Reason}, New York: W.W.  
Norton and Company, 1988.  
  
    Grossman, Sanford \& Oliver Hart (1983) ``An Analysis of 
the Principal Agent Problem'' {\it Econometrica,} January 1983,    7-45.  
  
Ito, Takatoshi and Charles Kahn (unpublished), ``Why is there Tenure?''    
Discussion paper No. 228, February 1986, Center for Economic    
Research, Dept. of Economics, University of Minnesota.    
    
 Lazear, Edward and Robert Moore. ``Incentives, Productivity,    
and Labor Contracts.'' {\it Quarterly Journal of Economics},   May    
1984,  275-295.  
   
Lipman, Mark.  {\it Stealing: How America's Employees are    
Stealing Their Companies Blind}, Robert Daley (ed.), New York:    
Harper's Magazine Press, 1973.    
    
Lipman, Mark and  W. McGraw. ``Employee Theft: A \$40 Billion    
Industry.'' {\it The Annals if the American Academy of Political and    
Social Science},  July 1988, 51-59.    
    
Lott, John. ``A Transactions-Cost Explanation for Why the Poor Are More Likely to
Commit Crime.''   {\it Journal of Legal Studies}, January 1990, 243-46.
    
 Murphy, Kevin M. and  Robert Topel.  ``Efficiency Wages    
Reconsidered: Theory and Evidence.'' In {\it Advances in the Theory    
and Measurement of Unemployment}, Yoram Weiss and Gideon Fishelson,    
eds. London: Macmillan, 1990.    
    
   
    
 Rossi, Peter, Richard Berk  and Kenneth Lenihan. {\it Money,    
Work, and Crime: Experimental Evidence}, New York: Academic Press,    
1980.    
    
 Shapiro, Carl and Joseph Stiglitz. ``Equilibrium Unemployment    
as a Worker Discipline Device.'' {\it American Economic Review},   June    
1984,  433-444.    
    
 Smith, Adam. {\it An Inquiry in the Nature and Causes of the    
Wealth of Nations}, Chicago: Encyclopedia Britannica Inc., 1952.    
    
Tillman, Robert.  ``The Size of the `Criminal Population': The    
Prevalence and Incidence of Adult Arrest.'' {\it Criminology}, 25,  561-579.    
    
 Woodbury, Stephen \& Robert Spiegelman. ``Bonuses     
to Workers and Employers to Reduce Unemployment: Randomized Trials in    
Illinois.'' {\it American Economic Review}, September 1987,     
513-530.   

   
 \pagebreak
 
  \begin{small} 
 \begin{center}    
  {Table 1}\\    
  {Percentage of Cleveland Retail Employees Self-Reporting Misbehavior}    
    
 \begin{tabular}{l|rr}    
 \hline    
  \hline    
 \hline    
Within the past year, how many  & About once a  & Once or\\    
 times did you  &   week or more  & more \\    
\hline    
 Take a long lunch or coffee break without approval?  &12.5 &52.7 \\    
 Fill out or punch a time card for an absent employee? &0.6 &3.1 \\    
 Do slow or sloppy work on purpose? & 1.0 &13.8\\    
Come to work while under the influence of alcohol &  &\\    
 or drugs?&1.4  &7.6\\    
 Come to work late or leave early without approval?&3.6 &31.0 \\     
 Use sick leave when not sick?&0.3 &18.1 \\     
 Get paid for more hours than were worked?&0.9 &7.9 \\     
 Ignore an instance of pilferage or shoplifting?&0.2 &5.9 \\     
 & & \\    
 \hline    
 \hline    
 & & \\    
 Use the discount privilege in an unauthorized manner?&0.8  &18.5\\    
 Take office or clerical supplies?&0.8 &11.6 \\    
 Take an item of store merchandise with a retail& & \\     
 value of less than \$5?&0.6  &1.9 \\     
 Take an item of store merchandise with a retail & & \\     
 value of more than \$5?&0.6 &1.9 \\     
 Purposely under-ring  a customer's purchase?& 0.2&2.6 \\     
 Damage an item of merchandise in order to buy it&  & \\     
  on discount?& 0.2  & 1.4\\     
Be reimbursed for more money than spent on& & \\      
business expenses?&0.0 &1.5 \\     
Take company equipment or tools?&0.1 &3.5 \\     
Borrow or take money from employer?&0.5 &3.4 \\     
Take personal property of co-workers or customers?&0.0 &0.5 \\     
Shortchange or overcharge a customer on purpose?&0.2 &1.4 \\     
 & & \\    
 \hline    
 \multicolumn{3}{l}{{\it Source:} Clark \& Hollinger (1985), p. 35.}\\    
 \multicolumn{3}{l} {{\it Notes:} $n= 816$ to 828, depending on the    
question. Items below the double line}\\    
 \multicolumn{3}{l} {are  financial.}\\    
 \hline    
  \hline    
 \hline    
  \end{tabular}    
 \end{center}    
 \end{small}    
    
   
%---------------------------------------------------------------    
   \newpage
    FOOTNOTES
     
*Assistant Professor,   Anderson Graduate School of Management, University of
California, Los Angeles,  and Olin Fellow, Yale Law School.  I
would like to thank Robert Chirinko, Philip Cook, Hadi 
 Esfahani  and several anonymous referees  for helpful comments, and Michael Kim
and George Michaelides
for research assistance.    

1. Smith (1776), 1-10, p. 44. 
 
 
 2.  Lipman (1973), p.  154.    

 3. Bankruptcy protection would make
it possible for the rich worker to suffer more than the poor worker
from a monetary penalty. In particular, suppose that the penalty
consists of restitution of the value of the stolen goods, but that
the worker has resold them at a fraction of their value in the
legitimate market. This would correspond to a penalty of $c(v)>v$.
The poor worker can go bankrupt; the rich worker suffers a net loss
of $c(v)-v$ if he is caught. The vulnerability of richer workers to
civil damages is thus another reason why high wages deter
misbehavior.  


 4. E.g.,
``There was a series of conveyor belts moving the goods around
the plant, and the thieves were working both floors. A guy on the
second floor would send the goods down to the first floor on a belt,
and the first-floor guy, if the coast was clear, would take the goods
off and stash them. If the coast was not clear, if someone happened
to be watching him, he would toss the goods onto another belt leading
straight into the incinerator.''  (Lipman (1973), p.  154).  

 5. These are not always  trivial tasks. One reason
why the government and  not the victim prosecutes criminal
cases is because punishing criminals is a public good; thus, the
government may not look kindly on companies that tolerate employee
crime. Also, the employer may have difficulty drawing lines
separating what behavior is permissible from what is not. If
employees are told they should feel no guilt as a result of
nondissipative transfers, they may lose their inhibitions regarding
dissipative transfers. 

 6. This will not satisfy the assumption that
$\stackrel{Limit}{x \rightarrow 0} U'(x) =\infty$, but that is only a
sufficient, not a necessary, condition. 

 7. If the  
 employer can precommit in the two-period satiation model, the bonding effect can
dominate the satiation effect under certain conditions.  Implicitly
differentiating equation (11) gives
   \begin{equation} \label{e200}
     d w_1/ dw_2  =  \alpha U'(w_2^*)/[U'(w_1+v)-U'(w_1)]    
       \end{equation}
 This expression is always negative, but if it is greater than one in magnitude,
the employer  can reduce his costs  by increasing $w_2$ above $w_2^*$ and reducing
$w_1$. This might be the case if  $v$ and $U''$  were small, so the difference
$U'(w_1+v)-U'(w_1)$ would be small.   In the numerical example,   $d w_1/dw_2 = -
.57$, so this is not the case.


 8. An entrance fee paid
some years in advance of employment would overcome this problem, but
only if the individual could not borrow against future income (which
would reduce his future net income by the amount of the repayment).
This is problematic, because an entrance fee is ordinarily funded
either out of initial wealth or through borrowing. If funded out of
initial wealth, that leaves less wealth available later at the time
of employment, so the worker is more tempted to steal. If funded out
by borrowing,   the debt must be repaid later, defeating the
purpose of the satiation wage. A third alternative is to fund the
entrance fee in installments ending before employment; one
implementation of this would be to underpay entry-level positions
requiring little trust relative to senior positions. 

 9. {\it The Chicago Reader},
21 December 1990, p. 23. 

 10. Some care must be taken in
determining whether a job requires trust. It might seem that 
security guards must be trusted, but they are 
poorly paid. In 1988, median weekly earnings of full-time ``Guards
and police, except public services'' were \$273, compared to \$522
for ``police and detectives, public service'' and \$288 for
``Laborers, except construction,'' (BLS, pp.  196-198). But not only
is it easy for the security guard to steal; it is also easy for the
employer to catch him, since he is an obvious suspect. Thus, it is not always
clear how much trust is needed in a job.

 11. Eaton \& White (1982) give another reason why
an employer might prefer a rich worker: he can post a higher bond to
be forfeited in case of misbehavior. 

 12.
The alert reader will wonder whether the reduced effectiveness of
monetary incentives is also a concern when the worker begins poor,
but is made richer by the efficiency wage premium. This can be
handled with some care; the employer must provide the wage premium as
part of the incentive pay.     

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

   
\end{document}    
    
    
