(1997) incetive compatibility constraints as an explanation for the use of prision sentence instead...

8/3/2019 (1997) Incetive Compatibility Constraints as an Explanation for the Use of Prision Sentence Instead of Fines

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I n c e n t i v e C o m p a t i b i l i ty C o n s t r a i n ts a s a n

E x p l a n a t i o n f o r t h e U s e o f P r is o n S e n t e n c e s

I n s t e a d o f F i n e s

STEVEN D . LEVITT

H a r v a r d S o ci ety o f F e ll ow s a n d N a t i o n a l B u r e a u o f E c o n o m i c R e se a rc h

E-m ai l : s l e v i t t @f as .harv ard . e du

I n s t a n d a r d m o d e l s o f o p t i m a l d e t e r r e n c e , w h i c h a s s u m e p e r f e c t i n f o r m a t i o n o n t h e

p a r t o f t h e s o c ia l p l a n n e r , f in e s d o m i n a t e j a i l s e n t e n c e s a s a n i n s t r u m e n t f o r p u n i s h i n g

c r i m e . I n t h e r e a l w o r l d , h ow e v e r , p u n i s h m e n t u s i n g p r is o n s is q u i t e c o m m o n . T h i s

p a p e r p r o v i d e s a n e x p l a n a t i o n f o r t h a t e m p i r i c a l o b s e r v a ti o n . I f c r i m i n a l s e i t h e r h a v e

p r i v at e i n f o r m a t i o n a b o u t t h e i r o w n w e a l th , o r h a v e a s u b s ta n t i a l p o r t i o n o f t h e i r w e a l t h

i n t h e f o r m o f h u m a n c a p i ta l , t h e s o c ia l p l a n n e r c a n n o t s i m p l y i m p o s e a f in e o n a

c r i m i n a l , w h o c a n a lw a y s c l a i m t o h a v e i n s u f f i c i e n t w e a l t h t o p a y t h e f i n e . R a t h e r ,

b e c a u s e o f t h e n e e d f o r i n c e n t i v e c o m p a t i b i l i t y , i t i s a s if t h e s o c i al p l a n n e r o f f e rs t h e

c r i m i n a l a c h o i c e : e i t h e r p a y t h e f i n e o r g o t o j a i l . T h a t a d d i t i o n a l c o n s t r a i n t o n t h e

s o c i a l p l a n n e r d r a m a t i c a l l y re d u c e s t h e e f f e c t i v e n e s s o f f i n e s v is -a-v i s a p e r f e c t i n f o r m a -

t i o n w o r l d . M a n d a t o r y s e n t e n c i n g g u i d e l i n e s e x a c e r b a t e t h e p r o b l e m s a s s o c i a te d w i th

i n c e n t i v e c o m p a t i b i l i t y b y r e s t r i c t i n g a j u d g e ' s a b i l i ty t o t a i l o r p e n a l t i e s t o i n d i v i d u a l

c r i m i n a l s . © 1 9 97 b y E l s e v i e r S c i e n c e I n c .

I . I n t r o d u c t i o n

A s i z ab l e l i t e ra t u r e h a s a ri s e n in r e c e n t y e a r s c o n c e r n i n g t h e o p t i m a l p u n i s h m e n t o f

c r i m i n a l a c t s. 1 R e l a t i v e ly l i tt l e a t t e n t i o n , h o w e v e r , h a s b e e n d i r e c t e d t o t h e q u e s t i o n o f

w h e t h e r c r i m i n a l s s h o u l d b e p u n i s h e d u s i n g fi n es o r j a i l s e n t e n c e s , g e c k e r ( 19 6 8) a n d

P o s n e r ( 1 97 7 ) a r g u e i n f o r m a l l y f o r t h e u s e o f f i n es w h e r e p o s s i b l e t o a v o i d t h e s o c i a lc o s ts o f m a i n t a i n i n g p r i s o n s , t h e p r i v a t e d i s u ti l it y o f i n c a r c e r a t i o n , a n d t h e s o c i a l w a s te

I would like to t hank Peter Dia mond, ChristineJolls, Louis Kaplow, Mirth Polinsky, Matthew Rabin, two anonymo us

referees, and participants in the Harvard Law School Research Seminar in Law and Economics for helpful discussions

on the topic and com ments on earlier drafts of the paper. All remaining errors are my own. Financial support of the

National Science Foundation is gratefnlly acknowledged.

llncl uded in this recen t literature are And reoni (1991), Kaplow (1990, 1992), Kaplow and Shavell (1994), Lott

(1987), Polinsky and Rubinti~ld (1991), a nd Polinsky and Shavell (1984, 1991, 1992). The classic works in this area are

Becker (1968) and Stigler (1970).

International Review of Law and Economics 17:179-192, 1997© 1997 by Elsevier Science Inc.655 Aven ue of the America s, New Ynrk, NY 10010

0144-8188/97/$17.00PII S0144-8188 (97) 00002-1



180 Incentivecompatibility constraints

o f i d l e h u m a n c a p i t a l i n j a i ls . 2 T h e a n a l y si s o f P o l i n s k y a n d S h a v e l l ( 1 9 84 ) c o n f i r m s t h a t

i n t u i t i o n f o rm a l l y u n d e r t h e a s s u m p t i o n t h a t t h e s oc i al p l a n n e r h a s p e r fe c t k n o w l e d g e

o f e a c h i n d i v i d u a l ' s w e a l t h , h a s a c o s tl e ss m e a n s o f e n f o r c i n g f i n es o n c e t h e c r i m i n a l i s

c a u g h t , a n d c a n c o s t l es s ly t a i l o r p u n i s h m e n t s t o e a c h i n d i v i d u a l . I n t h a t s c e n a r i o , t h e

s o c i a l p l a n n e r ' s o p t i m a l a p p r o a c h i s t o f u ll y e x p l o i t f i ne s , o n l y u s i n g j a i l t e r m s i f

m o n e t a r y s a n c t i o n s a r e i n s u f f i c i e n t t o d e t e r c r i m i n a l a c ti v it ie s . I n p r a c t i c e , h o w e v e r ,

r e l i a n c e o n i n c a r c e r a t i o n a s p u n i s h m e n t is e x t en s iv e . A t y e a r - e n d 1 9 94 , t h e c o m b i n e d

U .S . j a i l a n d p r i s o n p o p u l a t i o n e x c e e d e d o n e m i l l io n . I n c o n t r a s t, f i ne s a r e r a r e l y u s e d

e x c l u s iv e l y e x c e p t f o r m i n o r c r i m e s s u c h a s tr a f fi c v i o l a t i o n s a n d s o m e f e d e r a l c r i m e s . 3

E v e n w h e n f i n es a r e u s e d , t h e d o l l a r a m o u n t s l e v i e d a r e t y p i c a l ly s m a l l .

T h r e e c o m m o n a r g u m e n t s a r e p u t f o r t h a s e x p l a n a t i o n s f o r t h e l i m i t e d u s e o f f in e s

a s p u n i s h m e n t d e s p i t e t h e t h e o r e t i c a l p r e d i c t i o n s . A f ir st a r g u m e n t is t h a t f in e s a r e

" u n j u s t" b e c a u s e t h e r i c h a r e a b l e t o p a y f i n es , w h e r e a s t h e p o o r s e r v e j a i l s e n t e n c e s . I f,

h o w e v e r , t h e s o c ia l p l a n n e r k n e w t h e p r e c i s e m o n e t a r y e q u i v a l e n t o f a j a i l s e n t e n c e f o r

a p a r t i c u l a r i n d i v id u a l , a n d i m p o s e d a f i n e o f t h a t m a g n i t u d e o r g r e a t e r , r e d i s t r i b u t i n g

t h e r e v e n u e t o e i t h e r t h e v i c t i m o f t h e c r i m e o r t h e p o o r , i t i s h a r d t o se e h o w s u c h a

f i ne c o u l d b e d e e m e d u n ju s t.

A s e c o n d a r g u m e n t a g a i n s t t h e u s e o f f in e s is th a t t h e t y p ic a l c r i m i n a l h a s e x t r e m e l y lo w

w e a l t h . A s a r e s u l t, fe a s i b l e f i n e s m i g h t b e s o s m a l l a s to b e i n c o n s e q u e n t i a l a s d e t e r r e n t s .

U n d e r m i n i n g t h is a r g u m e n t , h o w e v e r , is t h e f a c t t h a t e v e n i f a c r i m i n a l d o e s n o t h a v e

s u b s t a n t i a l physica l a s se ts , h e o r s h e t y p i c al l y d o e s h a v e h u m a n c a p i t a l t h a t i s c a p a b l e o f

g e n e r a t i n g a f lo w o f f u t u r e i n c o m e w i th w h i c h t o p a y a fi n e . T h e r e i s n o l e g a l r e s t ri c t io n

o n t h e g o v e r n m e n t ' s a b i li ty t o c o l l e c t f in e s i n i n s t a l lm e n t s t o t a k e a d v a n t a g e o f f u t u r e

e a r n i n g s . N o n e t h e l e s s , a l t h o u g h m o n t h l y p a y m e n t s a r e s t a n d a r d f o r c h i l d s u p p o r t a w a r d s,

t h e y a re r a r e f o r c r i m i n a l p u n i s h m e n t s i n t h e U n i t e d S t a te s [ H i l l s m a n e t a l. ( 1 9 8 2 )] .A fi n a l a r g u m e n t f o r t h e u s e o f p r i s o n s r a t h e r t h a n f i n es is t h e v a l u e o f i n c a p a c i t a t i o n

o f r e p e a t o f f e n d e r s . A c c o r d i n g t o p r i s o n e r s u rv e ys , t h e m e d i a n p r i s o n e r c o m m i t s 1 2 to

1 5 s e r io u s n o n - d r u g c r i m e s p e r y e a r w h e n n o t b e h i n d b a r s [ V i sh e r ( 1 9 86 ) , P i e h l a n d

D i I u l i o ( 1 9 95 ) ] . A l t h o u g h t h e i n c a p a c i t a t i o n a r g u m e n t is c o m p e l l i n g , t h e p u z z l e o f w h y

p r i s o n t e r m s a r e n o t c o m b i n e d w i t h w e a l t h - e x h a u s t i n g fi n e s r e m a i n s .

T h i s p a p e r o f f e r s a n a l t e r n a t i v e e x p l a n a t i o n f o r t h e l i m i t e d u s e o f f in e s . T h e f u n d a -

m e n t a l p r e m i s e o f th e p a p e r i s t h a t t he g o v e r n m e n t c a n n o t e n f o r c e f in e s e x c e p t u n d e r

t h e t h r e a t o f f u r t h e r p u n i s h m e n t , i n p a r t i c u l a r p r is o n s e n t e n c e s . 4 W h e n i m p o s i n g f in e s ,

t h e s o c i a l p l a n n e r is t h e r e f o r e i m p l i c i t l y o f f e r i n g t h e c r i m i n a l a c h o i c e : E i t h e r p a y t h e

f i n e, o r i f y o u r e f u s e / a r e u n a b l e , y o u w i ll b e r e q u i r e d t o s p e n d t i m e i n j a i l . 5 P u t i n t o

s t a n d a r d e c o n o m i c j a r g o n , o n l y fi n es t h a t a r e i n c e n t i v e c o m p a t i b l e w i ll b e p a i d . A d o p t -i n g t h a t a s s u m p t i o n , w h i l e m a i n t a i n i n g t h e o t h e r b a s i c a s s u m p t i o n s o f t h e p r e v i o u s

2 T h e d i s t i n ct i o n b e t w e e n p r i s o n s a n d j a i ls is u n i m p o r t a n t t o t h e a r g m n e n t s t h a t f ol lo w . C o n s e q u e n t l y , t h o s e t w o

t e r m s a r e u s e d i n t e r c h a n g e a b l y i n t h e p a p e r .

3 T h e u s e o f fi n e s i s m o r e e x t e n s iv e i n m a n y o t h e r c o u n t r i e s [ s ee G i l te s p i e ( 1 9 8 1 ) ] . T h e r e a r e a l so s o m e i n d i c a t i o n s

t h a t i n t e r es t i n t h e u s e o f f i n e s i s o n t h e i n c r e a s e i n th e U n i t e d S t a te s [ M c D o n a l d ( 1 9 9 2 ) ] . W a l d f o g e l ( 1 9 95 ) e x a m i n e s

t h e u s e o f f i n e s i n f e d e r a l f r a u d c a s e s. W e i s b u r d e t a l. ( 1 9 9 1 , p p . 1 5 0 - 1 5 7 ) c o n s i d e r t h e u s e o f f i n e s f o r a r a n g e o f

w h i t e - c o l l a r c r i m e s .

4 As a c o n c r e t e e x a m p l e , t r a ff i c v i o l a ti o n s a r e t y p ic a ll y p u n i s h e d u s i n g f i n e s. T h e g o v e r n m e n t h a s o n ly l i m i t e d s u c c es s

i n c o l le c t i n g s u c h f in e s , a n d t h e r e f o r e i t r e s o rt s t o m o r e s e r i o u s f o r m s o f p u n i s h m e n t , i n c l u d i n g c o n f i s c at i o n o f

v e h i c l e s , r e v o c a t i o n o f d r i v i n g p r i v i l e g e s , a n d t r a f fi c sc h o o l .

5 T h i s i g n o r e s a n y d i f fi c u lt i e s t h at t h e s o c i al p l a n n e r m i g h t h a v e i n e n f o r c i n g j a i l t e r m s . E n f o r c i n g j a il t e r m s i s l ik e ly

t o b e m u c h l es s o f a n i s su e b e c a u s e t h e c r i m i n a l p r e s u m a b l y i s p r e s e n t a t h i s o r h e r s e n t e n c i n g .



S.D . LEWTT 181

l i t e r a t u r e , i t is d e m o n s t r a t e d t h a t t h e u s e f u l n e s s o f fi n e s is g r e a t l y r e d u c e d r e l a ti v e to t h e

e a r l i e r p a p e r s t h a t a s s u m e p e r f e c t i n f o r m a t i o n a n d e n f o r c e a b i l i ty o f f in e s.

T h e r e a r e a t l e a s t t h r e e r e a s o n s w h y g o v e r n m e n t s m a y h a v e d i f f ic u l ty c o l l e c t i n g f i ne s

e v e n i f a g e n t s h a v e s u f f ic i e n t w e a l th , p e r h a p s i n t h e f o r m o f h u m a n c a p i ta l . O n e r e a s o n

is t h e e x i s t e n c e o f p r i v a te i n f o r m a t i o n o n t h e p a r t o f i n d i v i d u a ls c o n c e r n i n g t h e i r o w n

w e a l t h ( e i t h e r p h y s i c a l a s se t s o r h u m a n c a p i t a l ) . W i t h p r i v a t e i n f o r m a t i o n , a g e n t s w i ll

h a v e a n i n c e n t i v e t o r e p o r t w e a l t h l e ve l s b e l o w t h e t r u e v a l u e , s i m p l y r e f u s i n g t o p a y a

g i v en f in e d u e t o ( s u p p o s e d ) i n ab i li ty . S e c o n d , e v e n i f t h e g o v e r n m e n t c a n a c c u r a t e l y

a ss es s a n i n d i v i d u a l ' s w e a l th , t h e r e m a y b e n o d i r e c t m e a n s t o c o m p e l p a y m e n t o f a f i n e.

T h a t is c e r t a in l y t h e c a s e w i t h r e s p e c t to f u t u r e r e t u r n s o n h u m a n c a p i ta l , t h e m o s t

v a l u a b l e a ss e t f o r m o s t c r i m i n a ls . A l t h o u g h a c r i m i n a l m a y b e c a p a b l e o f g e n e r a t i n g a

s t e a d y f lo w o f i n c o m e t h a t t h e g o v e r n m e n t c o u l d t a k e a s a f i n e , t h e r e i s n o w a y f o r t h e

g o v e r n m e n t t o f o r c e th e c r i m i n a l t o e a r n t h a t i n c o m e b e c a u s e t h e i n d i v i d u a l ' s e f fo r t is

u n o b s e r v e d (a s w e l l a s i n a l i e n a b l e ) a n d is t h e r e f o r e o u t s i d e t h e g o v e r n m e n t ' s c o n t r o l .

A l t h o u g h p h y s i c a l a s se t s a r e c e r t a i n l y e a s ie r t o c o n f i s c a t e , f o r m a n y c r i m i n a l s w i t h

s i z a b le h o l d i n g s , e . g. , d r u g t r a f fi c k e r s a n d p a r t i c i p a n t s i n o r g a n i z e d c r i m e , i t is l i k e ly t o

b e e x t r e m e l y d i ff i c u l t t o l o c a t e t h o s e a s s e ts . F i n a ll y , a l t h o u g h t h e s o c i a l p l a n n e r m a y b e

a b l e t o c o n f i s c a t e a ss e ts , t h e c o s ts o f d o i n g s o m a y b e p r o h i b i t i v e r e l a t i v e t o t h e r e v e n u e

g e n e r a t e d , e s p e c i a l l y f o r s m a l l f in e s .

T o u n d e r s t a n d w h y i n c e n t i v e c o m p a t i b i l i t y l i m i ts t h e e f f e c t i v e n e s s o f fi n e s, i t i s u s e f u l t o

c o n s i d e r t h e t w o p u r p o s e s s e r v e d b y f in e s i n a w o r l d w i th p e r f e c t i n f o r m a t i o n a n d c o sf le ss

e n f o r c e m e n t o f fi ne s . T h e f ir st p u r p o s e o f fi n e s is to p r o v i d e a g r e a t e r l e v e l o f d e t e r r e n c e

f o r a g iv e n l i k e l i h o o d o f d e t e c t i o n . I f t h e s o c i al p l a n n e r c a n i m p o s e b o t h a f in e e q u a l t o

w e a l t h and the m a x i m u m j a i l s e n te n c e , d e t e r r e n c e is g r e a t e r t h a n u t i l iz i n g t h e m a x i m u m

j a i l s e n t e n c e a l o n e . I f i n c e n t iv e c o m p a t i b i l i ty i s r e q u i r e d , h o w e v e r , t h e c o m b i n e d p u n i s h -m e n t u s in g b o t h f in e s a n d j a i l c a n n o t b e a n y g r e a t e r th a n t h e p u n i s h m e n t u s i ng t h e

m a x i m u m j a i l s e n t e n c e a l o n e . I f t h e s o c i al p l a n n e r a t t e m p t s t o i m p o s e a s ti ff er p e n a l t y , th e

c r i m i n a l c a n s i m p l y r e f u se t o p a y t h e f i n e , i n s t e a d a c c e p t i n g t h e m a x i m u m j a i l s e n t e n c e .

T h u s , i n a w o r l d w i t h i n c e n t i v e c o m p a t i b i l i t y c o n s t r a i n t s , i n t r o d u c i n g f i n e s ( w e a k ly ) l o w e r s

r a t h e r t h a n r a is e s t h e d e t e r r e n t e f fe c t o f a g i v e n le v e l o f d e t e c t io n .

T h e s e c o n d u s e o f f i n es in a p e r f e c t i n f o r m a t i o n w o r l d i s t o m i n i m i z e t h e s o c i a l c o s ts

o f p u n i s h i n g o f f e n d e r s . G i v e n t h a t a c r i m e o c c u r s , i t is s o c ia l ly m o r e e f f i c i e n t t o u s e

f in e s th a n p r i s o n s f o r p u n i s h m e n t , d u e b o t h t o t h e c o st s o f m a i n t a i n i n g p r i s o n s a n d t h e

w a s t e d h u m a n c a p i t al a s s o c ia t e d w it h i n c a r c e r a t i o n . A l t h o u g h t h is j u s t i f i c a t i o n o f f i ne s

r e m a i n s r e l e v a n t , it s p r a c t i c a l u s e f u l n e s s i s r e d u c e d i f t h e s o c i a l p l a n n e r c a n n o t t a i l o r

t h e p u n i s h m e n t t o t h e i n d i v i d u a l ' s t y p e ( e i t h e r b e c a u s e t h e i n d i v i d u a l ' s t y p e is p r i v a tei n f o r m a t i o n a n d is , t h e r e f o r e , n o t k n o w n t o t h e s o c ia l p l a n n e r , o r b e c a u s e o f m a n d a t o r y

s e n t e n c i n g g u i d e l i n e s t h a t r u l e o u t s u c h t a i l o r i n g ) . B e c a u s e t h e t y p i c a l c r i m i n a l is l i k e ly

t o h a v e a l o w d is u t i li t y o f p r i s o n ( in d o l l a r t e r m s ) r e l a ti v e to t h e p o p u l a t i o n a s a w h o l e ,

t h e f i n e m u s t b e l o w r e l a ti v e t o t h e j a i l s e n t e n c e t o b e i n c e n t i v e c o m p a t i b l e . T h e

a v a i l a b il i ty o f a lo w f i n e a s a p o t e n t i a l p u n i s h m e n t , h o w e v e r , w i ll m a k e c r i m e m o r e

a t t r a c t i v e to t h e r e s t o f t h e p o p u l a t i o n . T h a t r e d u c t i o n i n d e t e r r e n c e c a n e a s i l y o u t -

w e i g h t h e s o c i a l b e n e f i t s o f a v o i d i n g i n c a r c e r a t i o n c o st s.

D e s p i t e t h e a b o v e li m i t a t io n s o n i m p l e m e n t i n g f in e s, th e m o d e l p r e s e n t e d i n th is

p a p e r s h o w s t h a t t h e r e a r e s o m e s i t u a t io n s w h e r e f i n e s m a y b e e f fe c t iv e d e s p i t e t h e

p r e s e n c e o f in c e n t i v e c o m p a t i b i l i t y c o n s t r a i n t s . F i n e s a r e e s p e c i a l l y u s e f u l f o r c r i m e s

w h e r e t h e p r i v a t e b e n e f i t s to c r i m e ( s u b t r a c t i n g o f f t h e c o st s o f c o m m i t t i n g t h e c r i m e )a r e g r e a t e r f o r t h e r i c h t h a n t h e p o o r , s u c h a s t a x e v a si o n . F o r t h o s e c r i m e s , l a r g e f i n es

w i ll b e p r e f e r r e d t o j a i l b y t h e t y p i c a l t a x e v a d e r , b u t w i l l n o t b e a t t ra c t i v e t o m o s t



182 I n c e n t i v e c o m p a t ib i li ty c o n s t r a i n t s

n o n - o f f e n d e r s . 6 F i n e s a r e a l so e f f ec t iv e w h e n t h e r e is a b i g g a p b e t w e e n t h e p r i v a t e

b e n e f i t s t o c r i m e f o r c r i m i n a l s a n d n o n - c r i m i n a l s . W h e n t h a t is t h e c a s e, a n y r e d u c e d

d e t e r r e n c e a s s o c i a t e d w i t h t h e a v a i la b i l it y o f f in e s i s u n l i k e l y t o a f f ec t t h e n o n - c r i m i n a l ' s

d e c i s i o n . A c r i m e s u c h a s c h i l d m o l e s t a t i o n , w h i c h p r o v i d e s l a r g e p r i v a t e b e n e f i t s to a

f ew m e m b e r s o f s o c ie t y , b u t n e g a t i v e p r i v a t e b e n e f i t s t o m o s t p e o p l e , i s o n e e x a m p l e . I n

t h is c a se , h o w e v e r , t h e o p t i m a l f i n e i s l i k el y t o g r e a t l y e x c e e d a n i n d i v i d u a l ' s w e a l t h .

T h e r e m a y a ls o b e s t r o n g i n c a p a c i t a t i o n a r g u m e n t s f o r th e u s e o f p r i s o n s r a t h e r t h a n

f i n e s i n p u n i s h i n g c h i l d m o l e s t e r s .

F i n e s a r e m o r e u s e fu l w h e n t h e j a i l / f i n e t r a d e - o f f is s i m i la r f o r c r i m i n a l s a n d n o n -

c r i m i n a l s b e c a u s e t h e i n c e n t i v e - c o m p a t i b i l i t y c o n s t r a i n t b i n d s l e ss ti g h t l y i n s u c h c a se s .

T h e v a l u e o f f i n es a l so t e n d s t o b e g r e a t e s t w h e n t h e s o c i a l e x t e r n a l i t y t o c r i m e i s s m a l l

r e l a t iv e to t h e c o s t s o f d e t e c t i o n a n d i n c a r c e r a t i o n . T h e r e l i a n c e o n f i ne s fo r t r af f ic

o f f e n s e s a n d o t h e r m i n o r c r i m e s i s c o n s i s t e n t w i t h t h is l as t p o i n t .

T h e s t r u c t u r e o f th e p a p e r i s a s f o ll o w s. S e c t i o n I I p r e s e n t s a s i m p l e m o d e l i n w h i c h

i n d i v id u a l s h a v e p r i v at e i n f o r m a t i o n a b o u t t h e i r o w n t yp e s, a n d t h e s o c i al p l a n n e r h a s

a c c e s s o n l y to j a i l s e n t e n c e s a s a n i n s t r u m e n t f o r p u n i s h i n g c r i m i n a l s . ( I n t h e p r e s e n c e

o f p r i v at e i n f o r m a t i o n , t h e r e c a n n o t b e o n l y f in e s as p u n i s h m e n t b e c a u s e a g e n t s w o u l d

r e p o r t l o w w e a l t h a n d r e f u s e t o p ay . ) I n S e c t i o n I I I, f i n e s a r e i n t r o d u c e d a s a n

a d d i t i o n a l i n s t r u m e n t f o r t h e s o c ia l p l a n n e r . B e c a u s e o f p r i v a te i n f o r m a t i o n , h o w e v e r ,

a n y p u n i s h m e n t i n v o lv i n g f in e s m u s t b e i n c e n t i v e c o m p a t i b l e . S e c t i o n I V e x p l o r e s

c o n d i t i o n s u n d e r w h i c h f i n e s a r e m o r e o r l es s e f fe c ti v e a n d d e r iv e s g e n e r a l p r o p o s i t i o n s

c o n c e r n i n g t h e u s e f ul n e ss o f f in e s i n t h e m o d e l . T h e m o d e l e m p l o y e d i n t h i s p a p e r i s

i n t e n t i o n a l l y sp a r s e . T h e b e n e f i t o f s u c h a n a p p r o a c h is t h a t t h e a d v e r s e e f f e ct s o f

i n c e n t i v e c o m p a t i b i l i t y c o n s t r a i n t s a r e h i g h l i g h t e d . T h e c o s t, h o w e v e r , i s t h a t s o m e

m e a s u r e o f r e a l i s m a n d g e n e r a l i t y is s a c r i fi c e d . S e c t i o n V t h e r e f o r e c o n s i d e r s t h e e f f e c to f g e n e r a l i z i n g t h e m o d e l i n n u m e r o u s w a ys . S e c t i o n V I o f f e rs a b r i e f s e t o f c o n c l u s i o n s .

I I . O p t i m a l P u n i s h m e n t i n a J a i l -O n l y W o r l d

A g e n t i , a s s u m e d t o b e r i s k n e u t r a l , m a x i m i z e s t h e f o l l o w i n g e x p e c t e d u t i l i ty f u n c t i o n

{013 i f n o c r i m e i s c o m m i t t e d

E ( U i ) = i - e ~J 8 i i f a c r i m e i s c o m m i t t e d ( 1)

w h e r e 13i i s t h e p r i v a t e b e n e f i t t o a g e n t i o f c o m m i t t i n g t h e c r i m e , e~ i s t h e l i k e l i h o o d o f

d e t e c t i o n g i v e n th a t t h e c r i m e i s c o m m i t t e d , J i s t h e l e n g t h o f th e j a i l te r m i f d e t e c t e d , a n d

8 i i s a m e a s u r e o f t h e d i s u t il i ty o f j a i l t o a g e n t i. F o r a l g e b r a i c s i m p l i c i t y , i t is a s s u m e d t h a tt h e i n d i v i d u a l d e ri v e s a l l b e n e f i ts f r o m t h e c r i m e b e f o r e t h e d e t e c t i o n o c c u rs ; t h e s u b s t a n -

t iv e r e s u lt s o f t h e a n a l y si s a r e u n c h a n g e d w h e n t h i s a s s u m p t i o n i s a l t e r e d .

T h e s o c i al p l a n n e r c o m m i t s t o a le v e l o f e~ a n d J b e f o r e t h e a g e n t ' s d e c i s i o n a b o u t

w h e t h e r o r n o t t o c o m m i t t h e c r i m e , so as t o m a x i m i z e s o c i a l w e l f ar e W g i v e n b y

N

M a x W = ~ ] ~ U 7 1 3 i , O i, ~ , y ) ] - c (~ , , y ) * [ L + ~ y ~ ] - e (~ ,)a , J i = 1

s . t . E [ U ~ E a r g m a x E [ U i ] V i ( 2 )

6 I n a d d i t i o n , t h e s o c i a l c o s t s o f i d le h u m a n c a p i t a l a s s o c i a te d w i t h j a i l t e r m s a r e p r e s u m a b l y g r e a t e r w h e n t h e

f o r e g o n e e a r n i n g s o f t h e c r i m i n a l is h i gh . T h e d e c l i n e i n f u t u r e e a r n i n g s a s s o c i at e d w i th i m p r i s o n m e n t i s g r e a t e r f o r

h i g h - i n c o m e o f f e n d e r s [ L o t t ( 1 9 9 2 ); W a l d f o g e l ( 1 9 9 4 ) ] .



S.D. LEVITT 18 3

w h e r e U ~ / re fl ec ts a g e n t i 's u t i li t y -m a x i m i z i n g c h o i c e o f b e h a v i o r , c is t h e n u m b e r o f

a g e n t s c o m m i t t i n g t h e c r i m e ( w h i c h d e p e n d s o n t h e s oc ia l p l a n n e r ' s c h o i c e o f p o li -

c i e s ) , L is t h e s o c i a l e x t e r n a l i t y a s s o c i a t e d w i t h t h e c r i m e , ~ is t h e e x t e r n a l c o s t b o r n e

b y s o c i e ty o f i n c a r c e r a t i n g c r i m i n a l s t h a t a r e d e t e c t e d ( a s s u m e d t o i n c r e a s e l i n e a r ly w it ht h e n u m b e r o f p ri s o n e r- y e a rs s e r v e d ), a n d e is th e c o s t o f e n f o r c e m e n t a s s o c ia t e d w i th

a g i v e n p r o b a b i l i t y e t o f d e t e c t i o n . 7 T h e s o c ia l p l a n n e r m a x i m i z e s W s u b j e c t t o t h e

i n c e n t i v e - c o m p a t i b i l i ty c o n s t r a i n t f o r e a c h a g e n t w i th r e s p e c t t o c o m m i t t i n g t h e c r i m -

i n a l ac t. P r iv a t e b e n e f it s t o c r i m e a r e i n c l u d e d i n t h e s o c i al w e l f a re f u n c t i o n ; e x c l u d i n g

s u c h b e n e f i t s d o e s n o t a l t e r t h e p a p e r ' s c o n c l u s i o n s .

T h e f o l l o w i n g a s s u m p t i o n s a r e m a d e :

(A1 ) 0 < [3 < L V i

( A 2 ) J e [ 0 , J m ~ ](A3 ) ~ , > o

(A4) e ' ( e t ) > 0 , d ' ( cQ > 0( A 5 ) i e l P , J R }

(A6) 0~ > 0p

( A 7 ) A n a g e n t ' s ty p e i is p r i v a te i n f o r m a t i o n

A 1 s a ys th a t t h e s o c ia l c o st s o f c r i m e o u t w e i g h t h e p r i v at e b e n e f i t s t o c r i m e f o r a ll

i n d iv i d u a ls ; i f d e t e r r e n c e w e r e c o s tl es s , t h e s o c i a l p l a n n e r w o u l d w a n t n o c r i m e s c o m -

m i t te d . T h e b a si c c o n c l u s i o n s o f th e m o d e l a r e u n c h a n g e d i f th is a s s u m p t i o n is r e la x e d ,

a l l o w i n g s o m e c r i m e s t o b e b e n e f i c i a l f r o m a s o c ia l p e r s p e c t iv e . A 2 im p o s e s a m a x i m u m

j a il s e n t e n c e . T h i s a s s u m p t i o n is s t a n d a r d i n a n a ly s e s s u c h a s t h is o n e t o a v o i d t h e

B e c k e r ( 1 9 6 8 ) r e s u l t o f i n f in i t e p u n i s h m e n t s , a n d i t c a n b e m o t i v a t e d b y c o n s t i t u t i o n a l

r e s tr i ct i o n s , b y t h e n e e d f o r m a r g i n a l d e t e r r e n c e , b y s o c i e ta l d e si r e s f o r h o r i z o n t a le q u i t y , o r s i m p l y b y t h e f a c t t h a t p e o p l e h a v e f i n i t e l iv es . A 3 sa y s t h a t t h e r e a r e c o s t s

b o r n e b y s o c i e ty o f m a i n t a i n i n g p r i s o n s , a n d t h a t t h e s e c o s t s o u t w e i g h a n y p o s s i b le

b e n e f i t s o f i n c a p a c i t a t i n g p o t e n t i a l r e p e a t o f f e n d e r s . I n o t h e r w o r d s , if p r i s o n t e r m s d i d

n o t h a v e d e t e r r e n c e v a lu e , th e s o c ia l p l a n n e r w o u l d n o t c h o o s e t o i n c a r c e ra t e c ri m i-

n a ls . s A 4 i m p l i e s t h a t e n f o r c e m e n t is c o st ly , a n d t h a t t h e r e a r e d e c r e a s i n g r e t u r n s t o

e x p e n d i t u r e s o n e n f o r c e m e n t . A 5 li m i ts t h e a n a l ys is to t h e c a s e o f t w o t y pe s , h e r e a f t e r

d e s c r i b e d a s " r ic h " a n d " p o o r . " F o r s im p l ic i ty , it is a s s u m e d t h e r e i s a n e q u a l n u m b e r o f

e a c h o f th e t w o ty p e s. T h e r a t i o n a l e f o r c a l li n g t h e t w o t y p e s ri c h a n d p o o r is g i v e n b y

A 6 : T h e d i su t il it y o f g o i n g t o j a il i s a s s u m e d t o b e g r e a t e r f o r t h e r i c h t h a n t h e p o o r .

T h i s is p r e s u m a b l y d u e t o th e g r e a t e r f o r e g o n e c o n s u m p t i o n o f t h e r i c h w h i le i n c a r-

c e r a t e d a n d a l a r g e r d e c l i n e i n p o s t c o n v i c t i o n e a r n i n g s f o r t h e r i c h [ L o t t (1 9 9 2 ) ] , b u tis p e r h a p s a l so a f u n c t i o n o f r e l e v a n t p s y c h o l o g i c a l c os t s to j a il t h a t a r e g r e a t e r f o r t h e

r i ch t h a n t h e p o o r . A 7 i m p l ie s t h a t t h e so c ia l p l a n n e r c a n n o t m a k e p u n i s h m e n t s

d i r e c tl y c o n d i t i o n a l o n t h e i n d i v i d u a l ' s t y p e ( i. e. , J i = J V i) a n d s o m u s t c o n s i d e r e a c h

7Using the terminology of Polinsky and Shavell (1992), enforcement costs are modeled in this paper as entirely

"fixed." The results are not substantively altered by allowing some portion of the enforcement costs be "variable."

8A3 seems to be a reasonable assumption empirically. Studies of the relationship between prison populations and

aggre gate crime rates find that the margin al social costs o f incarceratio n are approx imately equal to the m argina l social

benefit due to crime reducti ons [Maxwell and Moody (1994); Dono hue and Siegelman (1994); Levitt (1996)]. To t he

exten t that a substantial portion of the cr ime-r educing effect of higher prison po pulations is due to increased

deter renc e, incapacitation effects alone would not justify curr ent levels of incarceration. Ehrlich (1981) and Levitt

(1997) provide evidence that deterrence is at least as strong a factor in reducing crime as incapacitation.



184 Incent ive comp at ib i li ty cons traints

i n d i v i d u a l ' s i n c e n t i v e - c o m p a t i b i l i ty c o n s t r a i n t w h e n c h o o s i n g o p t i m a l p o l ic i es . 9 A s m e n -

t i o n e d p r e v io u s ly , t h e r e a r e o t h e r r e a s o n s b e s i d e p r i va t e i n f o r m a t i o n t h a t p u n i s h m e n t s

w o u l d n o t b e t yp e d e p e n d e n t , i n c l u d in g m a n d a t o r y s e n t e n c in g g u i d e li n es [ C h a m p i o n

( 1 9 8 9 ) ] a n d t h e p r o h i b i t i v e c o s t s o f t a i l o r in g p u n i s h m e n t s t o i n d iv i d u a ls . A l t h o u g h Iw il l r e f e r t o A 7 as t h e p r i v a t e i n f o r m a t i o n a s s u m p t i o n h e r e a f t e r , a n y o f t h e s e o t h e r

e x p l a n a t i o n s a r e e q u a l l y c o m p a t i b l e w i t h t h e f o r m a l m o d e l . A l t h o u g h a n i n d i v i d u a l ' s

t y p e is p r iv a t e i n f o r m a t i o n , t h e s o c i a l p l a n n e r is a s s u m e d t o k n o w t h e v a l u e s o f 13r~ 13R,

0 / ~ a n d OR.

T h e s o l u t i o n t o t h e i n d i v i d u a l 's m a x i m i z a t i o n p r o b l e m is s t r a i g h t fo r w a r d ; t h e c r i m e

is c o m m i t t e d o n l y i f t h e e x p e c t e d p u n i s h m e n t is le ss t h a n t h e p r iv a t e b e n e f i t t o c ri m e :

0 i f O~J ~ ~i / / O i

E [ U ~ = ~ i - e ~JO i i f a j < ~ i / o i ( 3 )

G i v e n e q u a t i o n ( 3 ), t h e s o c i a l p l a n n e r c h o o s e s c~ a n d J to m a x i m i z e s o c ia l w e lf a re .L e m m a 1 f ol lo w s d ir e c tl y f r o m t h e s e t u p o f t h e p r o b l e m :

LEMMA 1:

( i ) T he soc ia l p l a nn e r a l w ay s se t s J = j . . . . . •

( i i ) I f bo t h age n t s c om m i t the c r im e a t t he soc ia l op t i m um , t he l e ve l o f e n f orc e m e n t oL m us t be

e qua l t o ze ro .

( i ii ) T he soc ia l ly op t i m a l c ho i ce o f a~ {O , 131-/(] . . . . 0e ), [3R /(] . . . . OR)}.

PR OOF: ( i ) N o t e i r s t t ha t t he l e ve l o f de t er re nce i n e qu a t i on ( 3 ) de pe nds on e~ a n d J on l y t h rou gh

t h e ir p r o d u c t . H o l d i n g e tJ f i x e d i n e q u a t i o n ( 2 ), Ui*( • ), c( • ), a nd t he soc i a l c os t s o f i nc arc e r -

a t i on are una f f e c t e d as t he ra ti o o f eL t o J c hange s. En f orc e m e n t c o s t s , how e v e r , a re s t ri c tl yi nc re a s i ng i n eL, bu t a re n o t a f un c t i on o f J . T he re fore , f o r a g i v e n l e ve l o f de t er re nce , soc ia l w e l fa re

i s m a x i m i ze d by s e t t i ng J as l a rge as pos si b l e.

( i i ) A s sum e t ha t a l l ow i ng bo t h t y pe s t o c om m i t t he c r i m e i s t he soc i a l l y op t i m a l so l u t i on t o t he

soc ia l p l an ne r ' s p rob l e m i n e q ua t i on ( 3 ). B e c au se e n f orc e m e n t i s c os tl y , an d t he on l y be ne f it o f

e n f orc e m e n t i s de te r renc e , i f no de t er re nce oc c ur s a t t he soc ia l op t i m u m , t he c os t -m i n i m i z i ng

enforcement leve l (e~ = O) m u st be chosen.

( i i i) Se t t i ng J = J . . . .. b y p ar t ( i ) o f th i s l e m m a, t he soc ia l p l a nn e r t he n c hoose s e~ t o m ax i m i ze

soc ia l w e l fa re . T he re are f o u r pos s i b le c ase s t o c ons ide r : bo t h t y pe s c om m i t t he c r im e , o ne t y pe or t he

other commits the cr ime , or ne i ther type commits the cr ime . Because enforcement i s cos t ly , the soc ial

p l a nn e r s e t s e~ as l ow as pos s ib l e w h i l e s t il l de te r r ing one or bo t h t y pe s. T he c u t o f f v a l ue s f o r ~ c om e

d i rec t ly f ro m t he age n t s ' m a x i m i za t i o n p rob l e m . I f bo t h t y pe s c om m i t t he c r im e a t t he soc ia lo p t i m u m , t h e n o l = 0 b y L e m m a l ( i i ) .

L e m m a 1 (i) s ay s t h a t t h e s o c ia l p l a n n e r p u n i s h e s c r i m i n a l s w i th t h e h i g h e s t p o s s i b le

j a i l s e n t e n c e , l ° E n f o r c e m e n t i s c o st ly , s o t h e c h e a p e s t m e a n s o f o b t a i n i n g a g i v e n l ev e l

o f d e t e r r e n c e is t o s e t J = J m ax , l o w e r i n g c~, t h e p r o b a b i l i t y o f d e t e c t i o n , a s f a r a s p o s s i b l e

° E v e n w i t h p r iv a t e i n f o r m a t i o n i t m a y b e p o s s ib l e i n a d y n a m i c c o n t e x t t o e n c o u r a g e t h e p a y m e n t o f f i n e s i f t h e

s o ci a l p l a n n e r i s a b l e t o v a r y t h e a m o u n t o f e n f o r c e m e n t r e s o u r c e s d i r e c t e d a t a p a r t i c u l a r c r i m i n a l . T h e s o c ia l p l a n n e r

c a n t h r e a t e n t o i n c r ea s e f u t u r e e n f o r c e m e n t m o r e i f c r i m i n a l e l e ct s t o g o t o j a i l r a t h e r t h a n p a y t h e f in e . T h i s l in e o f

a r g u m e n t i s s i m i l a r to t h a t o f P o li n s k y a n d R u b i n f e l d ( 1 9 9 1) .

1 ° T h is re s u l t c o n t ra s t s w i t h K a p l o w ( 1 9 9 0 ) , w h o f i n d s t h a t o p t i m a l j a i l s e n t e n c e s a r e o f t e n l es s t h a n t h e m a x i m u m

a l l ow e d b e c a u s e o f t h e d e a d w e i g h t l o ss a ss o c i a te d w i t h j a i l s e n t e n c e s s e r v e d b y i n f r a m a r g i n a l c r i m i n a ls . T h e K a p l o w

r e s u l t d o e s n o t a r i s e i n t h e s i m p l e ~la od el d e v e l o p e d h e r e b e c a u s e t h e r e a r e o n l y t w o t yp e s ; t h e r e f o r e , t h e r e w i l l n e v e r

b e a n i n f r a m a r g i n a l t y p e s e r v i n g a j a i l s e n t e n c e i n t h i s m o d e l .



S.D . LEVITT 185

w h i l e s t il l d e t e r r i n g t h o s e c r i m e s f o r w h i c h i t is s o c i a ll y d e s i r a b l e t o d o s o. B y L e m m a

1 ( ii ) , if e n f o r c e m e n t i s c o s tl y e n o u g h , t h e s o c i a l p l a n n e r w i ll p r e f e r t o s e t th e d e t e c t i o n

r a t e e~ e q u a l t o z e r o a n d w i ll l e t b o t h t y p e s c o m m i t t h e c r i m e . P a r t ( ii i) o f L e m m a 1

i d e n t i fi e s t h e r a n g e o f e n f o r c e m e n t l ev e ls t h a t m u s t b e c o n s i d e r e d w h e n s e a r c h i n g f o r

a so c i a l o p t i m u m . B e c a u s e e n f o r c e m e n t i s c o st ly , t h e s o c i a l p l a n n e r s e t s t h e d e t e c t i o n

r a t e a t t h e l o w e s t l e v e l c o n s i s t e n t w it h d e t e r r e n c e .

G i v e n L e m m a 1, t h e s o c ia l p l a n n e r ' s p r o b l e m s i m p li f i e s t o a c o m p u t a t i o n o f s o ci a l

w e l f a r e a t t h e t h r e e p o t e n t i a l l y o p t i m a l l e v el s o f ~ . W h i c h o f th o s e c h o i c e s o f ~ is

o p t i m a l w il l d e p e n d o n t h e p a r a m e t e r v a l u e s o f th e m o d e l ; f o r d i f f e r e n t se ts o f

p a r a m e t e r s , i t m a y b e o p t i m a l t o d e t e r b o t h t yp e s, ex a c t ly o n e t y pe , o r n e i t h e r t yp e .

I I I . I n t r o d u c i n g F i n e s a s a n A d d i t i o n a l I n s t r u m e n t i n a J a i l -O n l y W o r l d

N o w , a s s u m e t h a t i n s t e a d o f p u n i s h i n g c r i m i n a l s e x cl u si v e ly b y s e n d i n g t h e m t o j a i l , t h e

s o c ia l p l a n n e r c a n o f f e r th e c r i m i n a l t h e o p t i o n o f p a y i n g a f i ne a n d f o r e g o i n g t h ep r i s o n s e n t e n c e . I t is a s s u m e d , h o w e v e r , t h a t t h e s o c ia l p l a n n e r c a n n o t m a n d a t e t h a t t h e

c r i m i n a l p a y t h e f i n e i f t h e c r i m i n a l r e fu s e s . A s d i s c u s s e d in t h e I n t r o d u c t i o n , t h a t

a s s u m p t i o n c a n b e m o t i v a t e d i n t h r e e w a ys . F i rs t, b e c a u s e t h e s o c ia l p l a n n e r d o e s n o t

k n o w a n a g e n t ' s w e a lt h , it m a y b e i m p o s s i b l e to d e t e r m i n e w h e t h e r t h e a g e n t ' s w e a l t h

i s s u f f i c i e n t t o c o v e r t h e f i n e . S e c o n d , t h e c r i m i n a l ' s w e a l t h m a y b e h e l d i n t h e f o r m o f

h u m a n c a p i t a l , a n d , t h e r e f o r e , i t w i ll b e d i f f i c u l t t o e x t ra c t . F in a l l y , t h e g o v e r n m e n t m a y

s i m p l y n o t h a v e t h e m e a n s o f c o l l e c t i n g f in e s w h e n t h e r e i s n o f u r t h e r s a n c t i o n a n d t h e

c r i m i n a l r e f u se s to c o o p e r a t e ; t h e l i m i t e d s u cc e ss o n t h e p a r t o f th e g o v e r n m e n t i n

e n f o r c i n g c h i l d s u p p o r t p a y m e n t s a n d p a r k i n g v i o l a ti o n s a r e t w o e x a m p l e s o f t h a t

d i f fi c u h y , u A l t h o u g h n o r e v e n u e c a n b e c o l l e c t e d fr o m a c r i m i n a l w h o r e f u s e s to p a y

a f in e , i t is a s s u m e d t h a t t h e c r i m i n a l c a n b e s e n t t o j a i l . I n p r a c t i c e , t h e n , t h e s o c i a l

p l a n n e r o f f er s a n i n d i v i d u a l w h o h a s b e e n c a u g h t c o m m i t t i n g a c r im e t h e o p t i o n o f

e i t h e r p a y i n g f i n e F o r s e r v i n g j a i l t e r m j .1 2 A s b e f o r e , a n a g e n t ' s w e a l t h is p ri v a t e

i n f o r m a t i o n s o t h a t p u n i s h m e n t s c a n n o t b e m a d e d i r e c t l y c o n d i t i o n a l o n w e a l th . I t is

a s s u m e d t h a t a l l f i n e s t h a t a r e c o l l e c t e d a r e r e d i s t r i b u t e d a s a l u m p s u m a c r o s s a l l

i n d i v i d u a l s .

I m p o s i n g t h e f u r t h e r a s s u m p t i o n o f q u a si - l i n e a r p r e f e r e n c e s , t h e i n d i v i d u a l ' s u t il it y

f u n c t i o n b e c o m e s

I 0 + c t f F i f n o c r i m e is c o m m i t t e d

E [ U / ] = [ [ 3 i - ct * M i n [ J 0 i , F ] + c~fF i f a c r i m e is c o m m i t t e d ( 4 )

w h e r e f i s t h e p e r c e n t a g e o f t h o s e a g e n t s w h o c o m m i t a c r i m e t h a t e l e c t t o p a y t h e f i ne

i f d e t e c t e d . T h e " M i n " t e r m i n th e s e c o n d l i n e r e fl e c t s t h e i n c e n t i v e c o m p a t i b i l i t y

r e q u i r e m e n t ; t h e a g e n t h a s t h e o p t i o n o f c h o o s i n g b e t w e e n t h e t wo fo r m s o f p u n i s h -

m e n t . T h e l a s t t e r m i n b o t h l i n e s o f t h e u t i li t y f u n c t i o n i s t h e l u m p s u m r e d i s t r i b u t i o n .

T h e a s s u m p t i o n o f q u a s i d i n e a r it y i m p l i e s th a t e a c h a g e n t v al u e s a n e x t r a d o l l a r o f

i n c o m e i d e n t i c a l l y , i .e ., u ti l it y i s t r a n s f e r a b l e . T h e c o m b i n a t i o n o f a u t i l it a r i a n s o c i a l

l l F o r e x a m p l e , o n l y 5 4 % o f p a r e n t s w i th c h i l d s u p p o r t a w a r d s r e g u l a rl y r ec e i v e p a y m e n t [ G o v e r n m e n t A c c o u n t i n g

O f f i c e ( 1 9 9 2 ) ] , b u t p a y m e n t s h a v e r e p e a t e d l y b e e n s h o w n t o b e h i g h l y r e s p o n s iv e t o t h r e at s o f f u r t h e r p u n i s h m e n t .

1 2A m o r e r e al is ti c a s s u m p t i o n w o u l d a l l o w t h e s o ci a l p l a n n e r t o o f f e r a m o r e c o m p l i c a t e d m e n u o f c o n t ra c t s

i n v o l v in g c o m b i n a t i o n s o f f in e s a n d j ai l t e r m s . T o m a k e t h e u n d e r l y i n g i n t u i t i o n a s t r a n s p a r e n t a s p o s si b le , h o w e v e r ,

t h e s i m p l e s t c a s e is e x a m i n e d h e r e . T h e m o r e g e n e r a l c a s e is d i s c u s s e d i n S e c t i o n V , b u t i t i s w o r t h n o t i n g h e r e t h a t

t h e a s s u m p t i o n o f e i t h e r f i n e s o r j a i l i s n o t a s r e s tr i c t iv e a s i t f i rs t s e e m s .



186 Incentive compatibi l i ty constraints

w e l f ar e f u n c t i o n a n d q u a s i - l i n e a r p r e f e r e n c e s r u le s o u t t h e u s e o f th e c r i m i n a l j u s t i c e

s y s te m fo r r e d i s t r i b u t i v e p u r p o s e s . I t s e e m s r e a s o n a b l e t o a s s u m e t h a t t h e s o c i a l p l a n n e r

h a s a c c e s s to a m o r e d i r e c t m e a n s o f a c h i e v i n g r e d i s t r i b u t i o n i f t h a t is a n o b j e c t iv e . 13

T h e s o c i a l w e l f a r e f u n c t i o n i s n o w g i v e n b y

N

M ax W = Z £ I U 'a/X[3i' 0 i ' c~ , J , F )] - c(oL, J, Is ) * L+ (1 - f (~ , J , F ) ) * c~Jt I - e (cQc 2 , J , F i - 1

s . t . E [U ~i] E a r g m a x E [ U i ] g i ( 5 )

T h e s o c i al p l a n n e r ' s p r o b l e m d i f fe r s in t h r e e w a y s f r o m t h e j a i l - o n l y w o r l d . F i rs t, t h e r e

a r e n o w t h r e e i n s t r u m e n t s a v a i la b l e : c~, J , a n d F . S e c o n d , a d d i t i o n a l i n c e n t i v e c o m p a t -

i b il it y c o n s t r a in t s o n t h e p a r t o f t h e a g e n t s h av e b e e n i n t r o d u c e d d u e t o t h e f in e o p t i o n .

F i n a ll y , t h e s o c i a l c o s t a s s o c i a t e d w i th i n c a r c e r a t i n g c o n v i c t e d c r i m i n a l s is b o r n e o n l y b y

t h e f r a c t i o n o f c r i m i n a l s ( 1 - f l w h o e l e c t t o s e r v e a j a i l s e n t e n c e i f d e t e c t e d , r a t h e rt h a n o n a l l d e t e c t e d c r i m i n a l s .

A s s u m e f u r t h e r ,

( A8 ) ~ [ 0 , ~ ]

i .e ., t h e r e is n o e x o g e n o u s l y i m p o s e d m a x i m u m f in e . A s s u m p t i o n A 8 r u le s o u t a ll

s i t u a t i o n s w h e r e t h e m a x i m u m f i n e is s o l o w t h a t i n t r o d u c i n g f i n e s h a s a d v e r s e e f fe c t s

d u e t o p o s s i b le u n d e r d e t e r r e n c e . O f c o u r s e , t h e s o ci a l p l a n n e r c a n ( a n d w i ll ) s e t t h e

a c t u a l f i n e b e l o w t h e m a x i m u m a l l o w a b l e fi n e . 14

T h e o u t c o m e o f th e a g e n t ' s u t i li ty m a x i m i z a t i o n p r o b l e m is a s f ol lo w s:

I ~ i f ( ~ , . ~ o t J O a n d ] 3 i ~ o~F)E [ U ' ~ , ] = f 3 i - - e L F + o t t ~ " i f ( O i > F / J a n d [ 3 i > e t F ) ( 6 )

(3 i o tJ O i+ o t F i f (O i < ~ F / J a n d [3 i > o t JO i )

T h e f i rs t l i n e is t h e u t i l it y o f th o s e n o t c o m m i t t i n g a c r i m e , t h e s e c o n d l i n e c o r r e -

s p o n d s t o th o s e w h o c o m m i t t h e c r i m e a n d c h o o s e t o p a y t h e f in e w h e n c a u g h t . T h e

t h i r d l i n e r e f le c t s t h o s e c r i m i n a l s w h o o p t f o r j a i l i f d e t e c t e d .

P a r t s ( i) a n d ( ii ) o f L e m m a 1 e x t e n d i n a s t r a i g h t f o r w a r d m a n n e r t o a f i n e - a n d rj a i l

w o r l d . T h e f o l lo w i n g l e m m a h e l p s t o f u r t h e r c h a r a c t e r i z e p o s s ib l e s o c ia l o p t i m a i n t h e

f i n e - a n d r j a i l w o r l d :

LEMMA 2:

( i ) I f the poo r ty pe c om m i t t i ng a c r i m e p re fe r s a g i v e n f i n e t o a g i v e n j a i l t erm , t he r i c h ty pe w i l l

a l so p re f e r the f i n e t o j a i l w h e n c onv i c t e d o f a c r im e .

( i i) I f on l y the r ic h ty pe c om m i t s t he c r i m e i n a soc i a l op t i m um , t ha t op t i m u m w i l l i nv o l v e the

r ic h c h o o s in g t h e f i n e r a t h e r t h a n s e r v i n g t h e j a i l s e n te n c e w h e n c a u g h t.

l Z N o n e t h el e s s, i t i s w o r t h n o t i n g t h a t f i n e s m i g h t b e a u s e f ul t o o l f o r a c h i e v i n g r e d i s t ri b u t i o n o f i n c o m e f i o m t h e

r i c h t o t h e p o o r i f t h e a s s u m p t i o n o f q u a s i -l i n e a r i t y is r e l a x e d . I f t h e r i c h h a v e a l o w e r m a r g i n a l u t i l i ty o f i n c o m e , i t

m i g h t b e s o c ia l ly b e n e f ic i a l t o a ll o w t h e r i c h t y p e to c o m m i t a c r i m e t h a t o t h e r w i s e w o u l d b e o p t i m a l l y d e t e r r e d , p a y i n g

a f i n e t h a t i s t h e n d i s t r i b u t e d a s a h n n p s u m .

1 4 In p r a c t i c e , a r e s t r i c t i o n o n t h e m a x i m u m f i n e i s t h e c r i m i n a l ' s a b i l i t y to p a y . I n w h a t f o ll o w s , i t i s a s s u m e d t h a t

t h e m a x i m u m f i n e is s u c h t h a t t h e c r i m i n a l c a n c o v e r t h e f i n e , e i t h e r t h r o u g h c u r r e n t a s se t s o r u s i n g t h e f l o w o f f u t u r e

i n c o m e . F o r c r i m e s r e q u i r i n g g r e a t e r p u n i s h m e n t t h a n t h a t, f i n e s wi ll b e e v e n l es s e f f e ct i v e t h a n t h e f o l l o w i n g a n a ly s is

s u g g e s t s .



S.D. LEXq~T 187

( i i i ) Th e soc ial ly op t im al choice o f o t~{O , f3v /OvJ . . . . . D R / 0 R J . . . .. . D R / 0 1 " J . . . . . }"

PROOF:

( i ) T h i s r esu l t f o l l ow s t ri v ia l ly up on i n spe c ti on o f e qua t i on ( 4 ) g i v e n t he as s um p t i on t ha t OR >0p.

( i i ) T h i s i s m os t e as il y p r ov e d by c on t rad i c ti on . A s su m e t ha t a t t he soc ia l op t i m um on l y t he r i ch

t y pe c om m i t s t he c ri m e , an d g i v e n t he soc ia l p l a nn e r ' s c ho i ce o f J an d F , e l e ct s t o go t o a i l i f caugh t .

For t he c ho i c es o f the t w o t y pe s t o be i nc e n t i v e c om p a t ib l e , i t m us t b e t he c ase t ha t

O R < F/J .. .. . and [~R > a J . . . . OR (IC for the rich)

Op > De/otJ ..... an d 13p < e~F (IC for the po or )

C o m b i n i n g t h e t w o c o n d i t io n s o f t h e IC c ons t ra i n t . f o r t he poor , 0 e > F/Jma×. B u t t h a t i s a

contradic t ion, because OR < F/ J ..... f r o m t h e IC c ons t ra i n t o f t he r i ch , a nd OR > 0v by a s s u m p t i o n

A 6 .

( i i i) T he re are i v e pos s i b l e c ase s : bo t h t y p e s c om m i t t he c r i m e , on ly t he r i ch c om m i t t he c r i m e an d

p a y t h e i n e i f d e te c te d , on l y t h e p o o r c o m m i t t h e cr im e a n d e it he r p a y t h e i n e o r g o t o j a i l , o r n e i th e r

t y pe c om m i t s t he c r i m e . Be c ause e n f orc e m e n t i s c os tl y , the soc i a l p l a nn e r c hoose s t he l ow e s t e~

c ons is t en t w i t h i n du c i n g a g i v e n s e t o f b e hav i or s. I f bo th t y pe s c om m i t t he cr i m e , o t = 0 i s op t i m a l

b y L e m m a I . I f o n ly t h e r ic h c o m m i t t h e cr im e , i t m u s t b e t h e c a se th a t D R > D e , s o th e b i n d i n g

c ons t ra i n t on t he po or i s t he j a i l s e n te nc e , i .e . , e~ = Dv /O v J . . . . . . I f on l y t he po or c o m m i t t he c r im e ,

t h e o p t i m a l et d e p e n d s u p o n w h e t h e r th e p o o r p r e fe r t o s o r e t he j a i l s e nt en c e o r p a y t h e f i n e . I f t h e

po or p re f e r a i l , t he low e s t e t t ha t w i l l de te r t he ri c h i s t he sam e as i n t he a i l -on l y w or l d : DR/0VJ . . . . "

I f t h e p o o r p r e fe r t h e i n e , h o w e v er , m a n i p u l a t i o n o f t h e IC cons traints reveals tha t o~ m us t be h igh er

t o de te r t he r ic h : f ~ R /O v J .. . . . I f n e i t he r t y pe c om m i t s t he c r im e , one o f t he abov e v a l u e s o f e~ m us tb e b i n d i n g .

Parts (i) and (ii) of Lemma 2 are a direct consequence of the assumption that the

trade-off betwee n fines and jail is mor e favorable for the rich. Part (iii) defines th e set

of enforcement levels that must be checked when seeking a social optimum. These

en fo rc eme nt levels are identical to those in the jail-only world, except t hat a new,

possibly optimal, en fo rc eme nt level exists for the case where the poor type commits the

crime a nd pays the fine, but the rich type is deterred. Because the jai l/ fi ne trade-off is

more favorable to the rich than the poor, a fine that is attractive to the poor must be

accom panie d by an increased level of enfor ceme nt if the rich are to be deterred.

I V . C o m p a r i n g S o c i a l W e l f a r e i n a J a i l - O n l y W o r l d t o a F i n e- a n d -J a il W o r l d

The precedi ng sections broadly out lined the possible outcomes in jail-only and fine-

and-jail worlds, respectively. A complete accounting of the exact solutions to the two

models is both tedious an d u nreveal ing. A more useful exercise is to consi der what

effect the int rod uct ion of fines has on social welfare vis-a-vis a world that previously did

not have fines available as instruments. Because the model developed here is quite

simple, it is actually the case that the availability of fines has no imp act whatsoev er on

social welfare in m any circumstances. I n m ore genera l settings discussed in Section V,

it is clear that in tro duc in g fines must m ake at least a marg inal co ntr ibu tio n to social

welfare. Nonetheless, examining this simpler model provides insight into both the

reasons why fines are less useful in the presence of private information, and theconditions un de r which fines cont inue to be effective punishments .

The analysis of this section proceeds in two steps. First, the cond itio ns und er which



188 Incent ive comp at ib i li ty cons traints

i n t r o d u c i n g f in e s d o e s o r d o e s n o t i n c r e a s e s o c ia l w e l f a re a r e o u t l in e d . S e c o n d , c o n -

s i d e r a t i o n is g i v e n t o h o w s p e c i fi c p a r a m e t e r s o f t h e m o d e l ( e .g ., t h e r e la t iv e p r i v a t e

b e n e f it s t o c r i m e f o r th e r i c h a n d p o o r t y p e s a n d t h e m a g n i t u d e o f t h e e x t e r n a li t y

a s s o c i a t e d w i th a p a r t i c u l a r c r i m e ) a f f e c t t h e u s e f u l n e s s o f f in e s .

T h e f o l l o w i n g p r o p o s i t i o n a d d r e s s e s t h e f i rs t o f t h e s e i s s ue s :

PROPOSITION 1: I n t ro du c i n g - fi ne s l e ads t o an i nc re ase i n soc i a l w e lf a re i f a nd on l y i f t he

- f i ne -and- j a i l soc i a l op t i m um i nv o l v e s

( i ) p re c is e ly one ty pe c om m i t t i ng t he c r im e ,

( i i ) t ha t t y pe c hoose s t o pa y t he - f i ne w he n de te c te d .

PR OOF: I f bo t h t y pe s c om m i t t he c r im e i n t he -f ine -and- ja i l w or l d , t he op t i m a l ot i s ze ro by L e m m a

1 . T h i s w as a f e as i b l e s tra t egy i n t he j a i l -on l y w or l d , how e v e r , so soc ia l w e l f a re c an no t h av e

i m prov e d .

I f both types are de terred in the - fine -and-jai l wor ld , soc ial we l fare can no t ha ve increased becauset he on ly e f fe c t o f - fi ne s i n suc h an e qu i l i b r i u m i s to i n t rodu c e t w o a dd i t i on a l i nc en t iv e -com pa t ib i l it y

c ons tra in t s . Be c ause no c os tl y j a i l s e n t e nc es are ac t ua l l y i m p l e m e n t e d i n t h is e qu i li b r ium , t he re i s

no soc ia l c os t a s soc ia t e d w i t h de t er re nce us i n g j a i l s e n te nc e s .

I f e xac t ly o ne t y pe com m i ts t he c r im e , a nd t ha t t y pe el e ct s t o go t o j a i l ra t he r t ha n p ay t he - f i ne

i n a ja i l - a n d - f i n e w o r ld , t h e n o n c e a g a i n , - fi n es c a n n o t h a v e h a d a p o s i t i v e i m p a c t o n s o c ia l

w e l fa re , i nas m uc h as t h is ou t c om e w as f e as i b l e i n a j a i l -on l y w or l d .

T o p r o v e su ff ic ie n cy , i t n ee d s o n ly b e n o t e d t h a t b y a s s u m p t i o n A 8 , a n y e q u i l i b r i u m o f t h e

j a i l -on l y w o r l d i s s t i ll ob t a inab l e i n t he - f i ne -and - j a i l w or ld . T he ref ore, i f the soc i a l p l a nn e r s e l e ct s

t he ou tc om e i n t he p ropos i ti on , i t m u s t be a soci a l im prov e m e n t .

P r o p o s i t i o n 1 d e m o n s t r a t e s t h e s u b s t a n ti a l l im i t s t h a t t h e i n c e n t i v e - c o m p a t i b i l it yc o n s t r a i n t i n d u c e d b y p r i v a te i n f o r m a t i o n p l a c e s o n t h e u s e f u l n e s s o f f in e s . T h e o n l y

b e n e f i t t o fi n e s in t h e p r i v a te i n f o r m a t i o n w o r l d is t h e a v o i d a n c e o f c o s tl y a i l t e rm s ; t h e

c a s e h i g h l i g h t e d i n t h e p r o p o s i t i o n is t h e o n l y i n s t a n c e w h e r e s u c h a b e n e f i t is r e a li z e d .

P r o p o s i t i o n 1 is i n s ta r k c o n t r a s t t o m o d e l s w i th p e r f e c t i n f o r m a t i o n a n d p e r f e c t l y

e n f o r c e a b l e f in e s i n w h i c h i n t r o d u c i n g f in e s u n a m b i g u o u s l y r a is e s w e l fa re , b o t h b e -

c a u s e o f t h e i n c r e a s e d d e t e r r e n c e p o t e n t i a l a n d t h e a b i li ty to m i n i m i z e j a il t i m e t h r o u g h

t h e u s e o f i n d i v id u a l l y t a i lo r e d f i n e s. T h e i n c e n t i v e c o m p a t i b i l it y c o n s t r a i n t s a r i s i n g

f r o m p r i v a te i n f o r m a t i o n a d v e r s e l y a f f e c t b o t h o f t h o s e c h a n n e l s . W i t h p r iv a t e i n f o r-

m a t i o n , t h e c r i m i n a l w il l n e v e r p a y a f i n e o r a c c e p t a fi n e- ja il c o m b i n a t i o n t h a t is m o r e

p u n i ti v e t h a n t h e m a x i m u m ja i l- o n ly p u n i s h m e n t , s o d e t e r r e n c e c a n n o t i n c r e a se w i th

t h e i n t r o d u c t i o n o f f in e s . P r iv a t e i n f o r m a t i o n a l so g r e a tl y r e d u c e s t h e s o c i al p l a n n e r ' sa b il it y t o t a il o r p u n i s h m e n t s t o in d i v i d u a l c r i m i n a l s , b e c a u s e t h e c r i m i n a l ' s t y p e is

p r i v a t e i n f o r m a t i o n .

A l t h o u g h P r o p o s i t i o n 1 h i g h l ig h t s t h e w e a k n e s s o f f in e s as a n i n s t r u m e n t i n t h e

p r e s e n c e o f p r iv a t e i n f o r m a t i o n , t h e f o l lo w i n g p r o p o s i t i o n p o i n t s o u t t h a t t h e r e is o n e

s e t o f c i r c u m s t a n c e s i n w h i c h t h e a v a il ab i li ty o f f i n e s u n a m b i g u o u s l y i n c r e a s e s s o c ia l

w e l f a r e :

PROPOSITION 2: T h e i n t rodu c t i on o f -f ine s un am b i guo us l y i nc re ase soc ia l w e l fa re i f t he j a i l -on l y

soc ia l op t i m um i nv o l v e s t h e r i ch c o m m i t t i ng t he c r im e a n d t he po or suc c e ss f u ll y de t e r red .

PR OOF: I f t he r i ch t y pe c om m i t s t he cr i m e i n t he j a i l -on l y op t i m u m , bu t t he po or ty pe doe s no t ,

t h e n i t m u s t b e t r u e t h a t ~3R > f 3p . B e c a u s e OR > O p , i t i s a l w ay s pos si b l e f o r t he soc ia l p l a nn e rt o i n t rodu c e a_ fi ne suc h t ha t t he e n f orc e m e n t l e ve l e t is unc ha nge d , t he r ic h c o n t i n ue t o c om m i t t he

c r im e , t h e po or c o n t i nu e t o be det e rre d , an d t hose r i ch t y pe s w ho a re de t ec t ed e le c t t o p ay t he f i n e



S.D . LEVITT 189

r a t h e r t h a n g o to j a i l . I n s p e c t i o n o f eq u a t i o n ( 5 ) s h o w s t h a t s o c i a l w e l fa r e m u s t h a v e i m p r o v e d w i t h

t he f i ne .

P r o p o s i t i o n 2 st a te s t h a t f in e s u n a m b i g u o u s l y i n c r e a s e s o c i a l w e l f a r e i f t h e i n i t i a lj a i l -o n l y e q u i l i b r i u m h a s t h e r i c h t y p e c o m m i t t i n g t h e c r i m e w i t h t h e p o o r t y pe su c -

c e s sf u ll y d e t e r r e d . T h i s r e q u i r e s t h a t t h e p r i v a t e b e n e f i t s to c r i m e f o r t h e r i c h a r e

s u b s t a n t i a l l y g r e a t e r t h a n t h e p r i v a t e b e n e f i t s t o c r i m e f o r t h e p o o r , i n a s m u c h a s t h e

r ic h a r e m o r e s e n si ti v e t o j a i l p u n i s h m e n t s . T a x e v a s i o n a n d o t h e r w h i t e - c o ll a r c r i m e s

a r e p o s s i b l e e x a m p l e s o f c r i m e s t h a t m a y s a ti sf y t h a t c o n d i t i o n , a5 L o w - i n c o m e i n d i v i d -

u a l s a r e u n l i k e l y t o h a v e s u f f i c i e n t i n c o m e o r a c c e s s t o r e a p l a r g e b e n e f i t s f r o m s u c h

c r i m e s .

W h i l e P r o p o s i t i o n s 1 a n d 2 o u t l in e g e n e r a l c o n d i t i o n s u n d e r w h i c h f i n es w il l o r w il l

n o t i n c r e a s e s o c ia l w e l fa r e , i t i s p e r h a p s m o r e i n t e r e s t in g t o c o n s i d e r h o w c h a n g i n g t h e

v a lu e s o f th e u n d e r l y i n g p a r a m e t e r s o f th e m o d e l a f fe c ts t h e u s e f u ln e s s o f f in e s . I n s o m e

c a se s , t h e l o g i c is t r a n s p a r e n t . F o r i n s t a n c e , t h e g r e a t e r i s t h e s o c i al c o st o f i m p r i s o n -m e n t ( ~ ) , t h e m o r e v a l u a b l e a r e f in e s b e c a u s e t h e y p r o v i d e a n a l t e rn a t i v e to i n c a r c e r -

a t i o n . A l s o , a s P r o p o s i t i o n 2 p o i n t s o u t , h i g h e r p r i v a t e b e n e f i t s t o c r i m e f o r t h e r i c h

v is -a-v i s t h e p o o r a r e a l s o a s s o c i a t e d w i th f i n e s b e i n g e f f e c ti v e .

T h e r e l a t i o n s h i p b e t w e e n o t h e r p a r a m e t e r s o f t h e m o d e l a n d t h e e ff e c ti v e ne s s o f

f i n e s is m o r e s u b t le . F o r e x a m p l e , e x t r e m e l y h i g h p r i v a t e b e n e f i t s to c r i m e f o r t h e p o o r

v is -a-v i s t h e r i c h a l s o m a k e f i n e s v a l u a b l e b e c a u s e t h e s o c i a l p l a n n e r c a n o f f e r a f i n e lo w

e n o u g h t o e n t i c e t h e p o o r t y p e t o p a y i t r a t h e r t h a n g o t o j a i l w i t h o u t h a v i n g t o b e

c o n c e r n e d t h a t t h e r i c h w il l a l s o f i n d t h e c r i m e a t t r a c ti v e n o w t h a t t h e f i n e o p t i o n e x is ts .

S i m i l a r d i s u t il i t ie s o f j a i l f o r r i c h a n d p o o r t y p e s a r e a l so a s s o c i a t e d w i t h f i n e s b e i n g

e f fe c t iv e . If t h e r i c h a r e v e r y a v e r s e t o p r i s o n t e r m s , t h e p o o r w i ll b e t h e f ir st to c o m m i t

t h e c r i m e , e v e n i f t h e i r p r i v a t e b e n e f i t f r o m t h e c r i m e i s l o w e r t h a n t h a t o f t h e r i c h .W h e n f in e s a r e i n t r o d u c e d , e n f o r c e m e n t w i ll n e e d t o b e r a i s e d t o d e t e r t h e p o o r t yp e .

T h e c o s t o f i n c r e a s e d e n f o r c e m e n t o ff se ts t h e b e n e f i t s o f f ew e r j a i l t e r m s s e r v e d.

F i n e s a r e a l so m o r e e f fe c t iv e w h e n t h e e x t e r n a l i t y ( L - [3 i) a s s o c i a t e d w i t h a c r i m e i s

s m a l l r e la t iv e to t h e c o s ts o f i m p r i s o n m e n t ( ~ ) a n d m a r g i n a l e n f o r c e m e n t c o st s ( e' ( ~ ) ) .

I n s u c h a c a s e, i t w i ll o f t e n n o t b e w o r t h w h i l e t o p u n i s h o f f e n d e r s w h e n t h e o n l y f o r m

o f p u n i s h m e n t is i n c a r c e r a t i o n , b e c a u s e t h e s o c i al co s ts o f p r e v e n t i n g c r i m e m a y

o u t w e i g h t h e s o c i al c o st s o f a l lo w i n g i t to o c c u r . W h e n f i ne s , a le s s s o c i a ll y c o s tl y m e a n s

o f p u n i s h m e n t , a r e i n t r o d u c e d , i t n o w m a y b e s o ci al ly b e n e f i c i a l t o p u n i s h t h e c r i m e .

T r a f f ic v io l a t i o n s a r e a g o o d e x a m p l e o f s u c h a s it u a t i o n .

V . E x t e n s i o n s a n d G e n e r a l i z a t i o n s o f t h e B a si c M o d e l

T h e r e su l ts o f t h e p r e v i o u s s e c t i o n s a re s t r ik i n g : U n d e r t h e p a r t i c u l a r m o d e l i n g a s s u m p -

t i o n s u s e d , f i n es d o m i n a t e j a i l t e r m s a s p u n i s h m e n t s w i th p e r f e c t i n f o r m a t i o n , b u t i n

m a n y c i r c u m s t a n c e s t h e y a r e c o m p l e t e l y u se l es s i n t h e p r e s e n c e o f pr i v a te i n f o r m a t i o n .

A l t ho ugh t he i n t u i t i on t ha t m o t i v a t e s t he r e duc e d ef fi cac y o f i n e s i s qu i t e robus t, t he p re ci se r e su l t

t ha t f i ne s p rov i de no i nc re m e n t t o soc ia l w e l fa re is no t. I n t h i s s e c t i o n , tw o g e n e r a l i z a t i o n s o f

t h e m o d e l a r e d i s c u s s e d .

O n e r e s t r i c t i o n o n t h e m o d e l i s t h e a s s u m p t i o n t h a t t h e so c ia l p l a n n e r p u n i s h e s

c r i m i n a l s u s in g f i n e s 0 r j a i l s e n t e n c e s , b u t n o t c o m b i n a t i o n s o f th e t w o, a l t h o u g h t h is

~ ST his p o i n t a s s u m e s t h a t n o t o n l y t h e f i n a n c i a l b e n e f i t , b u t a l s o t h e m a r g i n a l u t il i ty o f t h e g a i n s f r o m t h e c r i m e a r e

g r e a t e r f o r t h e r i c h t h a n t h e p o o r , b e c a u s e p r i v a t e b e n e f i t s h e r e a r e e x p r e s s e d i n u d l i t y t e r m s .



190 I n c e n t i v e c o m pa t i b il it y c o n s t r a i n t s

limitation is not as restrictive as if first seems. With private information, the social

pla nne r cann ot enforce a p un ish men t that involves both J, nax a n d a fine, because no

fur ther additi onal jail term can be imp osed on a criminal who claims insuffici ent wealth

an d refuses to pay the fine. 16 Ther efo re, the basic incenti ve-c ompa tibi lity constraint isstill present, even when combi nation s of pun ishm ents are allowed.

Combination punishments can sometimes be useful, because they allow the social

pl an ne r to substitute a fine for some por tion of the socially costly jail sent ence. T he

social gains from com bin ati ons are generall y not very large, however, for two reasons.

First, only the p oor type serves jail time in the f ine-and-jail world, by Lem ma 2(ii). Any

reduct ion in the jail sentence of the poor must be count er-bala nced by an increased

level of enf or cem en t for the rich to con tin ue to be deterred. If the mar gina l cost of

det err ence is high relative to the social costs of incarcer ation, access to co mbi nat ion s of

fines and jail may not increase social welfare at all. Second, in n umer ical si mulations of

the model, jail sent ences were f ou nd to be relatively inf req uen t in a fine-and-jail

world. 17 Con sequ entl y, ther e is relatively little gain to society fro m a m arg in al red uc ti on

in time served.

A second extension of the model is to allow for a continuum of types. The existence

of a continuum makes separating equilibria more likely; for most sets of parameter

values some types comm it the crime and others do not. A separating eq uili briu m is a

necessary (but not sufficient) co ndi tio n for fines to increase social welfare by Proposi-

tion 1. Not surprisingly, therefore, fines are mo re effective with a con ti nu um of types.

For example, as long as some types comm it the crime, while others do not, it is possible

to show that the int ro duc tio n of fines will increase social welfare. Th e mag nit ud e of that

increase, however, turns o ut to be smaller than one might first suspect, precisely for the

reasons put forth in this paper. A fine that makes the marginal criminal indifferentbetween paying the fine or serving the prison sentence will not be attractive to the

infr amar gina l criminal, and therefor e it will have only an infinites imal impac t on social

welfare. If the social planner wants to obtain a substantial social benefit from fines, a

lower fine will nee d to be i mposed so that mor e criminals will choose the fine. The

existence of that lower fine, however, will make the crime seem attractive to others who

previously were dete rred by the possibility of a prison term. The social pl an ne r is then

faced with either (i) incr easing the level of enfo rce men t, which is costly, or (ii)

accepting a higher crime rate, which is also socially costly. Although the precise social

gains or losses depend on the specific case, it is clear that the presence of costs

associated with the int ro duc tio n of fines makes their use less attractive tha n is the case

in a perfect information world in which fines strictly dominate prison terms as punish-m e n t .

V I . C o n c l u s i o n s

Models that assume perfect infor matio n on the part of the social plan ner predict a

strong reliance on fines, a predic tion that is incon siste nt with real-world practice. I n this

1 6 W h i le J . l ax i s t r e a t e d a s e x o g e n o u s l y g i v e n i n t h e m o d e l , i t i s a l s o p o s s i b l e t h a t s o c i e t y ' s m a x i m u n l a c c e p t a b l e

m a x i m u m j a i l s e n t e n c e c h a n g e s w i t h t h e i n t r o d u c t i o n o f fi n e s. F o r i n s ta n c e , i f s o c ie t y th i n k s t h a t t h o s e c r i m i n a l s w h o

r e f u s e t o p a y t h e f i n e a r e a c t u a ll y a b l e t o p a y t h e f i n e b u t a r e l y i n g a b o u t t h e i r w e a l t h , a j a i l t e r m g r e a t e r t h a n J m , × m a y

b e j u s t i f i e d . O n t h e o t h e r h a n d , i f t h e r i c h p a y f i n e s a n d o n l y t h e p o o r g o t o . ja il , s o c i e ty m a y c o n c l u d e t h a t t h e r e i s

i n j u s t ic e in t h is a r r a n g e m e n t a n d t h a t l o w e r t h e m a x i m u m a c c e p t a b l e j a i l s e n t e n c e .

1 7F ull d i s c u s s i o n o f t h e n u m e r i c a l s i m u l a t i o n s w e r e i n c l u d e d i n p r e v i o u s v e r si o n s o f th e p a p e r , b u t h a v e b e e n

o m i t t e d d u e t o s p a c e c o n s t r a i n t s . R e s u l t s a r e a v a i l a b le f i- o m t h e a u t h o r o n r e q u e s t .



S.D. LEVITt 191

paper, it is dem ons tra ted that private infor mat ion greatly reduces the usefulness of fines

due to the additional incentive-compatibility constraint that binds the social plann er.

Although caution is warranted in drawing positive conclusions from a model as limited

as the o ne p rese nted here, this pape r provides a possible theoretical justif ication for theheavy reliance o n jail sen tences in the real world.

Even with private inf orma tion , there are nu me ro us situations where fines are a

valuable ins tr ume nt to the social plann er. Fines are more useful for crimes that are

com mit ted by the rich, no t only because they have more resources to pay fines, but also

because of the direction in which the incentive-compatibilityconst raint binds. Fines are

also useful when the social externality of crime is small relative to the en fo rc eme nt and

in car cer ati on costs. Possible examples o f such crimes i ncl ude traffic xfiolations an d m ost

other misdemeanors, all of which are frequently pun ishe d using fines in practice. Fines

can also be useful when the private benefits to crime are much higher for one segment

of the p opula tion th an the rest because unde rde ter ren ce of the latter type is not l ikely

to be an issue.

Although the assumption that a criminal's type is completely private information is

und oub tab ly extreme, the as sumption of perfect informat ion on the part of the social

planner is l ikewise unrealistic. The court has some information about an individual 's

wealth a nd disutility of jail. If used effectively, that inf orm atio n can certainly be welfare

improv ing. In li ght of the inf orm atio nal restrictions, however, the relatively limited use

of fines in practice may be justified.The results of this pape r have implications for policies such as man dat ory sen ten cin g

guidelines that l imit udicial discretion. Although there are o ther justifications for such

policies [Cham pion (1989)], on e negative conse quenc e is that if judges cann ot tailor

punishments to the situation of individual criminals, it is as if the criminal's type iscompletely private information, exacerbating the problems associated with incentive

compatibility.

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