## E v a l u a t i n g U

. S

. F ue l E c o no m y S t a n d a rds

In a M od e l w i t h P rod uc e r a n d H ous e h ol d H e t e ro ge n e i t y

M a r k R

. J a c obs e n *

U ni ve r s i t y of C a l i f o r ni a

, S a n D i e go

S e pt e m be r 2010

A b s t r ac t

T h i s p ap e r emp l o y s an e mp i ri cal l y es t i mat ed mo d el t o s t u d y t h e eq u i l i b r i u m eff ect s o f an i n creas e

i n t h e U

. S. co rp o rat e av e rag e fu el eco n o my (C A F E ) s t a n d ard s

. T h e mo d el cap t u res h et ero g en ei t y

amo n g p ro d u ce rs an d a mo n g h o u s eh o l d s t o d es cri b e d i ffer en ces i n res p o n s es t o t h e r eg u l at i o n

. A

d i s t i n g u i s h i n g feat u re o f t h e mo d el i s t h at i t co n s i d ers t h e fact t h at s o me fi rms ar e u n co n s t rai n ed

b y C A F E r eg u l at i o n

, w h i l e o t h ers ch o o s e ei t h er t o v i o l at e t h e reg u l at i o n (p ay a fi n e) o r t o me et

t h e s t an d ard

. By t ak i n g t h i s h et ero g en ei t y i n t o acco u n t

, I fi n d t h at t h e p ro fi t i mp act s o f CA F E

fal l al mo s t en t i rel y o n d o mes t i c p ro d u c ers

. In ad d i t i o n

, t h e mo d el d ev el o p s u t i l i t y

- co n s i s t en t

w el f are an al y s es t h at al l o w d i re ct co mp ari s o n o f t h e C A F E s t an d a rd w i t h g as o l i n e t ax es

,

co n s i d eri n g t h e s i mu l t an eo u s h o u s eh o l d d eci s i o n o f v eh i cl e an d mi l es t ra v el ed

. I fi n d t h at

i n creas ed g as o l i n e t ax es w o u l d r ed u ce g as o l i n e co n s u mp t i o n fo r ab o u t o n e

- s i x t h t h e w el fa re co s t

o f a co rr es p o n d i n g i n cremen t t o t h e C A F E s t an d ard

. F i n al l y

, t h e mo d el ac co u n t s fo r t h e d y n ami c

effe ct s o f CA F E o n u s ed v eh i cl e mark et s

– ef fect s t h at t u rn o u t t o b e i mp o rt an t t o t h e w el far e

i mp act s

. T h e co n s u m er s u rp l u s ch an g es i n u s ed c ar mark et s mak e u p n e arl y h al f o f t h e g ro s s

w el f are co s t s o f an i n creas e i n t h e C A F E s t an d ard

. T h es e effe ct s fal l d i s p ro p o rt i o n at el y o n l o w

i n co me h o u s eh o l d s

. Co n t r ary t o p rev i o u s fi n d i n g s

, t h e o v eral l w el fa re co s t s ar e r eg res s i v e.

* D ep art men t o f E co n o mi cs

, 9 5 0 0 G i l man D ri v e, L a J o l l a, C A 9 2 0 9 3

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. E mai l :

m3 j aco b s @ u cs d

. ed u

. I t h an k L a w ren ce G o u l d er

, T i mo t h y Bres n ah an

, L i r an E i n av

, F ran k W o l ak

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an d s emi n a r p a rt i ci p an t s fo r t h ei r h el p fu l s u g g es t i o n s

. Fi n an ci al s u p p o rt fo r t h i s w o rk f ro m t h e

B. F. H al ey an d E

. S. Sh a w Fel l o w s h i p Fu n d i s g rat e fu l l y ack n o w l ed g ed

.1 1. I n t r od u c t i on

G a s ol i ne us e i n t he U ni t e d S t a t e s i s a s s oc i a t e d w i t h c ons i de r a bl e e xt e r na l c os t

, l a r ge l y

a s s oc i a t e d w i t h e nvi r onm e nt a l a nd ge opol i t i c a l c o nc e r ns

. T he s e i nc l ude e c onom i c a nd

s e c ur i t y r i s ks a s s oc i a t e d w i t h oi l i m por t s a s w e l l a s t he i m pl i c a t i ons o f c l i m a t e c ha nge a nd

l oc a l a i r pol l ut i on. R e gul a t i on t a r ge t e d t ow a r d t he r e duc t i on of ga s ol i ne c ons um pt i on w a s

i nt r oduc e d f ol l ow i ng t he 1973 oi l c r i s i s

, i n t he f o r

m of t he c or por a t e a ve r a ge f ue l e c onom y

( C A F E ) s t a nda r ds

. 1 T he s e s t a nda r ds i m pos e a l i m i t on t he a ve r a ge f ue l e c onom y of t he

ve hi c l e s s ol d by a pa r t i c ul a r c om pa ny i n e a c h ye a r

, w i t h s e pa r a t e l i m i t s f or pa s s e nge r c a r s a nd

l i ght dut y t r uc ks

.

S ubs t a nt i a l i nc r e a s e s i n t he s t r i nge nc y of U

. S

. f ue l e c onom y s t a nda r ds a r e pl a nne d f or

t he pe r i od 2010 t o 2020

, c o r r e s pondi ng t o t he gr o w i ng s a l i e nc e of c onc e r ns a s s oc i a t e d w i t h

ga s ol i ne us e

. 2 T hi s pa pe r c ont r i but e s a n e m pi r i c a l e xa m i na t i on of t he a c t i ons a ut om obi l e

pr oduc e r s t a ke t o m e e t f ue l e c onom y s t a nda r ds a nd m e a s ur e s t he w e l f a r e c os t a s s oc i a t e d w i t h

a n i nc r e a s e i n t he s t r i nge nc y o f C A F E

. I e xa m i ne t he m e c ha ni s m s t hr ough w hi c h t he

s t a nda r ds w or k, a nd m ode l di s t r i but i ona l i m pl i c a t i ons a c r os s bot h pr oduc e r s a nd c ons um e r s

.

A num be r o f pr i o r s t udi e s ha ve c ons i de r e d f ue l e c onom y s t a nda r ds i n t he c on t e xt of

c om pa r i ng a l t e r na t i ve pol i c y i ns t r um e nt s : P a r r y e t a l

. ( 2007) pr ovi de a s ur ve y a nd di v i de

a

ut om obi l e r e l a t e d e xt e r na l i t i e s i n t o t hos e a r i s i ng f r om ga s ol i ne us e a nd t hos e f r om m i l e s

dr i ve n, s how i ng t ha t ga s ol i ne t a xe s r e duc e a g r e a t e r num be r of i m p or t a nt e xt e r na l i t i e s t ha n do

C A F E s t a nda r ds

. 3 F ur t he r m o r e

, t he or y s ugge s t s t ha t ga s ol i ne t a xe s a r e s upe r i or t o f ue l

e c onom y s t a nda r ds e ve n w he n c ons i de r i ng t he ga s ol i ne e xt e r na l i t y i n i s ol a t i on. P r i c i ng t he

e xt e r na l i t y di r e c t l y a l l ow s m or e f l e xi bi l i t y i n t ha t t a xe s bot h r e duc e m i l e s dr i ve n a nd

i nf l ue nc e ve hi c l e c hoi c e w hi l e C A F E s t a nda r ds op e r a t e onl y on t he l a t t e r c ha nne l

. 4 I of f

e r

1 Imp o rt an t rat i o n al es fo r C A F E reg u l at i o n i n ad d i t i o n t o a r ed u ct i o n i n g as o l i n e u s e i n cl u d e

p ro t ect i o n i s m an d t h e co rr ect i o n o f ma rk et f ai l u res i n d eman d fo r fu el eco n o my

. Po rt n ey et al

. (2 0 0 3 )

p ro v i d e a d i s cu s s i o n o f t h e m ark et fai l u re rat i o n al e. G o l d b erg (1 9 9 8 ) d i s cu s s es p ro t e ct i o n o f t h e

d o mes t i c au t o mo b i l e i n d u s t ry

.

2 2 0 0 8 av er ag e fu el eco n o my i n t h e U

. S

. w as 2 7

. 0 mp g ( N H T S A 2 0 0 9 a)

. T h e E n erg y In d ep en d en c e

an d Se cu ri t y A ct o f 2 0 0 7 r eq u i res an i n cr eas e t o 3 5

. 0 m p g b y 2 0 2 0

. A 2 0 0 9 W h i t e H o u s e

an n o u n cem en t cal l s fo r ev en s t ri ct er reg u l at i o n t o 3 5

. 5 mp g b y 2 0 1 6 ( E P A 2 0 0 9 ).

3 Fo r ex a mp l e fu el e co n o my s t an d a rd s d o n o t d i re ct l y ad d res s au t o mo b i l e acci d en t s o r co n g es t i o n

.

4 C A F E s t an d ard s m ay i n cr eas e mi l es d ri v en s i n ce effi ci en t cars ar e ch eap e r t o o p er at e. Sm al l an d

V an D en d e r (2 0 0 7 ) fi n d t h at t h i s reb o u n d eff ect can o ff s et 5

- 1 0 % o f t h e g as o l i n e s av i n g s f ro m C A F E

.2 c onf i r m a t i on t ha t t hi s r a nki ng hol ds i n m y m ode l

, but t he f oc us o f m y pa pe r l i e s i ns t e a d w i t h

t he m e c ha ni s m s a nd di s t r i but i ona l i m pl i c a t i ons o f C A F E i n pa r t i c ul a r

.

T hi s r e qui r e s e xpl i c i t l y m ode l i ng p r oduc e r be ha vi or unde r C A F E

, bui l di ng on a

l i t e r a t ur e f oc us e d on pr oduc e r r e s pons e t o r e gul a t i on: A us t i n a nd D i na n ( 2005 ) c ons i de r a

r e pr e s e nt a t i ve c a r pr oduc e r t ha t f a c e s a r e gu l a t o r y f ue l e c onom y c ons t r a i nt

. U s i ng de m a nd

e l a s t i c i t i e s f r om t he l i t e r a t ur e

, t he y e s t i m a t e t he c ha nge s i n ve hi c l e f l e e t t ha t r e s ul t a nd

c ons i de r s ur pl us c ha nge s i n t he m a r ke t f or ne w c a r s

. G ol dbe r g ( 1998) de ve l ops a n ol i gopol y

m ode l of p r oduc e r be ha vi o r a nd c ons i de r s t he i m p l i c a t i ons of C A F E f or i nt e r na t i ona l t r a de

. 5

K l e i t ( 2004) de ve l ops a m ode l ba s e d on G e ne r a l M ot or s ’ r e s pons e t o C A F E

, m ode l i ng p r i c i ng

be ha vi or

. S i m i l a r l y, G r e e ne ( 1991) c ons i de r s t he pr i c i ng a nd f l e e t m i x be ha vi or o f U

. S

.

dom e s t i c f i r m s i n r e s pons e t o C A F E s t a nda r ds

. 6

A nde r s on a nd S a l l e e ( 2009 ) a l s o c ons i de r pr od uc e r r e s pons e

, but i ns t e a d of f oc us i ng

on pr i c e s a nd f l e e t s t he y e xa m i ne a l oophol e i n t he r e gul a t i on. T he y f i nd e vi de nc e t ha t f i r m s

ha ve f a i l e d t o t a ke f ul l a dva nt a ge of t he l oophol e i n s pi t e of i t s ve r y l ow c os t

. T hi s s ugge s t s

t ha t t he c ur r e nt s t a nda r d, a t l e a s t i n r e c e nt ye a r s w he n ga s ol i ne pr i c e s a r e hi gh, m a y be a l m os t

non

- bi ndi ng. 7 I n c ont r a s t

, m y w o r k c e nt e r s a r ound a pe r i od of l ow ga s ol i ne p r i c e s i n t he l a t e

1990’ s w he r e I f i nd t ha t t he r e gul a t i on s ubs t a nt i a l l y i nf l ue nc e d f i r m be ha vi o r

. T he e f f

e c t s

dur i ng t hi s pe r i od a l l ow i ns i ght i nt o how pr oduc e r s a nd c ons um e r s m a y r e s pond t o m o r e

s t r i nge nt r e gul a t i on l i ke t ha t c u r r e nt l y be i ng a dopt e d.

I a ddr e s s t hr e e m a i n c ha l l e nge s unm e t i n t he a bove l i t e r a t ur e

. F i r s t i s t he t r e a t m e nt of

he t e r oge ne ous r e s pons e a c r os s f i r m s

, w hi c h ha s be e n m a s ke d by t he r e p r e s e nt a t i ve pr oduc e r

m ode l us e d i n ne a r l y a l l p r i or s t udi e s

. G ol dbe r g ( 1 998) t a ke s a n i m po r t a nt s t e p, m ode l i ng

c e r t a i n f i r m s a s pa yi ng t he pe na l t i e s a s s oc i a t e d w i t h vi ol a t i on. M y m ode l i nc l ude s t hi s gr oup

of f i ne

- pa yi ng f i r m s but a l s o e nc om pa s s e s t he be ha vi or of a s e pa r a t e

, c e nt r a l gr oup i nc l udi ng

F or d, G M

, a nd C hr ys l e r : I a r gue t ha t t he s e f i r m s d o not vi ol a t e t he s t a nda r d o r pa y a ny f i ne s

,

but i ns t e a d f a c e a s ha dow c os t i n m e e t i ng t he c ons t r a i nt

. I n c ont r a s t t o t he l i t e r a t ur e

, I m ode l

5 T h e p ro d u c er mo d el i s b as ed o n d em an d el as t i ci t i es es t i mat ed i n G o l d b erg (1 9 9 5 ).

6 L i k e A u s t i n an d D i n an (2 0 0 5 ), G re en e d ev el o p s a mo d el t o p red i ct t h e co s t o f reg u l at i o n s t art i n g

fro m an u n d i s t o rt ed s t at e b u t d o es n o t ex a mi n e e mp i ri cal p ro d u cer res p o n s e d i rect l y

.

7 A g en cy p ro b l ems o r mark et fai l u res w i t h i n t h e fi r m mi g h t al s o acco u n t fo r a f ai l u re t o t ak e fu l l

ad v an t ag e o f t h e l o o p h o l e, w h i ch i n v o l v es re w ard s fo r t h e p ro d u ct i o n o f fl ex

- fu el v eh i cl es

.3 t he he t e r oge ne ous be ha vi or of t he s e f i r m s i n a s i ng l e f r a m e w or k a nd pr ovi de e m pi r i c a l

e s t i m a t e s of s ha dow c os t f or f i r m s t ha t c hoos e t o j us t m e e t t he c ons t r a i nt

.

A s e c ond unm e t c ha l l e nge i s t he s i m ul t a ne ous m e a s ur e m e nt of w e l f a r e e f f

e c t s a c r os s

m a r ke t s f or ve hi c l e s a nd ga s ol i ne

. T he l i t e r a t ur e o n C A F E ha s ge ne r a l l y pr e s e nt e d m e a s ur e s

of c ons um e r s ur pl us i n i ndi vi dua l c a r m a r ke t s

. S t u di e s of ga s ol i ne pr i c e s e ns i t i vi t y

ne c e s s a r i l y c ons i de r ut i l i t y i n ga s ol i ne m a r ke t s a s w e l l

, but ha ve t ypi c a l l y e s t i m a t e d t he t w o

de m a nd e qua t i ons s e pa r a t e l y. 8 I n c ont r a s t

, I m a ke us e of r e c e nt w or k i n B e nt o e t a l

. ( 2009 ) t o

a l l ow c ons i s t e nt e qui l i br i um w e l f a

r e a na l ys i s a c r os s m a r ke t s

. 9 I f u

r t he r i nt e gr a t e m y m ode l o f

pr oduc e r pr o f i t s unde r C A F E

, a l l ow i ng a m e a s ur e of ove r a l l e qui va l e nt va r i a t i on i n a n

e qui l i br i um s e t t i ng.

T he t hi r d m a i n c ha l l e nge I a ddr e s s c onc e r ns t he m a r ke t f or us e d c a r s

. A l l p r i or

e m pi r i c a l s t udi e s of C A F E t o m y know l e dge ha ve f oc us e d on t he m a r ke t f or ne w ve hi c l e s

, but

r e gul a t i ons i nf l ue nc i ng ne w c a r pr oduc t i on ne c e s s a r i l y ha ve dyna m i c e f f

e c t s on us e d c a r

m a r ke t s t hr ough t i m e

. I m ode l t he e f f

e c t s a s ne w c a r s be c om e us e d, c a pt ur i ng p r e vi ous l y

ove r l ooke d w e l f a r e i m p l i c a t i ons of a c ha ngi ng us e d c a r f l e e t

.

M y m a i n r e s ul t s r e f l e c t t he s e i nnova t i ons

. I e xa m i ne t he e f f

e c t s of C A F E a t t he

m a nuf a c t ur e r l e ve l a nd f i nd t ha t a l m os t a l l pr o f i t i m pa c t s of t he c ur r e nt s t a nda r d a r e f e l t by

dom e s t i c f i r m s

. A ke y m e c ha ni s m be hi nd t hi s r e s ul t i s s ubs t i t ut i on i n t he m a r ke t f or l a r ge

,

hi gh

- hor s e pow e r ve hi c l e s : W he n dom e s t i c f i r m s c ut pr oduc t i on of t he s e ve hi c l e s i n o r de r t o

m e e t t he s t a nda r d, t he unc ons t r a i ne d a nd f i ne

- pa yi ng f i r m s w i l l i nc r e a s e pr oduc t i on i n t he i r

pl a c e

. T he s ubs t i t ut i on pa t t e r n pr ot e c t s f i ne

- pa yi ng f i r m s f r om pr of i t i m pa c t s a nd a l s o ha r m s

t he e f f i c a c y of C A F E i n r e duc i ng ga s ol i ne us e

. 1 0 I m por t a nt pol i c y s t e ps t ow a r d a ha r m oni z e d

s t a nda r d m a y be a bl e t o m i t i ga t e t hi s e f f

e c t

.

A t t he a ggr e ga t e l e ve l

, I f i nd t ha t a 1 m i l e

- pe r

- ga l l on i nc r e m e nt t o t he s t r i nge nc y o f

C A F E r e duc e s l ong r un ga s ol i ne us e by 3 %

. S ho r t r un e f f

e c t s a r e m uc h s m a l l e r

,

8 Fo r ex a mp l e G o l d b erg (1 9 9 5 ) an d W es t (2 0 0 4 ) es t i mat e d e man d fo r v eh i cl es an d g as o l i n e s ep ar at el y

,

co rrect i n g fo r t h e s i mu l t an ei t y w i t h t h e t ech n i q u e i n t ro d u ced b y D u b i n an d McF ad d en

.

9 T h e d e man d eq u at i o n fo r mi l es i s d eri v ed u s i n g Ro y ’s i d en t i t y an d t h e co n d i t i o n al i n d i rect u t i l i t y

fu n ct i o n d e s cri b i n g v eh i cl e ch o i ce. A s i n g l e s et o f u t i l i t y p ara met ers res u l t s t h at c an b e u s ed t o d e ri v e

a m eas u re o f eq u i v al en t v ari at i o n

.

1 0 T h e d eg ree o f i mp er fect s u b s t i t u t i o n i n t h e l u x u ry v eh i cl e mark et co n t ro l s t h e ex t en t t o w h i ch g ai n s

i n d o mes t i c av erag e fu el eco n o my a re o ffs et

.4 de m ons t r a t i ng t he s i gni f i c a nc e of e xpl i c i t l y m ode l i ng t he gr a dua l pe ne t r a t i on o f f ue l e c onom y

s t a nda r ds t hr ough t he us e d c a r f l e e t

. I f i nd t ha t t he a ggr e ga t e w e l f a r e c os t s a s s oc i a t e d w i t h

t he s e ga s ol i ne s a vi ngs a r e a bout s i x t i m e s l a r ge r f o r a C A F E s t a nda r d t ha n a c om pa r a bl e

ga s ol i ne t a x. 1 1

F i na l l y, one of m y m o r e s t r i ki ng c onc l us i ons i s t ha t t he pr og r e s s i vi t y of a C A F E

s t a nda r d c a n be ove r t ur ne d by l ong r un e f f

e c t s i n t he us e d c a r m a r ke t

. T he i ni t i a l l y

pr ogr e s s i ve a s pe c t of t he s t a nda r d i s i nt u i t i ve a nd c onf i r m e d he r e : w e a l t hi e r hous e hol ds t e nd

t o buy m o r e ne w ve hi c l e s

, a nd t hus be a r m uc h of t he i ni t i a l bu r de n. I f i nd

, how e ve r

, t ha t

c ha nge s i n us e d c a r pr i c e s ove r t i m e a nd l ong r un s hi f t s i n t he c om pos i t i on of t he us e d c a r

f l e e t e ve nt ua l l y ove r w he l m t hi s

, m a ki ng t he t o t a l e f f

e c t r e gr e s s i ve

. P r i o r s t udi e s of f ue l

e c onom y r e gul a t i on ha ve ove r l oo ke d t hi s r e s u l t w i t h t he i r f oc us on ne w c a r m a r ke t s a nd a

r e pr e s e nt a t i ve c ons um e r

.

T he r e s t of t he pa pe r i s or ga ni z e d a s f ol l ow s

. S e c t i on 2 de s c r i be s t he C A F E r e gul a t i on

a nd i nt r oduc e s t he m ode l

. S e c t i on 3 de m ons t r a t e s t he i m por t a nc e of f i r m he t e r oge ne i t y a nd

c a t e g or i z e s f i r m s e m pi r i c a l l y. S e c t i on 4 de s c r i be s a n e s t i m a t i on pr oc e dur e us i ng f i r s t o r de r

c ondi t i ons on f i r m be ha vi or

. S e c t i on 5 of f

e r s a n a l t e r na t i ve s our c e of e vi de nc e f or f i r m

pr i c i ng be ha vi or

. T he w e l f a

r e a nd di s t r i bu t i ona l i m pa c t s of a c ha nge i n C A F E pol i c y a r e

m e a s ur e d i n S e c t i on 6 us i ng t he e s t i m a t e d pa r a m e t e r s

. C onc l us i ons a r e of f

e r e d i n S e c t i on 7

.

2. R e gu l at i o n an d M od e l of P r od u c e r B e h avi or

a. F u e l E c on om y R e gu l at i on

C A F E s t a nda r ds a r e e nf or c e d a t t he l e ve l of a m a n uf a c t ur e r ’ s f l e e t of ne w v e hi c l e s i n a

gi ve n m ode l ye a r

. E a c h m a nuf a c t ur e r ’ s pr oduc t i o n i s di vi de d i nt o t w o s e pa r a t e l y r e gul a t e d

1 1 A u s t i n an d D i n an (2 0 0 5 ) i s t h e o n l y s t u d y t o my k n o w l ed g e t o o ff er co mp a rab l e es t i mat es

. T h ey

ap p ro x i mat e co n s u me r s u rp l u s ch an g es u s i n g n e w ca r a n d g as o l i n e d em an d el as t i ci t i es b u t d o n o t

i n cl u d e u s ed ca r mark et s o r i n t eg r at e d e m an d s i n a u t i l i t y fra me w o rk

. T h e fi n d t h at g as o l i n e t ax es

h av e 6 0 t o 7 0 % l es s d i s t o rt i o n ary co s t t h an an eq u i v al e n t C A F E s t an d ard

.5 f l e e t s : pa s s e nge r c a r s a nd l i ght dut y t r uc ks

. 1 2 T he r e gul a t i on de f i ne s a f i r m ’ s c o r por a t e

a ve r a ge f ue l e c onom y, f or e a c h of t he t w o f l e e t s

, a s :

( 1 )

w he r e q j i s t he qua nt i t y of m ode l j pr oduc e d by t he f i r m a nd m pg j i s t ha t m ode l ’ s f ue l

e c onom y m e a s ur e d i n m i l e s

- pe r

- ga l l on

. T he s um m a t i on i s t a ke n ove r a l l m ode l s i n t he f l e e t

.

T he 2009 l i m i t w a s 27

. 5 m pg f or pa s s e nge r c a r s a nd 23. 1 m pg f o r l i ght dut y t r uc ks

.

T he pa s s e nge r c a r s t a nda r d ha s be e n he l d c ons t a nt a t 27. 5 m pg f o r e ve r y ye a r s i nc e 1990

.

T he l i ght t r uc k s t a nda r d ha s i nc r e a s e d gr a dua l l y ov e r t i m e but

, c onve ni e nt f or m y a na l ys i s

,

w a s he l d f i xe d a t 20

. 7 m pg i n a l l ye a r s be t w e e n 19 96 a nd 2004. T he r u l e s a l l ow f o r t he

ba nki ng of “ c r e di t s

, ” de f i ne d i n t e r m s o f qua nt i t y w e i ght e d de vi a t i ons f r om t he s t a nda r d, f or

up t o t h r e e ye a r s

. F or e xa m pl e

, i f t he f i r m ’ s c a r f l e e t ha s a f ue l e c onom y of 28

. 5 m pg i t

a c c um ul a t e s c r e di t t ha t c a n be us e d t o of f

s e t a 26. 5 m pg f l e e t i n a ny of t he ne xt t hr e e ye a r s

. 1 3

S i m i l a r l y, t he f i r m m a y bo r r ow a ga i ns t f ut ur e c r e d i t s

, a s l ong a s i t r e pa ys t he de bt w i t hi n t hr e e

ye a r s

. I f t he f i r

m f a i l s t o r e pa y a de bt w i t h i n t h r e e ye a r s i t i s f ound i n vi o l a t i on of t he

r e gul a t i on a nd a s s e s s e d a f i ne of $50 f or e a c h m i l e pe r ga l l on be l ow t he s t a nda r d m ul t i pl i e d

by t he t ot a l num be r o f ve hi c l e s i n t he f l e e t

. T he f i ne w a s i nc r e a s e d t o $55 a f t e r t he e nd of m y

s a m pl e pe r i od.

T he ba nki ng a nd bor r ow i ng s c he m e pr oduc e s a c o m pl e x s e t of dyna m i c i nc e nt i ve s f or

t he f i r m

. I n pa r t i c ul a r

, i t c a n be s how n t ha t a de c i s i on m a de i n t he c ur r e nt pe r i od c a n a f f

e c t

t he f i r m i n a l l f ut u r e pe r i ods a nd c onve r s e l y t ha t a f i r m ’ s r e gul a t or y c om pl i a nc e s t a t us i n t he

c ur r e nt pe r i od c a n de pe nd on t he e nt i r e hi s t or y. T hi s i s t r ue i n s pi t e of t he t h r e e ye a r

e xpi r a t i on of c r e di t s a nd i s de m ons t r a t e d i n A ppe n di x B

. T he dyna m i c f e a t ur e s o f t he

r e gul a t i on ge ne r a t e e f f

e c t i ve va r i a t i on i n t he s t r i ng e nc y of t he s t a nda r d t hr ough t i m e

. S e c t i on

1 2 T h e r eg u l at i o n s u b d i v i d es t h e p as s en g er car fl e et i n t o t h o s e p ro d u ced mo r e an d l es s t h an 7 5 %

d o mes t i cal l y

. W h i l e t h i s d i v i s i o n may h av e h ad s o me i mp act i n i t i al l y

, fi r ms h av e s i n ce b een ab l e t o

eq u al i ze t h e fu el eco n o my o f t h e t w o g ro u p s o f p as s en g er c ars w i t h o u t m aj o r s t ru ct u ral ch an g es ( N RC

, 2 0 0 2 ). T h e e as e o f mo v i n g cars ab o v e an d b el o w t h e “i mp o rt ” t h r es h o l d an d t h e l a ck o f co mp l et e d at a

o n t h e fr act i o n o f d o mes t i c p art s i n e ach v eh i cl e l ead m e t o co n s i d er p as s en g er ca rs as a s i n g l e g ro u p

.

1 3 T h e ex amp l e as s u m es t h at t h e o v eral l s al es o f t h e fi r m are t h e s a me i n t h e t w o y e ars

, s i n ce t h e

n u mb er o f c red i t s ea rn ed i s w ei g h t ed b y q u an t i t y

.6 5 e xpa nds on t he de t a i l s of t hi s va r i a t i on a nd p r ovi de s a r e duc e d f or m e m pi r i c a l a na l ys i s of

pr oduc e r pr i c i ng r e s pons e

.

b

. M od e l of P r od u c e r B e h avi or

A ut om obi l e pr oduc e r s a r e a s s um e d t o be ol i gopol i s t s i n a di f f

e r e nt i a t e d pr oduc t s

m a r ke t a nd e qui l i b r i um i s de f i ne d a s a s e t of pr i c e s s uc h t ha t e a c h f i r m i s m a xi m i z i ng pr o f i t s

gi ve n t he a c t i ons of a l l ot he r s

. 1 4 F i r m s a r e t r e a t e d c ons i s t e nt l y i n t ha t he t e r oge ne i t y e nt e r s

onl y t hr ough pa r a m e t e r s

. T he m a xi m i z a t i on p r obl e m s pe c i f i e d he r e i s w r i t t e n i n t e r m s of a n

i ndi vi dua l f i r m c ondi t i ona l on t he be ha vi or o f i t s c om pe t i t or s

.

I nt r oduc i ng C A F E r e gul a t i on i nt o t he f i r m ’ s p r of i t f unc t i on i nvol ve s m ode l i ng t he

c os t a s s oc i a t e d w i t h a vi ol a t i on of t he s t a nda r ds

. I w i l l a s s um e t ha t t hi s c os t c om e s f r om t w o

s our c e s : T he f i r s t i s t he f i ne l e vi e d by t he r e gul a t o r

, w hi c h va r i e s l i ne a r l y w i t h t he de gr e e of

vi ol a t i on. T he s e c ond i s a f i xe d c os t o f vi o l a t i on, e nc om pa s s i ng t he l e ga l

, pol i t i c a l

, a nd

c or por a t e i m a ge l os s e s a l s o r e s ul t i ng f r o m i nf r a c t i ons

.

A ve nue s f or c om pl i a nc e w i t h C A F E r e gul a t i on w i l l be ba l a nc e d a ga i ns t t he c os t s of a

vi ol a t i on. C om pl i a nc e i nvol ve s s e l l i ng m or e hi gh

- e f f i c i e nc y ve hi c l e s ( a nd f e w e r l ow

e f

f i c i e nc y one s ) a s a f r a c t i on of t he t o t a l

, w hi c h I c a pt ur e t hr ough t he f i r m ’ s c hoi c e o f p r i c e i n

a B e r t r a nd s e t t i ng. I n t he l ong

- r un

, f i r m s w i l l a l s o i nve s t i n ne w t e c hnol ogi e s

. 1 5 I do not

e s t i m a t e a t e c hnol ogi c a l f r ont i e r di r e c t l y i n t he m o de l

, but a m a bl e t o c ons i de r t he r ol e o f

t e c hnol ogy i n a n e xt e ns i on t o t he ove r a l l w e l f a r e a na l ys i s

. 1 6

W i t h t he s e c om pone nt s I m ode l e a c h f i r m a s m a xi m i z i ng pr of i t ne t o f t he c os t s of

vi ol a t i on, s ol vi ng:

( 2 )

1 4 T h e p ri c es o f o t h er fi rms en t er t h ro u g h res i d u al d e man d

. A l l el s e eq u al

, an i n cre as e i n t h e p ri c e o f a

car b y o n e fi rm s h i ft s t h e r es i d u al d em an d f aced b y o t h er fi r ms o u t w a rd

.

1 5 K l i er an d L i n n (2 0 0 8 ) co n s i d er t h e q u es t i o n o f t ech n o l o g y an d fu el eco n o my s t an d ard s

, ex ami n i n g a

“med i u m

- ru n ” cas e w h e re t e ch n o l o g y en t ers w i t h an i n t ermed i at e s co p e

.

1 6 My ex t en s i o n o f t h e mo d el t o i n cl u d e t e ch n o l o g y fo l l o w s A u s t i n an d D i n an (2 0 0 5 )

. T h e ex t en s i o n

rel i es o n t h e g en er al res u l t t h at co s t

- mi n i mi zi n g f i r ms e q u al i ze t h e marg i n al co s t s o f co mp l i an c e

acro s s av ai l ab l e ch an n el s

. Fo r an ex p l an at i o n i n t h e s p eci fi c co n t ex t o f fu el e co n o my s ee A n d ers o n

an d Sal l e e (2 0 0 9 )

.7 w he r e p j , c j , a nd q j a r e r e s pe c t i ve l y t he pr i c e

, c os t

, a nd qua nt i t y of a pa r t i c ul a r m ode l j m a de

by f i r m i

. J i s t he s e t o f a l l c a r s m a de m y f i r

m i

. P i s t he ve c t or of pr i c e s of a l l c a r s i n t he

m a r ke t

, a nd Q i r e f e r s t o t he qua nt i t i e s of a l l m ode l s m a nuf a c t ur e d by f i r m i

. I i s a n i ndi c a t or

f unc t i on t a ki ng t he va l ue of 1 i f t he f i r m i s i n vi ol a t i on of t he s t a nda r d a nd 0 ot he r w i s e

. T he

f unc t i ons F C a nd F T r e pr e s e nt t he f i ne s f a c e d f or t h e c a r a nd t r uc k f l e e t s r e s pe c t i ve l y. H i

r e pr e s e nt s t he f i r m

- s pe c i f i c c om pone nt of c os t t ha t i s f i xe d c ondi t i ona l on vi ol a t i on.

T he l e ve l of t he f i ne s de pe nds o n f l e e t s i z e a nd de vi a t i on f r om t he s t a nda r d

. I us e t he

f unc t i ona l f or

m di r e c t l y f r om t he r e gul a t i on, w hi c h i s a dm i ni s t e r e d by t he N a t i ona l H i ghw a y

T r a f f i c S a f e t y A dm i ni s t r a t i on ( N H T S A ) :

( 3 )

w he r e d

c a r

f l e e t i s t he l e ve l of t he s t a nda r d f or t he m a nuf a c t ur e r ’ s c a r f l e e t

, 27. 5 m i l e s pe r

ga l l on, a nd C A F E

c a r

f l e e t t he c or por a t e a ve r a ge f ue l e c onom y f or t he f i r m ’ s c a r f l e e t a s de f i ne d

i n ( 1 )

. N ot e t ha t f l e e t f ue l e c onom y i s c om put e d a s t he h a r m oni c m e a n i n or de r t o m a t c h t he

N H T S A r ul e pr e c i s e l y. T he e xp r e s s i on f or t he l i g ht dut y t r uc k f l e e t

, F T

, i s a na l ogous w i t h t he

s t a nda r d f i xe d a t 20

. 7 i n 2001.

T he f i r m l e ve l f i xe d c om pone nt s o f c os t

, H i , r e pr e s e nt ot he r l os s e s t ha t a r e i nc u r r e d

w he n vi ol a t i ng t he r e gul a t i on. 1 7 C or po r a t e publ i c i m a ge a nd l e ga l l i a bi l i t y f o r e nvi r onm e nt a l

da m a ge m a y be i m por t a nt f a c t or s

. A f i r m ’ s pol i t i c a l c a pi t a l

, va l ua bl e i n t i m e s o f f i na nc i a l

di s t r e s s or w he n ne got i a t i ng s t r i nge nc y o f r e gul a t i on, c oul d a l s o be e r ode d by vi ol a t i ons

.

A l l ow i ng t he m a gni t ude of t he s e c os t s t o va r y a c r o s s f i r m s i s i m por t a nt : F or e i gn c om pa ni e s

m a y ha ve l e s s e xpos ur e t o U

. S

. e nvi r onm e nt a l l a w s ui t s or l e s s ne e d f or U

. S

. pol i t i c a l c a pi t a l

.

S i m i l a r l y, f i r m s t ha t s pe c i a l i z e i n h i gh pe r f or m a n c e c a r s m a y be l e s s a ve r s e t o a r e put a t i on f or

e nvi r onm e nt a l vi ol a t i ons t ha n a r e f ul l

- l i ne a ut om a ke r s

.

1 7 So me o f t h es e co s t s m ay b e arg u ed t o v ary w i t h t h e s e v eri t y o f v i o l at i o n

. T h e d i s t i n ct i o n i s

i rrel ev an t fo r t h e p u rp o s es o f es t i mat i n g t h e s h ad o w co s t o f fi r ms n ev e r o b s erv ed t o v i o l at e t h e

s t an d ard

. It co u l d

, h o w ev e r, s o me w h at i n fl u en ce t h e g r o u p o f fi r ms o b s erv ed t o v i o l at e s i n ce t h ey

mu s t w ei g h t h e d eg re e t o w h i ch t h ey f al l b el o w t h e s t a n d ard

.8 T he s e c os t s a r e di f f i c ul t t o m e a s ur e di r e c t l y, s o i n w or ki ng w i t h t he m ode l I m us t r e l y

on t w o ke y a s s um pt i ons t o bound H i : i ) F or f i r m s t ha t ha ve c om pl i e d hi s t or i c a l l y t he c os t s i n

H

i a r e a t l e a s t l a r ge e nough t o j us t i f y t he i r de c i s i on. i i ) F or f i r

m s r e gul a r l y f ound i n vi ol a t i on

of t he s t a nda r d t he c os t s a r e s m a l l e nough t ha t t he vi ol a t i on i s c ons i s t e nt w i t h pr o f i t

m a xi m i z a t i on.

A f i na l i m po r t a nt s i m pl i f i c a t i on i s t ha t t he i nd i c a t or f o r vi ol a t i ons

, I

, i s de f i ne d f o r a

s i ngl e ye a r i n a s t a t i c ve r s i on of t he pr ob l e m w he r e a s t he r e gul a t i on i n f a c t a l l ow s ba nki ng

a nd bor r ow i ng of c r e di t s

. A dyna m i c m ode l

, a s s how n i n A ppe ndi x B

, i nvol ve s opt i m i z a t i on

ove r a l l ye a r s s i m ul t a ne ous l y w i t h a s t a t e s pa c e de pe ndi ng on t he f i r m ’ s e nt i r e h i s t or y. 1 8 T he

a

ppr oxi m a t i on t o r e qui r e c om pl i a nc e i n a s i ngl e ye a r bot h p r ovi de s a t r a c t a bl e m ode l a nd i s

c ons i s t e nt w i t h a dyna m i c a l l y opt i m i z i ng f i r m ’ s be ha vi or i n a pe r i od of s t a bl e de m a nd w i t h

c onve x c os t s of c om pl i a nc e

. 1 9

Sol v i ng f or F i r

m B e hav i or

E qua t i on ( 2 ) c a n be di vi de d i nt o t hr e e c a s e s

, de pe ndi ng on t he s t a t e of t he i ndi c a t or I

.

I n t he f i r s t c a s e

, I i s e qua l t o 0 a t t he unc ons t r a i ne d opt i m um s how n be l ow

. I n ot he r w o r ds

, i f

t he f i r m m a xi m i z e s pr of i t s w i t hout r e ga r d t o I i t w i l l a l r e a dy m e e t o r e xc e e d t he s t a nda r d.

T he m a xi m i z a t i on p r obl e m i n ( 2 ) c a n t he n be r e du c e d t o a s t a nda r d m ul t i

- pr oduc t pr of i t

m a xi m i z a t i on pr obl e m s ubj e c t t o t he r e s i dua l de m a nd c ur ve s gi ve n by t he q j ’ s :

( 4 )

I n t he s e c ond c a s e

, t he m a xi m um i n ( 2 ) i s r e a c he d w he n I i s e qua l t o 1

. P r of i t s a r e

m a xi m i z e d w he n t he f i r m i s vi ol a t i ng t he s t a nda r d a nd pa yi ng a l l a s s oc i a t e d c os t s

. A f t e r

r e pl a c i ng I a nd e l i m i na t i ng c ons t a nt t e r m s ( 2 ) r e du c e s t o:

1 8 It may s e em t h at co mp l i an ce s t at e co u l d b e d et e rmi n ed v i a a mo v i n g s et o f s ev en

- y ea r w i n d o w s

, an

al read y d i f fi cu l t i n t ert emp o r al p ro b l em

, b u t i n fact t h e acco u n t i n g o f c red i t s an d d eb i t s can l e ad t o

d ep en d en ce o n t h e en t i re h i s t o ry

.

1 9 Co n v ex i t y o f co mp l i an c e co s t s ( w h i ch fo l l o w s fro m s t an d ard as s u mp t i o n s o n t h e mu l t i

- p ro d u ct

d eman d s y s t em) cau s es t h e co s t o f r ep ay i n g b o rro w ed c red i t s t o ex ce ed t h e i n i t i al g ai n

. N o t e al s o t h at

t h i s i s ab s en t d i s co u n t i n g : In a mo d el t h at p ermi t s b o r r o w i n g

, a fi rm w o u l d l i k e t o b o rro w i n t h e earl y

y ears o f t h e r eg u l at i o n an d p ay b ack l at e, l et t i n g t h e v al u e o f t h e p er mi t s ri s e w i t h t h e d i s co u n t rat e

. In

t h e cas e o f C A F E

, h o w ev er

, t h e t h ree

- y ear l i mi t o n b o r ro w i n g mi t i g at es t h e i mp o rt an ce o f t h i s e ffe ct

.9 ( 5 )

I n t he t h i r d c a s e

, t he m a xi m um i n ( 2) i s r e a c he d w h e n t he f i r m i s j us t c om pl yi ng w i t h

t he s t a nda r d. I n o t he r w or ds

, I i s e qua l t o 0 bu t a n y s m a l l r e duc t i on i n f ue l e c onom y w oul d

c a us e t he f i r m t o vi ol a t e t he s t a nda r d. T he s ol ut i o n t o ( 2 ) f or a c ons t r a i ne d f i r m c a n be

w r i t t e n a s t he m a xi m i z a t i on:

( 6 )

w he r e t he c ons t r a i nt a bove i s t he de f i ni t i on of

. F o r e c onom y of not a t i on I ha ve

om i t t e d t he c a s e w he r e a f i r m m a y be c ons t r a i ne d i n one f l e e t but not t he ot he r

, a l t hou gh t hi s

pos s i bi l i t y i s c ons i de r e d i n bot h t he e s t i m a t i on a nd pol i c y s i m ul a t i ons

.

T he f i r s t or de r c ondi t i ons f o r e a c h of t he s e t hr e e c a s e s a r e w r i t t e n out e xpl i c i t l y i n

S e c t i on 4 a s e s t i m a t i on e qua t i ons

.

3. H e t e r oge n e ou s R e s p on s e t o C A F E : T h r e e T y p e s of F i r m s

I de ve l op a da t a s e t a nd m e t r i c t o e xa m i ne t he d i vi s i on of m a j or a ut om a ke r s i nt o t he

t hr e e c a t e gor i e s i de nt i f i e d by t he t he o r e t i c a l m ode l a bove

. T he a na l ys i s i s ba s e d on hi s t or i c a l

r e s pons e t o C A F E a nd m y de f i ni t i ons o f t he gr oup s be l ow a r e f ol l ow e d by t w o pr opos e d

m e t r i c s f or c a t e gor i z i ng f i r m s

. 2 0 I n c ont r a s t t o G ol d be r g ( 1998)

, I not onl y c ons i de r f i r

m s t ha t

a r e a f f

e c t e d by t he C A F E f i ne s

, bu t a l s o f i r m s t ha t a r e c ons t r a i ne d by t he r e gul a t i on. I w i l l

f i nd t ha t t hi s ne w gr oup of c ons t r a i ne d f i r m s be a r s m uc h of t he bur de n o f pol i c y a nd

i nf l ue nc e s t he e f f i c i e nc y of t he r e gul a t i on.

2 0 G i v en en o u g h v ari at i o n t h ro u g h t i me

, fi r ms may h av e mo v ed f ro m o n e cat eg o ry t o an o t h er

, b u t t h i s

d o es n o t ap p ea r t o h av e b e en t h e cas e fo r t h e maj o r p ro d u cers i n t h e U

. S. m ark et

.10 G r oups

I

. T he f i r s t gr oup c ons i s t s of t hos e f i r m s w hos e c a r a nd t r uc k f l e e t s e xc e e d t he s t a nda r d.

M or e pr e c i s e l y, gi ve n t he s e t of p r i c e s a nd ve hi c l e s of f

e r e d by ot he r m a ke r s

, t he pr of i t

m a xi m i z i ng qua nt i t y f or e a c h m ode l r e s ul t s i n a f l e e t of ne w ve hi c l e s t ha t i s unc ons t r a i ne d by

t he r e gul a t i on. T oyot a a nd H onda a r e t he t w o l a r g e s t f i r m s i n t hi s c a t e gor y; t he i r c a r a nd

t r uc k f l e e t s ha ve w e l l s ur pa s s e d t he s t a nda r d e ve r y ye a r s i nc e 1978. T hi s gr oup c or r e s ponds

t o e qua t i on ( 4 ) a bove

.

I I

. T he s e c ond gr oup i s c om p r i s e d of f i r m s t ha t vi ol a t e t he s t a nda r d a nd pa y t he

a s s oc i a t e d f i ne s

. B M W a nd M e r c e de s ( unt i l i t s m e r ge r w i t h C hr ys l e r ) a r e t he t w o l a r ge s t

f i r m s i n t hi s gr oup

. T he y ha ve bot h vi ol a t e d t he s t a nda r d f or e a c h m ode l ye a r s i nc e 1987 a nd

ha ve pa i d a bout $500 m i l l i on i n f i ne s a s a r e s ul t

. T he y c or r e s pond t o e qua t i on ( 5) a bove

.

I I I

. T he t hi r d

, a nd a r gua bl y m os t i m por t a nt

, c a t e gor y c ons i s t s of f i r m s t ha t a r e c ons t r a i ne d

by C A F E a s m ode l e d i n e qua t i on ( 6)

. T he s e a r e f i r m s t ha t

, i n t he a bs e nc e of r e gul a t i on

,

w oul d c hoos e t o pr oduc e a f l e e t t ha t f a l l s be l ow t h e C A F E s t a nda r d, but a l t e r t he i r f l e e t s uc h

t ha t i t j us t m e e t s t he s t a nda r d w he n r e gul a t i on i s i n t r oduc e d. I m pl i c i t l y

, t hi s m e a ns t ha t t ot a l

c os t s a s s oc i a t e d w i t h vi ol a t i ng t he s t a nda r d a r e l a r ge r t ha n t he f or gone pr of i t s f r om

c om pl i a nc e

. I s how be l ow t ha t t he t r a di t i ona l “ bi g t hr e e ” pr oduc e r s

, F or d

, G M

, a nd C hr ys l e r

,

f

a l l i nt o t hi s c a t e gor y.

C A F E c om pl i a nc e s t a t us f or e a c h f i r m i s c a l c ul a t e d a nnua l l y a nd a va i l a bl e f r om t he

N H T S A

. 2 1 F i gu r e 1 pl o t s t he r a w da t a f o r one f i r m i n e a c h c a t e gor y: T he be ha vi or of T oyot a

a nd B M W i s c l e a r

, w i t h T oyot a e xc e e di ng a nd B M W vi ol a t i ng t he s t a nda r d i n e v e r y ye a r

.

F or d, w hi l e not m e e t i ng t he s t a nda r d e xa c t l y i n a n y one ye a r

, a ppe a r s c ons t r a i ne d i n t he s e ns e

t ha t t hr ough t i m e i t s de vi a t i ons f r om t he s t a nda r d a l m os t pr e c i s e l y c a nc e l

. I n ot he r w or ds

, t he

c r e di t s t ha t i t e a r ns f r om a ye a r w he n i t i s s l i ght l y a bove t he s t a nda r d a r e o f f

s e t a l m os t e xa c t l y

by ye a r s w he n i t f a l l s be l ow t he s t a nda r d. F i gur e 2 pl ot s t he hi s t or y of t he l a r ge s t f i r m s i n

e a c h c a t e gor y, a s di vi de d by t he m e t r i c be l ow

.

2 1 N at i o n al H i g h w ay T r affi c S afet y A d mi n i s t rat i o n (2 0 0 9 a) an d (2 0 0 9 b ).11 T o i nc or po r a t e t he dyna m i c na t ur e o f t he r e gul a t i o n, w he r e c r e di t s f r om ove r

c om pl i a nc e m a y be us e d on a one

- t o

- one ba s i s t o o f f

s e t unde r

- c om pl i a nc e

, I a ggr e ga t e f i r m

de vi a t i ons f r om t he C A F E s t a nda r d t hr ough t i m e

. T hi s i s done i n T a bl e 1 f o r t he l a r ge s t

f i r m s

. I n t he l e f t ha nd ( c a r f l e e t ) pa ne l

, t he r ow f or H onda

, f or e xa m pl e

, i ndi c a t e s t ha t du r i ng

t he pe r i od 1990

- 2001 t he f i r m pr oduc e d a f l e e t t ha t e xc e e de d t he C A F E s t a nda r d by a n

a ve r a ge of 3. 96 m i l e s pe r ga l l on. M e r c e de s

, on t h e ot he r ha nd, pr oduc e d a f l e e t w hos e f ue l

e c onom y a ve r a ge d 3. 29 m i l e s pe r ga l l on be l ow t he s t a nda r d, pa yi ng pe na l t i e s f or vi ol a t i ng t he

r e gul a t i on i n a l m os t e ve r y ye a r

. F or d

, G M

, a nd C hr ys l e r ha ve a ggr e ga t e de vi a t i ons ve r y c l os e

t o z e r o

– m e a s ur i ng l e s s t ha n 0. 2 m i l e s pe r ga l l on a bove t he s t a nda r d. T hi s pl a c e s t he m i n t he

t hi r d gr oup

, f i r m s t ha t a r e c ons t r a i ne d by t he s t a nd a r d but not f ound i n vi o l a t i on. 2 2

T o f u

r t he r e m pha s i z e t he di f f

e r e nc e s i n t he t hr e e g r oups

, t he t a bl e a l s o s how s t he

f r a c t i on of ye a r s i n w hi c h t he f i r m ha d a f l e e t f ue l e c onom y t ha t f e l l be l ow t he s t a nda r d

.

N ot i c e t ha t t he f i r m s i n t he vi ol a t i ng gr oup w e r e b e l ow t he s t a nda r d i n e ve r y ye a r

, w hi l e t he

unc ons t r a i ne d f i r m s a r e a bove i n a l m os t e ve r y ye a r

. T he c ons t r a i ne d dom e s t i c f i r m s s pe nd

s om e ye a r s unde r t he s t a nda r d, a nd s om e ye a r s ove r

, us i ng c r e di t s f r o m t he good ye a r s t o

of f

s e t unde r

- c om pl i a nc e i n t he ba d ye a r s

.

T he s e c ond pa ne l r e pe a t s t hi s e xe r c i s e f or t he s e pa r a t e l y r e gul a t e d l i gh t dut y t r uc k

f l e e t

. T he s a m e g r oup of t hr e e dom e s t i c f i r m s i s i n t he c ons t r a i ne d s e c t i on, w i t h t he f l e e t s of

t he l a r ge s t t r uc k m a ke r s

, G M a nd F or d, a ga i n a ve r a gi ng l e s s t ha n 0. 1 m i l e s pe r ga l l on a bove

t he s t a nda r d. 2 3

4. D at a an d E s t i m at i on

I n o r de r t o de ve l op a m or e c om pl e t e unde r s t a ndi ng of a ut om ob i l e m a r ke t s i n t he

c ont e xt of C A F E r e gul a t i on

, m ode l s o f bot h t he de m a nd a nd s uppl y of a u t om obi l e s a r e

e s t i m a t e d. D e m a nd f o l l ow s t he m ode l i n B e nt o e t a l

. ( 2009 )

, w hi l e s uppl y i s g i ve n by t he

2 2 Si n ce I b eg i n t h e c al cu l at i o n i n 1 9 9 0 (a ft er t h e l ev el o f t h e s t an d ard w as fu l l y s t ab i l i zed ) t h e s l i g h t

o v er

- co mp l i an ce me as u red may cap t u r e t h e rep ay men t o f cr ed i t s o w ed f ro m t h e l at e 1 9 8 0 ’s

.

2 3 T h e t ru ck fl eet s o f V W

, Is u zu

, an d Mi t s u b i s h i are n o t d i fferen t i at ed as s h ar p l y b y t h e s e co n d m et ri c,

s o I p l ac e t h es e s mal l e r fi r ms acco rd i n g t o t h ei r av e rag e p er fo rm an ce

, w h i ch i n al l c as es co i n ci d es

w i t h p er fo r man ce i n t h e cen t ral 1 9 9 7

- 2 0 0 1 p eri o d I co n s i d er. V o l k s w ag en v i o l at ed t h e s t an d ard i n

each y ear s i n ce 1 9 9 6 an d w as fo r ced t o p ay a fi n e o n al l o f i t s 1 9 9 7

- 2 0 0 1 t ru ck fl eet s

. Is u zu an d

Mi t s u b i s h i b o t h h ad fl eet s w el l ab o v e t h e s t an d ard i n t h i s p eri o d

, an d d i d n o t p ay fi n es

.12 m ode l de s c r i be d i n S e c t i on 2. T he pa i r of m ode l s ha s t he a dva nt a ge of c ons i s t e nc y i n t he

s e ns e t ha t I e m pl oy t he s a m e da t a s our c e s a nd a s s u m pt i ons t hr o ughout

. I n b r i e f

, t he

hous e hol d l e ve l r e s ul t s f r om B e nt o e t a l

. , de s c r i be d i n t he f i r s t s ubs e c t i on be l ow

, a r e us e d t o

de r i ve a s e t of r e s i dua l de m a nd c ur ve s f a c e d by pr oduc e r s a nd t o a l l ow m e a s ur e m e nt of

w e l f a r e e f f

e c t s

.

T he s e c ond s ubs e c t i on de s c r i be s e s t i m a t i on of t he pr oduc e r m ode l

. T he c om put a t i ons

f

or t he unc ons t r a i ne d a nd f i ne

- pa yi ng c a s e s f ol l ow G ol dbe r g ( 1998)

. T he c ons t r a i ne d c a s e

,

f

or F o r d, G M

, a nd C hr ys l e r

, p r ovi de s a ne w c ha l l e nge i n s e pa r a t e l y e s t i m a t i ng t he s ha dow

c os t s of t he r e gul a t i on

. T he f i r s t o r de r c ondi t i ons of t he p r of i t

- m a xi m i z a t i on pr obl e m s a bove

a r e e m pl oye d i n e s t i m a t i on

. T he e s t i m a t e s pr ovi de a pr oduc e r l e ve l unde r s t a ndi ng o f

r e s pons e s t o f ue l e c onom y r e gul a t i on

.

a. H ou s e h ol d D e m an d

F or a m o r e de t a i l e d de s c r i pt i on of t he de m a nd e s t i m a t i on, s e e B e nt o e t a l

. ( 2009)

. T he

pr i m a r y da t a s our c e i s t he 2001 N a t i ona l H ous e hol d T r a ve l S ur ve y ( N H T S )

, w hi c h pr ovi de s

,

i n a ddi t i on t o de m ogr a phi c i ndi c a t or s

, hous e hol d l e ve l s ur ve y da t a on a ut om obi l e s ow ne d a nd

ve hi c l e m i l e s t r a ve l e d ( V M T )

. T he ve hi c l e da t a f o r bot h t he de m a nd a nd s uppl y s i de a r e

di vi de d i nt o t he f ol l ow i ng 10 ve hi c l e c l a s s e s

, 5 a ge c a t e gor i e s

, a nd 7 m a nuf a c t ur e r s :

Cl as s es A g e cat eg o ri es Man u f act u rers

Co mp a ct N e w c ars Fo rd

L u x u ry co mp act 1

- 2 y ears o l d Ch ry s l er

Mi d s i ze 3

- 6 y ears o l d G en eral Mo t o rs

Fu l l s i ze 7

- 1 1 y ears o l d H o n d a

L u x u ry mi d / fu l l s i ze 1 2

- 1 8 y ears o l d T o y o t a

Smal l S U V O t h er A s i an

L a rg e S U V E u ro p e an

Smal l t ru ck

L a rg e t ru ck

Mi n i v an

V e hi c l e c ha r a c t e r i s t i c s c om e f r om W ar d’

s A ut om o t i v e Y e ar book

, a nd pr i c e s f r om t he

N a t i ona l A ut om obi l e D e a l e r ’ s A s s oc i a t i on ( N A D A ) C ar G ui de

. A n a nnua l m e a s ur e of

ve hi c l e r e nt a l c os t ba s e d on t he c ha nge i n r e s a l e va l ue

, r e gi s t r a t i on

, a nd i ns ur a nc e c os t s i s

c ons t r uc t e d a nd gi ve n i n t he m ode l be l ow by

. F ue l e c onom y a nd l oc a l pr i c e s of ga s ol i ne

a r e us e d t o c om put e a m e a s ur e of pe r

- m i l e ope r a t i ng c os t f or e a c h hous e hol d a nd ve hi c l e

,13 . 2 4 ( T he

~ s ym bol t h r oughout i ndi c a t e s da t a a nd pa r a m e t e r s e s t i m a t e d w i t hi n t he

hou s e hol d pr obl e m

. )

T he ke y a dva nt a ge s of t h i s de m a nd m ode l i n a ppl i c a t i on t o C A F E s t a nda r ds a r e i ) t he

s i m ul t a ne ous e s t i m a t i on of t he c hoi c e o f ve hi c l e a nd m i l e s dr i ve n a nd i i ) t he m ode l o f

de m a nd f or us e d ve hi c l e s

. T h i s r e pr e s e nt s a n i m p or t a nt i m pr ove m e nt ove r pr e vi ous w or k

,

m uc h of w hi c h ha s e m pl oye d a t w o s t e p pr oc e dur e a nd ha s not c ons i de r e d t he us e d m a r ke t

. 2 5

T he s i ngl e s e t of pa r a m e t e r e s t i m a t e s

, obt a i ne d by us i ng t he i nf or

m a t i on i n bot h t he ve hi c l e

c hoi c e a nd V M T da t a

, a l l ow s t he num e r i c a l s i m ul a t i on of a n i nt e gr a t e d s e t of hous e hol d

de c i s i ons a nd c ons i s t e nt m e a s ur e m e nt of w e l f a r e e f f

e c t s unde r pol i c y s c e na r i os

.

S pe c i f i c a l l y, i ndi r e c t ut i l i t y f o r hous e hol d h c ondi t i ona l on t he d i s c r e t e c hoi c e of

ve hi c l e j i s gi ve n by:

( 7 )

w he r e i s hous e hol d h ’ s i nc om e a nd t he pr i c e of t h e out s i de good. T he ut i l i t y

pa r a m e t e r s a r e t o be e s t i m a t e d. S ubs c r i pt t i nd i c a t e s t he c hoi c e oc c a s i on

f

or hous e hol ds pur c ha s i ng m ul t i pl e ve hi c l e s

, s e e f ul l a r t i c l e f or a n i n de pt h di s c us s i on of t hi s

c om pone nt

. T he r a ndom c om pone nt o f ut i l i t y, gi v e n by

, i s dr a w n f r om t he t ype I

e xt r e m e va l ue di s t r i but i on

, w i t h t he p r o ba bi l i t y o f a gi ve n di s c r e t e c hoi c e j m a xi m i z i ng ut i l i t y

t he r e f or e t a ki ng t he l ogi t f o r m :

( 8 )

w he r e r e pr e s e nt s t he s e t of a l l ne w a nd us e d ve hi c l e s i n t he m a r ke t

.

2 4 al s o i n cl u d es a meas u r e o f p er

- mi l e m ai n t en an ce co s t s an d t h e p o rt i o n o f i n s u ran c e co s t s t h at

v ary w i t h an n u al mi l eag e

.

2 5 Fo r ex a mp l e, W es t (2 0 0 4 ), G o l d b e rg (1 9 9 8 ) an d T r ai n (1 9 8 6 ) u s e a t w o

- s t ep p ro ced u re t o

s eq u en t i al l y es t i mat e t h e d i s c ret e ch o i ce o f v eh i cl e an d t h e d em an d fo r V M T

.14 T he s e c o nd e qua t i on, f or t he c ont i nuous c hoi c e

, i s de r i ve d di r e c t l y f r om t he i ndi r e c t

ut i l i t y f unc t i on i n ( 7 ) us i ng R oy’ s i de nt i t y

, a nd i s g i ve n by:

( 9 )

w he r e i s m i l e s d r i ve n f o r hous e hol d h c ondi t i ona l on c hoos i ng ve hi c l e j

. W e a s s um e

i s m e a s ur e d i m pe r f e c t l y

, yi e l di ng t he e s t i m a t i on e qua t i on,

, w he r e

i s t he obs e r ve d s ur ve y r e s pons e on m i l e s dr i ve n a nd i s i

. i

. d

. G a us s i a n e r r o r

.

T o c om put e t he e s t i m a t e s

, w e a dopt a B a ye s i a n a ppr oa c h a nd us e a va r i a t i on of

A l l e nby a nd L e nk’ s i m pl e m e nt a t i on o f t he G i bbs s a m pl e r

. M e a n va l ue s f or t he e l a s t i c i t i e s of

m i l e s dr i ve n w i t h r e s pe c t t o ope r a t i ng c os t a nd i nc om e

, r e s pe c t i ve l y, a r e f ound t o be

- 0

. 69 a nd

0. 62, w i t h t he r e l a t e d e l a s t i c i t y of de m a nd f or ga s o l i ne e s t i m a t e d t o be

- 0. 32

. T he m e a n

e l a s t i c i t y of ne w ve hi c l e de m a nd w i t h r e s pe c t t o pr i c e i s e s t i m a t e d t o be

- 2. 0

. T he e s t i m a t e d

ut i l i t y pa r a m e t e r s a r e a l l ow e d t o va r y by hous e hol d i nc om e

, f a m i l y c om pos i t i on

, e duc a t i on,

M S A s i z e

, a nd r a c e

. T he s e s our c e s of va r i a t i on a l l ow a pa r t i c ul a r l y de t a i l e d vi e w o f t he

di s t r i but i ona l e f f

e c t s of pol i c y

.

b

. P r od u c e r C os t s

E s t i m a t i on of c os t pa r a m e t e r s de t e r m i ni ng pr oduc e r r e s pons e t o C A F E r e gul a t i on

r e pr e s e nt s t he f i na l s t e p i n us i ng t he pa i r of m ode l s f or pol i c y a na l ys i s

. I n or de r t o r e c ove r t he

c os t pa r a m e t e r s I m a ke us e of t he f i r m s ’ f i r s t or de r c ondi t i ons dr a w n f r om t he m od e l of

be ha vi or i n S e c t i on 2. W he r e t he r e s i dua l de m a nd f unc t i ons e nt e r I i nc o r por a t e e s t i m a t e s

f r om t he hous e hol d de m a nd s ys t e m j us t di s c us s e d. W e w i l l s e e t ha t a n e s t i m a t e o f c os t s m a y

be c om put e d di r e c t l y, a l ong t he l i ne s of G ol dbe r g ( 1998)

, f or t w o of t he t h r e e gr oups o f f i r m s :

t hos e t ha t a r e unc ons t r a i ne d or t ha t a r e pa yi ng t he f i ne

. F or t he t hi r d c l a s s

, t he c ons t r a i ne d

dom e s t i c f i r m s

, I i n t r oduc e a n e c onom e t r i c m ode l t o s e pa r a t e t w o c om pone nt s of c os t unde r a

pr e

- e xi s t i ng C A F E s t a nda r d: m a r gi na l pr o duc t i on c os t

, a nd t he s ha dow c os t of e xi s t i ng

r e gul a t i on.15 i

. C om put at i on f or U nc ons t r ai ne d and F i ne

- P ay i n g F i r

m s

F i r s t c ons i de r t he c a s e of t he unc ons t r a i ne d f i r m gi ve n i n e qua t i on ( 4 )

. T hi s i s a

s t a nda r d m ul t i

- pr oduc t pr of i t m a xi m i z a t i o n pr obl e m a nd t he s e t o f f i r s t or de r c ondi t i ons w i t h

r e s pe c t t o pr i c e m a y be w r i t t e n i n m a t r i x no t a t i on a s :

( 10 )

w he r e Q i i s t he ve c t or of qua nt i t i e s of e a c h t ype of ve hi c l e m a de by f i r m i

, a nd P i a nd C i t he

c or r e s pondi ng pr i c e a nd c os t ve c t or s

. D i i s t he j b y j m a t r i x of de r i va t i ve s of de m a nd w he r e

t he k

, t h e l e m e nt of D i i s :

. I c om put e t he m a t r i x D i f r om t he a ggr e ga t e hous e hol d

de m a nd s ys t e m

, a nd t he ve c t or s Q i a nd P i a r e da t a

. A n e s t i m a t e o f c os t s m a y t he n be

c om put e d di r e c t l y f r om ( 10 )

.

I n t he s e c ond c a s e

, w hi c h de s c r i be s f i r m s obs e r ve d t o be v i ol a t i ng t he s t a nda r d a nd

pa yi ng t he f i ne

, t he f i r s t or de r c ondi t i ons m a y be w r i t t e n a s :

( 11 )

w he r e a nd a r e ve c t or s w i t h t he e l e m e nt s de f i ne d a s t he pe r

- ve hi c l e f i ne f or e a c h c a r

a nd l i ght dut y t r uc k

. T he ve c t or s G i C a nd G i T a r e t he de r i va t i ve s of a nd w i t h r e s pe c t

t o ve hi c l e pr i c e

. 2 6 A s m e nt i one d

, t h i s c a l c ul a t i on a n d t he one a bove f or unc ons t r a i ne d f i r

m s

s o f a r f ol l ow t he a na l ys i s done i n G ol dbe r g ( 1998)

, w i t h t he e xc e pt i on t ha t I m ode l t he

a ve r a ge f ue l e c onom y c a l c ul a t i on us i ng t he r e gul a t i on’ s ha r m oni c m e a n f or m ul a r a t he r t ha n a

l i ne a r a ve r a ge

. T he r e s ul t i s t ha t t he de r i va t i ve s i n G i C a nd G i T a r e no l onge r l i ne a r

, but a r e

gi ve n by:

( 12 )

D e s pi t e t he c om pl e xi t y of t hi s e xpr e s s i on, a n e s t i m a t e of C i c a n s t i l l be c om put e d di r e c t l y

f r om t he da t a a s i n t he unc ons t r a i ne d c a s e

.

2 6 T h e * s y mb o l i n ( 1 1 ) i n d i cat es el em en t

- b y

- el e men t mu l t i p l i cat i o n

.16 i i

. E s t i m at i on P r oc e dur e f or C ons t r ai ne d F i r

m s

T he l a r ge s t dom e s t i c a ut om a ke r s f a l l i nt o ne i t h e r o f t he t w o c a t e gor i e s de s c r i be d by

G ol dbe r g, but i ns t e a d a r e c ons t r a i ne d by C A F E

. T he s ha dow c os t of s a t i s f yi ng t he r e gul a t i on

i s unobs e r ve d a nd m us t be i de nt i f i e d s e pa r a t e l y f r o m pr oduc t i on c os t i n or de r t o unde r s t a nd

t he i m pa c t s of pol i c y

.

F or c l a r i t y

, f i r s t r e w r i t e t he m a xi m i z a t i on p r obl e m gi ve n i n ( 6 ) i n ve c t or no t a t i on:

( 13 )

w he r e t he k

- t h e l e m e nt of L i C i s f or pa s s e nge r c a r s a nd 0 ot he r w i s e

. T he k

- t h

e l e m e nt of L i T i s f or l i ght dut y t r uc ks a nd 0 o t he r w i s e

. W e c a n w r i t e t he f i r s t

or de r c ondi t i on w i t h r e s pe c t t o pr i c e o f t he a s s oc i a t e d L a gr a ngi a n a s :

( 14 )

w he r e a nd a r e t he s c a l a r L a gr a nge m u l t i pl i e r s f or f i r m i a s s oc i a t e d w i t h t he pa s s e nge r

c a r a nd l i ght dut y t r uc k c ons t r a i nt s

, r e s pe c t i ve l y. I n t he pr e vi ous t w o c a s e s w e s a w t ha t a n

e s t i m a t e of C i c oul d be c om pu t e d di r e c t l y f r om t he f i r s t o r de r c ondi t i ons

. T hi s i s no l onge r

pos s i bl e s i nc e t he t e r m s r e pr e s e nt i ng t he s ha dow c os t of C A F E a r e a l s o unknow n

. T he

r e m a i nde r of t hi s s e c t i on de s c r i be s a n e c onom e t r i c a ppr oa c h f or e s t i m a t i ng a nd

, f r om

w hi c h t he r e m a i ni ng pa r a m e t e r s ne e de d f or t he pol i c y s i m ul a t i ons m a y be c om put e d

.

N ot i c e t ha t

, a t t he opt i m u m

, ( a nd s i m i l a r l y ) t a ke s t he s a m e va l ue a c r os s a l l

m ode l s p r oduc e d by a g i ve n m a nuf a c t ur e r

. T hi s r e s t r i c t i on, t ha t t he s ha dow c os t of t he

r e gul a t i on i s m a de e qua l a c r os s pr oduc t s

, w i l l be u s e d i n i de nt i f yi ng t he e c onom e t r i c m ode l

.

I nt ui t i ve l y, i t s t a t e s t ha t a t t he opt i m um f i r m s s e t t he s ha dow c os t of t he c ons t r a i nt s

, gi ve n by

t he λ t e r m s

, e qua l a c r os s m ode l s

.

A pr oxy f or t he pr i c e

- c os t m a r gi n i s a l s o i n t r oduc e d, c ons t r uc t e d us i ng t he de a l e r

m a r kups obs e r ve d i n t he da t a a nd t he r a t i o o f de a l e r t o m a nuf a c t ur e r m a r gi n s ugge s t e d i n

B r e s na ha n a nd R e i s s ( 1985)

. T h e y f i nd t ha t t hi s r a t i o i s a ppr oxi m a t e l y c ons t a nt a c r os s17 ve hi c l e s

– t ha t i s

, t ha t w hi l e m a r kups w i l l d i f f

e r w i de l y ba s e d on a t t r i but e s of t he ve hi c l e a nd

t he c or r e s pondi ng de m a nd e l a s t i c i t i e s

, t he f r a c t i on of t he t ot a l m a r kup ke pt by t he de a l e r i s

r oughl y c ons t a nt

. I a s s um e t ha t t hi s m e a s ur e

, B i , i nc l ude s e r r or a nd a c ons t a nt f a c t or

, a nd

c ons i de r t he f ol l ow i ng t w o f o r m s :

( 15 )

I n s pe c i f i c a t i on ( I ) i s a n a ddi t i ve c ons t a nt

, t he f i r

m ’ s pr i c e

- c os t m a r gi n

, a nd i s

m e a s ur e m e nt e r r or i nde pe nde nt of t he va r i a bl e s e n t e r i ng t he p r oduc e r ’ s opt i m i z a t i on pr obl e m

.

S pe c i f i c a t i on ( I I ) a dds a m ul t i pl i c a t i ve t e r m

, , a nd i s pr e f e r r e d s i nc e t he m ul t i pl i c a t i ve

f

a c t or i s i n ke e pi ng w i t h t he B r e s na ha n a nd R e i s s m ode l

. I s how t ha t t he c e nt r a l pa r a m e t e r

e s t i m a t e s of t he m ode l a r e r obus t a c r os s bot h s pe c i f i c a t i ons

, but f i nd t ha t m ode l ( I I )

, i nc l udi ng

t he m ul t i pl i c a t i ve f a c t or

, f i t s t he da t a s om e w ha t m or e c l os e l y.

R e a r r a ngi ng t he f i r s t or de r c ondi t i on i n ( 14 )

, w e c a n w r i t e t he pr i c e

- c os t m a r g i n i n

t e r m s of t he de m a nd s ys t e m a nd t he s ha dow c os t s of C A F E :

( 16 )

C om bi ni ng ( 16) w i t h t he f unc t i ona l f or m s c ons i de r e d f or B i i n ( 15 ) yi e l ds t he f ol l ow i ng t w o

m ode l s :

( 17 )

T he pa r a m e t e r s

, , , a nd

, a r e e s t i m a t e d by l e a s t s qu a r e s

. T he r e s ul t s a r e

pr e s e nt e d i n T a bl e 2

. M ode l I i s e s t i m a t e d f i r s t us i ng a s c a l a r va l ue a nd t he n a l l ow i ng i t t o

va r y f or e a c h m a ke

- f l e e t c om bi na t i on. S i m i l a r l y

, m ode l I I i s f i r s t e s t i m a t e d w i t h s c a l a r va l ue s

f

or a nd a nd t he n m o r e f l e xi b l y a l l ow i ng t o va r y w i t h m a ke

- f l e e t c om bi na t i on

.

W hi l e t he m ode l s a r e bot h i de nt i f i e d i n c r os s

- s e c t i on, da t a f or t he ye a r s 1997

- 2001 i s pool e d

due t o t he l i m i t e d num be r of obs e r va t i ons a va i l a bl e f or a s i ngl e ye a r

. I m pl i c i t l y

, t hi s a dds t he

a s s um pt i on of a c ons t a nt s ha dow c os t of C A F E a c r os s t he s e f i ve ye a r s

. R e c a l l

, how e ve r

, t ha t18 f i r m s c a n s hi f t t he C A F E r e qui r e m e nt s a c r os s t i m e

, s o t ha t i n a pe r i od o f s t a bl e de m a nd i t i s

not unr e a s ona bl e t o a s s um e t ha t t he y a r e a bl e t o e qua l i z e t he s ha dow c os t s

. 2 7

T he e s t i m a t e s f or a nd s how n i n T a bl e 2 a r e r obus t a c r os s s pe c i f i c a t i ons a nd

va r y s i gni f i c a nt l y a m ong m a nuf a c t ur e r s

. P e r ha ps not s ur pr i s i ngl y, t he m ode l s w i t h f i xe d

e f

f

e c t s by m a ke

- f l e e t f i t t he da t a c ons i de r a bl y be t t e r

. T o a t t a c h e c onom i c m e a ni ng t o t he

pa r a m e t e r s a nd t he di f f

e r e nc e s obs e r ve d a m ong f i r

m s

, I c om put e t he m a r gi na l e f f

e c t s of a uni t

c ha nge ( one m i l e pe r ga l l on) i n t he s t a nda r d on t he pr of i t s o f e a c h f i r m a nd f l e e t i n T a bl e 3. 2 8

I n t hi s t a bl e

, a nd a s t he c e nt r a l c a s e i n t he pol i c y s i m ul a t i ons

, t he va l ue s f r om m ode l ( I I b) a r e

us e d. A ppe ndi x A de m ons t r a t e s t he r obus t ne s s of t he r e s ul t s t o a l t e r na t i ve s pe c i f i c a t i ons of

t he f i xe d e f f

e c t s

, t he i nc l us i on of ye a r f i xe d e f f

e c t s

, a nd a “ pl a c e bo” t ype t e s t on

unc ons t r a i ne d f i r m s

.

T he hi ghe s t s ha dow c os t s di s pl a ye d i n T a bl e 3 a r e f or G M ’ s pa s s e nge r c a r f l e e t

.

I nt ui t i ve l y, t hi s f l e e t i s e s t i m a t e d t o be t he m os t c o ns t r a i ne d i n t he s e ns e t ha t t he p r i c i ng o f

c om pone nt ve hi c l e m ode l s r e f l e c t s t he l a r ge s t di s t or t i ons a t t r i but a bl e t o r e gul a t i on

. 2 9 A t t he

ot he r e nd of t he s pe c t r um

, F o r d’ s c a r f l e e t s how s t he s m a l l e s t e f f

e c t s f r om C A F E

. T he s e

e s t i m a t e s a r e c ons i s t e nt w i t h c a s ua l obs e r va t i on i n t he dom e s t i c a ut o i ndus t r y: a m ong

c a r m a ke r s

, F or d ha s a r e put a t i on f or i t s “ pr a c t i c a l ” c a r l i ne ( T a ur

us

, E s c or t

, F oc us ) w he r e a s

G M i s be s t know n f or a l i ne up of l a r ge r

, hi gh

- ho r s e pow e r ve hi c l e s w i t h c or r e s pondi ngl y l ow

f ue l e c onom y. I n t r uc k f l e e t s

, F or d a nd G M a r e s i m i l a r

, w hi l e C hr ys l e r

, w i t h i t s dom i na nc e i n

t he m i ni va n m a r ke t

, ha s t he l ow e s t m a r gi na l c os t s of C A F E

. ( M i ni va ns ha ve s i gni f i c a nt l y

be t t e r f ue l e c onom y t ha n m os t S U V s

. )

2 7 T h e s ev en

- y ea r l i mi t o n t h e w i n d o w o f b an k i n g an d b o rro w i n g an d l o n g ru n ch an g es i n m ark et

co n d i t i o n s may m ean t h at fi r ms ei t h er can n o t o r d o n o t w i s h t o eq u al i ze s h ad o w co s t s o v e r l o n g t i m e

h o ri zo n s

. In o r d e r t o l i mi t t h e i mp a ct o f t h es e l o n g ru n effe ct s

, I res t ri ct t h e t i me p eri o d fo r es t i mat i o n

t o t h e fi v e y ears l e ad i n g u p t o 2 0 0 1

— t h e y e ar fro m w h i ch t h e cro s s

- s e ct i o n o f h o u s eh o l d d e man d

d at a i s d ra w n

. N o t e al s o t h e s t ab i l i t y o f t h e C A F E s t an d ard t h ro u g h t h i s t i me p eri o d (s e e Sect i o n 2 a ).

2 8 T h e marg i n al eff ect s a re d eri v ed b y i n v ert i n g t h e (n o n l i n ear) t r an s fo rm at i o n p erfo rm ed o n t h e

co n s t rai n t w h en w ri t i n g i t i n t h e fo rm o f eq u at i o n ( 1 3 )

, an d co n v ert i n g t o d o l l ar u n i t s

.

2 9 T h e d i s t o rt i o n s ex ceed t h e $ 5 0 fi n e fo r v i o l at i o n

, s u g g es t i n g t h at d o mes t i c au t o mak ers h av e

s u b s t an t i al p ro fi t mo t i v es fo r co mp l i an ce i n ad d i t i o n t o t h e n o mi n al fi n es i mp o s ed fo r v i o l at i o n

. Se e

d i s cu s s i o n i n Sect i o n 2 b

.19 5. T i m e S e r i e s M od e l of P r i c e s

T he a na l yt i c a l m ode l a nd pa r a m e t e r e s t i m a t e s a bove a r e ba s e d on t he a s s um pt i on t ha t

f i r m s r e a c t t o C A F E by c ha ngi ng p r i c e s

, t he r e by a f f

e c t i ng de m a nd a nd t he c om pos i t i on of

t he i r f l e e t

. A n a l t e r na t i ve e s t i m a t i on pr oc e dur e i s a l s o pos s i bl e

, e xpl oi t i ng t i m e s e r i e s

va r i a t i on i ns t e a d a nd s e r vi ng a s a t e s t of t he a s s um pt i on m a de i n t he m a i n m ode l

.

T he e s t i m a t i on s t r a t e gy us e s a f i r m ’ s hi s t or y of c o m pl i a nc e

, a nd t he r e f or e i n f or m a t i on

a

bout how m a n y e xt r a c r e di t s i t ha s or obl i ga t i ons i t ow e s

, t o de r i ve a pr oxy f or how

c ons t r a i ne d i t i s i n a ny gi ve n ye a r

. P r i c e i s r e gr e s s e d on t he i n f or m a t i on a bout C A F E s t a t us t o

a s s e s s how f i r m s a l t e r p r i c e s ba s e d on t he r e gul a t i on. W hi l e t hi s m ode l m a ke s a ve r y

di f f

e r e nt s e t o f a s s um pt i ons a nd us e s di f f

e r e nt da t a s our c e s

, i t r e s ul t s i n a s e t o f e s t i m a t e s

c ons i s t e nt w i t h t he c e nt r a l r e s ul t s j us t p r e s e nt e d i n S e c t i on 4b.

R e c a l l t ha t t he r e gul a t i on a l l ow s bot h ba nki ng c r e d i t s f or t hr e e ye a r s a nd bo r r ow i ng

a ga i ns t t hr e e ye a r s w or t h o f f ut ur e c r e di t s

. I f t he f i r m hol ds c r e di t s l o nge r t ha n t hr e e ye a r s

t he y e xpi r e

, a nd i f i t f a i l s t o r e pa y bor r ow e d c r e di t s w i t hi n t hr e e ye a r s t he f i r m i s f ound i n

vi ol a t i on. T he f i r s t s i m pl e m e a s ur e of a nnua l “ f i r

m s t a t e ” I c ons t r uc t i s s i m pl y t he nu m be r o f

c r e di t s a f i r m ha s t ha t w i l l e xpi r e i f t he y go unus e d m i nus t he num be r of bor r ow e d c r e di t s i t

m us t r e pa y t o a voi d pe na l t y. A pos i t i ve va l ue m e a ns t ha t a f i r m m a y f r e e l y pr oduc e a f l e e t

t ha t i s l e s s t ha n t he s t a nda r d, s o t ha t t he f i r m i s l e s s c ons t r a i ne d by t he r e gul a t i on

. A ne ga t i ve

va l ue m e a ns t ha t a f i r m m us t e xc e e d t he s t a nda r d i n or de r t o a voi d a pe na l t y f or no t pa yi ng

ba c k bor r ow e d c r e di t s

, a nd i s t he r e f or e m o r e c ons t r a i ne d by t he r e gul a t i on.

I c ons t r uc t t hi s m e a s ur e f r om m y da t a s e t a s f ol l ow s

. D e f i ne t he va r i a bl e s :

w he r e a s be f or e d

t i s t he s t a nda r d a nd C A F E

t i s t he f i r m ’ s c e r t i f i e d f l e e t f ue l e c onom y i n ye a r

t

. P os i t i ve va l ue s of δ i ndi c a t e c r e di t s a nd ne ga t i v e va l ue s i ndi c a t e de bt s

. I c om put e t he

e vol ut i on of t he δ pa r a m e t e r s t hr ough t i m e f r om t h e i ni t i a l s t a t e (

, , a nd

) a nd t he c om pl e t e t i m e s e r i e s da t a on Y

t be gi nni ng w i t h t he 1978 i nc e pt i on of C A F E

.

F or e xa m pl e

, i n t he c a s e t ha t t he f i r m ha s c r e di t s a va i l a bl e ( s o a t l e a s t one δ

t i s20 pos i t i ve ) a nd us e s s om e of t he m ( s o Y

t i s ne ga t i ve ) t he s t a t e va r i a bl e s i n t he ne xt ye a r ( δ

t + 1 )

a r e de f i ne d a s :

A n a na l ogous s e t of r ul e s a ppl i e s f or c om put i ng t h e s t oc k a nd f l ow o f de bt s t h r ough t i m e a nd

f

or t he r e m a i ni ng c a s e s on Y

t

. T he s e a r e pr ov i de d i n A ppe ndi x B

. W i t h t hi s not a t i on

, m y f i r s t

m e a s ur e of t he f i r m ’ s s t a t e i s gi ve n s i m pl y by

. T h e e f f

e c t of a f i r m ’ s e xpi r i ng

c r e di t s ur pl us or de f i c i t on r e l a t i ve pr i c e s pr oxi e s f or r e s pons e t o c ha nge s i n t he e f f

e c t i ve

s t r i nge nc y of t he c ons t r a i nt a nd c a n be e s t i m a t e d a s :

( 18 )

w he r e t he l e f t ha nd s i de i s t he l og o f pr i c e of a pa r t i c ul a r c a r c l a s s f or e a c h f i r

m i a nd ye a r t

.

T he m ode l i s e s t i m a t e d s e pa r a t e l y f or e a c h c a r c l a s s

. T he f i r s t t e r m s on t he r i ght ha nd s i de a r e

f i xe d e f f

e c t s f o r ye a r a nd f i r m

, α t a nd α i

. N e xt i s a m a t r i x of ve hi c l e c h a r a c t e r i s t i c s X i t , w i t h

e s t i m a t e d c oe f f i c i e nt s γ

. 3 0 i s t he c oe f f i c i e nt on t he m e a s ur e of a f i r m ’ s c r e di t s or de bt s

,

a nd i s t he pa r a m e t e r of i nt e r e s t

. I t i ndi c a t e s how f i r m pr i c e s a r e r e l a t e d t o C A F E s t a t e

, a f t e r

c ont r ol l i ng f o r c a r c ha r a c t e r i s t i c s a nd m a ke a nd ye a r f i xe d e f f

e c t s

. F i na l l y

, c a pt ur e s

unobs e r ve d he t e r oge ne i t y i n ve hi c l e s a nd i s a s s um e d t o be unc or r e l a t e d w i t h

.

T he f i xe d e f f

e c t s by ye a r a r e pa r t i c ul a r l y i m por t a nt s i nc e t he y c ont r ol f or c ha nge s i n

t he popul a r i t y o f e a c h ve hi c l e c l a s s

— c om i ng f or e xa m pl e f r om ga s ol i ne p r i c e s

— ove r t i m e

.

3 0 T h e v eh i cl e ch aract eri s t i cs co n t ro l l ed fo r ar e fu el eco n o my r el at i v e t o w ei g h t an d h o rs ep o w er

, accel e rat i o n (h o rs ep o w er d i v i d ed b y w ei g h t ), w h eel b as e, an d v o l u me

.21 T he a va i l a bi l i t y o f C A F E c r e di t s i s be i ng us e d he r e t o r e f l e c t onl y d i f f

e r e nc e s i n p r i c e s a c r os s

m a nuf a c t ur e r s w i t hi n t he s a m e ye a r

, c ont r ol l i ng f o r f i xe d br a nd e f f

e c t s a nd f o r t he a ve r a ge

pr i c e of t he ve hi c l e c l a s s by ye a r

.

A s e c ond s pe c i f i c a t i on f ur t he r r e l a xe s t he a s s um pt i on t ha t f i r m s onl y c ons i de r c r e di t s

or de bt s e xpi r i ng i n t he c ur r e nt pe r i od

, a nd i ns t e a d us e s a m e a s ur e ba s e d on opt i m a l be ha vi or

gi ve n t he e xpi r a t i on da t e s f or a l l t h r e e vi nt a ge s of c r e di t s or de bt s i t m a y pos s e s s

. I a ga i n

a s s um e c onve xi t y of c om pl i a nc e c os t s

, c a us i ng t he f i r m t o r e pa y a de bt e ve nl y ove r t hr e e

ye a r s

, or

, a na l ogous l y, t o us e a c r e di t e ve nl y ove r i t s t hr e e ye a r l i f e

. 3 1 T hi s m e a s ur e of

a ggr e ga t e f i r m s t a t e ( a s a n opt i m a l de vi a t i on f r om t he c ons t r a i nt ) i s t he n gi ve n by:

i n t he c a s e t ha t a f i r m ha s c r e di t s

. F or t he c a s e of de bt s

, t he s i gn of S

t a nd t he i ne qua l i t i e s a r e

r e ve r s e d. I nt ui t i ve l y, S

t s i m pl y s pr e a ds t he us e of c r e di t s or de bt s e ve nl y ove r t hr e e ye a r s

,

w i t h t he nonl i ne a r i t i e s a r i s i ng be c a us e of t he c ons t r a i nt s i m pos e d by t he e xpi r a t i on da t e s

.

M ode l ( I I ) r e pl a c e s t he f i r m s t a t e i n ( 18 ) w i t h t hi s a ggr e ga t e m e a s ur e : 3 2

( 19 )

T he r e s ul t s f r o m e s t i m a t i ng m ode l s ( I ) a nd ( I I ) a r e pr e s e nt e d i n T a bl e 4

. T he poi nt

e s t i m a t e s a r e t he c ha nge i n ve hi c l e pr i c e ( f o r t he c l a s s gi ve n i n t he c ol um n he a di n g ) i n ye a r s

w he n a f i r m ha s a n e xt r a one

- m i l e

- pe r

- ga l l on c r e di t t ha t i t m a y us e

. F o r e xa m pl e

, t he t op l e f t

e s t i m a t e i ndi c a t e s t ha t

, c ont r ol l i ng f o r m a ke a nd y e a r f i xe d e f f

e c t s a nd c a r c ha r a c t e r i s t i c s

,

F or d pr i c e s c om pa c t c a r s 4. 6% hi ghe r i n ye a r s w he n i t c a n f r e e l y de vi a t e one m i l e pe r ga l l on

be l ow t he s t a nda r d.

3 1 N o t e t h at t h e as s u m ed fo r es i g h t h ere i s w i t h res p e ct t o t h e u s e o f cr ed i t s o r p ay men t o f d eb t s

, an d

n o t t o ran d o m fl u ct u at i o n s i n d e m an d t h at cau s e t h e i n i t i al accu mu l at i o n o f s u ch cr ed i t s o r d eb t s

. In

o t h er w o rd s

, t h e fi r m n o w re al i zes i t h as t h ree y ears i n w h i ch t o u s e a cr ed i t

, b u t i t s t i l l act s a cco rd i n g

t o a co n s t an t ex p ect at i o n o v er fu t u re d em an d s

.

3 2 In p ri n ci p l e, a mo r e co mp l ex mo d el co u l d b e es t i mat ed w i t h al l o f t h e δ v ari ab l es en t eri n g

s ep arat el y

. T h e s h o rt t i me s eri es i n t h e cas e o f C A F E ( s i n ce reg u l at i o n i s o n an n u al av e rag es )

, h o w ev er, p res en t s i n s u ffi ci en t v ari at i o n i n t h e i n d i v i d u al s t at e v ari ab l es t o mak e t h i s ap p ro ach

feas i b l e.22 T he pa t t e r n o f e s t i m a t e s a c r os s ve hi c l e c l a s s e s pr e s e nt e d i n T a bl e 4 s t r ongl y s uppor t s

t he m ode l of f i r m be ha vi or i n S e c t i on 4b: t he l a t t e r m ode l a s s e r t s t ha t ve hi c l e s w i t h h i gh f ue l

e c onom y ha ve a ne ga t i ve s ha dow c os t f r om r e gul a t i on, a nd s houl d t he r e f or e be pr i c e d hi ghe r

i n ye a r s w he n t he r e gul a t i on i s l e s s bi ndi ng

. T he p os i t i ve c oe f f i c i e nt s i n t he f i r s t c ol u m n of

T a bl e 4 be a r t hi s out

. S i m i l a r l y, ve hi c l e s w i t h t he l ow e s t f ue l e c onom y ( i n t he r i ght

- m os t

c ol um n of T a bl e 4) s houl d ha ve t he hi ghe s t s ha dow c os t s

, a nd t hus t he l ow e s t p r i c e s i n ye a r s

w he n r e gul a t i on i s l e s s bi ndi ng. T hi s i s a l s o s uppo r t e d. F i na l l y

, t he pr i c e of m i ds i z e ve hi c l e s

i s f ound t o be r e l a t i ve l y una f f

e c t e d by t he s t r i nge n c y of r e gul a t i on, w hi c h a ga i n f i t s t he

be ha vi or a l m ode l s i nc e m i ds i z e f ue l e c onom i e s t e nd t o be c l os e t o t he m e a n a nd t he r e f o r e

ha ve ne a r z e r o s ha dow c os t s a s s oc i a t e d w i t h r e gul a t i on.

W he n t hi s s a m e m ode l i s r e pe a t e d f o r t he l i ght dut y t r uc k f l e e t

, how e ve r

, a c l e a r

pa t t e r n no l onge r e m e r ge s

. W hy m i ght t hi s be ? W hi l e t he f i ve c l a s s e s of c a r s a r e w e l l

de f i ne d ove r t i m e a nd ha ve a s t a bl e r a nki ng i n t e r m s of f ue l e c onom y, t he s a m e i s not t r ue f or

t r uc ks

. T he r i s e of t w o br oa d c l a s s e s of l i ght t r uc k

— t he m i ni va n i n t he l a t e 80 ’ s a nd S U V i n

t he 90’ s

— c a us e s t he de m a nds a nd c ha r a c t e r i s t i c s of ve hi c l e s i n t he t r uc k f l e e t t o c ha nge

dr a m a t i c a l l y. F ue l e c onom y

, a nd i n pa r t i c ul a r t he r a nki ngs of t he va r i ous c l a s s e s by f ue l

e c onom y, c ha nge s ove r t he s a m pl e pe r i od. T he r e duc e d f or m m ode l of pr i c i ng be ha vi or i n

t hi s s e c t i on a s s um e s a f i xe d e f f

e c t of r e gul a t i on w i t hi n a c l a s s a nd i s not a bl e t o a dj us t f or t he

s hi f t i ng de m a nds a nd f ue l e c onom i e s of t he l i ght t r uc k c l a s s e s

.

T he e s t i m a t e s i n S e c t i on 4b

, on t he ot he r ha nd

, ba s e t he s ha dow c os t s a nd i m pl i c i t

pr i c i ng e f f

e c t s on r e l a t i ve f ue l e c onom y a nd de m a nd e l a s t i c i t i e s

. T he y c a n t he r e f o r e c a pt ur e

t he e f f

e c t s a s t he t r uc k m a r ke t c ha nge s ove r t i m e

. F ur t he r m or e

, s i nc e t he f ul l m ode l of f i r m

be ha vi or a l s o i nc or por a t e s i nf o r m a t i on f r om c r os s

- s e c t i ona l va r i a t i on, I a m a bl e t o us e t he

s hor t e r t i m e pe r i od be gi nni ng i n 1997 a f t e r m uc h o f t he r e a r r a nge m e nt i n t he t r uc k m a r ke t i s

c om pl e t e

.

6. S i m u l at i o n M od e l an d R e s u l t s

T he s i m ul a t i on m ode l c om bi ne s hous e hol d a nd pr oduc e r de c i s i ons i n t he a ut om obi l e

m a r ke t

, us i ng t he m ode l s a nd pa r a m e t e r s e s t i m a t e d i n S e c t i on 4. E qui l i br i u m i n c a r m a r ke t s

i s s ol ve d num e r i c a l l y a t 1 ye a r i n t e r va l s f or 10 ye a r s

. T he r e s ul t s c a pt ur e t he e f f

e c t s o f C A F E

s t a nda r ds on bot h ne w a nd us e d c a r m a r ke t s a s t he f l e e t t ur ns ove r

. A ge nt s opt i m i z e i n e a c h23 pe r i od a c c or di ng t o t he hous e hol d ut i l i t y f unc t i on a nd pr oduc e r p r obl e m de s c r i be d a bove

. 3 3

T he qua nt i t i e s a nd a t t r i but e s of ve hi c l e s a va i l a bl e i n t he us e d c a r m a r ke t a r e upda t e d t hr ough

t i m e

, a nd e vol ve a c c o r di ng t o t he f ul l hi s t or y of de m a nds

.

a. S t r u c t u r e of t h e N u m e r i c al M od e l

A ggr e gat e D e m and

A ggr e ga t e de m a nd f or ne w a nd us e d c a r s c om e s f r om t he hous e hol d ut i l i t y f unc t i on

de s c r i be d i n e qua t i ons ( 7 ) a nd ( 9 )

. H ous e ho l ds s i m ul t a ne ous l y m a ke t he di s c r e t e c hoi c e of

ve hi c l e a nd t he c ont i nuous c hoi c e of m i l e s

. S i nc e t he e s t i m a t e d ut i l i t y pa r a m e t e r s va r y w i t h

hous e hol d c ha r a c t e r i s t i c s

, t he 20, 429 hous e hol ds i n t he da t a s e t a r e c ons i de r e d i ndi vi dua l l y

.

T he r e s ul t i ng hous e h ol d

- l e ve l de m a nds a r e c om bi n e d t o a r r i ve a t a n a ggr e ga t e de m a nd f o r

e a c h of t he ne w a nd us e d ve hi c l e s

. 3 4 T he r e a r e a t ot a l of 225 di s t i nc t ve hi c l e s i n t he us e d

c a r m a r ke t a nd 59 i n t he br a nd

- di f f

e r e nt i a t e d ne w c a r m a r ke t

. A ggr e ga t e de m a nd f or m i l e s

dr i ve n, a nd t he r e f or e ga s ol i ne

, i s c a l c ul a t e d di r e c t l y f r om t he s ol ut i ons t o t he hous e hol d ut i l i t y

m a xi m i z a t i on pr obl e m s

.

Suppl y of N e w C ar s

T he s uppl y of ne w c a r s i s c om put e d by s ol vi ng t he pr oduc e r p r obl e m gi ve n i n

e qua t i on ( 2 ) f or e a c h of t he s e ve n f i r

m s c ons i de r e d. T hi s r e qui r e s t he us e of t he c os t

e s t i m a t e s de s c r i be d i n S e c t i on 4b, a nd t he de r i va t i ve s of t he ve hi c l e de m a nd f unc t i on, D i

.

N um e r i c a l l y, t he s i m ul a t i on a ddr e s s e s t he s pe c i a l c a s e s i n ( 2 ) by s ol vi ng t he f i r s t o r de r

c ondi t i ons gi ve n i n ( 4 )

, ( 5 )

, a nd ( 6 ) f or e a c h o f t he t hr e e c a s e s i ndi vi dua l l y, a nd t he n f i ndi ng

t he m a xi m um w he r e a l l c ondi t i ons a r e s a t i s f i e d. 3 5 T hi s s ol ut i on pr oc e dur e m us t be i t e r a t e d t o

3 3 T h e p e ri o d b y p eri o d s o l u t i o n o f t h e mo d el m ean s t h at w h i l e t h e fl eet ev o l v es en d o g en o u s l y w i t h

p o l i cy

, t h e ag en t s are n o t fo r w ard l o o k i n g i n t h at fu t u r e d em an d co n d i t i o n s are n o t p red i ct ed

. T h i s

l i mi t at i o n fo l l o w s fro m t h e s t at i c mo d el s o f c o n s u mer a n d p ro d u cer b eh av i o r, an d i s n eed ed t o m ak e

t h e mo d el co mp u t at i o n al l y t ract ab l e

.

3 4 E ach h o u s eh o l d i n t h e d at a i s as s u m ed t o b e rep res en t a t i v e o f a g ro u p o f h o u s eh o l d s p ro p o rt i o n al t o

i t s s amp l i n g w ei g h t

. T h e ch o i c e p ro b ab i l i t i es g i v en i n ( 7 ) ar e t h er efo re co mb i n ed u s i n g t h e w ei g h t s

p ro v i d ed i n t h e N H T S t o y i el d ag g reg at e d e man d s

.

3 5 Su b j ect t o t h e r es t ri ct i o n t h at co n s t rai n ed fi r ms h av e a s u ffi ci en t l y h i g h v al u e fo r H i t h at t h ey

co n t i n u e t o co mp l y w i t h t h e s t an d ard

.24 f i nd a n e qui l i b r i um

, s i nc e t he s ol ut i on f or a ny one f i r m de pe nds on t he pr i c e s s e t by a l l o f t he

ot he r s

. 3 6

Suppl y of U s e d C ar s

T he s uppl y of us e d c a r s a va i l a bl e of a pa r t i c ul a r c l a s s

, m a ke

, a nd a ge c a t e gor y

de pe nds on t he s t oc k ( gi ve n e ndo ge nous l y f r om de m a nd f or ne w c a r s i n p r e vi ous ye a r s ) a nd

t he r a t e a t w hi c h ve hi c l e s of t ha t t ype a r e s c r a ppe d. A t a ny gi ve n t i m e t i t i s c a l c ul a t e d by

a ddi ng t he pr e vi ous ye a r ’ s pr oduc t i on o f ne w c a r s t o t he pr e vi ous s uppl y of us e d c a r s

, a nd

de duc t i ng t he num be r of ve hi c l e s w hi c h a r e s c r a ppe d. S pe c i f i c a l l y:

w he r e a nd a r e t he qua nt i t y of us e d a nd ne w c a r s o f m a ke a nd c l a s s a va i l a bl e i n ye a r

t

, a n d r e pr e s e nt s t he a ve r a ge p r oba bi l i t y t ha t us e d c a r s of t ype a r e s c r a ppe d. T he

c om put a t i on i s pe r f o r m e d s e pa r a t e l y f o r t he t r a ns i t i ons be t w e e n e a c h of t he di f f

e r e nt a ge

c a t e gor i e s

.

T he pr oba bi l i t y t h a t a c a r i s s c r a ppe d i n a ny gi ve n ye a r i s de t e r m i ne d s i m ul t a ne ous l y

w i t h pr i c e s w he r e a h i ghe r c ur r e nt r e s a l e va l ue i m pl i e s a l ow e r r a t e of s c r a p

. T he r e l a t i ons hi p

i s c a pt ur e d s i m pl y i n t he m ode l a s :

( 20 )

w he r e i s a s c a l e pa r a m e t e r us e d f or c a l i br a t i on a n d i s a n e l a s t i c i t y c ont r ol l i ng t he

c ha nge i n s c r a p pr oba bi l i t y a s t he pr i c e of t he c a r c ha nge s

. 3 7 B a s e l i ne s c r a p r a t e s i nc r e a s e

w i t h c a r a ge

.

3 6 Mu l t i

- p ro d u ct o l i g o p o l y p ro b l e ms l i k e t h i s o n e h av e t h e p o t en t i al t o ex h i b i t mu l t i p l e eq u i l i b ri a,

al t h o u g h n o al t ern at i v e eq u i l i b ri a h av e ap p e ared i n my mo d el ev en u n d er w i d el y v ary i n g s t a rt i n g

v al u es

. T h e s t ab i l i t y o f t h i s p art i cu l ar s y s t em i s l i k el y d u e t o rel at i v el y s mal l c ro s s

- p ri ce el as t i ci t i es

an d t h e p r es en ce o f t h e mu ch l arg er, co mp et i t i v e u s ed c ar mark et

.

3 7 T h e el as t i ci t y i s s et t o

- 3 i n t h e cen t r al cas e, s ee Ben t o et al

. (2 0 0 9 ) fo r d i s cu s s i o n o f t h i s p ar am et er.25 E qui l i br i um

T he s ol ut i on t o t he num e r i c a l m ode l i s a s e t of ne w c a r pr i c e s

, us e d c a r pr i c e s

, a nd

t r a ns f e r s t o t he hous e hol d t ha t s i m ul t a ne ous l y c l e a r t he us e d c a r m a r ke t

, s ol ve t he p r oduc e r s ’

pr obl e m s s ubj e c t t o C A F E

, a nd ba l a nc e t he gove r n m e nt budge t

. S uppl y i n t he us e d c a r

m a r ke t a dj us t s a c c or di ng t o t he e l a s t i c i t y gi ve n i n ( 20 )

, w i t h a ggr e ga t e de m a nd de r i ve d f r om

t he s ol ut i on t o t he hous e hol ds ut i l i t y m a xi m i z a t i on pr obl e m s

. T he s ol ut i on t o t he s e c ond

c ondi t i on, e qui l i b r i um i n t he o l i gopol y p r obl e m f a c e d by pr oduc e r s

, i s a s e t of ne w c a r p r i c e s

t ha t m a xi m i z e s pr of i t s f or e a c h f i r m c ondi t i ona l on t he de c i s i ons of t he ot he r s

. T he m ode l

s ol ve s f or t he ne w c a r m a r ke t e qui l i br i um

, hol d i ng us e d c a r pr i c e s f i xe d

, a nd t he n s ol ve s t he

us e d c a r m a r ke t

. B e c a us e of t he i nt e r de pe nde nc e of de m a nds i n t he t w o m a r ke t s

, t hi s

pr oc e dur e i s i t e r a t e d t o c onve r ge nc e

. 3 8

T he t hi r d c ondi t i on

, ba l a nc e of t he gove r nm e nt bu dge t

, i s r e a c he d by a dj us t i ng t he

l e ve l of t he t r a ns f e r t o t he hous e hol d. I n t he s i m ul a t i on, t he gove r nm e nt r e c e i ve s r e ve nue

f r om p r e

- e xi s t i ng ga s ol i ne t a xe s a nd f r om t he f i ne s l e vi e d on vi o l a t or s of t he C A F E s t a nda r d.

I t r e t u r ns t he r e ve nue i n a f l a t l um p

- s um pa ym e nt t o hous e hol ds

. R e ve nue c ha nge s r e s ul t i ng

f r om t he C A F E s t a nda r d a r e t ypi c a l l y s m a l l ( t he i n c r e a s e i n f i ne s a nd t he de c r e a s e i n ga s ol i ne

t a x r e ve nue a c t i n oppos i t e di r e c t i ons ) s o t ha t r e l a t i ve l y l i t t l e a dj us t m e nt i s ne e de d i n t he

pa ym e nt s

. 3 9 T he s ol ut i on t o t he s ys t e m i s f ound us i ng B r oyde n’ s m e t hod, a de r i va t i ve

- ba s e d

qua s i

- N e w t on s e a r c h a l gor i t hm

.

b

. R e s u l t s

M y c e nt r a l pol i c y s i m ul a t i on i nvol ve s a n i nc r e m e n t of one m i l e pe r ga l l on t o t he

C A F E s t a nda r d. I di vi de t he num e r i c a l r e s ul t s f r o m t hi s s i m ul a t i on i n t o t h r e e pa r t s

. F i r s t

, I

pr e s e nt t he e f f

e c t s of t he pol i c y on e qui l i b r i um ga s ol i n e c ons um pt i on a nd w e l f a r e

, w i t h t he

l a t t e r br oke n dow n i nt o e f f

e c t s on c ons um e r a nd pr oduc e r s ur pl us

. S e c ond, I c om pa r e t he

3 8 Su b s t i t u t i o n p at t ern s b et w e en n e w an d u s ed v eh i cl es h av e t h e p o t en t i al t o mak e t h i s p ro b l em v ery

d i ffi cu l t co mp u t at i o n al l y

. In t h e ap p l i cat i o n h ere

, h o w ev er, co n v erg en ce b et w e en t h e t w o ma rk et s i s

reach ed i n r el at i v el y fe w s t ep s

.

3 9 T h i s i s n o t t ru e fo r i n cr em en t s t o t h e g as o l i n e t ax

, w h i c h h av e s u b s t an t i al rev en u e i mp l i cat i o n s

. T h e

met h o d i n w h i ch t h e r ev en u e i s ret u rn ed i s t h erefo re o f fi rs t

- o rd er i mp o rt an ce; t h i s i s s u e i s co n s i d ered

i n d et ai l i n Ben t o et al

. (2 0 0 9 )

.26 e f

f

e c t s of t he pol i c y on f ue l e c onom y a nd pr o f i t s a c r os s t he di f f

e r e nt pr oduc e r s

. T h i r d, I

e va l ua t e t he di s t r i but i on o f w e l f a

r e e f f

e c t s a c r os s h ous e hol d i nc om e gr oups

.

I a l s o pe r f o r m a s e c onda r y s i m ul a t i on w he r e a ga s ol i ne t a x t ha t r e duc e s ga s ol i ne

c ons um pt i on by t he s a m e a m ount a s t he C A F E s t a nda r d i s c ons i de r e d. A l l o f t he w e l f a r e

c ha nge s a r e e xpr e s s e d a s gr os s c os t s t ha t do not i n c l ude t he be ne f i t s a s s oc i a t e d w i t h t he

r e duc t i on i n ga s ol i ne us e i t s e l f

. 4 0 F i na l l y, I i nc l ude a n e xt e ns i on t ha t a l l ow s f or e ndoge nous

t e c hnol ogi c a l i m pr ove m e nt s i n f ue l e f f i c i e nc y i n r e s pons e t o t he C A F E s t a nda r d, a l l ow i ng a

m or e di r e c t c om pa r i s on of m y r e s ul t s w i t h t hos e i n A us t i n a nd D i na n ( 2005)

.

O v e r al l C hange i n G as ol i ne C ons um pt i on and W e l

f

ar e

T he f i r s t pa ne l of T a bl e 5 di s pl a ys t he c ha nge i n g a s ol i ne us e a nd f ue l e c onom y f r om a

one m i l e pe r ga l l on i nc r e a s e i n t he C A F E s t a nda r d. N ot i c e t ha t ga s ol i ne us e de c l i ne s i n t he

f i r s t ye a r by onl y 0. 8 pe r c e nt s i nc e t he s t a nda r d ha s not ye t ha d t i m e t o a f f

e c t us e d c a r s

. B y

ye a r 10, how e ve r

, ga s ol i ne us e ha s de c l i ne d 3

. 4 pe r c e nt f r om t he ba s e l i ne

. T he gr a dua l e f f

e c t

of t he s t a nda r d on t he us e d c a r f l e e t c a n be s e e n i n t he de c om pos i t i on of f ue l e c onom y

i m pr ove m e nt s a m ong ne w a nd us e d c a r s

. I nt e r e s t i ngl y, t he us e d f l e e t w i l l ne ve r f ul l y r e f l e c t

i m pr ove m e nt s i n ne w c a r f l e e t f ue l e c onom y due t o c ha ngi ng s c r a p r a t e s

. T hi s i s be c a us e

hi ghe r pr i c e s f o r l a r ge ve hi c l e s

, i nduc e d by t he i r r e l a t i ve s hor t a ge unde r C A F E

, r e s ul t i n

l ow e r s c r a p r a t e s ove r t i m e

. T hi s c r e a t e s a us e d c a r f l e e t w e i ght e d m or e he a vi l y t ow a r d l a r ge

ve hi c l e s

, a nd w i t h a c o r r e s pondi ngl y l ow a ve r a ge f ue l e c onom y r e l a t i ve t o ne w c a r s

.

T he s e c ond pa ne l of T a bl e 5 di s pl a ys t he ove r a l l w e l f a r e e f f

e c t a nd de c om pos e s i t i nt o

c ha nge s i n c ons um e r a nd pr oduc e r s ur pl us

. 4 1 N o t i c e f i r s t t ha t t he w e l f a r e l os s r i s e s t hr ough

t i m e

, r e f l e c t i ng t he i nc r e a s i ng i nc i de nc e of t he pol i c y on us e d c a r m a r ke t s i n t he l a t e r ye a r s

.

I nt ui t i ve l y, m uc h o f t he w e l f a r e l os s c om e s f r om t he s hi f t i n c om pos i t i on of t he ve hi c l e f l e e t

t ow a r d s m a l l ve hi c l e s : i n t he e a r l y ye a r s hous e hol d s w i t h a s t r ong pr e f e r e nc e f o r l a r ge

ve hi c l e s c a n s hi f t de m a nd t o t he us e d m a r ke t s a nd s o s uf f

e r s m a l l e r w e l f a

r e l os s e s

. O ve r

4 0 Se e fo r ex amp l e Pa rry et al

. (2 0 0 7 ) fo r es t i mat es o f t h e en v i ro n men t al an d s o ci al b en efi t s as s o ci at ed

w i t h r ed u ct i o n i n g as o l i n e u s e.

4 1 T h e w el far e l o s s i s m eas u red as t h e w ei g h t ed s u m o f e q u i v al en t v ari at i o n fo r each o f t h e h o u s eh o l d s

i n t h e mo d el

. T h i s i n cl u d es eff ect s o n p ro d u cer p ro fi t s

, s i n ce h o u s eh o l d s ar e as s u med t o o w n t h e

fi rms

. T h e d eco mp o s i t i o n s ep arat es t h e e ffe ct o n p ro d u cers fro m t h e t o t al w el far e co s t s

.27 t i m e

, how e ve r

, t he nu m be r o f l a r ge ve hi c l e s i n t he us e d m a r ke t i s a l s o di m i ni s he d, r e s ul t i ng i n

t he i nc r e a s i ng pa t t e r n o f w e l f a r e l os s e s

.

T hi s poi nt a l s o a ppe a r s c l e a r l y i n t he de c om pos i t i on of w e l f a

r e e f f

e c t s i nt o pr oduc e r

a nd c o ns um e r s ur pl us

. L os s i n p r oduc e r s ur pl us r e m a i ns r e l a t i ve l y s t a bl e ove r t i m e

, de c l i ni ng

s l i ght l y a s c om pe t i t i on f r om l a r ge ve hi c l e s i n t he u s e d m a r ke t de c l i ne s

. L os s i n c ons um e r

s ur pl us

, how e ve r

, r i s e s s ha r pl y ove r t i m e a s t he e f f e c t s of C A F E s t a nda r ds e nt e r t he us e d c a r

m a r ke t

.

D is t r i but i on of I nc i de nc e am ong P r oduc e r s

T a bl e 6 s how s t he e qui l i b r i um e f f

e c t s on t he s e ve n s i m ul a t e d pr oduc e r s a nd di s pl a ys

s t a r k c ont r a s t s be t w e e n pr oduc e r s of di f f

e r e nt t ype s

. F i r s t c ons i de r t he e f f

e c t s on f ue l

e c onom y: t he c ons t r a i ne d dom e s t i c f i r m s c om pl y w i t h t he s i m ul a t e d pol i c y a nd i nc r e a s e f ue l

e c onom y by one m i l e pe r ga l l on

. T he f or e i gn pr od uc e r s

, how e ve r

, a c t ua l l y r e duc e a ve r a ge

f ue l e c onom y i n r e s pons e t o t he i nc r e a s e d s t r i nge nc y. T hi s r e a c t i on i s of i nt e r e s t a s i t po i nt s

t o a n i m po r t a nt s our c e of i ne f f i c i e nc y i n C A F E s t a nda r ds a nd unde r s c or e s t he ne e d t o

c ons i de r he t e r oge ne i t y a m ong f i r m s i n pol i c y de c i s i ons

. I nt ui t i ve l y, C A F E s t a nda r ds c a us e

t he c ons t r a i ne d dom e s t i c m a ke r s t o s e l l a m or e f ue l e f f i c i e nt

— l i gh t e r or l e s s pow e r f ul

—

m i x of ve hi c l e s

. 4 2 T hi s m ove s t he r e s i dua l de m a nd c ur ve s f or ve hi c l e s w i t h hi gh ho r s e pow e r

a nd w e i ght t o t he r i ght f o r a l l ot he r p r oduc e r s

.

C ons i de r t he e f f

e c t of t hi s de m a nd s hi f t on unc ons t r a i ne d f i r m s : t he y c a n f r e e l y

s ubs t i t ut e i nt o a l e s s f ue l e f f i c i e nt f l e e t

, up t o t he a m ount of s l a c k i n t he s t a nda r d

, t a ki ng ove r

t he de m a nd f or l a r ge r ve hi c l e s

. 4 3 T he e f f

e c t on t he f i ne

- pa yi ng E u r ope a n pr oduc e r s c a n be

di vi de d i nt o t w o c om pe t i ng c om pone nt s : t he f i r s t e f f

e c t i s t he i nc r e a s e d m a r gi na l c os t of t he

f i ne

, w hi c h a c t s a s a n i nc e nt i ve t o i m pr ove f l e e t f u e l e c onom y. T he s e c ond i s t he out w a r d

m ove m e nt of r e s i dua l de m a nd f or l a r ge ve hi c l e s

, w hi c h a c t s i n t he oppos i t e di r e c t i on. T a bl e 6

s how s t ha t t hi s l a t t e r e f f

e c t dom i na t e s : t he vi o l a t i n g E ur ope a n p r oduc e r s

, l i ke t he

unc ons t r a i ne d f i r m s

, m ove i n t he di r e c t i on of a l e s s f ue l e f f i c i e nt f l e e t

.

T he di s t r i but i on of i nc i de nc e a m ong f i r m s a ppe a r s i n t he f i na l t w o r ow s of T a bl e 6:

T he c ons t r a i ne d dom e s t i c pr oduc e r s s uf f

e r e qui l i b r i um pr of i t l os s e s r a ngi ng f r om 4 t o 21

4 2 Red u ct i o n s i n en g i n e s i ze are c ap t u red as s h i ft s fro m l u x u ry t o n o n

- l u x u ry mo d el s

. Red u ct i o n s i n

w ei g h t an d w h eel b as e ap p ear as s h i ft s t o w ard mi d s i ze o r co mp act v eh i cl es

.

4 3 T h e s l ack i n t h e s t an d a rd w as ab o u t 4 mi l es p e r g al l o n fo r H o n d a an d T o y o t a i n 2 0 0 1

.28 pe r c e nt i n t he f i r s t ye a r

, w hi l e f or e i gn pr oduc e r s r e a l i z e i nc r e a s e d pr of i t s

. 4 4 T he pr of i t

i nc r e a s e s a r e r e a l i z e d by t a ki ng a dva nt a ge of i nc r e a s e d de m a nd f or l a r ge a nd l uxur y ve hi c l e s

,

w i t h H onda a nd T oyot a s e e i ng t he l a r ge s t ga i ns

. I c a nnot di s t i ngui s h s pe c i f i c c a r l i ne s

, bu t

t he di s t r i but i on o f m ode l s s ugge s t s t ha t H onda ’ s l u xur y A c ur a l i ne ( a nd T oyot a ’ s L e xus l i ne )

w oul d be r e s pons i bl e f or t he m a j o r i t y o f t he ga i ns

.

D is t r i but i on of W e l

f

ar e E f f

e c t s ac r os s I nc om e G r o ups

F i na l l y, I e xa m i ne t he di s t r i but i on of w e l f a r e e f f

e c t s a c r os s hous e hol ds by i nc om e

gr oup. M y a na l ys i s i s w e l l s ui t e d t o a ddr e s s i ng t he de ba t e ove r t he p r ogr e s s i vi t y of C A F E

s t a nda r ds s i nc e i t f ul l y m ode l s i n t e r a c t i ons w i t h t h e us e d c a r m a r ke t a nd i nc or por a t e s

c ons um e r he t e r oge ne i t y. I s how t ha t l ow

- i nc om e c ons um e r s

, w ho t e nd t o pur c ha s e us e d

ve hi c l e s

, a r e a f f

e c t e d s i gni f i c a nt l y by C A F E a nd t ha t t hi s e f f

e c t va r i e s i m por t a nt l y ove r t i m e

.

T he s e c ond c ol um n of T a bl e 7 di s pl a ys t he t ot a l w e l f a r e l os s a s a pe r c e nt a g e of

i nc om e

, w i t h t he t op a nd bot t om pa ne l s r e s pe c t i ve l y r e pr e s e nt i ng t he f i r s t a nd t e nt h ye a r of

t he s i m ul a t i on. I n ye a r 1

, t he w e l f a r e l os s i s s i m i l a r i n p r opor t i on a c r os s i nc om e gr oups due

t o t he l a r ge r a bs ol ut e i m pa c t o f di s t or t i ons i n ne w c a r m a r ke t s on w e a l t hy hous e hol ds

. 4 5 T h i s

i s a n a r gum e nt t ha t i s c om m onl y m a de t o s uppor t pr ogr e s s i vi t y of C A F E s t a nda r ds

, a nd I

c onf i r m t ha t i n t he f i r s t ye a r o f r e gul a t i on i t w or ks a s e xpe c t e d. I n c ont r a s t

, t he w e l f a r e

e f

f

e c t s i n t he t e nt h ye a r be c om e s ha r pl y r e gr e s s i ve

, w i t h l ow

- i nc om e hous e hol ds s uf f

e r i ng

w e l f a r e l os s e s ( a s a f r a c t i on o f i nc om e ) m or e t ha n t hr e e t i m e s a s l a r ge a s t hos e of t he hi gh

i nc om e gr oup. T hi s r e s ul t ha s be e n ove r l ooke d i n pr i or s t udi e s s i nc e i t a ppe a r s onl y w he n

c ons i de r i ng l onge r r un e f f

e c t s of C A F E i n us e d c a r m a r ke t s

. T he i nt ui t i on i s s i m pl y t ha t

C A F E w i l l

, ove r t i m e

, dr i ve up t he p r i c e of us e d v e hi c l e s a nd s hi f t t he c om pos i t i on o f t he

us e d ve hi c l e f l e e t t ow a r d s m a l l e r ve hi c l e s

. G i ve n t he s t r ong pr e f e r e nc e s f o r l a r ge ve hi c l e s

e s t i m a t e d us i ng t he hous e hol d da t a

, t he w e l f a r e e f f e c t s i n t he us e d m a r ke t r a pi dl y be c om e

i m por t a nt

.

4 4 Y ear 1 0 l o s s es are mo d e rat ed fo r d o mes t i c fi rms

, w h i l e fo r ei g n fi r ms b u i l d fu rt h er o n t h ei r p ro fi t

g ai n s

.

4 5 Pro d u c ers are as s u med t o b e o w n ed b y t h e h o u s eh o l d s i n p ro p o rt i o n t o i n co me

-- me an i n g a l o s s i n

p ro fi t s affe ct s h i g h

- i n co me h o u s eh o l d s mo r e t h an l o w

- i n co me h o u s eh o l d s

. H i g h i n co me h o u s eh o l d s

al s o b u y a l a rg er s h are o f n e w v eh i cl es

, me an i n g l o s s i n co n s u me r s u rp l u s i s s i mi l arl y d i s t ri b u t ed

.29 C

om par is on of t he C A F E St andar d and G as ol i ne T ax e s

T a bl e 8 o f f

e r s a c om pa r i s on of t he C A F E s t a nda r d w i t h a ga s ol i ne t a x. I n t he f i r s t

ye a r f ue l e c onom y s t a nda r ds a r e a f a r m or e c os t l y w a y t o r e duc e ga s ol i ne us e s i nc e t he i r

e f

f

e c t s ha ve not ye t e nt e r e d t he us e d f l e e t

. T he ye a r 10 c os t s of C A F E a r e c or r e s pondi ngl y

l ow e r

, a s f ue l e c onom y i m p r ove m e nt s s pr e a d t hr o ugh t he us e d f l e e t

, but s t i l l m o r e t ha n 6

t i m e s a s l a r ge a s t hos e a s s oc i a t e d w i t h t he ga s ol i ne t a x. I t ha s be e n e s t a bl i s he d i n t he

l i t e r a t ur e t ha t ga s ol i ne t a xe s a r e t ypi c a l l y m o r e e f f i c i e nt t ha n C A F E r e gul a t i on s i nc e t he y

ope r a t e bot h t hr ough c ha nge s i n m i l e s d r i ve n a nd c ha nge s i n ve hi c l e c hoi c e ; C A F E s t a nda r ds

a c t pr i m a r i l y t hr ough t he l a t t e r c ha nne l

. 4 6 T he m a gn i t ude of t he di f f

e r e nc e i n c os t s I f i nd

t he r e f or e r e f l e c t s t he ke y e l a s t i c i t i e s e s t i m a t e d i n t he de m a nd m ode l : c ons um e r s a dj us t dr i v i ng

pa t t e r ns ( i

. e

. m i l e s t r a ve l e d) f a

r m o r e e a s i l y t ha n t h e y a l t e r t h e i r c hoi c e of ve hi c l e

. N ot

s ur pr i s i ngl y, t he n

, a s s how n i n t he s e c ond r ow o f t he t a bl e

, t he e f f

e c t s of t he ga s ol i ne t a x e nt e r

a l m os t e xc l us i ve l y t hr ough t he m or e e f f i c i e nt m i l e s

- t r a ve l e d c ha nne l

.

T a bl e 8 a l s o o f f

e r s a n e xt e ns i on o f t he pr oduc e r m ode l t ha t a l l ow s e ndoge nous

t e c hnol ogi c a l i m pr ove m e nt i n f ue l e c onom y i n r e s pons e t o C A F E

. P r oduc e r s now ha ve t w o

i ns t r um e nt s t o c om pl y w i t h C A F E : t he y m a y a l t e r t he m i x of ve hi c l e s s ol d us i ng pr i c e s a s

be f or e

, a nd t he y c a n a l s o i m p r ove t he f ue l e c onom y of i nd i v i dua l m ode l s

. T he e xoge nous

f unc t i on r e l a t i ng i m pr ove m e nt i n f ue l e c onom y t o c os t s of pr oduc t i on i s t a ke n f r om t he

N a t i ona l R e s e a r c h C ounc i l a s s e s s m e nt of C A F E

, N R C ( 2002)

, a s i n A us t i n a nd D i na n ( 2005)

.

T he c os t s pe r ga l l on of ga s ol i ne s a ve d unde r C A F E a r e c ons i de r a bl y l ow e r a s a r e s ul t of t hi s

e xt e ns i on, but r e m a i n m or e t ha n t w i c e a s l a r ge a s t hos e of t he ga s ol i ne t a x.

T he t hi r d r ow of T a bl e 8 i ndi c a t e s t he f r a c t i on of t he w e l f a r e l os s bor ne by pr oduc e r s

.

I t i s ge ne r a l l y hi ghe r i n t he c a s e o f C A F E

, a s c a n b e e xpe c t e d gi ve n t ha t f ue l e c onom y

r e gul a t i on c ons t r a i ns f i r

m de c i s i ons di r e c t l y. I n t h e c a s e of e ndoge nous t e c hnol ogi c a l c ha nge

,

how e ve r

, t he c os t bo r ne by f i r m s f a l l s c ons i de r a bl y. T hi s i s i n a c c or da nc e w i t h t he c os t

e s t i m a t e s m a de by t he N R C ( 2002)

, w hi c h a l l ow r e l a t i ve l y i ne xpe ns i ve i m pr ove m e nt s i n f ue l

e c onom y. F i na l l y, I t r a ns l a t e t he c os t s pe r ga l l on i nt o e qui va l e nt c os t s pe r t on C O 2 a voi de d

i n t he bot t om r ow of t he t a bl e

.

4 6 Se e Parry et al

. (2 0 0 7 ) an d Po r t n ey et al

. (2 0 0 3 )

.30 7. C on c l u s i on

M y a ppr oa c h t o s t udyi ng t he e f f

e c t s of C A F E s t a n da r ds a l l ow s he t e r oge ne ous f i r m

r e s pons e a nd c ons i de r s e qui l i br i um i m pa c t s i n t he i nt e r r e l a t e d de m a nds f or ne w c a r s

, us e d

c a r s

, a nd ga s ol i ne

. T he pa r a m e t e r s a r e e s t i m a t e d w i t hi n t he p r oduc e r a nd hous e hol d m ode l s

a nd t he r e s ul t s c a n be us e d t o m e a s ur e ove r a l l w e l f a r e e f f

e c t s

, t he di s t r i but i on of c os t s a m ong

gr oups

, a nd t o de s c r i be unde r l yi ng m e c ha ni s m s t ha t i nf l ue nc e e f f i c i e nc y

.

I f i nd t ha t he t e r oge ne i t y a m ong f i r m s c a us e s t he pr of i t i m pa c t s of a n i nc r e a s e i n C A F E

t o f a l l a l m os t e xc l us i ve l y on dom e s t i c f i r m s

. I a l s o f i nd t ha t e qui l i br i um r e s pons e s

, dr i ve n by

f i r m he t e r o ge ne i t y, r e duc e t he e f f

e c t s of t he pol i c y on f i na l ga s ol i ne c ons um pt i on a nd

c ons e que nt l y i nc r e a s e t he e f f i c i e nc y c os t of t he r e g ul a t i on. E f f

or t s t o ha r m oni z e t he

r e gul a t i on a c r os s f i r m s

, t hus r e duc i ng t he i nc e nt i ve of unc ons t r a i ne d f i r m s t o s ubs t i t ut e i nt o

t he l a r ge ve hi c l e m a r ke t

, w oul d i m pr o ve t he e f f i c i e nc y pe r f or m a nc e of C A F E

. 4 7

I a l s o c onc l ude t ha t t he l ong r un e f f

e c t s of i nc r e m e nt s i n f ue l e c onom y s t a nda r ds a r e

not pr ogr e s s i ve l y di s t r i but e d a m ong i nc om e g r oup s a s m i ght be e xpe c t e d. A c om m on

a r gum e nt m a i nt a i ns t ha t s i nc e C A F E a f f

e c t s ne w c a r pr od uc e r s

, i t w i l l ha ve a g r e a t e r i m pa c t

on w e a l t hi e r hous e hol ds w ho pur c ha s e a di s pr opo r t i ona t e s ha r e of ne w ve hi c l e s

. B y

i nc l udi ng us e d c a r m a r ke t s a nd s i m ul a t i ng e f f

e c t s t hr ough t i m e

, how e ve r

, I f i nd t ha t i nc r e a s e d

pr i c e s a nd c ha nge s i n f l e e t c om pos i t i on f or us e d c a r s l e a d t o l a r ge r p r opor t i ona l w e l f a r e l os s e s

f

or l ow i nc om e hous e hol ds

. T hi s s ugge s t s t ha t C A F E s t a nda r ds

, i n m uc h t he s a m e w a y a s

ga s ol i ne t a xe s

, m us t be c om bi ne d w i t h pr ogr e s s i ve di s t r i but i ona l po l i c y i f t he r e i s a de s i r e t o

m a ke t he bur de n p r opor t i ona l a c r os s i nc om e gr oup s

.

I n a ggr e ga t e

, a nd a f t e r a c c ount i ng f o r c om pe t i t i on a m ong c a r pr oduc e r s a nd e f f

e c t s i n

t he us e d m a r ke t

, a one m i l e

- pe r

- ga l l on i nc r e m e nt i n t he s t a nda r d r e duc e s U

. S

. ga s ol i ne

c ons um pt i on by a bout 3 pe r c e nt

. I n t he f i r s t ye a r o f t hi s pol i c y 44 pe r c e nt of w e l f a r e c os t s a r e

bor ne by p r oduc e r s

, w i t h t hi s s ha r e f a l l i ng t o l e s s t ha n 20 pe r c e nt by t he t e nt h ye a r

. T he c os t s

i n l a t e r ye a r s c om e pr i m a r i l y f r om l os s e s i n c ons um e r s ur pl us a s t he e f f

e c t s of t he pol i c y e nt e r

t he us e d c a r f l e e t

.

4 7 T rad ab i l i t y o f cred i t s ac ro s s fi r ms o ff ers o n e p o t en t i al s o l u t i o n

. N o t i ce t h at t h e fi rm h et ero g en ei t y I

d es cri b e s u g g es t s l arg e d i s t ri b u t i o n al co n s eq u en ces t h at co u l d m ak e s u ch a s y s t em d i f fi cu l t t o

i mp l emen t

.31 A num be r o f i m po r t a nt c a ve a t s i n t he m ode l a nd p oi nt s f or f ut ur e r e s e a r c h r e m a i n.

P r i nc i pl e a m ong t he m i s c ons i de r a t i on o f i nduc e d t e c hnol ogi c a l c ha nge pr om pt e d by f ue l

e c onom y r e gul a t i on. F i r m he t e r oge ne i t y

, a l ong t h e l i ne s de s c r i be d i n t hi s pa pe r

, m a y

pot e nt i a l l y be us e d t o i de nt i f y d i f f

e r e nc e s i n i nc e nt i ve s t o de ve l op f ue l e f f i c i e nc y e nha nc i ng

t e c hnol ogy. A de e pe r unde r s t a ndi ng o f t he de m a nd

- s i de t r a de of f

s be t w e e n f ue l e c onom y a nd

ve hi c l e a t t r i but e s l i ke w e i ght a nd hor s e pow e r i s a l s o e s s e nt i a l i n a ppr oa c hi ng t hi s i s s ue

. M y

f i ndi ngs he r e pr ov i de a s t a r t i ng poi nt f or t hi s ongoi ng r e s e a r c h a nd pr e s e nt a ba s e of e m pi r i c a l

c onc l us i ons a bout f i r m be ha vi or a nd e f f i c i e nc y c os t s unde r C A F E r e gul a t i on.32 R e f e r e n c e s

A us t i n, D

. a nd T

. D i na n ( 2005)

, “ C l e a r i ng t he A i r : T he C os t s a nd C ons e que nc e s of H i ghe r

C A F E S t a nda r ds a nd i nc r e a s e d G a s ol i ne T a xe s

, ” J our nal of E nv i r onm e nt al E c onom i c s and

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. a nd J

. S a l l e e ( 2009 )

, " U s i ng L oophol e s t o R e ve a l t he M a r gi na l C os t of

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- E c onom y S t a nda r ds

. " W or ki ng pa pe r

, U ni ve r s i t y of C hi c a go

a nd M i c hi ga n S t a t e U ni ve r s i t y, ht t ps : / / w w w

. m s u. e du/

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, “ I m pa c t s of L ong

- R a nge I nc r e a s e s i n t he C or por a t e A ve r a ge F ue l E c onom y

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, " N e w V e hi c l e C ha r a c t e r i s t i c s a nd t he C os t of t he C or por a t e

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. " F e de r al R e s e r v e B ank of C hi c ago W or k

i ng P ape r 2008

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, Sum m ar y O f F ue l E c onom y

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N a t i ona l H i ghw a y T r a f f i c S a f e t y A d m i ni s t r a t i on ( 2009b)

, Sum m ar y O f C A F E F i ne s

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e c t i v e ne s s and I m

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A F E

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, “ T he E c onom i c s o f F ue l

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. ( 1986)

, Q ual i t at i v e C hoi c e A nal y

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. ( 2004)

, “ D i s t r i but i ona l E f f

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J

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W hi t e H ous e O f f i c e of t he P r e s s S e c r e t a r y ( 2009 )

, P r e s i de nt O bam a A nnounc e s N at i onal

F

ue l E f f

i c i e nc y P ol i c y

, ht t p: / / w w w

. w hi t e hous e

. gov/ t he _pr e s s _of f i c e / P r e s i de nt

- O ba m a

A nnounc e s

- N a t i ona l

- F ue l

- E f f i c i e nc y

- P o l i c y/

.T a bl e 1: A ve r a ge D e vi a t i on f r om C A F E S t a nda r d by F i r m

, 1990

- 2001T a bl e 2: E s t i m a t e s of a nd

T a bl e 3: F i r m a nd F l e e t M a r gi na l E f f

e c t sT a bl e 4: V e hi c l e P r i c e s a nd Q ua nt i t y of B a nke d o r B or r ow e d C A F E C r e di t sT a bl e 5: E f f

e c t on G a s ol i ne C ons um pt i on a nd W e l f a r e

of a 1 M P G I nc r e m e nt i n t he C A F E S t a nda r d

T a bl e 6: P r oduc e r R e s pons e t o a 1 M P G I nc r e m e n t i n t he C A F E S t a nda r dT a bl e 7: D i s t r i but i on of W e l f a r e E f f

e c t s of a 1 M P G I nc r e m e nt i n t he C A F E S t a nda r d

T a bl e 8: C om pa r i s on of I nc r e a s e i n C A F E a nd I nc r e a s e i n G a s ol i ne T a xF i gur e 1: T oyot a

, F or d

, a nd B M W : F l e e t F ue l E c onom i e sF i gur e 2: F l e e t F ue l E c onom i e s by F i r m T ypeA

- 1 A p p e n d i x A : A l t e r n at i ve S p e c i f i c at i on s a n d T e s t s

T hi s a ppe ndi x e xt e nds t he e c onom e t r i c m ode l of S e c t i on 4 t o c ons i de r di f f

e r e nt

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or m s

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m s

.

Y

e ar f i x e d e f f

e c t s

M y e s t i m a t i on of t he s ha dow c os t s us i ng a pool e d s a m pl e r e s t s on t he a s s um pt i on

of r e l a t i ve l y s t a bl e de m a nd c ondi t i ons ove r t he pe r i od 1997

– 2001. T he s e c ond c ol um n o f

T a bl e A 1 s how s t ha t t he e s t i m a t e s of a r e ne a r l y u nc ha nge d w he n i nc l udi ng f i xe d

e f

f

e c t s by ye a r

. T he e s t i m a t e d c oe f f i c i e nt s on ye a r a r e a l s o r e l e va nt a s t he y s i gna l

c ha nge s i n a ve r a ge m a r kups ove r t i m e : N one of t h e c oe f f i c i e nt s a r e s i gni f i c a nt l y

di f f

e r e nt f r om z e r o or one a not he r a nd t he i r m a gni t ude s a r e a l l l e s s t ha n 0. 05 i n a bs ol ut e

va l ue

. 1 T hi s l e nds s om e s uppor t t o t he a s s e r t i on t ha t a ve r a ge m a r kups

, a nd by a s s oc i a t i on

de m a nd c ondi t i ons

, w e r e s t a bl e ove r t he ye a r s c on s i de r e d.

St r uc t ur e of f

i x e d e f f

e c t s

T he r a t i o of m a r kups

, , i s t he f oc us of t he l i t e r a t ur e a nd a l s o t he pa r a m e t e r I

a l l ow t o va r y by m a ke a nd f l e e t i n t he c e nt r a l c a s e

. C ol um n 3 of T a bl e A 1 c ons i de r s t he

a l t e r na t i ve

, w he r e i s i ns t e a d a l l ow e d t o va r y a nd i s e s t i m a t e d a s a s c a l a r

. T he

c oe f f i c i e nt s of i nt e r e s t a r e s l i ght l y r e duc e d i n m a g ni t ude

, a l t hough a l l t ha t a r e s i gni f i c a nt

i n t he c e nt r a l s pe c i f i c a t i on r e m a i n s o.

P l ac e bo t e s t

A n i ns t r uc t i ve pl a c e bo t e s t i s t o i m a gi ne t ha t t he ot he r 4 m a nuf a c t u r e r s ( H onda

, T oyot a

, O t he r A s i a n, a nd E u r ope a n) a r e i n f a c t c o ns t r a i ne d by C A F E a r ound t he i r

a ve r a ge f ue l e c onom y. T hi s a l l ow s t he c ons t r uc t i o n of t he L i C a nd L i T va r i a bl e s

, a nd

e s t i m a t i on t oge t he r w i t h t he c ons t r a i ne d dom e s t i c f i r m s

. T he r e s ul t s a ppe a r i n c ol um n 4

of T a bl e A 1. W hi l e t he c oe f f i c i e nt s a r e m or e o f t e n pos i t i ve t ha n ne ga t i ve none i s

s i gni f i c a nt a t t he 5 % l e ve l

. T he c oe f f i c i e nt on E ur ope a n c a r s i s pos i t i ve a nd ha s t he

l a r ge s t t

- s t a t i s t i c ( 1. 63 )

, pe r ha ps pi c ki ng up t he e f f e c t s of t he C A F E f i ne s t ha t a l t e r t he

pr i c i ng of E u r ope a n i m por t s

. N ot e t ha t t he s e ve hi c l e s t e nd t o ha ve hi gh ba s e pr i c e s a nd

a r e pa r t o f a n a gg r e ga t e t ha t i nc l ude s c om pl yi ng c om pa ni e s

, s o w e s houl dn’ t e xpe c t t he

di f f

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- 1 A p p e n d i x B : D yn a m i c s of B an k i n g a n d B or r o w i n g i n U

. S

. C A F E R e gu l at i on

T hi s a ppe ndi x pr ovi de s a n out l i ne o f t he dyna m i c de c i s i ons m a de by f i r m s i n t he

c ont e xt of C A F E ba nki ng a nd bor r ow i ng

.

B ank i ng and bor r ow i ng r ul e s

U nde r t he r ul e s e s t a bl i s he d f or t he C A F E pr og r a m

, a s e t of c e r t i f i e d f l e e t f ue l

e c onom i e s i s pr oduc e d f or e a c h f i r m on a n a nnua l ba s i s

. D e vi a t i ons f r om t he s t a nda r d

a r e f i r s t us e d t o of f

s e t t he f i r m ’ s s t oc k o f c r e di t s o r de bt s

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, de vi a t i o ns f r om t he s t a nda r d a r e “ ba nke d” f o r

t hr e e ye a r s i nt o t he f ut u r e

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f

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. T he f ol l ow i ng e xa m pl e i l l us t r a t e s t he a c c ount i ng m e t hod us e d: t he “ de vi a t i on” i n

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a nd a ne ga t i ve va l ue i f i t i s be l ow

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f ut ur e

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. N ot i c e t ha t i n ye a r 9

t he f i r m ha s a n e xpi r i ng de bt t ha t i t f a i l s t o r e pa y, a nd s o i t i s f i ne d $50 pe r ve hi c l e

.B

- 2 A n i nt e r e s t i ng f e a t ur e of t hi s a c c ount i ng s ys t e m i s t ha t a f i r m ’ s a c t i on ha s t he

pot e nt i a l t o a f f

e c t vi ol a t i on i n a ny f ut ur e ye a r

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. F o r

e xa m p l e

, i f t he f i r m ha d de vi a t e d by

- 1 i ns t e a d o f

- 2 m i l e s pe r ga l l on i n t he f i r s t ye a r o f

r e gul a t i on, i t c oul d ha ve a voi de d vi ol a t i on a l t oge t h e r i n t he 9t h ye a r

. T hi s r e s ul t i s

s om e w ha t c ount e r

- i nt ui t i ve

, s i nc e one m i ght e xpe c t t he t h r e e

- ye a r l i m i t on ba nki n g a nd

bor r ow i ng t o l i m i t t he de pe nde nc e of c ur r e nt vi ol a t i ons on a c t i ons l ong i n t he pa s t

. T he s e t of ne c e s s a r y a nd s uf f i c i e nt c ondi t i ons f o r c om pl i a nc e c a n be w r i t t e n a f t e r

de f i ni ng t he e vol ut i on of t he pa r a m e t e r s t hr ough t i m e

. T he r e a r e f ou r c a s e s t ha t m us t

be c ons i de r e d. T he c a s e of pos i t i ve a nd ne ga t i ve Y i s pr ovi de d a s a n e xa m pl e i n t he

m a i n t e xt ; t he a c c ount i ng de f i ni t i ons i n t he r e m a i ni ng c a s e s a r e pr ovi de d be l ow

. N ot i c e

t ha t t he a c c ount i ng m e t hod m e a ns t ha t a f i r m c a n n ot c a r r y bo t h c r e di t s a nd de bt s a t t he

s a m e t i m e

, s o i f a ny i s pos i t i ve ( ne ga t i ve ) a l l of t h e ot he r s a r e w e a kl y pos i t i ve

( ne ga t i ve )

.

F or ( ≥ 0 a nd Y ≥ 0) o r ( < 0 a nd Y < 0 ) :

F or < 0 a nd Y ≥ 0 :

A f t e r c om put i ng t he e vol ut i on of c r e di t s a nd de bt s a s a bove

, t he c om pl i a nc e c ondi t i on

i t s e l f c a n be de f i ne d e a s i l y. A f i r m i s i n c om pl i a nc e w i t h r e gul a t i on i n a l l ye a r s t i f a nd

onl y i f :B

- 3 T he f i r m ’ s f u l l m a xi m i z a t i on pr obl e m ove r t i m e ( w i t hout di s c ount i ng) c a n t he n be

w r i t t e n a s :

w he r e

.

T he pr obl e m f or t he unc ons t r a i ne d f i r m r e duc e s t o pe r i od

- by

- pe r i od pr of i t

m a xi m i z a t i on s i nc e t he r i ght ha nd t e r m dr ops out

. F or c ons t r a i ne d f i r m s

, how e ve r

, t he

c ons t r a i nt i nc l ude s m ul t i pl e di s c ont i nui t i e s a nd t he c om pl e t e hi s t or y o f a f i r m ’ s a c t i ons

( s i nc e I de pe nds on t he e nt i r e t i m e s e r i e s of

, , a nd )

. I n or de r t o s i m pl i f y t he

pr obl e m f o r e s t i m a t i on I de f i ne c om pl i a nc e i n a s i ngl e ye a r a s Y

t ≥ 0

. T hi s i s a s uf f i c i e nt

c ondi t i on f or c om pl i a nc e i n t he dyna m i c m ode l

, b ut a bs t r a c t s f r om ba nki ng a nd

bor r ow i ng. I f de m a nds a r e c e r t a i n a nd s t a bl e ove r t i m e a nd a s s um i ng c onve x pr of i t s w i t h

r e s pe c t t o f l e e t f ue l e c onom y, how e ve r

, t he pe r i od

- by

- pe r i od s ol ut i on t o t he s t a t i c

pr obl e m c oi nc i de s w i t h t he s ol ut i on t o t he f u l l dyn a m i c pr obl e m a bove

.