Full text of Working Papers (Federal Reserve Bank of Chicago) : Price Ceilings as Focal Points for Tacit Collusion : Evidence From Credit Cards, Working Paper 2001-12

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sW +s2 , @ duj pd{  +s > s2 ,

+D6,

zkhuh F lv wkh ohyho ri wkh sulfh fhlolqj1
Ghqh

R

dv up 4*v vkruw0uxq ehvw uhvsrqvh wr up 5*v sulfh1 Wkxv/ zh fdq uhsuhvhqw up 4*v surwv zkhq
lw sod|v lwv ehvw uhvsrqvh wr up 5*v sulfh dw wkh fhlolqj e|
 +sW +F,> F,

+D7,

 +QF> QF,

+D8,

QF @ sW +QF,> QF @ sW2 +QF,

+D9,

dqg wkh qrqfrrshudwlyh surwv dv

zkhuh

65
Iru vlpsolflw| zh dvvxph wkdw
 +QF> QF, @ 3

+D:,

Qrwh wkdw doo ri wkh deryh fdq dovr eh uhsuhvhqwhg xvlqj htxlydohqw qrwdwlrq lq whupv ri sulfhv
dqg ghpdqg/ zkhuh
 +s > s2 , @ s G +s > s2 ,

2

+D;,

tt4T|L?t

Zh pdlqwdlq wkuhh dvvxpswlrqv uhjduglqj frpshwlwlrq=
+4, Wkh wzr jrrgv duh vxevwlwxwhv=
CG +s > s2 ,
A3
Cs2

+D<,

CsW
A3
Cs2

+D43,

+5, Sulfhv duh vwudwhjlf frpsohphqwv=

+6, Wkh rzq0sulfh hodvwlflw| ri ghpdqg lv juhdwhu lq devroxwh ydoxh wkdq wkh furvv0sulfh hodvwlflw|
ri ghpdqg=
CG +s > s2 ,
CG +s > s2 ,
?
Cs2
Cs



+D44,

@?}it ? |i 5t|@?@M*|) Lu A@U| L**tL?

Zh duh lqwhuhvwhg lq h{dplqlqj fkdqjhv lq wkh vxvwdlqdelolw| ri wdflw frooxvlrq dv wkh fhlolqj fkdqjhv1
Wklv vxvwdlqdelolw| zloo ghshqg rq wkh surwv iurp frrshudwlrq dqg wkh surwv iurp fkhdwlqj1 Zh
fdq uhsuhvhqw fkdqjhv lq wkh fhlolqj dv ehlqj htxlydohqw wr fkdqjh lq s2 / xqghu wkh dvvxpswlrq wkdw
up 5 wdflwo| frooxghv e| pdwfklqj wkh fhlolqj1
Frqvlghu uvw wkh vlpsoh fdvh lq zklfk F @ QF 0 wkdw lv/ wkh fhlolqj lv vhw dw wkh qrqfrrshudwlyh
sulfh1 Reylrxvo|/ vxvwdlqlqj wdflw frooxvlrq lv wulyldoo| hdv| lq wklv vlwxdwlrq1 Zh fdq qrwh/ krzhyhu/
wkdw zkhq F @ QF=
g +QF> QF,
g +sW +QF,> QF,
A
gs2
gs2

+D46,

66
Wkdw lv/ iru vpdoo fkdqjhv lq wkh fhlolqj/ wkh fkdqjh lq surwv iurp fkhdwlqj lv pruh srvlwlyh
wkdq wkh fkdqjh lq surwv iurp frrshudwlrq1 Wklv phdqv wkdw fkhdwlqj ehfrphv lqfuhphqwdoo|
pruh dwwudfwlyh wkdq frrshudwlrq/ dv wkh fhlolqj ulvhv voljkwo| deryh wkh qrqfrrshudwlyh sulfh1 Wkh
lqwxlwlrq ehklqg wklv lv idluo| fohdu= wkh ohiw0kdqg vlgh ri wkh deryh h{suhvvlrq doorzv up 4 wr
uh0rswlpl}h edvhg rq wkh fkdqjh lq s2 / zkloh wkh uljkw0kdqg vlgh grhv qrw ehfdxvh lw frqvwudlqv up
4 wr pdlqwdlq s @ F1
Nqrzlqj wkdw fkhdwlqj ehfrphv pruh dwwudfwlyh dv wkh fhlolqj ulvhv durxqg F @ QF/ zh wkhq
dgguhvv wkh lvvxh ri zkwd kdsshqv eh|rqg wkdw srlqw1 Wr orrn dw wklv pruh forvho|/ zh h{dplqh wkh
vhfrqg ghulydwlyhv ri surwv xqghu frrshudwlrq dqg fkhdwlqj1
Wkh vhfrqg ghulydwlyh ri wkh surw ixqfwlrq xqghu fkhdwlqj lv vlpsohu/ vr zh zulwh lw uvw=
2
g2 +sW +F,> F,
CsW CG +=,
W C G+=,
@
.
s

Cs2 Cs2
gs22
Cs22

Zh qrwh wkdw vrph whupv kdyh gursshg rxw ehfdxvh ri wkh hqyhorsh wkhruhp uhvxowv wkdw dw wkh
vkruw0uxq ehvw uhvsrqvh/
C+sW +F,> F,
@3
Cs
Khuh zh pdnh wkh vlpsoli|lqj dvvxpswlrq wkdw wkh vhfrqg ghulydwlyhv ri ghpdqg duh }hur1 Wklv
phdqv wkdw

g2 +sW +F,> F,
CsW CG +=,
@ 
2
Cs2 Cs2
gs2

Wklv h{suhvvlrq lv vwulfwo| srvlwlyh e| dvvxpswlrqv +4, dqg +5, 0 wkdw wkh jrrgv duh vxevwlwxwhv
dqg sulfhv duh vwudwhjlf frpsohphqwv1
Wkh vhfrqg ghulydwlyh ri surwv xqghu frrshudwlrq zlwk uhvshfw wr wkh fhlolqj lv=



 2
g2 +F> F,
CG +=, CG +=,
C G +=,
C 2 G +=, C 2 G +=,
.5
@F
.5
.
.
Cs Cs2
Cs2
Cs
gs22
Cs2
Cs22
Djdlq/ li wkh vhfrqg ghulydwlyhv ri ghpdqg duh }hur wkh h{suhvvlrq vlpsolhv wr=


CG +=, CG +=,
g2 +F> F,
@
5
.
Cs2
Cs
gs22
Wklv lv vwulfwo| qhjdwlyh e| dvvxpswlrq +6,/ wkdw wkh rzq0sulfh hodvwlflw| ri ghpdqg lv juhdwhu
wkdq wkh furvv0sulfh hodvwlflw| ri ghpdqg1 Wkxv/

g2 +sW +F,> F,
g2 +F> F,
A
3
dqg
?3
gs22
gs22

67
Dorqj zlwk wkh uvw uhvxow/ wkdw
g +sW +QF,> QF,
g +QF> QF,
A
gs2
gs2

+43,

wklv lpsolhv wkdw
g+sW +F,> F,
g+F> F,
A
gs2
gs2
iru dq| F A QF1 Wkxv/ wkh surwv iurp fkhdwlqj ulvh idvwhu wkdq wkh surwv iurp frrshudwlrq1

68



A@M*it
Wdeoh 4= Fuhglw Fdug Lqwhuhvw Udwh Fhlolqjv/ 4<:<04<;<
\hdu

4<:<

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74

73

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68

69

69

73

6:

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64

Qr Fhlolqj

9(

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66(

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67(

66(

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468

466

457

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449

448

433

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5(

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Vkduh ri Vwdwhv=

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Vrxufhv= Wkh Frvw ri Shuvrqdo Eruurzlqj lq wkh Xqlwhg Vwdwhv dqg Txduwhuo| Uhsruw ri Udwhv
ri Vhohfwhg Gluhfw Frqvxphu Lqvwdoophqw Ordqv/ ydulrxv lvvxhv1

69
Wdeoh 5= Fuhglw Fdug Sulflqj dqg Lqwhuhvw Udwh Fhlolqjv
4<:<

;3

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Vkduh ri Lvvxhuv dw Fhlolqj=
Doo Idflqj Fhlolqj

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3165

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318;

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vshflfdwlrq lqfoxghv d gxpp| yduldeoh iru hdfk vwdwh lq wkh vdpsoh1 Ohyho ri fhlolqj vshflfdwlrq
lqfoxghv d frqvwdqw whup dqg wkh ohyho ri wkh lqwhuhvw udwh fhlolqj lq wkh lvvxhu*v krph vwdwh1

6:
Wdeoh 6= Dyhudjh Lqwhuhvw Udwhv e| Fhlolqj
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Qr Fhlolqj

4913

4913

4;1:

4;1;

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4615

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441;

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816

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4<146

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4867

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5;4;7

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483:

649

} Uhsruwhg lq 4<;604<;7 grooduv1

44<4

6<
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31435
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31439WW
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313<3WW
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313:7WW
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KKL

314;5
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3=49:WWW
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314;7WWW
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31533WWW
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313;;WW
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314:4WWW
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31494WWW
+3=35:,

3=3<;
+=43;,

31434
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3=463
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313<7
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3=3;6
+3=386,

Sulflqj Htxdwlrq=

314<7WWW
+3=36<,

FF Ordqv
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Xqhpsor|phqw
Lqfrph

3=657WWW
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Suredelolw| ri Wdflw Frooxvlrq=
Frqvwdqw
Sulfh Fhlolqj

3=4;3WWW
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31458WW
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3=437W
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3=665WWW
+31399,
3=346WWW
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31663WWW
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3=334
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3=6:7WWW
+31369,
3=337WWW
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3=6:5WWW
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31337WWW
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4=534WWW
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31;;9WWW
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4<136WWW
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4=353WWW
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3=3:6WW
+3=366,
3144;WWW
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3=388
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3=343WWW
+3=336,

4314<WWW
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3=688WWW
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3=44;WWW
+3=385,
3144:WWW
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313<8WW
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31348WWW
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31755
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4=363WWW
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4<;4/4<;5

4=8:<WWW
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4<;6/4<;7
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3=94<
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4=:8;WWW
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4=57;WWW
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4164WWW

5=74;WWW
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4165WWW

\hv
483:

\hv
483:

5=76<WWW
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4<;:/4<;;



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4176WWW

5=9:;WWW
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4166WWW

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0Q0

Q2D
483:

Qr
483:

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483:

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W WW dqg WWW ghqrwh vljqlfdqfh dw wkh 3143/ 3138 dqg 3134 ohyhov1

5=57;WWW
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73

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4<;40;5

4<;60;7

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51;< +5:<,

3199 +8<,

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413: +49,

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4198 +54,

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41;5 +94,

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319; +78,

319: +49,

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04177 +7,

031:: +46:,

031<3 +9;,

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031:7 +596,

z@4

6136 +58;,

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31;5 +57,

31:: +73,

31:; +47,

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0516; +<,

~

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4137 +53,

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677

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564

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483:

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Qrwhv= _Dw Fhlolqj% urz lqfoxghv doo lvvxhuv iru zklfk s| @ F| 1 Lvvxhuv zlwk sa| ? F| duh
a @ 31 Qxpehuv lq sduhqwkhvhv duh qxpehu
dvvljqhg z
a @ 4/ dqg lvvxhuv zlwk sa|  F| duh dvvljqhg z
ri lvvxhuv lq fdwhjru|1 Xqlwv duh kxqguhgv ri edvlv srlqwv1 _Q% urz vkrzv wrwdo qxpehu ri lvvxhuv
lq vdpsoh1

74
Wdeoh := Hqwu| Uhjuhvvlrqv
Yduldeoh
Sulfh Hhfw

Prgho 4

Prgho 5

Prgho 6

31344WW

31356WWW

+31339,

+3133:,

Prgho 7

03135;WWW

Sulfh HhfwG;8;<

+31343,
Sulfh Hhfwn

3133:

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31359WW

31363WW

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031379
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319<8WWW

319<6WWW

31:46WWW

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031;4;WWW

031:<6WWW

031;:9WWW

031;:6WWW

+31445,

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phufldo edqnv zlwk srvlwlyh fuhglw fdug ordqv/ lq wkh |hdu iroorzlqj wkh phdvxuhphqw ri wkh sulfh
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75



6}hit
C<18

C=18

18<C<24

C>=24

1

Fraction of States (with >1 observation)

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

(0, 0.25]

(0.25,
0.50]

(0.50,
0.75]

(0.75,
1.00)

1

Share of Issuers at Ceiling

Iljxuh 4= Klvwrjudpv ri Zlwklq0Vwdwh Vkduh dw Fhlolqj/ e| Ohyho ri Fhlolqj

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10

12

14
1979-1984

16
1985-1986

18

20
1987-1988

22

24

26

1989

Iljxuh 5= Suredelolw| ri Wdflw Frooxvlrq yv1 Sulfh Fhlolqj/ e| \hduv

76

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10

12

14

16

18

20

22

24

26

Average
High HHI, CCLoans, Auto Rate and Low Income
Low HHI, CC Loans, Auto Rate and High Income

Iljxuh 6= Suredelolw| ri Wdflw Frooxvlrq e| KKL/ FF Ordqv/ Dxwr Udwhv dqg Lqfrph1
Full text of Working Papers (Federal Reserve Bank of Chicago) : Price Ceilings as Focal Points for Tacit Collusion : Evidence From Credit Cards, Working Paper 2001-12

FRASER
