BLS WORKING PAPERS
U.S. DEPARTMENT OF LABOR
Bureau of Labor Statistics
OFFICE OF PRICES AND LIVING
CONDITIONS
Is Adverse Selection Simply Moral Hazard?
Evidence from the 1987 Medical Expenditure Survey
Ralph Bradley, U.S. Bureau of Labor Statistics
Working Paper 360
May 2002
All views expressed in this paper are those of the author and do not reflect the views or policies of the Bureau of
Labor Statistics.
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lv wkh h{shfwhg xwlolw| jdlq iurp kdylqj d orzhu h{shfwdwlrq ri vlfnqhvv1 Qrwlfh
wkdw d fkdqjh lq h zloo orzhu wkh lqvxuhu*v uhlpexuvhphqwv/ exw wkh lqglylgxdo lv
qrw frpshqvdwhg iru wklv fkdqjh1 Wkxv/ wkhuh lv d qhz vrxufh ri pdunhw idloxuh1
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iru h{rjhqrxv dgyhuvh vhohfwlrq e| hvwlpdwlqj wkh vlpsoh fryduldqfh ehwzhhq
z dqg v> wkh uhvxow lv eldvhg ehfdxvh wkh hhfwv ri hruw kdyh ehhq ljqruhg1
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Grzg hw do1 +4<<4, glg qrw qg dgyhuvh vhohfwlrq lq wkhlu vwxg| hyhq wkrxjk lw
frxog vwloo eh suhvhqw1
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ri vl exw hlm grhv1 Lq wklv vlwxdwlrq/ wkh dgyhuvh vhohfwlrq sureohp lv frpsohwho|
hqgrjhqrxv zkhuh Chlm +z,@Cz @ 3> dqg |hw C+hl > zl ,@Chl ? 31
Zkloh wklv lv qrw d plfur wkhru| sdshu/ lw vhhpv sodxvleoh wkdw rswlpdo
lqwhuyhqwlrqv zloo ghshqg rq hqgrjhqhlw| ri dgyhuvh vhohfwlrq1 Wkh qh{w vhfwlrq
ghvfulehv krz L whvw iru wkh fruuhfw irup ri dgyhuvh vhohfwlrq1
6
Vshflfdwlrq ri wkh Hfrqrphwulf Prgho
Zkhq L vshfli| wkh phglfdo h{shqglwxuh prgho/ L dffrxqw iru wkuhh vw|ol}hg idfwv1
Iluvw/ wkhuh duh lqglylgxdov zkr gr qrw pdnh dq| phglfdo h{shqglwxuhv1 Vhfrqg/
hyhq zkhq wkh frlqvxudqfh udwh lv }hur iru ihh iru vhuylfh sodqv/ lqglylgxdov
43
vshqg d qlwh dprxqw rq phglfdo fduh1 Wklug/ wkh ghpdqg iru phglfdo jrrgv
lv dhfwhg e| wzr glhuhqw w|shv ri udqgrp yduldeohv/ wkh uvw lv wkh vhyhulw|
ri looqhvv/ dqg wkh vhfrqg lv wkh lqflghqfh ri dq dfflghqw1 D shuihfwo| khdowk|
shuvrq zkr lv lqyroyhg lq dq dfflghqw zloo ghvluh pruh phglfdo h{shqglwxuh
wkdq vkh zrxog li vkh kdg qrw ehhq lq dq dfflghqw1 Krzhyhu/ lw grhv qrw vhhp
srvvleoh wkdw wkh h{rjhqrxv vljqdo vkrxog eh deoh wr ehwwhu suhglfw wkh lqflghqfh
ri dq dfflghqw> li dq hyhqw fdq eh dqwlflsdwhg wkhq lw uhdoo| lv qrw dq dfflghqw: 1
Krzhyhu/ wkhuh duh hruwv wkdw wkh lqglylgxdo fdq pdnh lq rughu wr orzhu wkh
suredelolw| ri dq dfflghqw1 Lq wkh vhfrqg vxevhfwlrq ri wklv vhfwlrq/ L dwwhpsw
wr vshfli| d prgho wkdw kdv wkh suredelolw| ri dq dfflghqw ghshqghqw rq wkh
hqgrjhqrxv hruw fkrlfh1 Lq wklv vwxg|/ wkh dfflghqw lv d elqdu| yduldeoh dqg
lv ghqrwhg dv d= Li wkhuh lv dq dfflghqw/ d @ 4> dqg lv }hur rwkhuzlvh1 L srvlw
wkdw erwk wkh sodq dqg wkh lqglylgxdo kdyh dffhvv wr wkh vdph ghprjudsklf
dqg klvwrulfdo gldjqrvlv lqirupdwlrq1 Iru qrwdwlrqdo frqyhqlhqfh/ L gurs wkh l
vxevfulsw iru wkh lqglylgxdo1 Rqo| wkh lqglylgxdo fdq revhuyh khu h{ dqwh vljqdo1
Li wklv h{rjhqrxv vljqdo lpsuryhv wkh suhglfwlyh dffxudf| wkhq wkhuh lv h{rjhqrxv
dgyhuvh vhohfwlrq1
614
Dgyhuvh Vhohfwlrq dv Frpsohwho| H{rjhqrxv
Lq wklv vxevhfwlrq/ wkh lqglylgxdo gudzv erwk d vlfnqhvv yduldeoh v> dqg d elqdu|
dfflghqw yduldeoh/ d1 Vlqfh L dp lqwurgxflqj d qhz udqgrp yduldeoh wkdw dhfwv
wkh suhihuhqfhv iru phglfdo jrrgv/ L dxjphqw wkh phglfdo uhvwrudwlrq ixqfwlrq J
: Wkh h{rjhqrxv vljqdo vkrxog frph prvwo| iurp vhoi revhuydwlrq/ dqg shukdsv xqgrfx0
phqwhg idplo| klvwru|1 Wkh hqgrjhqrxv vljqdo frphv iurp fkrlfhv vxfk dv wkh surfolylw| wr
gulyh uhfnohvvo| ru sduwdnh lq gdqjhurxv uhfuhdwlrq hwf1
44
zlwk d wklug dujxphqw iru wkh dfflghqw yduldeoh1 Wkh h{ srvw xwlolw| lv vshflhg
dv
X @ h{siU+| um Fm +p, J+v> d> p,,j> p 3=
+44,
U lv wkh ulvn dyhuvlrq sdudphwhu dqg pxvw eh vwulfwo| srvlwlyh1 Lq rughu wr
nhhs wkh vshflfdwlrq frqvlvwhqw zlwk wkh suhylrxvo| phqwlrqhg vw|ol}hg idfwv/ L
vshfli| J+=> => =, dv d txdgudwlf orvv ixqfwlrq=
J+v> d> p, @ 4@5+v . d p,5 > li v . d A 3
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Fm +p, zloo eh htxdo wr p iru m @ 31 Iru m @ 4> lw lv d slhfhzlvh olqhdu ixqfwlrq
ri d ghgxfwleoh dqg frlqvxudqfh udwh1 Lq wkh gdwd vhw xvhg lq wklv vwxg|/ KPR
uhlpexuvhphqwv duh frqyhuwhg wr ihh iru vhuylfh htxlydohqwv1 Li Fm +p, lv 3 wkhq
p @ +v.d,@ iru dq| gudz ri +v.d, wkdw lv juhdwhu wkdq }hur1 Wklv jxdudqwhhv
wkh qlwhqhvv ri p lq fdvhv zkhuh wkh pdujlqdo rxw ri srfnhw sd|phqwv htxdo
}hur1; Wkh udqgrp vlfnqhvv yduldeoh v ghshqgv rq ghprjudsklf yduldeohv dqg
wkh h{lvwhqfh ri d fkurqlf frqglwlrq wkdw h{lvwhg ehiruh wkh lqglylgxdo vhohfwv
khu sodq w|sh1 Wkhvh fkdudfwhulvwlfv duh frqwdlqhg lq wkh yhfwru {= Wkxv/ rqh
fdq vshfli| v dv
v @ { . x
+46,
zkhuh H+x, @ 3 dqg xqghu wkh h{rjhqrxv dgyhuvh vhohfwlrq/ lw lv x wkdw lv
vwdwlvwlfdoo| ghshqghqw rq wkh h{ dqwh vljqdo z= Wkxv/ diwhu dffrxqwlqj iru wkh
; Wkhuh duh dfwxdoo| revhuydwlrqv lq wkh gdwd wkdw L xvh zkhuh 433( ri doo phglfdo h{shqgl0
xwxuhv duh uhlpexuvhg1
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lqglylgxdo*v h{ srvw phglfdo h{shqglwxuh zloo ghshqg rq {> d> Fm +=,> dqg x= Lq
wklv vwxg|/ li CFm +p,@Cp h{lwv/ lw zloo eh d frqvwdqw fm 5 ^3> 4`= E| vxevwlwxwlqj
+45, dqg +46, lqwr +44, dqg rswlpl}lqj zlwk uhvshfw wr p/ wkh uhvxowlqj h{ srvw
phglfdo h{shqglwxuh ixqfwlrq lv
p @ +{ . d 4
fm . x . KPRm ,@=
lv d vkdgrz sulfh ri wkh KPR h{shqglwxuh frqvwudlqw li m lv dq KPR +KP Rm @
4,= Wklv frqvwudlqw zdv ghvfulehg lq wkh suhylrxv vhfwlrq1
Lq wklv vwxg|/ L srvlw wkdw wkh suredelolw| ri dq dfflghqw lv lqghshqghqwo|
glvwulexwhg zlwk uhvshfw wr x= Lq hvvhqfh/ L dp dvvxplqj wkdw khdowk| shrsoh
kdyh wkh vdph fkdqfh ri jhwwlqj lqwr dq dfflghqw dv loo shrsoh1 Zkloh wklv vhhpv
uhvwulfwlyh/ lw doorzv ph wr lghqwli| wkh prgho lq wkh qh{w vxevhfwlrq zkhuh wkhuh
lv hqgrjhqrxv dgyhuvh vhohfwlrq1
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vhohfwlrq prgho/ L srvlw wkdw
z
x
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Diwhu wkh gudz ri z exw ehiruh wkh gudz ri x> wkh h{shfwhg lqgluhfw xwlolw| ri
ehlqj xqlqvxuhg lv
4
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h{siU+|,j Su+x { d . 4@mz,` Su+d,
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jlyhq wkh vshflfdwlrq lq +47,/ x lq +48, fdq eh lqwhjudwhg rxw/ dqg L jhw wkh
forvhg irup
Y3 +z, @ h{siU+|,,j
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Vxssrvh wkdw wkh lqglylgxdo kdv wkh fkrlfh ehwzhhq qrw sxufkdvlqj d khdowk
sodq/ dqg fkrrvlqj d ihh iru vhuylfh khdowk sodq +m @ 4, zlwk suhplxp u4 dqg
frlqvxudqfh f4 > zkhuh F4 +p, @ f4 p= Zkhq lqvxudqfh lv sxufkdvhg/ wkh h{shfwhg
lqgluhfw xwlolw| ixqfwlrq lqwhjudwhv wr
Y4 +z, @ h{siU+| u4 ,j
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Iru d gudz ri z> wkh lqglylgxdo zloo qrw sxufkdvh lqvxudqfh li Y3 A Y4 1 L qrz
kdyh d forvhg prgho wkdw h{solflwo| vkrzv wkh lqglylgxdo*v suhihuhqfh iru lqfrph
surwhfwlrq1 Qrwlfh wkdw zlwk d srvlwlyh ulvn dyhuvlrq +U A 3,> dq lqfuhdvh lq wkh
yduldqfh ri Y du+xmz, ghfuhdvhv wkh h{shfwhg xwlolw|/ ehfdxvh wkhuh lv d kljkhu
suredelolw| iru d juhdwhu lqfrph orvv1 Lq wklv h{dpsoh/ wkh fkrlfh wr lqvxuh
lqyroyhv wkh wudgh0r ehwzhhq sd|lqj wkh suhplxp u4 dqg jhwwlqj wkh dgglwlrqdo
lqfrph surwhfwlrq iurp f4= Y4 +z, Y3 +z, lv prqrwrqlf zlwk uhvshfw wr z rqo|
li wkhuh lv dgyhuvh vhohfwlrq +l1h1 xz 9@ 3,> dqg wkhuh zloo eh d z vxfk wkdw
Y4 +z, Y3 +z, @ 3= Dq| gudz ri z ehorz z zloo ohdg wkh lqglylgxdo wr irujr wkh
khdowk sodq1 Xvlqj +49, dqg +4:,/ wkh surshqvlw| wr sxufkdvh khdowk lqvxudqfh
lv dssur{lpdwhg e| wkh pdjqlwxgh ri wkh iroorzlqj glhuhqfh=
u4 @+4 f4 , . { . xmz +4 . f4 ,+4@5,+4 UY du+xmz,,
+4;,
Qrwlfh wkdw +4;, vkrzv krz wkh lqfuhdvh lq ulvn dyhuvlrq/ U> lqfuhdvhv wkh
surshqvlw| wr sxufkdvh khdowk lqvxudqfh1 Lw lv lpsruwdqw wr qrwh wkdw +4;, lv qrw
prqrwrqlf zlwk uhvshfw wr f4 = Wkh uhdvrq lv wkdw wklv fkdudfwhul}hv wkh h{ dqwh
ghpdqg iru lqvxudqfh dqg li Y du+xmz, lv odujh/ wkhuh lv d srvlwlyh suredelolw|
wkdw wkh lqvxuhg zrxog ryhu frqvxph phglfdo jrrgv1
Lq wklv vwxg| Fm +p, lv olqhdu zlwk vorsh fm 5 ^3> 4`> dqg wkh qr lqvxudqfh
vorsh lv f3 @ 4= D srolf| zlwk ixoo lqvxudqfh kdv fm @ 3= L dgg edfn wkh vxevfulsw
l wr lqgh{ wkh lqglylgxdo/ dqg L ghqrwh }lm @ i{l > dl > fm > KP Rm j> zkhuh f3 @ 4
dqg L vhw @ i@> @> 4@ 5 > j= L fdqqrw revhuyh wkh vljqdo zl exw li wkhuh
48
lv srvlwlyh qrq }hur pl > L fdq hvwlpdwh xl @ pl }lm = Li pl @ 3> L fdq rqo|
hvwlpdwh Su+pl @ 3, @ Su+xl }lm ,= L qrupdol}h zz @ 4 dqg xx @ 5x =
Wkhuhiruh L fdq hvwlpdwh wkh iroorzlqj orj olnholkrrg zkhuh wkh lwk lqglylgxdo*v
frqwulexwlrq lv=
L+pl A 3, oq+!+xl @ x ,@x ,
.
4
[
+4<,
L+sodq m fkrvhq,~L+pl @ 3, oq+Su+m lv fkrvhq> xl }lm ,, .
m @3
L+pl A 3,oq+Su+m lv fkrvhqmxl ,,
!+, lv wkh vwdqgdug qrupdo glvwulexwlrq ixqfwlrq1 Xvlqj +4;,/ L vshfli| Su+sodq
m fkrvhqmxl , dv + 4 ulm . {l @+ x , . 5 flm . 6 glm . 7 flm xl @ x . =8 8 U+4 .
flm ,+5x +4 57 ,, zkhuh ulm > flm > dqg glm duh uhvshfwlyho| wkh lqvxudqfh suhplxp/
wkh frlqvxudqfh udwh dqg wkh ghgxfwleoh ri wkh m wk srolf| dydlodeoh wr lqglylgxdo
l= Uhfdoo wkdw u3 @ 3> f3 @ 4 dqg g3 @ 3= Qrwlfh wkdw wkh odvw whup lq wklv
vshflfdwlrq dffrxqwv iru wkh hhfw ri ulvn dyhuvlrq rq wkh ghpdqg iru lqvxu0
dqfh1 L vshfli| Su+sodq m fkrvhq> xl }lm , dv wkh vwdqgdug elyduldwh qrupdo
+ 4 ulm . 5 flm . 6 glm . =8 8 +4 . flm ,U 5x > }lm > 7 ,= Wkh sdudphwhuv duh wkhq
> 4 > 5 > 6 > 7 > 8 > x > dqg U= L whvw iru dgyhuvh vhohfwlrq e| whvwlqj wkh qxoo
k|srwkhvlv/ 7 @ 3=
615
Hqgrjhqrxv Dgyhuvh Vhohfwlrq zlwk Hruw
L dxjphqw wkh prgho iurp wkh odvw vhfwlrq e| dgglqj d odwhqw hruw yduldeoh
wkdw qhlwkhu wkh sodq surylghu qru wkh hfrqrphwulfldq fdq revhuyh1 Lq rughu wr
49
lghqwli| wklv prgho/ L lpsrvh dgglwlrqdo uhvwulfwlrqv1< Lq wklv prgho/ lqglylgxdov
fkrrvh dq hruw ohyho ghqrwhg dv h ehiruh wkhlu gudz ri x= Dv phqwlrqhg lq wkh
suhylrxv vhfwlrq wkh phdq ri x lv lqyhuvho| uhodwhg wr h= Wkh udqgrp yduldeoh v
lv qrz prghoohg dv
v @ { . h h . x=
+53,
h ? 3= Wkh suredelolw| ri dq dfflghqw lv dovr lqyhuvho| uhodwhg wr h= Dv lq wkh
suhylrxv vxevhfwlrq/ d @ 4 li wkhuh lv dq dfflghqw/ dqg d @ 3 rwkhuzlvh1 Lq
rughu wr prgho wkh suredelolw| ri dq dfflghqw/ L lqwurgxfh d wklug odwhqw udqgrp
dfflghqw yduldeoh y= Dq dfflghqw grhv qrw rffxu li
y ? 3 . 4 h=
+54,
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Wkhuhiruh/
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h ? 3 ru 4 A 3
+56,
wkhq wkhuh lv hqgrjhqrxv dgyhuvh vhohfwlrq1 Dgglwlrqdoo|/ li H+x H+xmz,5 , ?
H+x H+x,,5 > wkhq wkhuh lv erwk h{rjhqrxv dqg hqgrjhqrxv dgyhuvh vhohfwlrq1
Qrwlfh wkdw z fdqqrw lpsuryh wkh iruhfdvwlqj dffxudf| ri wkh dfflghqw yduldeoh
y1 Wkh lqglylgxdo fdq rqo| dhfw wkh suredelolw| ri dq dfflghqw e| khu fkrlfh ri
h= Wkh h{ srvw xwlolw| lv qrz=
X @ h{siU+| um Fm +p, 4@5+d . v p,5 h,j
<
Dv lq wkh suhylrxv vhfwlrq/ L vwduw e| rplwwlqj wkh vxsvfulsw 4:
+57,
Ehiruh wkh gudz ri x> exw diwhu wkh gudz ri wkh h{rjhqrxv vljqdo z/ wkh
lqglylgxdo pxvw fkrrvh erwk dq hruw ohyho h dqg lqvxudqfh vwdwxv m1 Wkh h{ srvw
phglfdo h{shqglwxuh lv ghqrwhg pmd = Dv phqwlrqhg lq wkh suhylrxv vxevhfwlrq/
Fm +p, lv dozd|v olqhdu zlwk vorsh fm = Iurp wklv L jhw
pmd @ +{ . d fm @ . h h . x,@
+58,
Ehiruh wkh gudz ri x> exw diwhu wkh gudz ri wkh h{rjhqrxv vljqdo z/ wkh
lqglylgxdo pxvw fkrrvh erwk dq hruw ohyho/ h> dqg lqvxudqfh vwdwxv m1 L vshfli|
wkdw y lv lqghshqghqwo| glvwulexwhg iurp x dqg z= Zlwk wklv dvvxpswlrq/ wkh
h{shfwhg xwlolw| ri hruw diwhu gudzlqj z dqg fkrrvlqj erwk h dqg sodq m lv=
Ym +h, @
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+59,
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h{siU+| h, Su+x { . d . h h fm @mz> h,`
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wkh glvwulexwlrq ixqfwlrq iru y= Ohw hm +z, eh wkh rswlpdo hruw fkrvhq iru sodq
m jlyhq z= Lq prvw fdvhv/ wkh iroorzlqj vkrxog krog
h3 +z, A h4 +z,=
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Wkh lqwxlwlyh uhdvrq lv wkdw xqghu qr lqvxudqfh/ wkh lqglylgxdo lv ixoo| frpshq0
vdwhg iru khu hruwv/ dqg wkhuhiruh vkrxog surgxfh pruh hruw wkdq vkh zrxog
li vkh zhuh qrw ixoo| frpshqvdwhg iru lw1 Li wkh lqvxudqfh sodq kdv d ghgxfwleoh
g4 / wkhq h4 vkrxog eh lqfuhdvlqj lq g4 =
4;
Wkh srolf| kroghu fkrrvhv wkh sodq m 3 vxfk wkdw
Ym 3 +hm 3 , A Ym +hm , ;m 9@ m 3
Zkhq L gr pd{lpxp olnholkrrg hvwlpdwlrq ri wklv prgho/ L srvlw wkdw
3
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l wr lqgh{ wkh lqglylgxdo1 L sur{| iru hlm e|
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References
Baumgardner, J.R. 1991 “The Interaction Between Forms of Insurance Contract and Types of Technical
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Table 1
Summary Statistics
1987 National Medical Expenditures Survey
Variable
Age
Years of Schooling
Income
%White
%Male
% with Chronic Condition
% in Accident
Total Medical Expenditures
Out of Pocket Med. Exp.
% Uninsured
% Offered Employer Insurance
% Reject Offer
% Accept Offer
% with Non Employer Policy
% with No Medical Expenditures
N=921
Mean
Standard Deviation
37.01
13.19
$21,042
77.31%
53.96%
29.64%
20.09%
$824.88
$286.29
26.71%
82.95%
15.45%
84.55%
6.30%
18.13%
13.75
2.91
$15,074
41.91%
49.87%
45.69%
40.09%
$2,253.71
$516.73
19.58%
37.61%
13.06%
13.06%
24.31%
14.84%
Table 2a
Summary Statistics
for the Uninsured
Variable
Age
Years of Schooling
Income
%White
%Male
% with Chronic Condition
% in Accident
Total Medical Expenditures
Out of Pocket Med. Exp.
Total Health Plan Premium
Individual Premium Payment
N=246
Mean
Standard Deviation
35.73
11.93
$13,096
71.54%
56.10%
9.76%
7.72%
$199.97
$192.46
$1,027.69
$668.86
14.54
3.23
$10,625
45.21%
49.73%
29.73%
26.75%
$548.55
$494.22
$179.06
$411.77
Table 2b
Summary Statistics
for HMO Holders
Variable
Age
Years of Schooling
Income
%White
%Male
% with Chronic Condition
% in Accident
Total Medical Expenditures
Out of Pocket Med. Exp.
Total Health Plan Premium
Individual Premium Payment
NonHospital Deductible
NonHospital Coinsurance
N=172
Mean
Standard Deviation
37.10
13.74
$25,754
73.84%
54.65%
34.88%
22.09%
$1,171.00
$205.84
$953.99
$158.95
$244.51
12.86%
12.89
2.59
$15,954
44.08%
49.93%
47.80%
41.61%
$3,769.20
$302.79
$284.98
$242.47
$324.17
11.21%
Table 2c
Summary Statistics
for Fee for Service Holders
Variable
Age
Years of Schooling
Income
%White
%Male
% with Chronic Condition
% in Accident
Total Medical Expenditures
Out of Pocket Med. Exp.
Total Health Plan Premium
Individual Premium Payment
NonHospital Deductible
NonHospital Coinsurance
N=503
Mean
Standard Deviation
37.61
13.61
$23,316
81.31%
52.68%
37.57%
25.45%
$1,012.14
$369.47
$953.79
$148.05
$191.87
16.64%
13.62
2.82
$15,195
39.02%
49.98%
48.48%
43.60%
$2,013.63
$568.68
$477.38
$287.71
$165.46
13.71%
Table 3a
Insurance Type and
Availability of
Employer Insurance
Type of Insurance
No Insurance
HMO
Fee for Serivce
Total
Employer Provided Insurance
Yes
No
12.81%
13.90%
18.35%
0.33%
51.79%
2.82%
82.95%
17.05%
Total
26.71%
18.68%
54.61%
100%
Table 3b
Insurance Type and
Chronic Condition
Type of Insurance
No Insurance
HMO
Fee for Serivce
Total
Chronic Condition
Yes
No
2.61%
24.10%
6.51%
12.16%
34.09%
20.52%
82.95%
17.05%
Total
26.71%
18.68%
54.61%
100%
Table 3c
Insurance Type and
Incidence of Accident
Type of Insurance
No Insurance
HMO
Fee for Serivce
Total
Accident Occurred
Yes
No
2.06%
24.65%
4.13%
14.55%
13.90%
40.72%
82.95%
17.05%
Total
26.71%
18.68%
54.61%
100%
Type of Insurance
No Insurance
HMO
Fee for Serivce
Total
Table 3d
Insurance Type and
Zero Medical
Expenditures
Zero Medical Expenditures
Yes
No
11.29%
15.42%
1.30%
17.38%
5.54%
49.07%
82.95%
17.05%
Total
26.71%
18.68%
54.61%
100%
Table 4a
Parameter Estimates of Exogenous Adverse Selection
Parameters (x)
Medical Expenditure
Constant
Age
Male=1
Years of School
White=1
Chronic condition
Income
Accident
HMO
Co-insurance cj
Insurance Demand
Premium
Coinsurance
Deductible
Additional
Parameters
su2
Risk Aversion R
Correlation Signal
and Medical Residual
d4
Mean log-likelihood
Number of cases
Estimates
Std. err.
t-statistic
Prob.|t|=0
-0.5328
0.7528
-0.1165
0.3488
0.1206
0.6671
-0.0214
0.3545
-0.0661
-0.2496
0.2289
0.2045
0.0679
0.2223
0.0805
0.0840
0.0372
0.0882
0.0913
0.1004
-2.328
3.681
-1.714
1.569
1.497
7.938
-0.576
4.019
-0.724
-2.486
0.0199
0.0002
0.0865
0.1167
0.1344
0.0000
0.5649
0.0001
0.4690
0.0129
-2.8208
-1.4869
-4.6601
0.2544
0.1096
0.4773
-11.088
-13.565
-9.763
0.0000
0.0000
0.0000
0.9984
0.00016470108
0.0528
2.9234503e-005
18.893
5.6337909
0.0000
0.0000
0.5106
0.0613
8.332
0.0000
-2.10094
921
Table 4b
Parameter Estimates of Both
Exogenous and Endogenous Adverse Selection
Parameters (x)
Medical Expenditure
Constant
Age
male=1
Years of School
white=1
chronic cond
income
Accident
HMO
Coinsurance cj
Effort
Estimates
Std. err.
t-statistic
Prob.|t|=0
1.0049
0.9919
-0.0852
0.8171
0.1431
0.7246
-0.0528
0.1286
0.1408
0.1924
-1.5076
0.6433
0.2112
0.0684
0.2623
0.0849
0.1009
0.0394
0.1164
0.1118
0.1350
0.4197
1.562
4.697
-1.246
3.115
1.686
7.179
-1.341
1.105
1.259
1.425
-3.592
0.1183
0.0000
0.2128
0.0018
0.0917
0.0000
0.1799
0.2690
0.2082
0.1541
0.0003
Insurance Demand
Premium
Coinsurance
Deductible
-1.8155
-1.1647
-4.5805
0.1522
0.0893
0.4097
-11.930
-13.050
-11.181
0.0000
0.0000
0.0000
Effort/Accident
Constant
Insured (j>0)
Deductible
1.2948
-0.8218
2.6962
0.1222
0.1469
0.6320
10.597
-5.596
4.266
0.0000
0.0000
0.0000
Additional
Parameters
var(u)
Risk Aversion R
Correlation Signal
and Medical Residual
d4
Correlation Effort
Bound and Medical
Residual a4
Mean log-likelihood
Number of cases
1.0912
0.0201
54.302
0.0000
0.00009735
5.9085e-006
16.4768
0000
0.7835
0.0193
40.524
0.0000
-0.0580
0.1035
-0.561
0.5750
-2.02123
921
Figure 1
Relationship between Random
Illness u and Effort e
ei
ei
Uninsured
Insured
wi
E(ui |wi)
wi
wi
45°
E(ui |wi)