The Wel a e Implica ions o G ow h
Reg essions
Donal O’Neilly
May 10, 2005
Abs ac
Reg essions ela ing he g ow h a e in income o ini ial income
ha e been he sou ce o much ecen deba e in g ow h economics.
Recen esea ch has emphasised he impo ance o allowing o non-
linea i ies in hese models when explaining he e olu ion o income
o e ime. In his pape we a gue hese ex ended g ow h eg essions
a e also use ul in acili a ing wel a e compa isons ac oss income dis-
ibu ions, in a way ha is no possible using al e na i e measu es o
con e gence. To do his we exploi he simila i i es be ween he in-
come con e gence li e a u e and wo k on ax p og essi i y in he pub-
lic …nance li e a u e. We illus a e ou app oach using bo h egional
da a ac oss he Uni ed S a es, Japan and Eu ope and coun ywide
compa isons.
Keywo ds: G ow h Reg essions, Wel a e, Equali y o Oppo uni y, P o-
g essi i y
JEL Codes: O47
I would like o hank Oli e Swee man and Philippe Van Ke m o help ul commen s
on ea lie e sions o his pape .
yEconomics Dep ., NUI Maynoo h, Co. Kilda e, I eland. e-mail:[email protected].
1
1 In oduc ion
The ea ly li e a u e on income con e gence ac oss coun ies was domina ed
by c oss-sec ion s udies ha eg essed he g ow h a e o income on ini ial
income o examine whe he o no poo coun ies g ew as e han iche
coun ies. These eg essions a e some imes called “Ba o- eg essions” (e.g
Quah 1993a)1and as e g ow h among poo coun ies has become known
as -con e gence (e.g. Ba o and Sala-i-Ma in (1992) and Sala-i-Ma in
(1996a)). Howe e , his app oach has been he subjec o much deba e and
has been c i icised by many.2A a undamen al le el a numbe o au ho s,
including F iedman (1992) and Quah (1996), poin ou ha , by i sel , -
con e gence ells us li le abou he dynamic e olu ion o incomes. F iedman
(1992), quo ing Ho elling (1933), a gues ha " he eal es o a endency
owa ds con e gence would be in showing a cons an decline in he a i-
ance...among indi idual en e p ises." In he g ow h li e a u e his ype o
con e gence has been labelled as -con e gence. As no ed by Islam (2003)
one o he main a gumen s o he ejec ion o Ba o’s conclusions cen e ed
on he ailu e o adi ional g ow h equa ions o accommoda e non-linea
speci…ca ions. As a esul mo e ecen de elopmen s in g ow h econome -
ics has emphasised nonlinea i ies in he g ow h p ocess (Kalai zidakis e
al (2001), Fiaschi and La ezzi (2003) and Maasoumi e al (2005)). These
p ocedu es p o ide a mo e de ailed desc ip ion o he e olu ion o he dis-
ibu ion o ealised incomes o e ime han was possible using adi ional
linea Ba o- eg essions.3
Al hough he e ha e been signi…can econome ic and heo e ical de el-
1Some au ho s e e o hese eg essions as g ow h-ini ial le el eg essions and ese e
he label "Ba o-Reg ession" only o cases in which he g ow h eg essions include o he
con ols in addi ion o in i ial income. This dis inc ion is somewha a b i a y and unnec-
essa y o ou s udy.
2Fo ecen summa ies o his li e a u e see Isalm (2003) and Du lau e al (2005).
3O he c i ics o adi ional g ow h eg essions include Quah (1996), who a gues ha
he speed o con e gence es ima ed om g ow h eg essions may simply e‡ec small-
sample biases. Howe e , he la e acknowledges ha he deg ee o p ecision epo ed in
s anda d Ba o-Reg essions cas s doub on his explana ion. Lee, Pesa an and Smi h
(1997) discuss he econome ic p oblems ha a ise when using Ba o-Reg essions o es-
ima e he s uc u al pa ame e s o a g ow h model. Al hough impo an , his issues is
dis inc om, and no ele an o he ques ion we add ess in ou pape . Fo de ailed
summa ies o hese issues and he al e na i e app oaches o measu ing con e gence see de
la Fuen e (1997), Du lau and Quah (1999) and Islam (2003).
2
opmen s in he analysis o g ow h models o e ime he e has been e y li le
empi ical wo k de o ed o cha ac e ising he wel a e p ope ies o he ob-
se ed p ocesses. When making wel a e compa isons economis s ha e adi-
ionally ocused on he dis ibu ion o obse ed ou comes. Howe e in ecen
yea s a numbe o economis s ha e a gued ha wel a e compa isons should
place g ea e emphasis on equali y o oppo uni ies a he han obse ed ou -
comes (e.g Fleu bay (1995), Roeme (1998)). The equal-oppo uni y ame-
wo k s esses he link be ween he oppo uni ies a ailable o an agen and he
ini ial condi ions which a e inhe i ed o beyond he con ol o hese agen s.
A he indi idual le el hese condi ions may include cha ac e is ics such as
ace, gende o pa en al income. A a coun y-le el analysis one may be in-
e es ed in knowing o wha ex en he u u e oppo uni ies o a coun y a e
de e mined by hei ini ial income le el. F om his pe spec i e one possible
goal o policy make s could be o ensu e ha he oppo uni ies a ailable o
agen s a e un ela ed o ini ial endowmen s. This need no necessa ily elimi-
na e inequali y in obse ed ou comes. P oponen s o equali y o oppo uni y
accep inequali y o ou comes ha a ise om genuine choice o shocks ha
a e un ela ed o ini ial condi ions.
The ques ion ha we add ess in his pape is whe he g ow h eg essions
can con ibu e in a meaning ul way o s udies ha ocus, no on he he
e olu ion o ealised ou comes, bu a he on he equali y o oppo uni y
ac oss agen s. We show ha app op ia e conside a ion o nonlinea i es in
he g ow h p ocess is no only desi able when documen ing he e olu ion o
income o e ime bu is also an essen ial componen o a cohe en equal-
oppo uni y based wel a e amewo k. In pa icula , we ex end he wo k o
Benabou and Ok (2001) o show p ecisely how ‡exible o m g ow h eg es-
sions can acili a e wel a e compa isons in ways ha a e no possible using
some o he al e na i e con e gence concep s ha ha e been p oposed.
2 P og essi i y, G ow h and Wel a e
T ansi ion p obabili ies, MT(xjy), speci y he p obabili y ha an indi idual
wi h income y oday will ea n a mos xa ime T. A numbe o au ho s ha e
es ima ed associa ed ansi ion ma ices in he con ex o income con e gence
(e.g Quah (1993)). Howe e , hey a e almos always p esen ed as desc ip-
i e ools o unde s anding he e olu ion o obse ed incomes o e ime.
Howe e , in his su ey o wel a e heo e ic app oaches o he measu emen
3
o mobili y Maasoumi (1998) no es ha "Mobili y in any social hie a chy is
an indica ion o oppo uni y." Benabou and Ok (2001) make a simila poin
when no ing ha many people ca e abou mobili y "no because income
mo emen s a e in insically aluable, bu p ima ily because o he hope ha
i helps a enua e he e¤ec s o dispa i ies in ini ial endowmen s on u u e
income p ospec s (pg. 2)." In hei pape hey de i e condi ions unde which
a mobili y p ocess can be cha ac e ised as oppo uni y-equalising, as well
as p o iding c i e ia o de e mine i one p ocess is mo e equalising han an-
o he .4To do his hey abs ac om agen s’a e sion o isk and summa ise
u u e a ailable oppo uni ies o income p ospec s using he condi ional ex-
pec a ion unc ion de e mined by he unde lying mobili y p ocess:5
eT(y) = Z1
0
xdMT(xjy)(1)
Thus eT(y)summa ises he oppo uni ies a ailable a ime T o an agen
wi h cu en income y.6 7 While Benabou and Ok (2001) cha ac e ise u-
u e a ailable oppo uni ies using he unde lying ansi ion p ocess, M, i is
ela i ely s aigh o wa d o ecas hei esul s in e ms o he unde lying
g ow h p ocess. To do his we no e ha …nal ealised income, yT, can always
be w i en as he sum o ini ial income (y0), he expec ed change in income
gi en he ini ial le el (g(y0)) and a mean ze o esidual e m ( T); ha is:
yT=y0+g(y0) + T(2)
In his case he oppo uni ies a ailable o agen s a ime T, wi h ini ial
income y0, can be w i en as:
eT(y0) = y0+g(y0)(3)
4They conside mono onic mobili y p ocessese such ha o any y1; y2wi h y2> y1
hen MT(xjy1)MT(xjy2) o all x. This implies eT(y2)> eT(y1).
5The use o condi ional means o summa ise oppo uni y se s is discussed in mo e de ail
in hei pape . A majo ad an age o his app oach is ha i signi…can ly simpli…es he
compa ison o di¤e en oppo uni y se s. Fo a gene al discussion o some o he p oblems
ha a ise when e alua ing oppo uni y se s see Sen (1985).
6Benabou and Ok (2001) conside only mono onic mobili y p ocessese such ha o any
y1; y2wi h y2> y1 hen MT(xjy1)MT(xjy2) o all x. This implies eT(y2)> eT(y1).
7Fo ex ensions ha conside discoun ed li e ime u ili ies see Benabou and Ok (2001)
and Da danoni (1993).
4
W i ing he model in his way allows us o d aw close pa allels be ween
he income con e gence li e a u e and he public economics li e a u e on
ax/bene… p og essi i y (Lambe (1993)).8Following he ax li e a u e we
de…ne a g ow h p ocess as p og essi e i dg(y0)
y0
dy0<0, eg essi e i dg(y0)
y0
dy0>0
and p opo ional i dg(y0)
y0
dy0= 0. In ui i ely a g ow h p ocess is p og essi e
i low income coun ies expe ience as e g ow h a es han highe income
coun ies.
This amewo k is su¢ cien o allow us o cha ac e ises he wel a e p op-
e ies o g ow h p ocesses based on he p og essi i y o o he wise o he
p ocess. To see his le U(e)deno e he u ili y acc uing o an agen wi h
u u e oppo uni ies summa ised by e:We assume U0(e)>0. Following an
es ablished adi ion in public economics de…ne social wel a e as he a e age
u ili y ac oss ini ial income le els. Tha is
WF=ZU(eT(y)) (y)dy (4)
whe e (y)is he dis ibu ion o ini ial incomes.9We can hen es ablish
he ollowing heo em:10
Theo em 1
A mono one g ow h p ocess inc eases (dec eases) wel a e mo e han an
equal yield p opo ional g ow h p ocess applied o he same p e-g ow h in-
come dis ibu ion o all s ic ly conca e Uand o all possible ini ial income
dis ibu ions i and only i he g ow h p ocess is p og essi e ( eg essi e).
P oo : See Appendix
This heo em s a es ha p og ession in he g ow h p ocess, o e he en-
i e ange o income, is a necessa y and su¢ cien condi ion o he esul ing
8In he ax/bene… li e a u e, y0would ep esen he ax/bene… base, ewould ep-
esen …nal income and g(y0)would ep esen ne bene… s. See also Benabou and Ok
(2001).
9See Lambe (1993) sec ion 4.2 o a a ionalisa ion o his social wel a e unc ion.
10 See also Co olla y 3 o Benabou and Ok (2001) .
5

dis ibu ion o oppo uni ies o wel a e domina e he dis ibu ion o oppo u-
ni ies de i ed om an equal yield p opo ional mobili y p ocess, i espec i e
o he ini ial income dis ibu ion. An immedia e co olla y o his heo em
is ha a dis ibu ion o u u e oppo uni ies ac oss agen s gene a ed by a
p og essi e g ow h p ocess will wel a e domina e he ini ial dis ibu ion o
oppo uni ies p o ided a e age income does no decline.
I is impo an o no e he ole o p og essi e g ow h in he abo e analysis.
Since we a e only conside ing mono one g ow h p ocesses hen p og essi -
i y mus educe he a iance o u u e a ailable oppo uni ies ac oss agen s
ela i e o hose a ailable in he ini ial dis ibu ion.11 Howe e , in gene al
i is possible o he p ocess o be mono onic, o mean income o ise and
o inequali y (as de…ned by he a iance o Gini coe¢ cien o oppo uni ies)
o all and ye o Gene alised Lo enz cu es o c oss so ha unambiguous
wel a e ankings a e no possible. A simple example which illus a es his
possibili y is gi en in Table 1. The … s column shows he dis ibu ion o
ini ial incomes (oppo uni ies) and he second column shows a hypo he ical
dis ibu ion o u u e oppo uni ies de i ed om his dis ibu ion. The las 4
ows summa ise he espec i e dis ibu ions. The example is cons uc ed so
ha on a e age oppo uni ies ha e imp o ed and dispe sion in oppo uni ies
has allen. This is ue o each o he h ee s anda d measu es o inequali y
epo ed. Fu he mo e he g ow h p ocess is mono onic in ha he ankings
o coun ies in bo h dis ibu ions a e p ese ed. Despi e all o his i can be
easily shown ha he Gene alised Lo enz Cu es o hese wo dis ibu ions
c oss, which p e en s unambiguous wel a e ankings ac oss he wo dis ib-
u ions. The eason o his is ha he g ow h p ocess in his example is no
p og essi e o e he en i e ange. Fo example he g ow h a e o he second
iches pe son is la ge han he g ow h a e o he second poo es , which is
a iola ion o p og essi i y.
Lambe (1993) p o ides a mo e de ailed discussion o he es ic ions
ha mus be imposed on p e e ences in o de o he social wel a e unc ion
o be comple ely summa ised by mean income and a scala index o inequal-
i y. He also discusses he limi a ions ha hese es ic ions place on he
ype o inequali y indices which could summa ise social wel a e. This la e
discussion may ha e in e es ing implica ions o how one should measu e -
con e gence in c oss-coun y s udies o income inequali y. Howe e , he key
11 As men ioned ea lie , his need no imply a educ ion in he dispe sion o obse ed
ou comes.
6
esul ha eme ges om his analysis is ha in o de o make unanimous
wel a e compa isons ac oss dis ibu ions o oppo uni ies i ma e s how he
educ ion in inequali y is gene a ed. Simply compa ing he a iance o u u e
a ailable oppo uni ies wi h cu en oppo uni ies is no su¢ cien o es ablish
wel a e ankings.
The abo e analysis shows how p og essi i y in he g ow h p ocess can
be used o acili a e wel a e compa isons ac oss al e na i e g ow h p ocesses.
We now es ablish he ela ionship be ween p og essi i y in he g ow h p ocess
and measu es o con e gence de i ed om a adi ional g ow h eg ession.
To de e mine he p og essi i y o he g ow h p ocess we need o es ablish
whe he dg(y0)
y0
dy00 o all y0. Using he ac ha dg(y0)
y0
dy00 o all y0
i and only i dg(y0)
y0
dln(y0)0 o all y0;we can use he ollowing model o log
income o cha ac e ise p og essi i y:
ln yT= ln y0+m(ln y0) + "T(4)
whe e "Tis a mean ze o e o e m. P og essi i y o he g ow h p ocess
equi es dm(ln y0)
dln y00e e ywhe e. Howe e , equa ion (4) is simply a ‡ex-
ible o m Ba o- eg ession and ou p og essi i y condi ion is no hing mo e
han a nega i i y condi ion on he slope o a non-pa ame ic c oss-sec ional
g ow h-ini ial le el eg ession. Thus he p og essi i y equi emen s needed
o wel a e compa isons o al e na i e g ow h p ocesses can be s a ed in e ms
o he con e gence es ima es ob ained om a ‡exible speci…ca ion o a
Ba o- eg ession. This highligh s a po en ially impo an ole o g ow h e-
g essions ha ex ends beyond hei abili y o dis inguish be ween compe ing
heo ies o g ow h o hei capaci y p o ide a use ul summa y o he e olu ion
o ealised ou comes.
3 Empi ical Analysis
In his sec ion we illus a e ou app oach using egional da a se s aken om
Ba o and Sala-i-Ma in (1995), as well as coun y le el da a aken om he
Penn-Wo ld Tables Ve sion 6.1. The egional da a se s a e hose used by Sala-
i-Ma in (1996b) o s udy egional cohesion. Sala-i-Ma in es ima ed linea
Ba o- eg essions o he egions o he Uni ed S a es, Japan and Eu ope. In
7
o de o apply Theo em 1 howe e we mus conside ‡exible es ima o s o
he g ow h p ocess ha allow o possible nonlinea i ies. To do his we ex-
end Sala-i-Ma in’s empi ical analysis by es ima ing ‡exible nonpa ame ic
g ow h equa ions o each o hese da a se s. In pa icula we es ima e he
ollowing ‡exible o m g ow h equa ion:
ln yi;T
yi;0=N =m[ln(yi;0)] + i;T (5)
In each case we use he Nada aya-Wa son ke nel es ima o o ob ain a
‡exible es ima e o m[ln(y0)].12 The da es o which he analysis is conduc ed
depends on da a a ailabili y and di¤e s ac oss da a se s. The da a o he
US e e o eal annual pe sonal income pe capi a o each o he 48 con-
iguous s a es om 1900 o 1990. The Japanese da a measu e eal pe capi a
income be ween 1955 and 1990 o he 47 p e ec u es, as collec ed by he
Economic Planning Agency o Japan. Finally he Eu opean da a measu e
GDP pe capi a in each o 90 egions o Eu ope co e ing Ge many (11 e-
gions), Uni ed Kingdom (11 egions), I aly (20 egions), F ance (21 egions),
The Ne he lands (4 egions), Belgium (3 egions), Denma k (3 egions) and
Spain (17 egions).13
The nonpa ame ic es ima es,
^
m[ln(y0)], o he US s a es, he Japanese
p e ec u es and he Eu opean egions a e gi en in Figu es 1-3 espec i ely.
Ou p incipal conce n is he ex en o which he g ow h p ocess exhibi s p o-
g ession o eg ession o e he income ange; equi alen ly he ex en o which
he slope o
^
m[ln(y0)] is nega i e o posi i e a each alue o y0. Recalling
Theo em 1 we no e ha i is his ea u e o he g ow h p ocess ha acili-
a es wel a e compa isons ac oss he dis ibu ion o oppo uni ies. Figu es
1-3 show ha all he egional g ow h p ocesses exhibi p og essi i y o e
almos all o hei espec i e income anges. Indeed he only e idence o
12 Fo a mo e de ailed discussion o ke nel eg esison echniques see Blundell and Duncan
(1998).
13 Following Sala-i-Ma in (1995) he Eu opean GDP …gu es a e exp essed as de ia ions
om coun y speci…c means. Thus he es ima ed g ow h p ocess we p esen o he egions
o Eu ope should be in e p e ed as a common, wi hin coun y g ow h, p ocess. Mo e
de ails on hese da a, including maps illus a ing he egions unde conside a ion, a e
a ailable in Ba o and Sala-i-Ma in (1995).
8
eg essi e g ow h o hese da a occu s among high income Japanese p e ec-
u es. Howe e , e en hen he con…dence in e als a e such ha we canno
ule ou p og essi e g ow h o e his income ange. On he o he hand we
clea ly ejec he possibili y ha income g ow h is eg essi e o e he en i e
income ange o all he egional g ow h p ocesses. In his case Theo em 1
implies ha he e exis s a leas one ini ial income dis ibu ion o which
he obse ed g ow h p ocess wel a e domina es an equal yield p opo ional
g ow h p ocess. Fu he mo e, since he da a s ongly suppo s he hypo h-
esis o p og essi i y o e he en i e ange, ou da a a e consis en wi h a
scena io in which he dis ibu ion o u u e oppo uni ies de i ed om he
obse ed p ocess unambiguously wel a e domina es ha ob ained om a p o-
po ional g ow h p ocess o all possible ini ial income dis ibu ions in all o
he egions. Since a e age income has isen o e his pe iod in each o ou
egional da a se s, and since we can always iew he iden i y mapping as
a p opo ional g ow h p ocess, ou da a also suppo he hypo hesis ha
he dis ibu ion o oppo uni ies a ailable oday wi hin each o hese egions
wel a e domina es ha a ailable p e iously.
We can also apply ou app oach o examine income g ow h ac oss coun-
ies using he Penn Wo ld Table e sion 6.1. These da a p o ide na ional in-
comes con e ed o in e na ional p ices om 1950-2000. We use da a o he
pe iod 1960-2000. We begin by looking a he uncondi ional g ow h p ocess
o he OECD coun ies and o a wo ld sample o 83 coun ies o which
he e we e no missing da a.14 The non-pa ame ic es ima es o m[ln(y0)] o
bo h hese samples a e gi en in Figu es 4 and 5 espec i ely. The es ima ed
g ow h p ocess o he OECD coun ies exhibi a high deg ee o nonlinea i y.
P og essi i y is mos p onounced a low and high income le els. Howe e ,
he e is a middle ange o incomes o which he es ima ed g ow h p ocess is
app oxima ely p opo ional. Ne e heless he con…dence in e als a e such
ha he in e ences ha we can d aw om he sample o OECD coun ies
mi o hose p esen ed ea lie o he egional da a se s. We ejec eg essi e
income g ow h o e he en i e income ange bu canno ejec he hypo hesis
o p og essi i y o e all ini ial income le els. Thus he da a a e consis en
wi h wel a e imp o ing g ow h among he OECD coun ies.
The si ua ion o he en i e wo ld sample is di¤e en howe e . Figu e 5
highligh s impo an nonlinea i ies in he es ima ed g ow h p ocess o he
wo ld sample. Fo his sample howe e , he o e all endency is o eg essi e
14 A comple e lis o hese coun ies is gi en in Table 2.
9
Appendix:
P oo o Theo em 1
De…ne he expec ed g ow h a e o pe son wi h ini ial income y0as
(y0)g(y0)
y0.
=)Unde p opo ional g ow h hen he Lo enz cu e o oppo uni ies a
ime T, (eT(yi)), mus equal he Lo enz cu e o ini ial incomes o oppo -
uni ies (e0y0).
Tha is Lep op;T (p)=Le0(p) o all p2[0,1]
By de…ni ion eT(y0) = y0+g(y0).
Taking he a e age ac oss agen s we ge ha eT=e0(1+),whe e is he
a e age expec ed g ow h a e ac oss agen s =Xg(y0)
y0
N!and e0is a e age
ini ial income o oppo uni ies.
Hence he Gene alised Lo enz Cu e o u u e oppo uni ies de i ed om
a g ow h p ocess cha ac e ised by (y)can be exp essed as :
GLCeT(p)=e0(1+)LeT(p),
whe e LeT(p) is he Lo enz cu e o u u e oppo uni ies.
I ou obse ed g ow h p ocess is p og essi e, ha is 0(y)<0 o all y,
hen we can use he Jakobsson-Fellman heo em (Lambe (1993) page 150)
and ou assump ion o mono onici y o conclude ha :
GLCeT (p)=e0(1+)LeT(p)e0(1+)Le0(p)= e0(1+)Lep op;T (p) all p2
[0,1].
The … s inequali y ollows om ou assump ions o mono onici y and
p og essi i y and he las equali y ollows om s ep 1 o he p oo .
By de…ni ion his implies ha :
GLCeT (p)GLCep op;T (p) all p2[0,1].
16

Re e ing o Sho ocks’(1983) comple es he p oo in his di ec ion.
(Suppose GLCeT (p)GLCep op;T (p) o all p and any p e-g ow h in-
come dis ibu ion.
Then ollowing he logic abo e we can es ablish ha
LeT(p)Le0(p) o all p and all p e-g ow h income dis ibu ions
F om he Jakobsson-Fellman heo em we can hen conclude ha he mo-
bili y p ocess is p og essi e o all y0.
17
Table 1: Ambiguous Wel a e Rankings in he P esence o Declining Income
Dispe sion.
yi;0e(yi;0)
10 17
20 20
30 21
40 45
50 48
Mean Income=30 Mean Income=30.2
Gini=.266 Gini=.23
Coe¢ cien o Va =.527 Coe¢ cien o Va .=.496
ln=.636 ln=.489
18
Table 2: Full Sample o 83 coun ies included in he analysis
A gen ina Cos a Rica India Malawi Sweden
Aus alia Denma k I eland Malaysia Swi ze land
Aus ia Dominican
Republic
I an Nige ia Sy ia
Belgium Alge ia Iceland Nica agua Chad
Benin Ecuado Is ael Ne he lands Togo
Bangladesh Egyp Jamaica No way Thailand
Boli ia Jo dan Nepal T inidad
and Tobago
B azil Finland Japan New
Zealand
Tu key
Ba bados F ance Kenya Pakis an Tanzania
Canada Ghana Ko ea Panama Uni ed
Kingdom
Chile Gambia S i Lanka Pe u Uganda
China Guinea-
Bissau
Leso ho Philippines U uguay
Came oon G eece Mexico Po ugal Uni ed
S a es o
Ame ica
Congo,
Republic o
Gua emala Mali Pa aguay Venezuela
Colombia Hong Kong Mozambique Romania Sou h
A ica
Spain Hondu as Mau i ius Rwanda Zambia
El Sal ado Indonesia Senegal Zimbabwe
19
Table 3: Summa y S a is ics
Va iable A e age Minimum Maximum
Hi4.6 yea s .5 (GNB) 10.8 (NZL)
ni3.2% .3% (BEL) 11.68% (JOR)
Si16.6% 2.06% (UGA) 31.80% (NOR)
y1960 3699 381.5 (TZA) 14978.25 (CHE)
y2000 9560 481.87 (TZA) 33292 (USA)
20
.005 .01 .015 .02 .025 .03
G ow h Ra e 1900-1990
0.5 11.5
Log GDP 1900
nonpa ame ic es ima es 95% lowe CI
95% uppe CI
Figu e 1: Nonpa ame ic Es ima es o he G ow h P ocess ac oss he US
S a es.
.04 .045 .05 .055 .06
G ow h Ra e 1955-1990
12.5 13 13.5
Log GDP 1955
nonpa ame ic es ima es 95% lowe CI
95% uppe CI
Figu e 2: Nonpa ame ic Es ima es o he G ow h P ocess ac oss he
Japanese Pe ec u es.
21

-.02 -.015-.01 -.0050.005
G ow h Ra e 1950-1990
-.5 0.5 1
Log GDP 1950
nonpa ame ic es ima es 95% lowe CI
95% uppe CI
Figu e 3: Nonpa ame ic Es ima es o he G ow h P ocess Ac oss he Eu o-
pean Regions.
.02 .03 .04 .05 .06
G ow h Ra e 1960-2000
7.5 88.5 99.5
Log GDP 1960
nonpa ame ic es ima es 95% lowe CI
95% uppe CI
Figu e 4: Nonpa ame ic Es ima es o he G ow h P ocess Ac oss he OECD
Coun ies.
22
.01 .015 .02 .025 .03
G ow h Ra e 1960-2000
6 7 8 9 10
Log GDP 1960
nonpa ame ic es ima es 95% lowe CI
95% uppe CI
Figu e 5: Nonpa ame ic Es ima es o he Uncondi ional G ow h P ocess
Ac oss he Wo ld.
-.04 -.03 -.02 -.01 0
G ow h Ra e 1960-2000
6 7 8 9 10
Log GDP 1960
nonpa ame ic es ima es 95% lowe CI
95% uppe CI
Figu e 6: Nonpa ame ic Es ima es o he Condi ional G ow h P ocess
Ac oss he Wo ld.
23