The Welfare Implications of Growth Regressions

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