On Skill Heterogeneity, Human Capital, and Inflation. Radhika Lahiri Queensland University of Technology. and

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1 On Skill eerogeneiy uman Capial and Inflaion Radhika Lahiri Queensland Universiy of Technology and Elisabea Magnani Universiy of ew Souh Wales March 006 Absrac This paper examines he welfare coss of inflaion wihin a moneary dynamic general equilibrium framework wih human capial ha incorporaes endogenous ex ane skill heerogeneiy among workers. umerical experimens indicae ha overall welfare coss are more likely o decrease wih increases in skill heerogeneiy. An implicaion of his feaure is ha a greaer degree of skill heerogeneiy may be associaed wih a higher olerance for inflaion consequenly implying a posiive correlaion beween agen heerogeneiy and inflaion. Using a panel of several counries we empirically es his proposiion. Our evidence lends some suppor o his hypohesis.

2 . Inroducion The impac of agens heerogeneiy on he macroeconomic performance of an economy is cenral o a large and growing body of lieraure and remains an open area of research. owever boh in he inequaliy-growh lieraure and in he inequaliy-inflaion lieraure researchers have ofen focused on one aspecs of agens heerogeneiy namely income inequaliy. For example sudies based on a poliical economy perspecive of he inflaion-income heerogeneiy link provide a heoreical raionale for a posiive as well as a negaive correlaion beween he wo aggregaes. By developing a heory of he deerminaion of inflaion oucomes in democraic socieies Dolmas uffman and Wynne 000 documen a posiive correlaion beween income inequaliy and inflaion. Bhaacharya Bunzel and aslag 003 on he oher hand presen a heory and empirical evidence ha suppors a non-monoonic relaionship beween inequaliy and inflaion. Albanesi 000 analyzes a model in which he poor are more vulnerable o inflaion and are he weaker pary in he poliical process ha deermines inflaion leading o a posiive inequaliy-inflaion correlaion. In empirical sudies on he effec of inequaliy of aggregae oucomes he focus on one single dimension of agens heerogeneiy income inequaliy has been moivaed by he lack of suiable daa. Because human capial inequaliy has been srongly emphasized as being an imporan deerminan of income inequaliy his has led o he common use of income inequaliy as a good proxy for human capial inequaliy. See for example Glomm and Ravikumar 99 Sain-Paul and Verdier 993 Galor and Tsiddon 997 among ohers. owever recen evidence suggess ha income and human capial disribuion saisics can show very low correlaions Casello and Domenech 00. In addiion Casello and Domenech 00 also find ha human capial inequaliy measures provide more robus resuls han income equaliy measures in he esimaion of sandard growh and invesmen equaions. This moivaes our ineres in an invesigaion of he relaionship beween human capial heerogeneiy and inflaion. This paper considers he effec of he degree of skillheerogeneiy among workers on he welfare coss of inflaion. We address his issue in he framework of an equilibrium model wih ex-ane heerogeneiy of he ype sudied in

3 Kydland and Prasad 996 wih money inroduced via a cash-in-advance consrain on he purchases on consumpion. owever in our model skill-heerogeneiy is endogenous and depends on he exen of human capial accumulaion underaken by he represenaive household. Specifically he model of his paper suggess ha he welfare coss of inflaion are likely o decrease as skill heerogeneiy increases. The inuiion underlying his ineresing resul can be briefly described as follows. In our model and imporan parameer inversely represening heerogeneiy is he elasiciy of subsiuion beween skilled and unskilled effor. The impac of inflaion in cash-in-advance models involves subsiuion ou of aciviies subjec o he inflaion ax such as consumpion and work effor owards leisure. igher subsiuabiliy/low heerogeneiy means ha subsiuion ou of skilled effor is possible o a greaer degree han in he case of low subsiuabiliy/high heerogeneiy. Combined wih he fac ha he represenaive household values he leisure of he skilled worker more han ha of he unskilled worker inflaion would enail a greaer degree of subsiuion away from skilled effor. As a resul he oher variables would also be adversely affeced o a greaer degree han in he case of high skill heerogeneiy. Welfare coss of inflaion herefore end o decrease wih increases in heerogeneiy. To empirically es some of he implicaions of our model we use a new panel daa se of human capial inequaliy measures creaed by Casello and Domenech 00 o examine he inflaion experiences of a large panel of counries beween 960 and 989. We find ha he implicaions of our model are broadly consisen wih he empirical evidence on inflaion and human capial heerogeneiy. The remainder of he paper is organized as follows. In Secion we describe he economic environmen and in Secion 3 we briefly analyze he seady sae. The model is parameerized in Secion 4 in which we also find welfare coss of inflaion associaed wih differen levels of skill heerogeneiy. The key implicaion of he quaniaive experimens conduced in Secion 4 is ha welfare coss of inflaion are inversely relaed o he degree of heerogeneiy. In Secion 5 we es his implicaion using a panel of a number of counries. If we focus on he experience of indusrialized economies which as menioned above we believe our model o be more represenaive of he daa finds suppors a posiive inflaion-heerogeneiy correlaion. owever his is no rue of less

4 developed economies in which he inflaion heerogeneiy correlaion is found o be negaive. Secion 6 concludes. A descripion of he numerical procedure used o solve for he seady sae is presened in he Appendix which also includes he proofs of some of he analyical resuls of Secion 3.. The Economic Environmen The economy is populaed wih a coninuum of idenical infiniely lived households ha are uniformly disribued along he uni inerval [0 ]. As in Kydland we assume ha each household consiss of wo ypes of workers skilled ype and unskilled ype. owever we make he furher assumpion ha he produciviy of he ype worker is endogenously deermined by he household s skill accumulaion as we will describe laer. ousehold preferences are given by E 0 β u c n n where c represens household consumpion in ime and ni represens labor effor a ime of ype i agen i. The funcional form used for he momenary uiliy funcion is of he indivisible labor form as in ansen 985 and is given by where ψ and log c ψ a n ψ a n ψ are he underlying weighs assigned o he leisure of skilled and unskilled workers respecively. ouseholds ener period wih nominal money balances m carried over from he previous period. The governmen augmens hese money balances by a lump-sum ransfer equal o he increase in money supply where he aggregae money supply deermined according he following rule: M g M. M is 3 Specifically skilled and unskilled workers can work some given posiive number h < or no a all implying household consumpion ses are non convex. owever as in ansen 985 and Rogersen 988 he household consumpion se is made convex by allowing agens o rade employmen loeries. As in Prasad 996 his economy has wo independen employmen loeries one for skilled workers and anoher for unskilled workers. The expeced uiliy of each household is hen defined over oal household consumpion and he probabiliy of employmen of each ype of worker. 3

5 Thus he oal amoun of money balances held by a household a he beginning of period is he amoun m g M. To ensure ha money is valued in equilibrium we assume he presence of a cash in advance consrain on he purchase of he non-sorable consumpion good. Expendiure on he consumpion good herefore canno exceed he oal money balances available o he household i.e. p c m g M. 4 5 The growh rae of money g evolves according o: log g γ log g ξ. 6 ξ is i.i.d normal wih mean γ log g and variance uncondiional mean of log g. σ ξ and logg represens he In every period household expendiures consis of consumpion c invesmen in physical capial x invesmen human capial s and he amoun of m money balances p ha are o be carried over o he nex period. These expendiures mus no exceed oal household income which is he sum of income earned from skilled and unskilled labor capial money balances carried over from he previous period and he lump-sum moneary ransfer from he governmen. ouseholds herefore maximize expeced lifeime uiliy subjec o 5 and a sequence of bue consrains of he following form: c x s m p w n w n r k m g M p where household invesmen expendiure for physical and human capial in period- is respecively given by x k s h δ k k ; δ h. h In equaion 8 k and h respecively denoe he household s physical and human capial sock in period-; δ k and δ h are he corresponding raes of depreciaion

6 The represenaive firm in his economy akes he average skill accumulaion by he households as given and hires labor and physical capial K o produce z Y e K 0 where z is an exogenous produciviy shock ha follows an AR process of he form: z ρ ε 0 < <. z ρ ere ε is i.i.d wih zero mean and consan variance σ z. In 0 he aggregae ime- labor inpu labor given by is a CES funcion of skilled and unskilled { h }. The elasiciy of subsiuion beween he wo ypes of labor is given by. The funcion h capures he produciviy of skilled labor which is assumed o be increasing and concave wih 0. oe ha he degree of heerogeneiy in his model is refleced in wo parameers: a parameer ha impacs direcly on he skill differenial beween he wo ypes of labor effor considered h and a parameer ha describes he elasiciy of subsiuion beween hem namely. In addiion we make he assumpion ha he economy wide average sock of human capial equals he sock of human capial accumulaed by he household i.e. h. The represenaive household herefore indirecly influences he relaive wage raes of skilled and un-skilled labor and he renal rae of capial hrough is choice of human capial accumulaion. Y Taking ha choice as given he firm maximizes profis which are equal o w w r K. The opimaliy condiions for he firm s problem yield he Wih he excepion of skill accumulaion capial leers denoe aggregae economy wide per capia variables which an individual household regards as being ouside is sphere of influence while lower case leers denoe variables specific o he household. 5

7 6 following funcions for he skilled and unskilled wage raes and he renal rae for capial: 3 3 z h K e K z w 4 z K e K z w 5. z K e K z r For a value of g greaer han one boh M and p will grow wihou bound. In order o make he household s problem saionary some of he variables need o be ransformed. To ha end we define M m m ˆ and M p p ˆ. We can hen sae he household s problem as follows: { } 6 log max 0 0 ˆ h k m n n c n a n a c E ψ ψ β subjec o 7 ˆ ˆ ˆ ˆ h k g p g m k r n w n w h h k k c p m δ δ 8 ˆ ˆ g p g m c he process for echnology and moneary shocks he aggregae capial accumulaion rule given by 9 z z ε ρ 0 log log g g ξ α X K K δ as well as he economy-wide aggregae decision rules perceived by he households: K g z 3 Since he aggregae producion echnology is of he Cobb-Douglas form profis will be zero in equilibrium even hough aggregae labor effor is a CES funcion of skilled and unskilled labor. This is easily verified by subsiuing he

8 X X z g K and P ˆ Pˆ z g K. In equilibrium aggregae per capia quaniies urn ou o be equal o he choices of he represenaive household. In paricular i mus be he case ha n k K x and m ˆ ˆ m. Since he cash in advance consrain is assumed o be X binding in equilibrium we also have c. Pˆ 3. The Seady Sae In his secion we show ha since money is inroduced in our model via a cashin-advance consrain inflaion has a negaive has impac on he long-run oucomes of several variables as is ypically expeced of such models. Furhermore consisen wih some of he heoreical lieraure on he link beween inflaion and human capial we find ha inflaion has a negaive impac on human capial accumulaion. 4 The degree of skill heerogeneiy in our model has a furher impac on he magniude of disorions associaed wih inflaion as suggesed by some of he analyical resuls of his secion. The subsequen secion based on numerical experimens in fac indicaes ha i ends o weaken hem. Consequenly he welfare coss of inflaion end o decrease wih an increase in heerogeneiy. In he non-sochasic seady sae he firs order condiions wih respec o c n n mˆ k h and equilibrium condiions for his economy imply: C λ λ 3 { } 4 ψ a λ K { } 5 ψ a λ K β λ λ λ 6 g opimal wage and renal raes in he profi funcion. 4 For a survey see Gillman and Kejak

9 8 7 k K δ β 8 h K δ β 9 δ δ K K C h k ere λ and λ are he Lagrangian mulipliers associaed wih he household bue and cash-in-advance consrains respecively. From equaion 7 which is he equilibrium version of he firs order condiion for capial i is clear ha he capial o aggregae labor raio is independen of inflaion and is given by: δ β κ K. Of course his is no he case for oher variables as a glance a he opimaliy condiions suggess. Manipulaing 3-6 and 8 we can express oher variables such as consumpion and work-effor as funcions of human capial: 30 a g C ψ βκ 3 h κ δ β 3 h κ δ β ψ ψ 33 h κ δ β 34. K h δ β κ

10 9 In he above equaions ψ ψ. Also noe ha for an inerior soluion o work effor we need o impose <. Making he necessary subsiuions in 9 we can hen derive an implici equaion in human capial given by: 35. a g h k h κ δ β κ δ κ δ ψ βκ Toal differeniaion of he above equaion wih respec o and g yields a fairly complicaed expression for d : 36. g g d In equaion 36 ψ a βκ δ β κ κ δ κ h k and he expressions and are parial derivaives of he respecive funcions wih respec o. ow inflaion impacs on consumpion work effor physical and human capial is herefore difficul o discern analyically. everheless if we impose some resricions on parameer values and funcional forms i is possible o derive a few weak analyical resuls. Le Ω represen he elasiciy of he marginal reurn o human capial o changes in human capial invesmen. Also define Ω. To inerpre he laer expression noe ha. Then can be regarded as he average conribuion of skilled effor o aggregae effor. Consequenly we can inerpre

11 Ω as he elasiciy of his average conribuion o changes in human capial invesmen. We can hen summarize our analysis of equaions 36 and 3-34 in he following proposiions he proof of which is presened in he appendix: Proposiion : If i < and > 0 seady sae human capial invesmen is decreasing in he rae of inflaion i.e. d < 0; dc ii seady sae consumpion is decreasing in he rae of inflaion i.e. < 0. Proposiion : If he condiions of Proposiion hold and Ω > Ω d i seady sae skilled effor is decreasing in inflaion i.e. < 0 ; ii d he sign of is ambiguous; d iii seady sae aggregae effor is decreasing in inflaion i.e. < 0; dk iv he seady sae capial sock is decreasing in inflaion i.e. < 0. Firs le us consider he inerpreaion of he condiions < and > 0 in Proposiion. The firs of hese places an upper limi on he inverse of he elasiciy of subsiuion beween he wo ypes of labor. To inerpre he second condiion again recall ha i.e. is he average conribuion of skilled effor o he aggregae work effor in his economy. Then he condiion > 0 requires ha his average conribuion responds posiively o changes in human capial accumulaion. In Proposiion he addiional condiion requires ha he elasiciy of he reurn o human capial invesmen be greaer han he human capial elasiciy of he average conribuion of skilled effor o aggregae effor muliplied by he facor which is he inverse of he elasiciy of subsiuion beween he wo ypes of labor. One can perhaps inerpre he 0

12 above Proposiions as saing condiions under which inflaion-ax disorions as measured by he negaive impac of inflaion on human capial skilled effor and consumpion are imporan. owever one canno conclusively say wheher he associaed welfare coss of inflaion will be high or low; ha would depend addiionally on he magniude of he response of variables o increases in he inflaion rae. everheless i should be inuiively clear ha experimens varying he heerogeneiy parameers will impac on inflaion ax disorions and consequenly he welfare coss of inflaion in ineresing ways. In he subsequen secion on numerical experimens we will herefore use he condiions of Proposiions and o assis in he inerpreaion of our resuls. oe however ha he condiions in he above proposiion are only sufficien condiions for he response of human capial consumpion and oher variables o be negaive. umerical simulaions conduced and discussed in more deail in he following secion indicae ha as is ypical in models wih a cash-in-advance consrain on consumpion purchases consumpion and work effor physical and human capial are negaively relaed o he growh rae of money even when some of he above menioned condiions do no hold. Ineresingly higher inflaion is also shown o be associaed wih a shif in he percenage composiion of he work force beween skilled and unskilled labor. The inuiion for he negaive impac of inflaion on economic aggregaes is sraighforward and common o several cash-in-advance models in he lieraure. Inflaion acs as a ax on consumpion since i requires he use of cash. This leads economic agens o subsiue consumpion for aciviies ha do no require he use of cash such as leisure. The decline in work effor causes a decline in oupu and consequenly consumpion invesmen and he physical and human capial sock. owever i is also inuiively clear ha he magniude of he negaive response o inflaion in his economy is likely o be affeced significanly by he parameers of he funcions and. Specifically varying ψ or α which can be inerpreed parameers affecing he exen of ex ane heerogeneiy in his economy has an impac on he condiions of Proposiions and and consequenly he magniude of he disorions associaed wih inflaion. I is hen naural o expec ha welfare coss

13 compuaions relaive o an opimal moneary policy may yield significanly differen resuls as we allow some of hese parameers o vary. In he nex secion we herefore derive some conclusions regarding welfare coss based on numerical experimens using a plausibly parameerized version of he model. 4. Inflaion and Skill eerogeneiy: Resuls Based on Quaniaive Experimens In his secion we explore he relaionship beween inflaion and heerogeneiy by examining how long-run aggregae oucomes and welfare coss of inflaion change as we vary he levels of he parameers ha capure heerogeneiy. Firs we α specify ; 0 < α < so ha he parameers relevan o he degree of heerogeneiy are αψ and.the remaining parameers viz β δ δ a and g are k h aken direcly from relevan papers in he equilibrium business cycle lieraure such as ansen 985 and Cooley and ansen 989 Lahiri 00 and Canon00. The range of values for he parameer includes he value 0.4 chosen in he Prasad 996. The values for α are chosen such ha he produciviy differenial is around or higher as suggesed in Kydland 995. The parameer ψ even hough i can be inerpreed as a parameer represening heerogeneiy is however fixed a 0.59 he value chosen in Prasad 996. The reason for doing so will be discussed below wih reference o he measure of welfare cos considered in his paper. The oher fixed parameers are given by he following: β. 99 ;. 36 ; δ. 05 ; δ ; a. 86. appendix. k The numerical procedure used o calculae he seady sae is described in he To compue welfare coss of inflaion we calculae he increase in consumpion ha an individual would require o be as well off under he equilibrium allocaion associaed wih he opimal moneary policy. Specifically we solve for x in he equaion U * * * log c x ψn ψ n where h * * * c n n are levels of consumpion and work effor associaed wih moneary policy ha ses g > while U is he uiliy aained under he opimal policy which ses g β. We calculae his loss expressed as a percenage of oupu and also of consumpion for varying levels of each of he heerogeneiy parameers. oe ha since ψ is a preference parameer i

14 obviously affecs he measure of welfare coss iself. An experimen ha considers he effecs of varyingψ on welfare coss of inflaion is herefore inappropriae. Table below presens he seady sae values of variables and associaed welfare coss of inflaion as he moneary growh rae increases wih he heerogeneiy parameers fixed a α 0.; 0.4; ψ Figures a and b presen he seady sae values of variables as increases. The x line represens he policy wih inflaion g. 5 and he doed line represens he opimal policy g β. Figure c presens welfare coss of inflaion as increases. Figures a and b presen he percenage difference in he seady sae values of variables in he presence of inflaion relaive o heir seady sae levels when g β for differen values of. Figure c presens he elasiciy Ω and he weighed elasiciy Ω for differen values of where he * line represens he laer. Figures 3a-c and Figures 4a-c presen similar experimens wih he parameer α. Firs we examine he compuaions presened in Table. As menioned above he heerogeneiy relaed parameers in his case are fixed a α 0.; 0.4; ψ and he moneary growh raes are se a g β g.04; g.05; and g. 5. The usual feaures of cash-in-advance models are apparen: inflaion impacs negaively on consumpion work effor physical and human capial and oupu. 5 The composiion of work effor however seems o shif slighly in favor of unskilled labor as inflaion increases perhaps due o he relaively higher weigh assigned o leisure of he skilled ype. In a quaniaive sense he magniudes of welfare coss are higher han would be observed in a model wihou endogenous skill heerogeneiy or human capial such as in Cooley and ansen 989. ex we examine he effecs of varying he heerogeneiy parameers and how his variaion impacs on he magniude of disorions associaed wih inflaion. Firs consider Figures a and b. The response of variables o changes in appears similar regardless of he moneary policy in operaion and he magniude of he negaive impac of inflaion does no look very sriking. The magniude of he inflaion-ax disorions is however difficul o discern from hese figures and we herefore defer he discussion of 5 In a qualiaive sense hese resuls hold for oher combinaions of he heerogeneiy parameers as well. 3

15 hese disorions unil he analysis of Figures c and d. 6 Firs we aemp o gain some inuiion for how changes in affec he long run values of economic aggregaes in general regardless of wha he inflaion rae is. Increasing which is he inverse of he elasiciy of subsiuion beween differen ypes of labor amouns o increasing skill heerogeneiy in his economy along wo dimensions. One dimension is associaed wih he falling elasiciy of subsiuion heerogeneiy increases in he sense ha he wo ypes of labor are subsiuable o a lower degree in he producion process. Secondly i is clear from Figure a ha he equilibrium composiion of he work force becomes more heerogeneous as increases. For high subsiuabiliy he work force comprises almos enirely of he skilled ype of labor bu as he elasiciy of subsiuion increases i becomes more heerogeneous. Also lower subsiuabiliy encourages invesmen in human capial; o he exen ha he more expensive ype of effor is used i would be more economical o employ i if is marginal reurn were higher and human capial accumulaion ensures his. This is also refleced in he increasing skill differenial as increases. igher levels of human capial increase he overall produciviy of all inpus and consequenly we see in Figure b ha boh he skilled and unskilled wage raes increase. igher produciviy also encourages physical capial accumulaion. As a resul oupu and consumpion also increase. An ineresing feaure of Figure a is he invered U-shaped response of skilled and unskilled work effor. This feaure can probably be explained by he same raionale used o inerpre backward-bending labor supply curves. Iniially as he wage rae increases he subsiuion effec dominaes he income effec and work effor increases. Afer a cerain level he income effec akes over and he demand for leisure increases. So far we have no considered how inflaion-ax disorions are affeced as increases. From Figures a and b i is easy o discern he negaive impac of inflaion we discussed earlier. owever we canno commen on he magniude of hese disorions unil we discuss he percenage differences in he levels of variables relaive o he case in which he opimal policy prevails. These differences are shown in Figures a and b. 6 The size of he differences is relaively small in comparison o he lengh of he scale of he verical axis in all of he graphs. owever as will become clear from he analysis of percenage deviaions relaive o he opimal policy presened in Figures a and b hese differences can be quie significan. 4

16 owever before we discuss Figure we consider he overall measure of inflaion ax disorions as represened by he welfare cos of inflaion defined earlier. Figure c presens such welfare cos compuaions for differen values of. I is clear ha he welfare cos of inflaion relaive o boh consumpion as well as oupu decreases as increases. In oher words welfare coss of inflaion decrease as heerogeneiy increases. In order o inerpre his resul we urn o Figures ab and c. Recall ha < > 0 and Ω > Ω were some of he condiions saed in Proposiions and. For he funcional form of he produciviy funcion considered in his paper i is easy o check ha α. Since we do no vary α in his experimen he horizonal Ω line in Figure c a 0.9 represens his elasiciy. The upward sloping * line represens Ω. Furhermore i is easy o read he sign of from his figure as Ω 0 > iff > 0. Obviously he condiions < and > 0 do no appear o hold simulaneously for his experimen while he condiion Ω > Ω does no hold for values of greaer han 0.4. As menioned above hese were only sufficien condiions for he impac of inflaion o be negaive and numerical experimens confirm ha he impac of inflaion on all of he variables in his model is negaive even when he said condiions do no hold. owever some of hese condiions paricularly < appears o be of some imporance in deermining he magniude of inflaion ax disorions in his economy. For example noe ha in Figure a and b he larges disorions measured in erms of he percenage deviaion from he opimal level of he variables in quesion appear o be for values of much smaller han. As increases pas his range he decline in welfare coss is more gradual. The oher condiions do no seem o be playing a significan role in he sense ha hey do no correlae srongly wih he magniude of disorions shown in he figures. Why are inflaion ax disorions high for smaller values of? The answer o his quesion may be relaed o he fac ha he impac of inflaion in cash-in-advance models involves subsiuion ou of aciviies subjec o he inflaion ax such as consumpion and work effor owards leisure. igher subsiuabiliy in he lower range of values for means ha subsiuion ou of skilled effor is possible o a greaer degree in his case. Combined wih he fac ha he represenaive household values he leisure of he skilled 5

17 worker more han ha of he unskilled worker since ψ inflaion would enail a greaer degree of subsiuion ou of skilled effor. As a resul he oher variables would also be adversely affeced o a greaer degree han in he case of low subsiuabiliy. The oher condiion ha may be of some relevance is Ω > Ω ; one can perhaps asser ha he disorions o he lef of 0. 4 where his condiion holds are larger han he disorions beyond his value. The lef hand side of his inequaliy can be inerpreed as a facor of imporance in of he supply side of he skill accumulaion decision; one would expec a larger lefward shif in supply of human capial in response o he inflaion ax if he elasiciy of is marginal reurn was large. 7 The demand side response on he oher hand depends on he human capial elasiciy of he average conribuion of skilled effor o aggregae effor appropriaely weighed by he inverse of he elasiciy of subsiuion. If Ω is negaive and large he average conribuion of skilled effor increases when human capial accumulaion falls in response o he inflaion ax. The demand for skilled effor may increase due o his increase in average produciviy or alernaively fall given ha a smaller amoun of skilled effor may be needed in he producion process. When here is high subsiuabiliy he exen of shifs in demand may no be oo large and he corresponding weigh assigned o his elasiciy is low. In any case our numerical experimens sugges ha he supply side response of work effor dominaes and he overall impac is negaive. For larger values of increases and becomes posiive. This means ha he average conribuion of skilled effor decreases when human capial accumulaion falls. Again demand may fall or rise depending on he exen o which skilled effor is needed relaive o he decline in is average produciviy. The scenario in which inflaion ax disorions weaken is when he demand shifs posiively o couner he lefward shif in supply so ha equilibrium skilled effor does no fall oo much. Re-examining he percenage differences in skilled effor and unskilled effor relaive o he opimal case in Figure a here is evidence o sugges ha his inerpreaion may be plausible. Ω 7 Recall ha he marginal reurn is assumed o be decreasing in human capial. As he inflaion ax encourages a reducion in human capial accumulaion he marginal reurn o i would increase as a resul. If he elasiciy of his marginal reurn is high a greaer exen of subsiuion ou of skilled leisure is possible hus enhancing he negaive response of skilled effor o increases in inflaion. 6

18 We now urn o he discussion of experimens ha vary α. Firs we inerpre he changes in he seady sae variables in Figures 3a and b as α is increased from 0.05 o igher α represens a higher marginal reurn o human capial and herefore a greaer seady sae level of human capial. As a resul he skill differenial increases as does he produciviy of skilled and unskilled effor leading o increases in wage raes. Physical capial also increases as i is more producive when higher levels of human capial are used in he producion process. The increase in oupu and consumpion is anoher obvious implicaion of he increase inα. The income effec of wage increases appears o dominae he subsiuion effec in his case; boh skilled and unskilled effor decline as α increases. Looking a he welfare cos esimaes in Figure 3c we find ha welfare coss of inflaion relaive o consumpion increase very gradually while welfare coss relaive o oupu increase and hen decrease. oe ha he magniude of changes in his case is very small. To inerpre hese changes we examine Figures 4a and 4b. In his case is fixed a is calibraed value of 0.4 so he condiion < is no saisfied for his experimen. The size of he difference relaive o he opimal policy shown in Figures 4a and b seems o increase monoonically for mos variables excep for work effor and human capial accumulaion. From Figure 4c we see ha Ω > Ω holds for a small range of relaively low values of α while > 0 holds for values of α greaer han or equal o 0.. The work effor response appears consisen wih he inerpreaion given earlier wih reference o he experimen wih variaions in. ow he welfare cos measure which is by definiion he consumpion compensaion you have o give he represenaive household o make i as well off in erms of uiliy as in he case when he opimal policy is in place is direcly affeced by he variables ha ener he uiliy funcion consumpion and leisure. In absolue levels his compensaion obviously has o increase as α increases. This is because as is clear from Figures 4a and b he percenage difference in consumpion levels relaive o he opimal policy increases wihα while he percenage difference in leisure decreases wih α. Expressed relaive o consumpion or oupu however welfare coss may increase or decrease depending on how fas oupu or consumpion increase as α increases. This is wha seems o be happening in Figure 3c; welfare coss relaive o consumpion 7

19 increase very gradually while welfare coss relaive o oupu increase and hen decrease. In fac in simulaions for higher values of α no repored here he welfare coss of inflaion relaive o consumpion also sar o decrease as α increases. The inuiion underlying hese resuls is as follows. Boh ypes of work effor are decreasing in inflaion bu an increase in he produciviy differenial offses he oupu loss associaed wih a given rae of inflaion. In a relaive sense herefore he welfare coss of inflaion are nor likely o be high. Overall we may conclude ha high levels of heerogeneiy are likely o be associaed wih lower welfare coss of inflaion. An implicaion of his resul is ha economies in which agens are characerized by a higher degree of heerogeneiy experience lower coss of inflaion and as such are likely o experience higher inflaion raes. In oher words skill heerogeneiy could conribue oward explaining variaions in he inflaion experiences of differen counries a any given poin in ime. The scope of he nex secion is o empirically esimae he correlaion beween inflaion and skill heerogeneiy. 5. Inflaion and Skill eerogeneiy: An Empirical Analysis In order o es wheher agens heerogeneiy indeed affecs he policy maker s decision over he opimal inflaion level we compare he experiences of a number of counries over a period of ime saring in 960 and ending in our mos comprehensive case in 000. Our empirical sraegy is o conrol for differences in insiuional arrangemens across counries so as o shed ligh on he correlaion beween human capial inequaliy and inflaion. The daa on inflaion are drawn from The Inernaional Financial Saisics published by he Inernaional Moneary Fund. The sample comprises 08 counries of which 33 are defined as developed economies LDC 0 and 44 are defined by Cukierman and Webb 995 as democracies dummy for auhoriarian regime0. owever he number of counries acually used in he esimaion procedure is much smaller due o daa availabiliy consrains. 5. The Explanaory Variables. 8

20 The ype of heerogeneiy a work in he heoreical model is correlaed wih agens produciviy and affecs he agens subsiuabiliy in he producion process. A naural candidae for a measure of such heerogeneiy is human capial inequaliy. Differences in human capial aainmen indeed produce heerogeneiy ha affecs produciviy and he subsiuabiliy beween agens in addiion o he value assigned o non-working aciviies. Daa for agens heerogeneiy are provided by Casello and Domenech 00 and refer o human capial inequaliy. Using he recen informaion conained in Barro and Lee s 00 daa se abou educaional aainmens Casello and Domenech calculae a human capial Gini coefficien G A y dy where Ay is he Lorenz curve of he educaional aainmen disribuion. The Lorenz curve plos he cumulaive percenage of educaional aainmen human capial reached by he boom y-percen of he populaion. The Gini coefficien is a measure of human capial inequaliy ha ranges from zero o one: in he case of perfecly equal disribuion he Lorenz curve would coincide wih he 45-degree lines and he Gini coefficien would be zero. Casello and Domenech 00 propose wo Gini coefficiens namely G5 he Gini coefficien compued using he populaion aged 5 and plus and G5 he Gini coefficien compued using he populaion aged 5 and plus. While for he mos par we will use he former we will use he laer o check he robusness of our resuls. Boh measures of human capial inequaliy are available for all 08 counries in he daa se a imes of 5-year inerval saring from 960. I is now well esablished ha he conduc of moneary policy and specifically he rae of growh of he money sock is he primary facor deermining a counry s inflaion rae. The acual policy pursued by he moneary auhoriy depends on a number of facors some of which have an exquisiely poliical flavor. For insance here is now a large body of lieraure ha relaes cenral banks decisions o heir independence from or vulnerabiliy o poliical pressure which may work o deviae he cenral bank s aenion from he pursui of a price sabiliy goal e.g. Cukierman Webb and eyapi 99; Cukierman and Webb 995. The oher variables we include in our daa se reflec his ype of argumen. The measures of Cenral Bank independence CBI cenral bank vulnerabiliy vulnerabiliy and poliical insabiliy poliical change come from he 0 9

21 Cukierman and Webb 995 daa se. The CBI variable measures legal independence of cenral bank from poliical power. Cukierman e al. 99 code cenral bank independence following wo main principles. Firs of all hey code only a few narrow bu relaively precise legal characerisics. Secondly hey only use he wrien informaion from cenral banks charers. The legal characerisics as described in he charers define a few imporan issues namely: i he appoinmen dismissal and erm of office of he cenral bank s chief officer; ii he policy formulaion cluser and he resoluion of possible conflics over moneary policy beween moneary and fiscal auhoriies; iii he objecives of he cenral bank; iv limiaions on he abiliy of he cenral bank o lend o he public secor and regulaion of he modaliies wih which such lending can ake place. The way he single componens of cenral bank s legal independence are aggregaed is fully described in Cukierman e al. 99. The Cukierman-Webb 995 vulnerabiliy variable akes is origin from raw daa on he acual daes of changes of he governors of he cenral banks. To measure cenral bank vulnerabiliy o poliical insabiliy Cukierman and Webb esimae he probabiliy per monh of a change in cenral bank governor condiional on being a ime inerval ha follows a poliical ransiion. They show ha alhough his probabiliy decreases monoonically wih he number of monhs ha have elapsed since he las poliical ransiion he esimaed probabiliy of a change in governor a he cenral bank is more han wo imes larger in periods wihin six monhs afer a poliical ransiion han in periods ha are more removed from poliical change. They hen compue an index of he poliical vulnerabiliy of he cenral bank vulnerabiliy defined for each counry in he Cukierman-Webb 995 sample as he fracion of poliical ransiions ha are followed wih a lag of 0 o 6 monhs by a replacemen of he cenral bank governor. Cukierman and Webb 995 illusrae ha he highes level of cenral bank vulnerabiliy occurs in he face of high level poliical ransiions which is hen included among he explanaory variables. The las variable we include is he degree of openness openness of an economy o he res of he world. We measure his as he raio of he sum of impors and expors 0

22 over a counry s GDP. The argumen is ha he degree of exposure o inernaional rade may increase he abiliy of a cenral bank o pre-commi o a given low inflaion arge. The Cukierman-Webb variables described above are available for 67 counries from 950 o 989 alhough daa for economies ha achieved poliical independence or esablished a cenral bank afer he 950 sar laer. The Cukierman-Webb daa se includes all he major indusrial and developing economies bu excludes mos Easer European counries. Table repors he summary saisics for he main variables. 5. The Empirical Specificaion. We esimae a model of he form where π i α xi β ηi ε i π i is he inflaion measure in counry i in ime 37 xi is a se of explanaory variables specific o counry i in ime and η ε is he residual. We are ineresed in esimaing he βs. While he error componen i i ε i has he usual properies mean zero uncorrelaed wih iself uncorrelaed wih he vecor x he characerisics of he error componen η i define he esimaion sraegy we will adop. In paricular given he exreme heerogeneiy of inflaion experiences we observe in our sample and he exreme differences of he insiuional feaures of he counries considered we op for reaing he counry specific error componen η i as a fixed effec raher han a random variable. This amouns o esimaing he following equaion where π i π i α xi xi β ε i ε i π i π / T x x T ε ε T. In he acual esimaion he i i i / i i / dependen variable has been ransformed o reduce heeroskedasiciy of he error and hus improve he efficiency of he esimae. Also since a few counries had hree-digi inflaion raes in some years using he unransformed inflaion rae as a dependen variable would give undue weigh o hese oulying observaions. Insead we use π D as he dependen variable as in Cukierman e al The variable D π akes a value from zero o one. 5.3 The empirical resuls. 38

23 We begin by reproducing some of he resuls from he previous lieraure using our daa se. In his way he acual impac of human capial inequaliy on inflaion will be beer evaluaed. When he dependen variable D is regressed on openness only using a FE esimaor or simply OLS on he pooled cross-secion observaions he openness coefficien is negaive and highly saisically significan a resuls ofen highlighed in he empirical lieraure Romer 993; Lane 995. The FE coefficien and sandard error of openness is repored below D openness The negaive correlaion beween openness and inflaion is robus o he inclusion of CBI among he explanaory variables alhough i becomes saisically non-significan when variables represening he vulnerabiliy of he cenral bank and high-level poliical change are included among he regressors. The degree of independence of he cenral bank from poliical pressure CBI has ofen been found o have posiive alhough a hardly saisically significan effec on inflaion. Using our full sample we find a posiive and saisically significan coefficien in he OLS and FE regressions. The CBI coefficiens urn saisically non-significan and negaive in he case of developed democracies for which he FE regression resuls are as follows D 0.07 CBI For his very resriced group of counries he OLS esimae of CBI is negaive and highly saisically significan a resul ha reproduces he one found by Cukierman e al. 99. Our new empirical resuls are illusraed in ables 3-5. Table 3 repors he Fixed Effec esimaion resuls obained by using he full sample o esimae equaion 38. The lef hand side panel illusraes resuls where he dependen variable is D while in he righ hand side panel he dependen variable is he logarihmic ransformaion of he inflaion rae π. The Gini coefficien compued using he populaion of hose aged 5 and over is consisenly negaive and saisically significan. The sign of hese esimaes suggess ha counries where agens are differenly endowed wih human capial end o

24 have beer inflaion records once we keep consan hose insiuional facors ha may impac upon he commimen o price sabiliy. owever his suggesed link beween human capial inequaliy and inflaion does no consisenly apply o all counries. For insance Table 4 illusraes he Fixed Effec esimaion resuls obained by spliing he sample in on-auhoriarian and Auhoriarian regimes lef hand side panel and righ hand side panel respecively of Table 4. When such a disincion is made we noice ha he negaive correlaion beween G5 and inflaion does no hold for Auhoriarian regimes where a mildly saisically significan posiive correlaion beween hese wo variables emerges. The resuls illusraed in Table 5 furher illusraes ha he relaionship beween human capial inequaliy and inflaion may depend on oher feaures of he economy ha are broadly capured by he dummy variable for he sae of developmen. For Less Developed Counries LDC we again find he negaive correlaion beween he Gini coefficien of he human capial disribuion and inflaion we iniially found in he full sample esimaes. owever in a sample of more developed counries LDC0 we find ha human capial inequaliy increases inflaion a resul ha can be explained by our model where human capial inequaliy decreases he welfare coss of inflaion hus opening a space where he commimen o price sabiliy may be relaxed. oe ha hese resuls are robus o i changes in he dependen variable as illusraed in able 3 above ii changes in he populaion used o compue he human capial inequaliy measure G5 raher han G5. Also in mos cases he use of OLS as an esimaion echnique does no radically change he resuls. For insance our OLS esimaes for Cenral Bank vulnerabiliy vulnerabiliy which reproduce he resuls by Cukierman and Webb 995 are no dramaically alered when he Gini measure of human capial inequaliy is included among he regressions. In such a regression he G5 variable has a negaive mildly saisically significan coefficien which appears o be consisen wih our FE esimaes reproduced in able 3. These resuls are available upon reques. 6. Concluding Remarks 3

25 The objecive of his paper was o examine he link beween skill heerogeneiy and he coss of inflaion. This issue was addressed wihin a dynamic general equilibrium framework ha incorporaed ex-ane endogenous skill heerogeneiy among workers. umerical experimens based on a plausible parameerizaion of his model indicae ha welfare coss of inflaion relaive o an opimal moneary policy are likely o decrease as skill heerogeneiy increases. An implicaion of his feaure is ha a greaer degree of skill heerogeneiy would be associaed wih a greaer olerance for inflaion consequenly implying a posiive correlaion beween agen heerogeneiy and inflaion. An empirical sudy based on a panel of several counries lends some suppor o his hypohesis. If we focus on he experience of indusrialized economies he daa suppors a posiive inflaion-heerogeneiy correlaion. On he oher hand his is no rue of less wealhy economies in which he inflaion-heerogeneiy correlaion if found o be negaive. owever he model economy we sudy in his paper and is parameerizaion is represenaive of developed economies and o ha end is only capable of explaining he long run or cyclical feaures of such economies. We may herefore inerpre he resuls as supporive of he heoreical implicaions of our model. Appendix. A. Proof of Proposiion. d I is easy o check ha he numeraor of he expression for is posiive. The sign of d herefore depends on he sign of he denominaor. oe ha he parameers and are posiive. Given ha we have assumed < 0 i is hen clear ha he sign of dc he denominaor will be negaive if < and > 0. To see ha < 0 we ake he oal derivaive of equaion 30 and obain 4

26 dc βκ ψ ag βκ { The firs erm is obviously negaive. Since ψ ag d is negaive and he erm inside he brackes is posiive under our assumpions par ii of he proposiion follows. B. Proof of Proposiion. From condiion 3 we can derive: d δ h β κ d d Again since is negaive given he condiions of Proposiion hold he sign depend. d. d on he erm in brackes. We can hen check ha < 0 Muliplying boh sides by his amouns o Ω > Ω. iff >. d ψ ψ d ψ d Also. ψ ψ ψ d The firs erm on he righ hand side is posiive since is negaive. The second erm is d negave if < 0 i.e. if Ω > Ω. Overall he sign of ha and d d d dk d κ. d is ambiguous. Also noe I is easy o check ha pars iii and iv of he proposiions follow from he given assumpions. 5

27 C. umerical Procedure The numerical procedure used o solve for he seady sae of he model involves he consrucion of a grid of values for human capial and searching his grid for a value ha saisfies equaion 35. Once his is found equaions can be used o find he seady sae values of oher variables. Resuls are accurae up o hree decimal places. References Albanesi S. 000 Inflaion and Inequaliy Universia Bocconi IGIER Working Paper # 99. Barro R.J. and J. Lee 00 Inernaional Daa on Educaional Aainmen: Updaes and Implicaions Oxford Economic Papers July Bell L.A. and R.B. Freeman 00 The Incenive for Working ard: Explaining ours Worked Differences in he U.S. and Germany Labour Economics Bhaacharya J. Bunzel. and J. aslag 003 Inflaionary Finance in a Simple Voing Model Iowa Sae Universiy Working Paper # 030. Campillo M. and Miron J.A. 996 Why Does Inflaion Differ Across Counries? BER Working Paper #5540. Canon E. 00 Business Cycles in a Two-Secor Model of Endogenous Growh Economic Theory Casello A. and R. Domenech 00 uman Capial Inequaliy and Economic Growh: Some ew Evidence Economic Journal Chakrabory S. & Mausumi Das 003. "Moraliy uman Capial and Persisen Inequaliy Universiy of Oregon Economics Deparmen Working Papers Cooley T.F. and G.D. ansen 989 The Inflaion Tax and he Business Cycle American Economic Review Cukierman A. and S. Webb 995 Poliical Influence on he Cenral Bank: Inernaional Evidence The World Bank Economic Review Cukierman A. Webb S. and B. eyapi 99 Measuring he Independence of Cenral Banks and is Effecs on Policy Oucomes The World Bank Economic Review

28 Dolmas J. uffman G.W. and M.A. Wynne 000 Inequaliy Inflaion and Cenral Bank Independence Canadian Journal of Economics Easerly W. and S. Fischer 00 Inflaion and he Poor Journal of Money Credi and Banking 33 Par I Fischer S. 98 Towards an Undersanding of he Coss of Inflaion Carnegie- Rocheser Conference Series on Public Policy Galor O. and D. Tsiddon 997 The Disribuion of uman Capial and Economic Growh Journal of Economic Growh Glomm G. and B. Ravikumar 99 Public versus Privae Invesmen in uman Capial: Endogenous Growh and Income Inequaliy Journal of Poliical Economy ansen G.D. 985 Indivisible Labor and he Business Cycle Journal of Moneary Economics Kydland F.E. 984 Labor-Force eerogeneiy and he Business Cycle Carnegie- Rocheser Conference Series on Public Policy Lane P. 995 Inflaion in Open Economies manuscrip arvard Universiy. Lahiri R. 00 The Inflaion Tax Variable Time Preference and he Business Cycle Macroeconomic Dynamics Lucas R.E. Jr. 98 Discussion of Towards an Undersanding of he Coss of Inflaion: II Carnegie-Rocheser Conference Series on Public Policy Mulligan C.B. and X. Sala-i-Marin 996 Adopion of Financial Technologies: Implicaions for Money Demand and Moneary Policy Working Paper # 5504 Cambrie Mass.: BER. Prasad E. 996 Skill eerogeneiy and he Business Cycle Canadian Journal of Economics Romer D. 993 Openness and Inflaion: Theory and Evidence Quarerly Journal of Economics CVII Sain-Paul G. and T. Verdier 993 Educaion Democracy and Growh Journal of Developmen Economics

29 Table : Seady sae values as g increases. g β Opimal g.04 g. 05 g. 5 Policy uman capial Consumpion Skilled effor Unskilled effor Aggregae effor Capial sock Oupu Skill differenial Skilled wages Unskilled wages Uiliy Welfare cos Welfare cos as % of consumpion Welfare cos as % of oupu