ON THE DYNAMICS OF GROWTH AND FISCAL POLICY WITH REDISTRIBUTIVE TRANSFERS

Transcription

1 O THE DYAMICS OF GROWTH AD FISCAL POLICY WITH REDISTRIBUTIVE TRASFERS by* Hyun Park Unversty of Essex and Apostols Phlppopoulos Athens Unversty of Economcs and Busness May 25, 999 Abstract: Ths paper formalzes the effects of redstrbutve transfers on economc growth and the desgn of desrable fscal polces. We make two contrbutons to the lterature. Frst, we set up a dynamc general equlbrum model n whch the socety as a whole chooses dstortng taxes to fnance redstrbutve transfers as well as publc goods. Second, we delver analytc results for the long-run and the transtonal dynamcs of optmal (secondbest) fscal polces and endogenous growth. The focus s on unqueness and determnacy, and how ths s affected by dstrbutve and allocatve actvtes on the part of the government. Keywords: Redstrbuton. Publc goods. Economc growth. Dynamcs. JEL classfcaton: H2, H4, O4, E62. Correspondence to: A. Phlppopoulos, Athens Unversty of Economcs and Busness, 76 Patsson street, Athens 0434, Greece. Tel: Fax: Emal: aphl@aueb.gr * We thank T. Moutos and H. Polemarchaks for dscussons. All errors are ours.

2 I. ITRODUCTIO The lnk between nequalty, redstrbuton and economc growth (effcency) s a complex one. Concernng the effects of nequalty on economc growth, the conventonal argument (see e.g. Sandmo [995]) s that when nequalty leads to redstrbuton to the less endowed, ths has negatve ncentve effects at both the gvng end (redstrbuton requres hgher taxes whch dscourage nvestment) and the recevng end (moral hazard problems dscourage effort). Recently, ths argument has been combned wth poltcal economy models wth votng. For nstance, Persson and Tabelln [994a], Alesna and Rodrk [994] and Benabou [996] show that n unequal socetes, the less captal-endowed s the medan voter relatve to the average, the hgher s hs deal captal taxaton. 2 Thus, accordng to the conventonal argument, snce redstrbutve polces dstort economc ncentves, more unequal socetes grow faster. 3 Ths paper extends the above lterature by formalzng the effects of redstrbutve transfers on economc growth and the desgn of desrable fscal polces. We make two contrbutons to the lterature. Frst, we set up a dynamc general equlbrum model n whch the socety as a whole chooses dstortng taxes to fnance redstrbutve transfers as well as publc goods. Thus, we allow explctly for both dstrbutve and allocatve actvtes on the For the effects from growth to nequalty (.e. the Kuznets hypothess), see e.g. Aghon and Wllamson [998]. Here, we do not study ths causal relatonshp. For emprcal evdence about the twoway lnk between nequalty and growth, see also Barro [999]. 2 However, n most of these models, redstrbuton s not modelled explctly. It just takes the form of taxes on captal. As Alesna and Rodrk [994, p. 466] say, taxes on captal must be nterpreted as a metaphor for any knd of redstrbutve polcy that transfers ncome to unsklled labor. 3 Ths argument has been recently challenged (for a survey, see Aghon and Wllamson [998]). For nstance, n the presence of captal market mperfectons, redstrbuton can be good for growth because t creates opportuntes, mproves borrowers ncentves and reduces volatlty (see Aghon and Bolton [997] and Aghon and Howtt [998]). Or nequalty can lead to rent-seekng actvtes n a game between nterest groups, and therefore equalty s good for growth (see Benhabb and Rustchn [996] and Benabou [996]). Or, as Sandmo [995] argues, the tradeoff between equty and effcency ceases to exst once we ntroduce adverse selecton ssues. In ths paper, we take redstrbuton as gven wthout justfyng t. Ths s because we want to focus on how redstrbutve transfers affect the dynamcs of optmal growth and fscal polces. If we do not want to ntroduce captal market mperfectons, rentseekng actvtes, etc (see above), then we could justfy redstrbuton by assumng that an ndex of nequalty (see below) provdes drect dsutlty to households, or that ths ndex exerts a negatve producton externalty to prvate frms. Snce ths would also be ad hoc and would not affect our man results, we smply prefer to take redstrbuton as gven.

3 part of the government. 4 Second, we delver analytc results for the long-run and transtonal dynamcs of optmal (second-best) fscal polces and endogenous growth. The focus s on unqueness and determnacy, and how ths s affected by dstrbutve and allocatve polces. The model s as follows. A decentralzed economy s populated by prvate agents (households and frms) and a government. Dfferent households have dfferent captal endowments. The government taxes captal ncome to fnance transfer payments, publc consumpton servces and publc producton servces. Transfer payments redstrbute from those who are endowed more than the average and gve to those who are endowed less than the average. Publc consumpton servces provde drect utlty to households. Publc producton servces rase the productvty of frms, and are the engne of long-run growth (see Barro [990]). 5 These consumpton and producton servces are pure publc goods. When economc polcy s exogenous, the model has the followng features: Frst, when households nternalse the provson of redstrbutve transfers, moral hazard behavor reduces growth. The larger the number of ndvduals, the stronger the ncentve to free rde on each other, and hence the stronger the moral hazard problem. Second, the relaton between the economy s growth rate and the captal tax rate s an nverse U-curve. Thus, at low (resp. hgh) tax rates, an ncrease n the tax rate ncreases (resp. decreases) growth. Ths s as n e.g. Barro [990] and Alesna and Rodrk [994]. We then study what happens when the socety as a whole chooses economc polcy. In partcular, we endogenze polcy by assumng that the government s benevolent and maxmses the sum of all households well-beng. The man results along the optmal path are as follows: Frst, tax ncreases always reduce growth (compare t wth the nverse U-curve relaton above when polcy s exogenous). Second, the government fnds t optmal to redstrbute ncome from the rch to the poor, only when t can also provde publc producton servces (recall that t s the latter that generates long-run growth). Thrd, from the vewpont of the poor (resp. rch) ndvdual, taxes should ncrease (resp. decrease) wth 4 As Sandmo [995] states, to access the role of the publc sector n growth, we have to consder a somewhat wder role for fscal polcy. Specfcally, he says that the man focus of the lterature has been on cash transfers, whereas effects of the provson of socal goods have not receved the attenton that they probably deserve Tax fnancng of publc expendtures wll presumably ncrease the qualty of the labor force, so that an assessment of the effects of the welfare state polcy n effcency terms ought to consder these effects jontly. 5 In Glomm and Ravkumar [992] and Perott [993] the engne of growth s human captal. See also Fernandez and Rogerson [995, 996] for human captal and redstrbuton. 2

4 nequalty. Ths happens because redstrbuton requres taxes. In turn, snce the growth rate s negatvely affected by the tax rate, t follows that unequal socetes grow faster (see also the medan-voter models of Alesna and Rodrk [994] and Benabou [996]). Fourth, provson of government consumpton servces mples that the optmal tax rate changes over tme, and hence there are transtonal dynamcs. Ths enrches the results of Barro [990] and Alesna and Rodrk [994] who do not get transtonal dynamcs. Concernng the long-run, we focus on a steady state n whch all ndvduals are alke ex post (see also Bewley [982]). Then, we fnd a suffcent condton on the parameter values under whch there exsts a unque long-run tax rate, and n turn a unque Balanced Growth Path ( BGP ) along whch consumpton and captal grow at the same postve rate. In ths steady state, the relaton between antcpated redstrbuton and BGP s an nverted U-curve. amely, when the rate of redstrbuton s relatvely small, growth ncreases wth antcpated redstrbutve transfers, whle when the rate of redstrbuton s relatvely large, growth decreases wth antcpated redstrbutve transfers (see also Benabou [996]). Fnally, we study local stablty propertes around ths steady state. We can clam that the antcpaton of large redstrbutve transfers opens the door for ndetermnacy. That s, there can be many possble equlbrum paths for tax polcy, consumpton and captal accumulaton, each of whch s consstent wth a gven ntal condton and wth convergence to a unque steady state. The channel for ndetermnacy s moral hazard. Our results can also explan why ndvduals who start wth smlar endowments may consume and save at dfferent rates over tme; that s, the antcpaton of redstrbutve transfers can tself generate ncome nequalty. Furthermore, n combnaton wth the result that hgh redstrbuton s assocated wth a low BGP along the optmal path, we can also explan why ndetermnacy arses when redstrbuton has a detrmental mpact on growth. The rest of the paper s organsed as follows. Secton II presents the economc envronment. Secton III solves for second best polcy. Sectons IV and V study respectvely the long-run and transtonal dynamcs. Secton VI concludes. II. THE ECOOMIC EVIROMET 3

5 Consder a decentralzed closed economy populated by prvate agents (households and frms) and a government. Households purchase goods for consumpton and save n the form of captal. 6 We assume that there are =, 2,..., households. Frms produce goods and make rental payments for captal nput. For smplcty, there s a sngle frm. The government mposes taxes on households captal ncome to fnance publc producton servces, publc consumpton servces and redstrbutve transfer payments. We assume contnuous tme, nfnte horzons and perfect foresght. Dfferent households have dfferent ntal captal stocks. Household s ndexed by ts own captal stock, k, relatve to the average captal stock, k (where k K and K k = s the aggregate captal stock). Ths ndex, ( k k ), can be also thought as a measure of nequalty. The role of economc polcy It s convenent to start wth the role of economc polcy. The government receves tax revenues θrk from each household, where 0 θ < s the tax rate on captal ncome, r s the market return to captal, and k s household s stock of captal. On the other hand, each household receves a transfer payment δ from the government. We assume that δ s a lnear functon of relatve captal ownershp, ( k k ). Thus, each household receves: 7 δ = δ ( k k ) () 6 For smplcty, we do not nclude labor. Ths s because we want to focus on dfferences n captal endowments across ndvduals. Our results do not change f households supply nelastcally ther labor servces. However, our results do change f households make labor/lesure choces (see e.g. Alesna and Rodrk [994]). For detals, see Park and Phlppopoulos [998]. 7 For smlar state-contngent lnear rules, see Aghon and Howtt [998, chapter 9]. Of course, redstrbuton can take many forms n addton to transfers (e.g. progressve ncome taxaton, regulatons, mnmum wage laws, etc). See Benabou [996]. 4

6 where 0 δ < s a redstrbutve parameter. Equaton () mples that the government subsdses those households who are endowed less than the average. Thus, f k household s a recever. If k < k, household s a donor. > k, The government uses ts total tax revenues to fnance the provson of aggregate publc producton servces g, aggregate publc consumpton servces h, and transfer payments to each household δ. Thus, the government budget constrant at each nstant of tme s: 8 g + h + δ = θrk (2) = = For smplcty, we assume that a porton 0 < b < of total tax revenues s used to fnance publc producton servces, and a porton 0 < b < s used to fnance publc consumpton servces plus transfer payments. 9 Thus, (2) s decomposed to (3a) and (3b): g = b θrk (3a) = h + δ = ( b) θrk (3b) = = Households Household maxmzes ntertemporal utlty: 8 For smplcty, there s no publc debt. 9 See also Turnovsky and Fsher [995] for the exogenous decomposton of government expendtures between varous servces. We assume that b s exogenous n order to study how ths decomposton affects optmal growth and tax polcy. 5

7 0 ρt [ u( c, h)] e dt (4a) where c s household s prvate consumpton, h s aggregate publc consumpton servces (whch s a pure publc good), and the parameter ρ > 0 s the rate of tme preference. ote that all households dscount utlty by usng the same factor, ρ (see below). The functon u(.) s ncreasng and concave n ts two arguments, and also satsfes the Inada condtons. For smplcty, we assume that u(.) s addtvely separable and logarthmc. Thus, u c (, h) = logc + ν logh (4b) where the parameter ν 0 measures the weght gven to publc consumpton relatve to prvate consumpton. 0 Households consume and save n the form of captal. When household rents out k to frms, t receves a net captal ncome ( θ )rk. It also receves a proft share, π. Furthermore, t receves a transfer payment δ from the government. Usng equaton () for δ, household s flow budget constrant s: c + k = ( θ ) rk + π + δ ( k k ) (5) where a dot over a varable denotes tme dervatve, and the ntal captal stock s gven. 0 Ths functon allows for a balanced growth path. In Persson and Tabelln [994], θ = δ n equaton (5). 6

8 Households take prces/profts ( r, π ), tax polcy ( θ ) and publc goods ( h ) as gven. The control varables are c and k, so that the frst-order condtons for a maxmum are equaton (5) as well as the Euler condton: 2 c = c [( θ) r ρ δ ( )] (6) The frm Followng Barro and Sala--Martn [995, pp. 53-4] and Alesna and Rodrk [994], technology at the frm s level takes a Cobb-Douglas form. Thus, the sngle frm faces the producton functon: y = g K (7) α α where 0 < α < s a parameter, g s publc producton servces (whch s a pure publc good) and K s the aggregate captal stock (there s a sngle frm). At any pont of tme, the frm maxmzes profts, π : π α α = g K rk The frm acts compettvely by takng prces (r) and publc goods ( g ) as gven. The control varable s K, so that the frst-order condton for a maxmum s smply: 2 The necessary condtons (5) and (6) are completed wth the addton of the transversalty condton ρt lm[ u (.) k e ] = t c 0. It s known that there exsts a unque soluton to ths problem. The other argument n the utlty functon must also be bounded. Ths s taken as gven by households (see below). 7

9 r = g K (8) α α α whch equates the rate of return to the margnal product of captal. Decentralzed Compettve Equlbrum We now characterze a Decentralzed Compettve Equlbrum (DCE). Ths s for any gven tax polcy, θ. Usng (3a) nto (8), the return to captal s: r α α α = α ( bθ) ( θ) (9) whch s the return to captal perceved by prvate agents n a DCE. Ths s the return that drves prvate agents consumpton/captal decsons n equlbrum (see (5) and (6)). In the presence of externaltes, ths return s smaller than the realzed one (see below). Ths can also justfy economc polcy n the next secton. Usng (9) nto (3a), (3b) and (7), the economy-wde publc producton servces ( g ), publc consumpton servces ( h ) and output (y) are respectvely: g = ( αbθ) α K (0a) h = ( b) θ ( θ) K δ ( k k ) (0b) α α y = ( αbθ) K (0c) = 8

10 where (as we sad above) each household s captal, k, and hence aggregate captal, K, have been chosen by prvate agents who gnored externaltes. 3 We next calculate aggregate profts, π π =. The law of Walras mples y = RK + π, where R s the realzed return to aggregate captal, K. Ths s an accountng relatonshp, whch smply states that realzed captal payments and profts exhaust total y output. But snce (0c) mples R = ( αbθ) K α α, we smple have for aggregate profts: π = 0 (0d) so that, at an economy-wde level, all realzed ncome goes to captal. 4 We summarze. We have characterzed a Decentralzed Compettve Equlbrum (DCE). Ths s for any tax polcy θ on behalf of the government. In ths equlbrum: () Prvate decsons maxmze households utlty and frms profts (see (5) and (6), where r follows (9) and π follows (0d)). () The government budget constrant s satsfed (see (0a) and (0b)). In the next secton, the government chooses ts tax polcy, θ. 5 Before we choose the optmal θ, we pont out the followng results for gven θ. Frst, (6) and (9) mply that the economy s growth rate s G c [( θ ) ( θ ) ρ δ ( )]. The last term,.e. 3 (0c) shows that our model s a varant of Rebelo s [99] model,.e. at an aggregate level, output s lnear n captal. 4 Ths s because the model s a varant of Rebelo s [99] AK model. Thus, f captal s pad ts realsed margnal product, there s nothng left for profts or labor. As Barro and Sala--Martn [995, pp. 4-2] say, ths s because n the AK model, captal encompasses human captal, knowledge and publc nfrastructure, whle the zero wage rate can be thought as applyng to raw labor whch has not been augmented by human captal. Also note that: () Snce 0 < α < and θ > 0, R > r. Thus, the economy-wde return exceeds the return perceved by prvate agents. () R and r concde only when there are no externaltes. () The smlarty of realsed returns to socally optmal returns obscures an mportant dfference between them: realsed returns are based on prvate decsons that gnored externaltes. 5 Here, δ s exogenous. Alternatvely, δ could be chosen optmally. The assumpton that δ s exogenous s delberate: t helps us to study how commonly used redstrbutve polces, as n (), affect optmal growth and tax polcy. 9

11 δ ( ) > 0, s the effectve redstrbutve parameter. It arses because households nternalse the provson of redstrbutve transfers, and mples that moral hazard behavor reduces growth. Observe that when there s a large number of households (.e. ), the effectve redstrubutve parameter ncreases, so that free-rdng ncentves - and hence the moral hazard problem - become stronger. By contrast, when there s only one household (.e. = ), the effectve redstrbutve parameter becomes zero and there are no moral hazard problems. Second, G c ( α θ) ( θ ) G =. Thus, c > 0, f 0 < θ < α < ; θ αθ θ G on the other hand, c < 0, f α < θ <. In other words, when polcy s exogenous, θ the relaton between the economy s growth rate and the captal tax rate s an nverse U- curve. At low tax rates, 0 < θ < α <, an ncrease n the tax rate ncreases growth. At hgh tax rates, α < θ <, the growth rate declnes wth the tax rate. Ths result s smlar to that n e.g. Barro [990] and Alesna and Rodrk [994]. 0