Growth, Welfare, and Public Infrastructure: A General Equilibrium Analysis of Latin American Economies

Transcription

1 Volume 26, Number 2, December 2001 Growh, Welfare, and Public Infrasrucure: A General Equilibrium Analysis of Lain American Economies Felix K. Rioja Empirical sudies have found infrasrucure invesmen imporan for a counry s economic performance, bu have no provided clear guidelines for infrasrucure policy or is effecs on oher macroeconomic variables. This paper develops a general equilibrium model of a small open economy o sudy he effecs of public infrasrucure on oupu, privae invesmen and welfare. The model is parameerized and solved for hree Lain American counries: Brazil, Mexico, and Peru. Resuls show ha infrasrucure can have posiive effecs on oupu, privae invesmen and welfare. However, raising public infrasrucure invesmen pas a cerain hreshold can be derimenal. All hree counries are shown o have under-invesed in infrasrucure in he 1970s and 1980s. The gains from opimal infrasrucure policy are greaes for Peru, he counry wih lowes infrasrucure expendiure. I. Inroducion Mos economiss agree ha a counry s public infrasrucure is one of he pillars of economic growh. Publicly provided airpors, highways, srees, and waer sysems conribue o oupu growh because hey can increase produciviy of privae facors and decrease coss. Empirical sudies of developing counries and cross-counry regressions have found infrasrucure imporan for a counry s growh (e.g., Easerly and Rebelo (1993), Ford and Pore (1991), Canning and Fay (1993), among ohers). Papers in his lieraure have ypically used regression analysis on eiher growh accouning or seady sae equaions. While hese papers have been useful in poining ou he imporance of infrasrucure, heir mehodology does no allow for analyzing imporan general equilibrium feedback effecs among variables or for ou-of-sample policy experimens. This paper develops a general equilibrium framework ha yields quaniaive predicions ha can be used for policy analysis. In addiion o sudying he overall produciveness of infrasrucure, his paper sudies is effecs on oher macroeconomic variables such as privae invesmen and welfare. Some of he quesions addressed are: is privae business invesmen encouraged or deerred wih addiional public invesmen, and in wha proporion? How does addiional infrasrucure invesmen affec he populaion s welfare? Mos previous sudies of infrasrucure have only focused on he implicaions for Deparmen of Economics, Andrew Young School of Policy Sudies, Georgia Sae Universiy, Alana, GA 30303, U.S.A. prcfkr@langae.gsu.edu 119

2 oupu. 1 This paper ries o offer infrasrucure policy recommendaions ha are compued based on he larges welfare gains o he populaion. In order o address hese issues, a wo-secor general equilibrium model of a small open economy is consruced. The model provides an inernally consisen framework for policy analysis as suggesed by Lucas (1987). The model is grounded in he equilibrium heoreical lieraure of Uzawa (1974), Barro (1990), and Glomm and Ravikumar (1994). However, heir models are no quaniaively solved and do no emphasize we lfare and privae invesmen effecs. The model is parameerized o hree Lain American counries: Brazil, Mexico, and Peru. Resuls show ha infrasrucure can have posiive effecs on oupu, privae invesmen and welfare. However, raising public infrasrucure invesmen pas a cerain hreshold can be derimenal. All hree counries are shown o have under-invesed in infrasrucure in he 1970s and 1980s. The gains from opimal infrasrucure policy are greaes for Peru, he counry wih lowes infrasrucure expendiure. The paper proceeds as follows: Secion II describes he model. Secion III describes he soluion procedure and inuiion. The quaniaive evaluaion of he model and policy implicaions are analyzed in Secion IV, while Secion V offers concluding remarks. II. The Model There are many households inhabiing he small open economy. Households have hree sources of income. Firs, hey earn wages by supplying heir effor o firms. Second, hey earn a reurn on physical capial ha hey own by rening i o firms. Third, hey earn a reurn on heir ne holdings of foreign bonds, which hey can buy and sell a he world ineres rae. Households are uiliy maximizers, so hey decide on heir levels of consumpion, invesmen, and foreign bond holdings. They also decide on heir work effor and on how much capial o ren o firms in he economy. In he producion secor, here is a represenaive firm ha produces a final good using privae capial and labor. In addiion, here exiss an exernal inpu in producion, public infrasrucure, which is provided by he governmen. The governmen finances infrasrucure invesmen by axing oupu a a fla rae, and i has o balance is budge consrain every period. A wo-secor neoclassical general equilibrium model of a small open economy is formally described below. 1. Households A large number of idenical infiniely lived households, a represenaive firm, and a governmen populae he economy. Households have preferences over consumpion and leisure sreams c, given by he uiliy funcion { l } =0 1. Among he excepions are Looney and Frederiken (1997) and Blejer and Khan (1984) who sudy privae invesmen effecs. 120

3 RIOJA: GROWTH, WELFARE, AND PUBLIC INFRASTRUCTURE =0 β U ( c, l ), (1) where he discoun facor is 0< β <1. U ( ) is an insananeous feliciy funcion ha is assumed o display sandard properies. The amoun of labor supplied by he household is n, and he oal amoun of ime available o a person is normalized o uniy so ha l n 1. The household s budge consrain can be wrien as, + c + i + p b w n + R k + b. (2) + 1 This budge consrain has a sandard uses canno exceed sources accouning inerpreaion. The lef-hand side describes he uses of funds. Households can spend on consumpion c ), invesmen ( i ) (hey own capial), or purchase foreign bonds ha come due nex period ( b ) + 1 a price p. Thus p denoes he price of a bond ha delivers one uni of consumpion nex period. The sources side of Equaion (2) describes how he household earns income. The household rens capial ( k ) o he firm earning a ne reurn of R. The household also earns a wage rae of w for is work effor, n, and has ne holdings of foreign bonds, b, purchased las period which come due a ime. Since his is a small open economy, R is also he world ineres rae. This is a sandard assumpion in small open economy models as hese economies are oo small o affec he world ineres rae, bu can borrow and lend inernaionally a ha rae. This effecively ies heir domesic ineres rae o he world s rae. Privae capial evolves according o, where k = i + ( 1 δ ) k, + 1 K δ is he depreciaion rae of capial. The privae capial sock omorrow k ) is equal K o he amoun invesed oday ) ( ( + 1 i plus oday s surviving capial sock, ( δ K ) k ( 1. Finally a no-ponzi game condiion, lim b /(1 + R ) = 0, should be imposed on he household so ha, basically, i canno jus coninuously borrow forever. 2. Firm There are hree facors of producion in he economy: privae capial, public infrasrucure, and labor. The final good is produced according o he echnology, * ( K, k n ) y = f,. G 121

4 The producion funcion f saisfies sandard properies and exhibis consan reurns o scale over privae inpus so ha facor paymens exhaus revenues. The effecive aggregae sock of * public infrasrucure, K, is a publicly provided inpu in producion. 2 This effecive public G sock is relaed o he raw sock of infrasrucure, K, by G K = θ, (3) * K G G where 0#2 #1 is a measure of effeciveness. Ofenimes in developing counries he sock of public infrasrucure is no in perfec condiion, hence he service derived from using i is diminished. A each dae, he firm chooses levels of y, k, n so as o maximize ne-of-ax profi according o ( λ) y R k w n 1, (4) where λ is he ax rae on oupu. Alernaively, i will be useful o inerpre λ as he share of GDP ha he governmen uses for infrasrucure invesmen. 3. Governmen The revenue obained from axing oupu is used by he governmen o inves in infrasrucure I ). 3 The governmen balances is budge consrain as follows, ( G I G = λy. (5) Public capial evolves according o, K = I + 1 G + G ( δ ) K G G 1, (6) where δ is he depreciaion rae of public capial. Nex period s sock of infrasrucure, G ( K ), is equal o he amoun invesed his period, I ), plus he surviving sock, 1 G + (( 1 δ ) K ). G G ( G 2. Public infrasrucure is no privaely provided because privae agens are unwilling or unable o do so because i can be very hard o exclude free-riders or o charge users a compeiive price. 3. In his model, borrowing from abroad is no used o finance infrasrucure; only axaion can fund public invesmens. Even if agens where allowed o borrow, hey would have o pay he loans by increased axes sooner or laer. In order o undersand he full long run effecs of infrasrucure, he model should accoun ha evenually axpayers have o pay for i. 122

5 RIOJA: GROWTH, WELFARE, AND PUBLIC INFRASTRUCTURE 4. Marke Clearing and Foreign Secor The goods marke clearing condiion is: c + i + I + TB = y, (7) G where TB is he rade balance a ime. As in sandard inernaional finance models, he rade balance is he difference beween oupu y ) and domesic absorpion c + i + I ). The ne ( holdings of foreign bonds evolves as follows, ( G p b = b + TB. (8) + 1 This equaion is basically he counry s balance of paymens. In seady sae, he rade balance simply becomes ( p 1) b. 4 III. Soluion Procedure and Inuiion In general, an analyic soluion for his economy is no possible due o nonlineariies. The model mus be solved numerically. Firs, he Euler equaions of he sysem are obained. They are described by, βu c, + 1 / U c, = 1/ ( R + ( 1 δ ) + 1 k, βu c, + 1 / U c, = p, U l, / U c, = w. The subscrips c and l on U denoe he marginal uiliies of consumpion and leisure, respecively, a ime. The basic uni of analysis for he model s soluion is composed of hese hree Euler equaions, he governmen budge consrain (Equaion (5)), he household s budge consrain (Equaion (2)), and he ransversaliy condiion, lim β Λ k = 0, (where Λ is + 1 he lagrangian muliplier used for Equaion (2) in he maximizaion procedure). The Euler equaions can be described inuiively. The firs equaion describes he relevan margins ha he household mus consider when deciding on invesmen. Hence, he marginal rae of subsiuion beween consumpion oday and consumpion omorrow ( β U ) mus be U c, + 1 / c, equal a he margin o he ne reurn on invesmen in erms of consumable oupu, 1/( R + (1 δ )). The second Euler equaion describes he decision on he level of ne foreign + 1 K 4. The descripion of he inernaional secor is similar o Rebelo and Vegh (1995) and Correia, Neves, and Rebelo (1993). 123

6 asses o be held. Basically, he marginal rae of subsiuion mus equal he price of foreign bonds. The reurn on foreign bonds and capial has o be equal so ha boh asses are held. Hence, hese wo Euler equaions can be combined yielding: R = (1/ p ) 1 δ, where R + 1 K +1 is simply he world ineres rae, which is exogenous from he small counry s poin of view. 5 Finally, he hird Euler equaion describes he working decision. The marginal rae of subsiuion beween consumpion and leisure ( U l, / U c, ) mus be equal a he margin o he real wage rae, w. How does infrasrucure affec he Euler equaions? Infrasrucure has a crucial effec on he marginal producs of privae facors. Any addiional public invesmen is financed in he model by raising axes (i.e., raising, λ, he share of GDP ha goes o infrasrucure invesmen). The addiional infrasrucure has wo effecs on he ne-of-ax rae of reurn, R 1 λ f k, K n w = 1 λ f k, K n. 6 The firs effec (arising = ( ) ( ), and on he wage rae ( ) ( ), K G, N G from a direc resource cos) obviously decreases he wage rae because of he higher ax necessary o fund more infrasrucure (i.e., λ w ). Conversely, his resource cos canno affec he ne reurn, R, which is fixed a he world rae of ineres. This implies ha, ceeris paribus, inpus need o adjus o keep he marginal produc of capial equal o R. On he oher hand, he second effec (a resource benefi) works opposie o he firs effec since he addiional infrasrucure enhances he produciviy of he exising privae facors (i.e., w ). This resource benefi also ends o raise he marginal produc of capial, bu K G canno because i is fixed a R. Neverheless, he resource benefi should parially (oher inpus may also adjus) offse he increase in λ (he resource cos) keeping he ne-of-ax marginal produc of capial consan a R. 7 Consequenly, public invesmen has boh a resource cos and a resource benefi. This is why i should no be obvious ha infrasrucure invesmen (paid for by axaion) always increases GDP or privae invesmen. The nex secion describes which of hese effecs dominaes and under wha condiions. Wih ime subscrips removed, he Euler equaions and consrains above describe he seady sae of he model. This seady sae is compued numerically since he non-lineariies complicae a closed-form soluion. Once i is calculaed, he macroeconomic effecs of policy experimens involving addiional (or less) infrasrucure invesmen can be quanified. IV. Quaniaive Evaluaion of he Model 1. Parameerizaion The model has o be solved, parameerized and simulaed in order o evaluae is 5. Using he expression for he world ineres rae, he seady sae rade balance is TB = ( p 1) b = [( R δ K ) /( R + 1 δ K )] b. Given ha R is he world ineres rae and TB is a percenage of GDP, b can easily be deermined. 6. The subscrips K and N denoe he marginal producs of capial and labor, respecively. 7. Baxer and King (1993) discuss hese wo effecs in a closed economy seing. 124

7 RIOJA: GROWTH, WELFARE, AND PUBLIC INFRASTRUCTURE quaniaive implicaions. The specific funcional forms for uiliy and echnology are assumed o be: U ( c, l ) γ 1 γ 1 σ [ c l ] 1 =, 1 σ Y = K k n. φ α 1 α G The benchmark values for he parameers used in his paper are presened in Table 1. Individual esimaes for Brazil, Mexico, and Peru are used when available. For example, Elias (1992) esimaes he capial share of income, which corresponds o he parameer, in hese hree counries as: 45%, 69%, and 66% in Brazil, Mexico, and Peru, respecively. Table 1 Benchmark Parameers Parameer Descripion Brazil Mexico Peru α Privae capial coefficien λ Infrasrucure share (% of GDP) a Trade Balance (% of GDP) Rebelo and Vegh (1995) repor he average share of GDP ha was spen on infrasrucure invesmen in he 1970s and 1980s. Mexico had he highes share wih 7.6% of GDP spen of infrasrucure invesmen. Brazil and Peru spen 6.3% and 5.6% respecively. Daa from he World Developmen Indicaors (1998) is used o compue he average rade balance (as percen of GDP) over his same ime period. Brazil and Peru ran rade balance surpluses of 0.42% and 0.64%, while Peru had a defici of 1.61%. The res of he parameers used are esimaes for developing counries, since individual counry esimaes are no available. Firs, he coefficien of public capial in he producion funcion, φ, is se o 0.10 in he benchmark. This choice is an average of Hulen s (1996), Canning and Fay s (1993) and Easerly and Rebelo s (1993) esimaes, which are all in he low end of esimaes. Nex, he depreciaion rae of privae capial, δ K, is se o 10% per year or 2.5% per quarer. This figure is in Elias s (1992) esimaed range for capial depreciaion in Lain America. The depreciaion rae of public capial, on he oher hand, is esimaed by he World Bank o be abou wice ha of privae capial (World Developmen Repor 1994). Hence, i is se o 5% per quarer in he benchmark. Preference parameers are se as follows. A value of 0.35 is used for he consumpion share γ. Such value implies a leisure share of 0.65, which is consisen in he model wih he allocaion of roughly one-hird of a household s ime o marke aciviies. Nex, he curvaure parameer, σ, is se o 2.33, which comes from Osry and Reinhar s (1992) esimaes for developing counries. The world ineres rae is se o 1% per quarer following Rebelo and Vegh (1995) which implies an annual reurn of 4%. This parameer choice for he ineres rae implies ha he discoun rae, β, equals Finally, he 1994 World Developmen Repor esimaes ha he average effeciveness of public infrasrucure in Lain America is abou 75%, 125

8 so 2 is se o Resuls The long-run effecs of increasing infrasrucure invesmen are presened in Table 2. The addiional public invesmen is funded by axaion increases (i.e., by increasing he share of GDP devoed o infrasrucure invesmen, λ). Hence, λ is alernaively raised by 1% of GDP, 5% of GDP, and 10% of GDP above he counry s individual benchmark. Then, he resuling effecs on GDP ( y ), privae invesmen ( i ), and welfare (measured by ω) are compued for each counry. 8 Brazil Mexico Peru Table 2 Long-Run Effecs of Raising Infrasrucure Invesmen (percen change from benchmark) λ y i ω y i ω y i ω Consider, for example, he resuls for Brazil. A 1% -of-gdp increase in public infrasrucure invesmen increases oupu by 2.23%. A he same ime, privae invesmen and welfare rise by 1.14%. Hence, he resource benefi of higher infrasrucure invesmen exceeds he resource cos. Among he hree counries, he 1%-of-GDP public invesmen increase has is larges posiive effecs for Peru. Oupu in Peru rises by 3.96% and welfare by 2.89%. These effecs are wice he size of he ones in Brazil and Mexico. Considering ha Brazil and Mexico have been invesing larger shares of GDP in infrasrucure, he resul is no surprising. Peru has only been invesing an average of 5.6% of GDP in infrasrucure, while Brazil and Mexico have invesed 6.3% and 7.6% of GDP, respecively. Hence, he gains of a 1% raise are larger in Peru which is he more infrasrucure-deprived counry of he hree. Overall, raising λ by 1% above is b enchmark has posiive effecs in all hree counries. Table 2 also describes he effecs of raising λ by 5% and 10%. For example, in Brazil s case, raising λ by 10% has a posiive effec on GDP of 10.4%, bu privae invesmen and welfare are boh negaively affeced! The reason for his, however, follows from he inuiion 8. As in Lucas (1987), he measure of welfare change is an equivalen change in aggregae consumpion. I is a number ω so ha consumers are indifferen beween: (i) a raise in λ which provides more revenue o fund more infrasrucure, and (ii) keeping λ he same bu reducing consumpion by ω percen. 126

9 RIOJA: GROWTH, WELFARE, AND PUBLIC INFRASTRUCTURE explained in Secion III. Recall ha a raise in λ has boh a resource cos and a resource benefi. Increasing λ by 10% means ha while infrasrucure invesmen is being raised by ha amoun, his mus be funded by an increase in axes (he resource cos). Hence he resource cos has exceeded he resource benefi a his poin. Privae invesmen and welfare are boh adversely affeced due o he large increase in axaion. These adverse effecs of a 10% raise in λ can be seen in Brazil and Mexico s case. In Peru s case, however, he effecs of such increase do no quie become negaive. However, hey do become very small: privae invesmen only rises by 0.30% and welfare by 0.68%. Given Peru s low benchmark infrasrucure expendiure, even wih a 10% rise, he resource benefi is slighly larger han he resource cos. Summarizing Table 2, addiional infrasrucure invesmen can be beneficial, bu oo much may be derimenal. In order o give concree policy recommendaions, he analysis can be exended even furher. A governmen official may ask, how much should infrasrucure invesmen be increased in order o ge he maximum welfare gains? Figures 1 hrough 3 aemp o answer his quesion. These figures plo he change in welfare for differen levels of infrasrucure invesmen. Brazil s case is depiced in Figure 1. 3 Figure 1.- Welfare Effecs of Infrasrucure:Brazil Welfare Change Infrasrucure Invesmen (share of GDP) Figure 1 Welfare Effecs of Infrasrucure : Brazil The horizonal axis measures he share of GDP devoed o infrasrucure invesmen ( λ). Brazil s benchmark is λ= 6.3, which is marked by a verical line as a poin of reference. Clearly, reducing public infrasrucure invesmen (moving o he lef of he benchmark) has adverse effecs on welfare (measured on he verical axis). Conversely, raising λ has a firs a posiive effec, which laer diminishes and evenually becomes negaive (as Table 2 indicaed). The peak of his curve is around λ= 10. Therefore, he larges welfare gains can be obained by devoing abou 10% of GDP o public invesmen. A corresponding plo for Mexico is described in Figure

10 2 Figure 2.- Welfare Effecs of Infrasrucure:Mexico 0-2 Welfare Change Infrasrucure Invesmen (share of GDP) Figure 2 Welfare Effecs of Infrasrucure : Mexico Noe, however, ha Mexico is much closer o opimal infrasrucure invesmen han Brazil. Peru s case, shown on Figure 3, is much more sriking since i sars from he lowes benchmark λ= 5.6. Peru s plo shows he larges poenial gains of opimal infrasrucure policy, wih a poenial welfare increase of abou 6% above benchmark. 8 Figure 3.- Welfare Effecs of Infrasrucure:Peru 6 4 Welfare Change Infrasrucure Invesmen (share of GDP) Figure 3 Welfare Effecs of Infrasrucure : Peru Anoher ineresing feaure of he plos is ha he opimal share of infrasrucure invesmen is around 10% of GDP for all hree counries. One of he mos imporan deerminans of his opimal share is he coefficien of public infrasrucure in he producion 128

11 RIOJA: GROWTH, WELFARE, AND PUBLIC INFRASTRUCTURE funcion, Ν (as shown in Barro s (1990) simpler model). This coefficien was parameerized o 0.10 using an average of fairly conservaive esimaes cied in Secion IV, A. Good individual esimaes for his parameer are unforunaely no available for hese hree counries, so a conservaive average was used for all hree. This yields an approximaely equal opimal share of public infrasrucure for all hree counries. However, even using his a low, conservaive esimae from he lieraure shows ha hese counries have all under-invesed in infrasrucure. Hence, he poin remains ha here are gains o raising infrasrucure invesmen in hese counries. V. Conclusions This paper quanifies he effecs of infrasrucure invesmen on GDP, privae invesmen, and welfare using a calibraed general equilibrium model of a small open economy. The model is parameerized o daa from Brazil, Mexico, and Peru, bu could poenially be applied o oher counries. For hese hree counries, resuls indicae ha, devoing addiional resources o infrasrucure invesmen pays-off in erms of ne increases in GDP. In addiion, here exis sizable posiive effecs on privae business invesmen. More highways and public communicaion neworks encourage privae companies o inves because using hese public inpus can increase produciviy of privae facors. This paper also conribues o he lieraure by sudying he welfare effecs of infrasrucure policy, which can be very imporan in guiding policymakers decisions. Resuls show ha here is a range over which infrasrucure invesmen in he hree counries is welfare improving. However, very high levels of infrasrucure invesmen can adversely affec welfare due o increased axaion necessary o fund i. In any even, all hree counries under-invesed in infrasrucure in he 1970s and 1980s, so here is room for increased infrasrucure invesmen ha would be beneficial. Poenial exensions o his work would sudy he neglec of mainenance and repair of infrasrucure neworks in developing counries. Policymakers have ofen emphasized building brand new infrasrucure over mainaining exising neworks in opimal shape. The deerminans of an opimal mix beween hese wo expendiures should be sudied. References Barro, R.J. (1990), Governmen Spending in a Simple Model of Endogenous Growh, Journal of Poliical Economy, 98, s103-s125. Baxer, M., and R. King (1993), Fiscal Policy in General Equilibrium, American Economic Review, 83(3), Blejer, M.I., and M.S. Khan (1984), Governmen Policy and Privae Invesmen in Developing Counries, IMF Saff Papers, June, Canning, D., and M. Fay (1993), The Effec of Transporaion Neworks on Economic Growh, Working Paper, New York: Columb ia Universiy. Correia, I., J. Neves, and S. Rebelo (1993), Business Cycles in a Small Open Economy, Working Paper, 16-93, Porugal: Banco de Porugal. 129

12 Easerly, W., and S. Rebelo (1993), Fiscal Policy and Economic Growh: An Empirical Invesigaion, Journal of Moneary Economics, 32, Elias, V. (1992), Sources of Growh: A Sudy of Seven Lain American Economies, San Francisco, CA: ICS Press. Ford, R., and P. Pore (1991), Infrasrucure and Privae Secor Produciviy, OECD Working Paper, 91. Glomm, G., and B. Ravikumar (1994), Public Invesmen in Infrasrucure in Simple Growh Model, Journal of Economic Dynamics and Conrol, 18, Hulen, C. (1996), Infrasrucure Capial and Economic Growh: How well you use i may be more imporan han how much you have, NBER Working Paper, No Looney, R.E., and P.C. Frederiken (1997), Governmen Invesmen and Follow-on Privae Secor Invesmen in Pakisan, , Journal of Economic Developmen, 22(1), Lucas, R.E., Jr. (1987), Models of Business Cycles, Oxford, UK: Basil Blackwell Ld. Osry, J.D., and C. Reinhar (1992), Privae Saving and Terms of Trade Shocks, IMF Saff Papers, 39, Rebelo, S., and C. Vegh (1995), Real Effecs of Exchange Rae Sabilizaion: An Analysis of Compeing Theories, NBER Working Paper, No Uzawa, H. (1974), Sur la heorie economique du capial collecif social, Cahiers du Seminaire d Economerie, World Bank (1994), World Developmen Repor 1994, Washingon, D.C.. 130