Filling potholes: macroeconomic effects of maintenance versus new investments in public infrastructure

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1 Journal of Public Economics 87 (2003) locae/ econbase Filling poholes: macroeconomic effecs of mainenance versus new invesmens in public infrasrucure Felix K. Rioja* Deparmen of Economics, Andrew Young School of Policy Sudies, eorgia Sae Universiy, Alana, A 30303, USA Received 6 December 2000; received in revised form 20 Augus 2001; acceped 16 Ocober 2001 Absrac The mainenance of exising public infrasrucure has ofen been negleced in favor of building new infrasrucure in developing counries. This paper develops a dynamic general equilibrium model ha analyzes he reasons and effecs of such neglec. Firs, he opimal level of mainenance is shown o depend on he size of new invesmens as a share of exising public infrasrucure and on he produciviy of infrasrucure. Second, he model is parameerized and solved numerically for a sample of Lain American counries. Quaniaive resuls show ha reallocaing funds from new infrasrucure o mainenance can have posiive effecs on hese counries DP Elsevier B.V. All righs reserved. Keywords: Public infrasrucure; Mainenance; rowh JEL classificaion: E62; H50; O40 1. Inroducion ood roads, canals, and navigable rivers, by diminishing he expense of carriage, pu he remoe pars of he counry more nearly upon a level wih hose in he neighboring own. They are upon ha accoun he greaes of all improvemens. Adam Smih, 1776 *Tel.: ; fax: address: prcfkr@langae.gsu.edu (F.K. Rioja) / 02/ $ see fron maer 2002 Elsevier B.V. All righs reserved. doi: /s (01)

2 2282 F.K. Rioja / Journal of Public Economics 87 (2003) A counry s roads and waer sysems are he foundaions on which economic aciviy akes place. Mos economiss agree ha public infrasrucure is imporan for a counry s growh. In developing counries, much aenion is usually devoed o building new public infrasrucure projecs. However, filling he poholes ha invariably appear wih ime and usage receives much less aenion. The mainenance of exising public infrasrucure has been negleced in favor of saring new, highly visible projecs. This paper boh presens evidence and quanifies he macroeconomic effecs of such neglec. In addiion, he paper derives he opimal level of mainenance and quaniaively evaluaes he effecs of redisribuion beween he wo expendiures. In general, mainenance is defined as hose aciviies ha allow public infrasrucure o efficienly deliver he oupus for which hey were buil (yamfi e al., 1992). A well mainained road should las years before resurfacing is necessary. Lack of mainenance can cause severe deerioraion requiring resurfacing in as soon as 5 years. The World Bank repors ha an addiional $12 billion spen on imely road mainenance in Africa during he las decade could have saved $45 billion spen in reconsrucion. Similarly, in he case of power lines, spending $1 million o reduce line losses could have saved $12 million in generaing capaciy (World Developmen Repor, 1994). Mainenance disregard leads o road deerioraion, irrigaion canal blockage, leaks, and power line breakdowns reducing he economy s producive capaciy. Alhough he World Bank has conduced a number of counry sudies of he adverse effecs of deficien infrasrucure mainenance (hese are discussed in he background secion), his opic has no been sudied exensively in he academic lieraure. An excepion ha does no direcly concenrae on mainenance, bu provides moivaion for his paper, is Devarajan e al. (1996) (henceforh DSZ). These auhors find empirical suppor in developing counries for curren public expendiures (like mainenance) having posiive effecs on DP, while capial expendiures (like new infrasrucure) have negaive effecs on DP. DSZ argue ha much has already been spen on infrasrucure (ofen a mainenance s expense), so a he margin an exra dollar spen on mainenance may be more producive. However, mos of he focus of he academic research has been on he effec of overall public invesmen on economic growh. Seminal empirical work in his area (using growh accouning and cross-counry regression analysis) includes Easerly and Rebelo (1993), Canning and Fay (1993), Canning (1998, ) and Hulen (1996) (among ohers). Neverheless, recen compelling empirical evidence (by DSZ and he World Bank) sugges ha o fully undersand he effecs of public infrasrucure, one should also sudy mainenance s role. iven ha moivaion, in his paper I aemp o describe he deerminans of 1 There are also a number of papers ha sudy he effecs of public expendiures in he US. These include: Aschauer (1989), Baina (1999), Fernald (1999), Holz-Eakin and Schwarz (1995), Nadiri and Mamuneas (1994), Morrison and Schwarz (1996), and Munnell (1992). Sudies of infrasrucure in OECD counries include Demeriades and Mamuneas (2000).

3 F.K. Rioja / Journal of Public Economics 87 (2003) opimal infrasrucure policy, he reasons for mainenance neglec, and o quanify he radeoffs associaed wih spending on new infrasrucure versus repairing exising infrasrucure given limied resources. For ha purpose, his paper consrucs a dynamic general equilibrium model ha 2 incorporaes boh ypes of expendiures and can be used for policy analysis. Following he Lucas (1987) program, he model is inernally consisen and micro-foundaions based. As Lucas suggess, he model makes a quaniaive connecion beween policies and heir consequences. The model has hree secors: households, firms, and a governmen. The public infrasrucure sock is a governmen provided inpu in firms producion. As i is commonplace in developing counries, new public projecs are mosly financed by inernaional donors (ypically by governmens of indusrial counries or inernaional organizaions). The mainenance of exising public infrasrucure, conversely, is financed by axaion. In he model, he depreciaion rae of infrasrucure is endogenous: i 3 depends on he level of mainenance and on usage. Firs, a simplified version of he model is solved obaining closed form soluions. The Ramsey soluion for he opimal level of mainenance shows ha i depends on he size of new invesmens as a share of exising public infrasrucure and on how producive infrasrucure is. Second, he model is solved numerically and parameerized using hisorical daa from seven Lain American counries. Quaniaive resuls show ha reallocaing some of he donor aid away from new invesmens and owards mainenance can have posiive effecs on DP. The paper is organized as follows. Secion 2 discusses he background of various findings; Secion 3 presens he model. Secion 4 derives closed form soluions o a simplified version of he model. Secion 5 is he quaniaive evaluaion, and Secion 6 concludes. 2. Background The World Bank has conduced mos of he research on he issue of mainenance 4 of infrasrucure. These sudies have concenraed mosly on one paricular ype of 2 Previous relaed heoreical work includes: Barro (1990), Devarajan e al. (1998), lomm and Ravikumar (1994), and Rioja (1999). However, hese papers do no analyze he opimal mix and radeoffs beween mainenance and new public invesmens as done in he presen paper. 3 The choice of depreciaion rae for privae capial was sudied by Haavelmo (1960). This concep was also used by Auerbach (1979) and Abel (1981) o sudy he choice of asse life problem. These wo papers examine how producers choose asse life when faced wih inflaion and a corporae income ax code (like in he US) ha allows hisoric depreciaion raher han replacemen cos depreciaion. Abel concludes ha inflaion may increase or decrease he durabiliy of capial depending on he raio of he nominal discoun rae o depreciaion rae being greaer or less han a criical value, which depends on ax parameers. 4 Oher researchers have sared sudying he role of mainenance of privae capial. For insance, Mcraan and Schmiz (1999) sudy is effec on business cycles using Canadian daa.

4 2284 F.K. Rioja / Journal of Public Economics 87 (2003) infrasrucure: roads. Their findings are surprising. For example, beween 1979 and 1984, 6000 km of paved road were buil in Brazil. During his same period, anoher 6000 km of roads wen from fair o poor and 2000 km wen from good o poor due o mainenance neglec (Harral, 1988). In Chile, he main norh-o-souh highway, which runs 3000 km, was paved in he 1960s. In he 1970s, half of his highway collapsed due o poor mainenance requiring is reconsrucion a grea expense. While mainenance disregard can cause larger expendiures in he fuure, i can also impose an addiional, immediae, cos o users. Consider he following example from Zambia repored in Roh (1996). In 1992, he Federaion of Zambian Road Hauliers commissioned a sudy on he effecs of bad road 5 condiions on a vehicle s operaing coss. The sudy compared he exra coss of damaged shocks, springs, brake shoes, cluch, ec., due o coninuous ravel on a pohole-filled road in order o deliver producs. These esimaed coss are shown in Table 1. In general, hese rucks were delivering producs o he marke or bringing needed inpus for producion. The increases in operaing coss o he Zambian company due o an un-mainained road were large (abou $14 000). The resuling increases in he coss of inpus should decrease he supply of heir good. Infrasrucure in poor condiion, consequenly, should affec a counry s oup he aggregae level. The ways of financing mainenance and new infrasrucure in developing counries should also be described briefly. Mainenance expendiures, which fall under he curren public expendiures classificaion, have been ypically financed Table 1 Addiional operaing coss due o poholes Quaniy Iem Exra annual cos (dollars) 10 Exra ires and ubes Exra cluch and pressure plae Exra wheel bearing Exra se of brake shoes Exra se of springs Exra spring hangers and bushes 452 Welding Exra seering assembly Exra shock absorbers 510 Toal exra coss Two ses of vehicles were used for he experimen. Each se was composed of a ruck and 22-wheel racor railer. For a whole year, one se of vehicles was assigned o deliver goods back and forh using he pohole-filled road, while he oher se of vehicles used he road in good condiion.

5 F.K. Rioja / Journal of Public Economics 87 (2003) by hese counries governmens from general ax revenue (DSZ, 1996). New public infrasrucure consrucion, however, has been ypically financed by foreign official sources using: bilaeral loans (from an indusrial counry s governmen o he developing counry s governmen); mulilaeral loans (from an inernaional organizaion like he World Bank or a regional developmen bank); and ourigh grans from hese sources. According o he World Developmen Repor 1994, bilaeral and mulilaeral sources made up as much as 80% of public infrasrucure funding up o he early 1990s (p. 90). While privae lending for infrasrucure has increased since he mid 1990s, he fac is ha official sources from abroad have been largely responsible for financing he consrucion of public infrasrucure in he developing world. Table 2 furher describes some of he characerisics of his financing for seven Lain American counries and seven African counries. Firs, noe ha a good porion of official deb in hese counries is rouinely forgiven. Beween 1989 and 1999 abou 22% of official deb in Lain America and 33% of official deb in Africa was forgiven. Second, official deb has liberal grace periods ha average 5 years. Finally, he average mauriy of hese loans is abou 20 years, which is again quie generous compared o he average mauriy of privae loans of 7 years Table 2 Official deb characerisics in Lain America and Africa Counry % Deb Average grace Average a forgiven b period b mauriy Lain America Argenina Brazil Chile Colombia n.a Mexico Peru Venezuela Average Africa Cameroon Dem. Rep. Congo Coe ˆ d Ivoire Ehiopia Nigeria Souh Africa n.a Sudan n.a Average Source: lobal Developmen Finance, a As percen of Toal Deb b Average over

6 2286 F.K. Rioja / Journal of Public Economics 87 (2003) (no shown). Basically, developing counries finance infrasrucure a exremely generous erms from indusrial counries and inernaional organizaions, and a good porion of hose loans are in pracice donaions as hey are laer forgiven. 3. The model The framework is grounded in he neoclassical growh model. In brief, he model has a represenaive household who earns income from rening is capial and effor o a privae firm. The household allocaes his income beween consumpion and invesmen o augmen is capial sock so as o maximize uiliy. Firms produce a final good, so hey decide on he amouns of labor and capial o hire for producion. Public infrasrucure is a governmen-provided inpu in 6 producion. Donaions from foreign counries finance new public infrasrucure invesmens. However, he governmen mus raise revenues by axing oup he firm level o pay for mainenance of public infrasrucure. A formal descripion of each of hese secors follows Households The represenaive household chooses a sream of consumpion hc j maximize is uiliy funcion, ` 50 so as o ` O b u(c ), (1) 50 where 0, b, 1. The household earns a wage rae, w, for he labor, l, i supplies o he firm. Labor is supplied inelasically, so l 5 1, and populaion is fixed. Also, he household receives a reurn, r, on he privae physical capial, k, i rens o he firm. Hence, each period he household mus also choose a level of invesmen, i, o augmen capial sock. Privae capial evolves according o, k 5 i 1 (1 2 d )k, (2) 11 where d denoes he depreciaion rae of privae capial. Household oal income is allocaed beween consumpion, c, and invesmen, i. The household s budge consrain is hen, c 1 i # wl 1 rk. (3) 6 The model builds on previous heoreical work of Barro (1990) and lomm and Ravikumar (1994) by inroducing mainenance and exploring is role.

7 F.K. Rioja / Journal of Public Economics 87 (2003) Firms There are many idenical compeiive firms in he marke. The represenaive firm decides on how much privae capial and labor inpus o hire in order o produce he final good. In addiion, he sock of public infrasrucure, K, is a publicly provided inpu. Then he producion echnology of he represenaive firm can be characerized by y 5 f(k, k, l ) where f exhibis consan reurns o scale 7,8 (CRTS) o privae inpus. The governmen axes he firm s oup rae l [ [0, 1]. Hence, he firm s ne-of-ax profi funcion is: P 5 (1 2 l )f(k, k, l ) 2 wl 2 rk. (4) The oal ax revenue collec by he governmen from firms equals ly overnmen The governmen allocaes ax revenues, ly, o mainenance of exising public 9 capial, m. Then he governmen s budge consrain is: l y 5 m. (5) In addiion, inernaional donors give D aid o his counry every period. This aid is earmarked for he consrucion of new public projecs. This is very common in acualiy in developing counries as new airpors, highways, waer sysems, ec., 10 are financed by inernaional aid. Then he public capial evoluion equaion is: K 5 D 1 (1 2 d (m,k ))K. (6) 11 Tha is, nex period s public capial sock (K 11) equals new invesmen his period, D, plus he surviving public capial sock his period, (1 2 d (m, k ))K. Noe ha he depreciaion rae of public capial, d (m, k ), is endogenous, and i depends on mainenance expendiures and on usage. More mainenance reduces 7 iven he compeiive srucure and he CRTS assumpion, ne-of-ax revenues will be exhaused by paymens o he privae facors of producion. 8 Feehan (1998) saes ha a consensus in he public inpus lieraure has emerged o model producive public inpus (e.g., infrasrucure) as facor augmening. The producion funcion here follows his lieraure. 9 Hence, l can be inerpreed as he share of DP ha is devoed o mainaining and repairing infrasrucure. For simpliciy, he model absracs from governmen consumpion. 10 As documened in Secion 2, even when par of he funds o finance new infrasrucure are borrowed from indusrial counries governmens or inernaional organizaions, much of his deb is effecively laer forgiven or never fully repaid. Hence, for simpliciy and as a saring poin o sudy he mainenance versus new infrasrucure issue, new infrasrucure financing is modeled as a gif in his paper.

8 2288 F.K. Rioja / Journal of Public Economics 87 (2003) his depreciaion rae ( d / m, 0) as roads and waer sysems are kep in beer condiion. Conversely, higher accumulaion of privae capial (i.e., a proxy for higher use of infrasrucure) leads o higher infrasrucure depreciaion ( d / k. 0). For example, he larger he number of rucks raveling on he highway, he 11 faser he highway will develop poholes. The governmen seeks o maximize he well being of is consiuens: max o 50 b u(c ), subjec o he above consrains (5) and (6). Hence, he governmen chooses l opimally which implicily deermines he public infrasrucure sock K given he level of donor aid as Eq. (6) describes. ` 3.4. Marke clearing The goods marke clearing condiion is: y 5 c 1 i 1 m. (7) The economy s oupu ( y ) mus equal expendiures: consumpion plus invesmen plus mainenance. 4. Equilibrium in a simplified version In his secion, a simplified version of he above model is solved. Much inuiion can be gained from simplifying assumpions which allow for closed-form descripion of he privae decision rules and opimal public policy. Assume ha preferences are characerized by a simple logarihmic funcion and ha he producion funcion has Cobb Douglas form: u(c ) 5 log c 12a y 5 K k l (8) wih u 1 a # 1. Furhermore, assume ha privae capial depreciaes compleely afer each period, hence d 5 1. Finally, assume ha he depreciaion rae of public capial only depends on mainenance expendiures, i.e., d (m ). 11 Mcraan and Schmiz (1999) have used a similar specificaion for an endogenous depreciaion rae. One possible alernaive specificaion suggesed by a referee would be d (m, c ), where consumpion proxies for higher use of he infrasrucure. Consumer driving o sores and shopping malls increase he wear on roads. As consumpion will be a funcion of he sae variable, k, resuls should be similar. Hence, we use he simpler specificaion d (m, k ) for racabiliy in he analysis. In any even, he alernaive specificaion has also been used in he quaniaive analysis of Secion 5 for compleeness.

9 F.K. Rioja / Journal of Public Economics 87 (2003) The privae secor s problem The household s problem is o choose c and k subjec o heir budge consrain. 11 so as o maximize uiliy ` max O b log(c ) hc,k11j 50 subjec o c1 k 11 # wl 1 rk, given k 0, w, r, and l,; The firm s problem is o choose k and l each period so as o maximize profi according o: 12a max(1 2 l )K k l 2 wl 2 rk, hk,lj subjec o k $ 0 and given l and K. To define a compeiive equilibrium for he economy, denoe an arbirary ` governmen policy p 5 hl j. Then a p-compeiive equilibrium is a se of 50 ` ` allocaions hc, k, l j and a se of prices hw, r j ha solve he households problem; he firm s problem; and saisfy he marke clearing condiions, c 1 k 11 # (1 2 l )y and l5 1. iven he public good naure of infrasrucure and he disorionary axaion, he second welfare heorem does no hold. However, i is possible o compue a compeiive equilibrium by solving an arificial planning problem as in lomm and Ravikumar (1994). The arificial planning problem is firs wrien recursively using a value funcion. Then a linear guess for he value funcion depending on he wo sae variables k and K is hypohesized. This guess is subsiued ino he problem s sandard Euler equaion. Finally, he undeermined coefficiens are compued and checked for consisency. Applying his mehod, he decision rules for privae capial and consumpion are 11 k 5 ab(1 2 l )K k c 5 (1 2 ab )(1 2 l )K k I is sraighforward o show ha hese decision rules are a unique soluion o he privae secor s problem (see lomm and Ravikumar (1994), Proposiion 2) The public secor s problem A he same ime, he governmen seeks o deermine is opimal policy wih respec o mainenance. Inernaional donaions for new infrasrucure are aken as given, bu he governmen mus decide on l [ [0, 1], he share of DP devoed o mainaining he exising infrasrucure. Assume ha he governmen s objecive

10 2290 F.K. Rioja / Journal of Public Economics 87 (2003) funcion is o maximize he well-being of he populaion. Hence he governmen s ` opimal policy will be a sequence hlj50 ha solves ` maxo b log(c (p)) subjec o K 50 5 D 1 (1 2 d (m ))K 11 12a m # l K k (p)l (p) given k0 and K 0. The privae decision rules compued in Secion 4.1 above can be used o solve he governmen s opimal policy problem, which can be re-wrien as ` maxo b log (1 2 ab )(1 2 l )K k s. hl j K 50 s 5 D 1s1 2 d (m ) dk k 5 ab(1 2 l )K k m 5 l K k 0 # l # 1, given k 0, and K 0. Furhermore, assume a simple funcional form for he depreciaion rae of public capial, d cm, wih c $ 0. This funcion is convenien since if nohing is spen on mainenance (m 5 0), public infrasrucure 12 depreciaes compleely (d 5 1). The soluion o he governmen s problem is: d SD bu (1 1 ab ) D l* 5]]]] 2 ]]]]]]] ] (9) 1 1 b(u 1 a) (1 1 b(u 1 a))ck k K Hence he opimal share of DP devoed o mainenance, l *, depends on parameers, he raio of donaions o exising infrasrucure (D /K ), and oher 13 ` sae variables. iven a. 0, a 1 u # 1, and ha he sequence hkj50 is bounded above, he above soluion will be he unique soluion o he public policy problem. The firs condiion, a. 0, implies ha in equilibrium he marginal produc of privae capial is posiive. The second condiion, a 1 u # 1, implies ha here are non-increasing reurns o scale o augmenable facors. Finally, he ` hird condiion ensures ha o b log(c ) is bounded above. Inuiion for his ` Furher assume ha he sequence hm j 50 is bounded above so ha d $ 0 for all. 13 Devarajan e al. (1998) and lomm and Ravikumar (1994) compue he opimal share of DP ha should be devoed o overall infrasrucure invesmen. Their measure is no direcly comparable o l *, since l* is he opimal share of DP ha should be devoed o mainenance of infrasrucure.

11 F.K. Rioja / Journal of Public Economics 87 (2003) soluion is described below, while he specifics of he derivaion are lef for Appendix A The deerminans of opimal mainenance The deerminans of he opimal share of DP devoed o mainenance, l *, have some inuiive appeal and can be analyzed by sudying Eq. (9). Firs, consider how he raio of inernaional donaions o exising public capial sock (D /K ) affecs opimal mainenance l *. This relaionship is clearly negaive as can be easily deermined by looking a Eq. (9): l * (1 1 ab ) ]]] 52 ]]]]]]],0 (D /K ) (1 1 b(u 1 a))ck k Inuiively, if new infrasrucure invesmen as a share of exising infrasrucure sock rises (le s say because donors raise aid), hen he opimal mainenance expendiure should decrease. Tha is, if he counry is o receive increased funding o build a few more bridges, i is opimal for he counry s policymakers o cu mainenance expendiures. Policymakers in his model care abou how large he overall public capial sock is (which affecs oupnd consumpion and hence heir objecive funcion). As donors fund more new (and ofen highly visible) projecs adding o he infrasrucure sock, i is opimal o decrease mainenance, which has o be financed by axes. This is suppored by he Brazilian experience beween 1979 and 1984 described in Secion 2. During his period, according o Harral (1988), 6000 km of new paved roads were buil, while 2000 km wen from good o poor condiion and 6000 km wen from fair o poor due o mainenance neglec. I would be erroneous, however, o imply ha infrasrucure aid causes a disservice o developing economies. Perhaps he correc policy implicaion would be o re-allocae porions of his aid o mainenance. More on his in he quaniaive evaluaion secion below. In order o gain ye more inuiion o his soluion, assume ha D 5 0. Tha is, assume foreign donors sop financing new infrasrucure enirely. The opimal mainenance share of Eq. (9) simplifies o: bu l* 5 ]]]]. (10) 1 1 b(u 1 a) Recall ha he parameer u, infrasrucure s coefficien in he producion funcion, describes how producive infrasrucure is. Consider a counry where infrasrucure is very producive (i.e., u is high). Should policymakers choose o spend more or less on mainenance of heir infrasrucure nework in his case? The answer is obained by compuing

12 2292 F.K. Rioja / Journal of Public Economics 87 (2003) l* b(1 1 ab ) ]] 5 ]]]]].0. u [1 1 b(u 1 a)] 2 This simply says ha he more producive he infrasrucure, he more i should be mainained, which is inuiively appealing. 5. Quaniaive evaluaion The simplified version of he model yields a closed form soluion for he opimal mainenance expendiure policy which provides valuable inuiion. This secion aemps o exends ha analysis by quanifying he macroeconomic effecs of changes in public expendiures. The saring poin of he quaniaive evaluaion, however, is he acual average allocaion (called benchmark allocaion) beween mainenance and new invesmens according o he daa of seven Lain American counries (Argenina, Brazil, Chile, Colombia, Mexico, Pernd Venezuela). Hence, in his secion we do no assume he governmen is choosing mainenance spending opimally; i simply balances is budge wih he allocaion given by he hisorical daa. Raher, households and firms opimize aking governmen expendiure policy as given by he daa. The quesions addressed in his secion are: saring from he benchmark allocaion, How would he economy be affeced if a fracion of donor aid (earmarked o build new roads and bridges) was redisribued owards mainenance of exising infrasrucure? Conversely, how would he economy be affeced if mainenance was reduced devoing hose resources o new infrasrucure consrucion insead? These are quesions ha policymakers in developing counries ofen face. The direcion and magniude of he effecs of such redisribuions are no readily apparen. This secion shows ha hese effecs depend on he iniial relaive shares of DP devoed o each ype of expendiure and on parameers. Funcional forms and parameer values are needed o numerically solve he complee version of he model. The funcional forms for uiliy and producion funcions are given as in Eq. (8). The funcion used for he depreciaion rae of m public capial is d (cm /k ), where c, m. 0. This funcion is decreasing in mainenance and increasing in privae capial (i.e., he more privae economic aciviy, he higher he wear on infrasrucure). The numerical soluion proceeds as follows. Firs, he firs-order condiions

13 F.K. Rioja / Journal of Public Economics 87 (2003) (FOCs) for he household and firms are derived. Second, he model is parameerized using esimaes from he lieraure for Lain American counries. Third, he sysem of equaions composed of he FOCs, he governmen budge consrain (Eq. (5)), he infrasrucure accumulaion equaion (6), and he goods marke clearing condiion (7) are solved numerically. Fourh, he effecs of policy experimens varying he mix of public expendiures are compued Parameerizaion An average of parameer esimaes of seven Lain American counries (Argenina, Brazil, Chile, Colombia, Mexico, Pernd Venezuela) are used for he quaniaive evaluaion. When parameers specific o hese Lain American counries are no available, esimaes from averages of developing counries are used. Some key parameers come from Vicor Elias s (1992) deailed growh accouning sudy of hese seven counries. As such deailed growh accouning sudy of African counries was no available, we do no aemp a quaniaive evaluaion for ha coninen. Table 3 liss he parameers used, and he parameer choices are explained in he ex below. Firs, echnology parameers are deermined as follows. Capial s share of income is on average 54% in hese seven counries according o Elias (1992); hence, a is se o Nex, he coefficien on public infrasrucure, u, has been esimaed by Hulen (1996), Canning and Fay (1993), and Easerly and Rebelo (1993) wih an average value of The esimae is for an average of developing counries including he seven counries being sudied. Unforunaely, here are no available esimaes of his parameer specifically for hese Lain American counries. A sandard depreciaion rae for physical capial of abou 10% per year is used in he benchmark (hence d ). This figure falls in Elias s (1992) esimaed 14 Table 3 Benchmark parameers Parameer Value Descripion a 0.54 Capial share u 0.10 Public infrasrucure coefficien d 0.10 Privae capial depreciaion rae m Public capial depreciaion rae funcion parameer c 100 Public capial depreciaion rae funcion parameer l 0.01 Share of DP devoed o mainenance d 0.05 Share of DP devoed o new infrasrucure b 0.99 Discoun rae 14 As his is sandard, he FOCs are repored in par B of Appendix A.

14 2294 F.K. Rioja / Journal of Public Economics 87 (2003) range for depreciaion in Lain America. Noe, however, ha his figure is an average for srucures and equipmen across he economy. Public infrasrucure capial, conversely, is mosly composed of srucures. According o reenwood e al. (2000), he depreciaion rae of srucures is abou 6% per year in he US. In developing counries, however, he depreciaion rae of infrasrucure is on average wice as much according o he World Developmen Repor 1994; hence d in he benchmark. To be consisen wih his, he parameers m and c are calibraed so ha d is 0.12 in he benchmark. Of course, his public capial depreciaion rae will vary in various policy experimens (e.g., larger mainenance expendiures will reduce d ). Easerly and Rebelo (1993) esimae ha overall public invesmen is abou 6% of DP in hese seven Lain American counries. According o yamfi e al. (1992) and Fay (2001), only abou 1% of DP is spen on mainenance of exising infrasrucure (hence l 5 m/y ). The remainder 5% of DP is spen on new infrasrucure consrucion (hence, d 5 D/y ). Noe ha as described in Secion 4, mainenance is financed by axes, while new invesmens are financed by inernaional donors. This allocaion is used as benchmark in he soluion. Finally, a sandard discoun rae of E is used as in, for example, Rebelo T and Vegh (1995) Quaniaive resuls of public expendiure reallocaion This secion describes he quaniaive consequences of reallocaing resources beween mainenance and new public invesmen. Table 4 presens he long-run (seady sae) effecs of various reallocaions. The saring poin is denoed Benchmark 1: where mainenance (my) is 1% of DP and new invesmen (dy) is Table 4 Long run effecs of public expendiures reallocaion (Benchmark 1) my dy d DK Dy Dc * 5.0* 0.12* D in percen change. *Denoes benchmark.

15 F.K. Rioja / Journal of Public Economics 87 (2003) % of DP (hese appear sarred in Table 4). Noe also ha in his benchmark he depreciaion rae of public capial, d, is 12% for reasons discussed above Reducing mainenance o build new infrasrucure Wha would be he effecs of policymakers reducing mainenance expendiures, for insance by 0.5% of DP, and allocaing hose resources o build new infrasrucure? The firs row in Table 4 (i.e., my 5 0.5; dy 5 5.5) describes he effecs. Firs, as less is spen on mainenance, he depreciaion rae of public infrasrucure would rise o 0.15 per year. This would in urn reduce he sock of public infrasrucure (DK ) by 15% in he long-run from is benchmark level. As he surviving sock of public capial (an essenial inpu in producion) has diminished, oupu (Dy) and consumpion (Dc) are adversely affeced falling by 23.48%. Hence, given he presen levels of expendiure in Lain American counries, reallocaing resources away from, for example, filling poholes in favor of building new bridges would affec hese economies adversely. This resul agrees wih Devarajan e al. (1996), who find empirically ha raising capial expendiures may have adverse effecs on oups described in Secion Reducing consrucion of new infrasrucure o raise mainenance Wha would be he effecs of policymakers insead raising mainenance by 0.5% of DP by reducing new invesmen expendiures? The hird row in Table 4 (i.e., my 5 1.5; dy 5 4.5) describes he effecs. As more is spen on mainenance, his reduces he depreciaion rae of public capial d from 0.12 o Wih a lower d, more public capial survives in he long run; he public infrasrucure sock is 7.09% larger. Under his policy, even hough less is invesed in new infrasrucure, 7.09% more of he public capial sock survives in he long run hanks o more mainenance. This affecs oupnd consumpion posiively (Dy 5Dc %) as public capial is an essenial inpu in producion. Once again, his resul agrees wih empirical findings of Devarajan e al. (1996) ha higher curren expendiures (like mainenance) have posiive effecs on DP in developing counries How much is oo much and wha is he opimal mix? Higher mainenance expendiures appear beneficial o he economy, bu how much is oo much? Consider, for example, raising my from 1.0 o 4.0 (by redisribuing donor aid worh abou 3% of oupu). The effecs of such redisribuion are presened in he column my 5 4.0; dy on Table 4. The depreciaion rae of public capial is significanly reduced o Neverheless, 15 This noaion is adoped o make public expendiure reallocaion clear. Suppose z is he percenage of DP o be redisribued from one use o he oher. Then, he share of DP devoed o mainenance is denoed my 5 l 1 z, while he share of DP devoed o new public invesmen is denoed dy 5 d 2 z. Naurally, z 5 0 in he benchmark as here is no redisribuion.

16 2296 F.K. Rioja / Journal of Public Economics 87 (2003) he public infrasrucure sock would be 23.8% smaller in he long run. The reason is ha so much has been aken away from new consrucion ha less of he infrasrucure will survive in he long-run even hough more is spen on mainaining i. This reallocaion would have adverse effecs on oupnd consumpion of 25.73%. Therefore, oo much mainenance can be deleerious. Wha is he opimal mix under he Benchmark 1 specificaion? Resuls on Table 4 show ha he highes gains in oupre obained when mainenance receives abou 2% of DP and new public invesmen abou 4.0% of DP (i.e., my 5 2.0; dy 5 4.0). iven ha hese Lain American governmens presenly spend abou 1% of DP on mainenance, doubling hese expendiures by redisribuing donor aid of abou 1% of DP away from new projecs yields he highes long-run gains in oupu. Fig. 1 graphically illusraes he effecs on oupu described on Table 4. The horizonal axis measures mainenance (as a percen of DP), while he verical axis measures he long run effecs on DP of various reallocaions. The verical line a my simply marks he saring poin for all he Benchmark 1 experimens. As described above, lowering my below is benchmark reduces DP, Fig. 1. Oupu effecs of redisribuions: Benchmark 1.

17 F.K. Rioja / Journal of Public Economics 87 (2003) while raising my has posiive effecs over some range. The curve peaks around 16 my 5 2.0% of DP where he posiive effec on long-run DP are larges Effecs of parameer changes This subsecion sudies how he resuls are affeced by changing some of he benchmark parameers. Firs, he iniial expendiure posiion is changed from my 5 1.0, dy o my 5 0.5, dy This case is labeled Benchmark 2 where he governmen iniially only spends 0.5% of DP on infrasrucure mainenance. In fac, his allocaion is no far from realiy for some of he poorer Lain American counries, which spend very lile on mainenance. Table 5 repors resuls of shifing expendiures for his Benchmark 2 (Fig. 2 describes hese effecs graphically). As in Benchmark 1, here are gains o re-allocaing owards mainenance. Raising my from 0.5 o 2.0 helps reduce he public capial depreciaion rae from 0.12 o 0.07 per year. Hence, he infrasrucure sock will be 28.3% larger in he long run. This resuls in an oupnd consumpion gain of 5.56%. The poenial gains in Benchmark 2 are larger han in Benchmark 1. This can be explained since in Benchmark 2 counries iniially spend only 0.5% of DP on mainenance versus 1% of DP in Benchmark 1. Because so lile is spen on mainenance under Benchmark 2, here are larger poenial gains a he margin. The second change involves raising he coefficien of public infrasrucure, u, from 0.10 o 0.15 keeping everyhing else as in he original benchmark. This higher u is reasonable as i is abou wha Easerly and Rebelo (1993) esimae for developing counries. This case is referred o as Benchmark 3. As Table 5 shows, a 1% raise in mainenance has a larger posiive effec on oupu han in he original Benchmark 1 (Dy is 3.28% here versus 1.87% in he original). This resul is expeced since, in counries where infrasrucure is more producive, a larger surviving sock of infrasrucure (due o more mainenance spending) would raise oupu by more. For visual comparison wih he original, Fig. 3 displays he wo cases. Finally, he hird change involves calibraing he model more specifically o Brazil as i is ofen useful o look a one counry in deail raher han a a composie of counries. Key Brazilian parameer esimaes available are used o calibrae he model: a (Elias, 1992); l ; d (Easerly and Rebelo, 1993). This means ha Brazilian expendiure on mainenance and on new infrasrucure has been somewha higher han he Lain American average. Resuls of reallocaions for his Benchmark 4 are presened on Table 5. A 1% raise in mainenance from 1.22 o 2.22 would raise oupu by 2.52%. Compare his o he average Lain American counry (Benchmark 1) where an equal-size raise in 16 The quaniaive evaluaion was also performed using he specificaion where depreciaion of public capial depends on consumpion raher han privae capial: d (m, c). The resuls obained are virually idenical and are available from he auhor on reques.

18 2298 F.K. Rioja / Journal of Public Economics 87 (2003) Table 5 Long run effecs of public expendiures reallocaion my dy d DK Dy Dc Benchmark * 5.5* 0.12* Benchmark 3 (u ) * 5.0* 0.12* Benchmark 4 (Brazil) * 6.08* 0.12* D in percen change. *Denoes benchmark. mainenance would raise oupu by a lower 1.87%. This resul can be explained because Brazil has spen more (as percen of DP) ha he average Lain American counry on infrasrucure. Consequenly, he infrasrucure nework in Brazil is larger han in he average Lain American counry. Hence, he same raise in mainenance (as percen of DP) would raise Brazilian DP by more han in he average counry case. Overall he Brazilian calibraion is qualiaively similar

19 F.K. Rioja / Journal of Public Economics 87 (2003) Fig. 2. Oupu effecs of redisribuions: Benchmark 2. o he one for he average of seven Lain American counries as here are gains o increasing mainenance in boh cases. 6. Conclusions The consrucion of new, highly visible public infrasrucure projecs has received grea aenion in many developing counries. Repairing and mainaining exising infrasrucure has generally been negleced. However, he empirical evidence form developing counries (i.e., Devarajan e al., 1996), shows ha curren public expendiures like mainenance have a posiive effec on oupu, while public capial expendiures have a negaive effec on oupu. More new infrasrucure a mainenance s expense may no be beneficial o hese counries. Hence, policymakers may have overemphasized building new infrasrucure as a recipe for developmen. This paper conribues o he lieraure by developing a dynamic general equilibrium model from which he opimal Ramsey expendiure on mainenance is

20 2300 F.K. Rioja / Journal of Public Economics 87 (2003) Fig. 3. Oupu effecs of redisribuions: comparing Benchmark 1 and 3. derived. Is key deerminan is he size of donor-financed new invesmens as a share of exising infrasrucure, which is negaively relaed o he opimal mainenance expendiure. Tha is, policymakers may find i opimal o cu mainenance if donors raise funding for new consrucion. This can parially explain he overemphasis on new infrasrucure. In addiion, donors ofen ie heir aid o highly visible projecs. According o he World Developmen Repor (1994), like minisries of public works, donor agencies find i easier o measure heir achievemens in new projec approvals (p. 91). A policy recommendaion for indusrial counries is o no earmark all infrasrucure aid for new consrucion. Raher, par of his aid could go o an escrow accoun commied o mainaining he infrasrucure for a number of years. Anoher conribuion of he paper is o quaniaively evaluae he radeoffs of various redisribuions of funds beween he wo expendiures using parameers from seven Lain American counries. Reallocaions, wihoddiional donor aid or axaion, can have posiive effecs on a counry s DP. Resuls show ha an opimal allocaion in hese counries implies mainenance should receive abou 2%

21 F.K. Rioja / Journal of Public Economics 87 (2003) of DP. Presenly, mainenance expendiures in Lain America appear below his opimal allocaion. Poenial exensions of he model include allowing he governmen a choice no only on mainenance, blso on he amoun of infrasrucure invesmen and on governmen consumpion. This could be done in a Ramsey framework in which he governmen s problem would now have wo or hree decision variables. Alernaively, his could be done in a poliical economy model where, for insance, he median voer was allowed o choose he levels of expendiures. In any even, filling poholes appears o deserve much more aenion han i has received. Acknowledgemens I am graeful o Jim Alm, Shana Devarajan, Ellen Mcraan, Shannon Mudd, yan Pradhan, and seminar paricipans a he 1999 Economeric Sociey Lain American meeings and he Federal Reserve Banks of Alana and Kansas Ciy for useful commens. Appendix A A.1. Derivaion of opimal mainenance expendiure Afer subsiuing he privae decision rules in, he public policy problem can be wrien as a dynamic program: V(k, K ) 5 ln s(1 2 ab )(1 2 l)k k d1 bv(k9, K 9 ) s. K9 5 D 1s1 2 d (m) dk k9 5 ab(1 2 l)k k m 5 lk k Noice ha following Bellman s noaion, ime subscrips are removed from he variables (e.g., k is simply k). According o his noaion, all prime variables denoe nex period s value (e.g., k11 is k9). The firs-order condiion (FOC) for l is given by (afer he envelope condiions are subsiued), S D 1 bu d m ab 2]] 2 ]S]?]?K D 2] sabkk d5 0 (1 2 l) K9 m l k9

22 2302 F.K. Rioja / Journal of Public Economics 87 (2003) Subsiuing he privae decision rules for k9 and K 9, hen rearranging he equaion, 1 d m K ab ]] 52Sbu?]?]?]]]]]] D2S]] D 1 2 l m l D 1s1 2 d (m) dk 1 2 l or by combining erms, (1 1 ab ) d m K ]]] 52bu?]?]?]]]]]]. (1 2 l) m l D 1s1 2 d (m) dk iven: d cm m 5 lk k, hen d / m 52c and m/ l 5 K k. Subsiuing hese wo derivaives ino he equaion, (1 1 ab ) K ]]] 5 buckk ]]]]]]. (1 2 l) D 1s1 2 d (m) dk Invering and rearranging his equaion, (1 1 ab ) D 1s1 2 d (m) dk (1 2 l) 5 ]]]?]]]]]] u 11 a (buc) K k Subsiuing d (m) s funcional form, f h jg (1 1 ab ) D clkk K (1 2 l) 5 ]]]?]]]]]]]] u 11 a (buc) K k Finally solving for l and re-insering ime subscrips so ha all variables are clearly disinguished from parameers, bu (1 1 ab ) D l* 5]]]] 2]]]]]]] S] D 1 1 b(u 1 a) (1 1 b(u 1 a))ck k K B.1. Firs-order condiions for he complee version of he model The firs-order condiions (FOCs) for he complee version of he model are sandard. Tha is, hey are obained by solving he household s problem (i.e., maximizing uiliy subjec o heir budge consrain); and he firm s problem (i.e., maximizing profi). They are described by: u (c) 5 b(r91(1 2 d ))u (c9) c c r 5 (1 2 l)f (k, n) K

23 F.K. Rioja / Journal of Public Economics 87 (2003) These equaions plus he governmen budge consrain (Eq. (5)), he infrasrucure accumulaion equaion (6), and he goods marke clearing condiion (7) deermine he equilibrium in he model. References Abel, A.B., Taxes, inflaion, and he durabiliy of capial. Journal of Poliical Economy 89 (3), Aschauer, D., Is public expendiure producive? Journal of Moneary Economics 23 (2), Auerbach, A.J., Inflaion and he choice of asse life. Journal of Poliical Economy 87 (3), Barro, R., overnmen spending in a simple model of endogenous growh. Journal of Poliical Economy 98, S103 S125. Baina, R., On he long run effec of public capial on aggregae oupu: esimaion and sensiiviy analysis. Empirical Economics 24 (4), Canning, D., Fay, M., The effec of ransporaion neworks on economic growh. Columbia Universiy Working Paper. Canning, D., A daabase of world socks of infrasrucure, World Bank Economic Review 12 (3), Canning, D., The conribuion of infrasrucure o aggregae oupu. World Bank Policy Research Paper no. 2246, Washingon, DC. Demeriades, P.O., Mamuneas, T.P., Ineremporal oupnd employmen effecs of public infrasrucure capial: evidence from 12 OECD economies. The Economic Journal 110 (465), Devarajan, S., Xie, D., Zou, H., Should public capial be subsidized or provided? Journal of Moneary Economics 41 (2), Devarajan, S., Swaroop, V., Zou, H., The composiion of public expendiure and economic growh. Journal of Moneary Economics 37 (2), Easerly, W., Rebelo, S., Fiscal policy and economic growh: an empirical invesigaion. Journal of Moneary Economics 32 (3), Elias, V., In: Sources of rowh: A Sudy of Seven Lain American Economies. ICS Press, San Francisco, CA. Fay, M., Financing he fuure: infrasrucure needs in Lain America, Working Paper no. 2545, The World Bank. Feehan, J.P., Public invesmen: opimal provision of Hicksian public inpus. Canadian Journal of Economics 31 (3), Fernald, J., Roads o prosperiy: assessing he links beween public capial and produciviy. American Economic Review 89 (3), lobal Developmen Finance, In: CD-Rom. The World Bank, Washingon, DC. lomm,., Ravikumar, B., Public invesmen in infrasrucure in a simple growh model. Journal of Economic Dynamics and Conrol 18 (6), reenwood, J., Hercowiz, Z., Krusell, P., The role of invesmen-specific echnological change in he business cycle. European Economic Review 44 (1), yamfi, P., uierrez, L., Yepes,., In: Infrasrucure Mainenance in LAC: The Cos of Neglec and Opions for Improvemen, Vol. 1. Lain American and Caribbean Technical Deparmen, The World Bank. Haavelmo, T., In: A Sudy in he Theory of Invesmen. The Universiy of Chicago Press, Chicago, IL.

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