MAMS:* A framework for analyzing MDG and poverty reduction strategies

Transcription

1 MPIA Nework Session Paper MAMS:* A framework for analyzing MDG and povery reducion sraegies Hans Lofgren Carolina Diaz-Bonilla DECPG World Bank A paper presened during he 5h PEP Research Nework General Meeing, June 18-22, 2006, Addis Ababa, Ehiopia.

2 MAMS:* A framework for analyzing MDG and povery reducion sraegies Hans Lofgren Carolina Diaz-Bonilla DECPG World Bank Submission dae: May 1, 2006 Paper submied for presenaion a he Ninh Annual Conference on Global Economic Analysis, Addis Ababa, June 15-17, 2006 Conac: Hans Lofgren, MC2-200, 1818 H S., NW, Washingon, DC 20433, USA. Ph Fax: hlofgren@worldbank.org. *MAMS MAquee for MDG Simulaion; MDG Millennium Developmen Goal 1

3 Inroducion his paper documens a dynamic Compuable General Equilibrium (CGE) model ha is designed o analyze sraegies for achieving he Millennium Developmen Goals (MDGs) and, more broadly, sraegies for growh and povery reducion in developing counries. Our reference o he erm maquee (French for model, skech, or layou) reflecs ha he model is designed o capure he key processes for MDG achievemen in a manner ha is applicable o a wide range of counries. When applying he model o any given counry, he key requiremen is he developmen of a counry-specific daabase ha, among oher hings, summarizes he findings from secor sudies on MDGs. In addiion, i may ofen be necessary o adap pars of he model srucure o counryspecific condiions. An economywide approach is needed in MDG analysis given ha he pursui of key MDG-relaed policies ypically has effecs across he economy ha feed back ino he processes ha deermine MDG achievemen. In is reamen of hese processes, our approach considers he imporan roles ha are played by he provision of MDG-relaed services (including healh and educaion), as well as he social and economic saus of he populaion (including per-capia household consumpion and MDG achievemens in relaed areas), incenives, and he sae of infrasrucure. In his process, exernal financing needs depend on economic performance in general, including growh in domesic governmen revenues. he model may be solved in a muli-pass mode, one period a a ime saring wih he base year and moving forward, or in a single-pass mode, simulaneously for all ime periods covered. I may be divided ino hree modules wihin-period and beweenperiod modules of a core CGE model and an MDG module all of which are inegraed ino a simulaneous sysem of linear and non-linear equaions. 1 he wihin-period module (in essence a saic CGE model) capures he bulk of he producion, consumpion, 1 his model is an exension of he saic, sandard CGE model in Lofgren e al. (2002) and he MDG model in Bourguignon e al. (2004). In addiion o adding ime and incorporaing he MDG module, he model exends he earlier model by endogenizing facor produciviy (which depends on economic openness and governmen capial socks), and racking he asses (liabiliies) of he differen insiuions (facor endowmens, domesic governmen debs, and foreign debs). he compuer code is wrien in GAMS. 2

4 invesmen and rade decisions of he economy in any given ime period. he beweenperiod module provides linkages over ime by updaing seleced parameers (including facor supplies, populaion, and facor produciviy) on he basis of exogenous rends and pas endogenous variables. he MDG module capures he processes ha deermine MDG achievemen, mos imporanly he provision of services in he areas of educaion, healh, waer and saniaion, and oher public infrasrucure. he size and skill composiion of he labor force is endogenized, in large measure depending on he evoluion of educaion. he MDG module has feedback effecs ino he res of he economy, mos imporanly via he labor marke. In he model, growh depends on he accumulaion of producion facors (labor a differen educaional levels, privae capial, and oher facors such as land, if presen) and changes in facor produciviy, which is influenced by he accumulaion of governmen capial socks and openness o foreign rade. For each ime period, he model equaions give a comprehensive accoun of decisions and relaed paymens involving producion (aciviies produce oupus using facors and inermediae inpus), consumpion (by households and he governmen), invesmen (privae, including FDI, and governmen), rade (boh domesic and foreign), axaion, ransfers beween insiuions (households, governmen, and he res of he world), and links beween facors and insiuions. hey also cover he marke consrains, macro balances, and dynamic updaing equaions under which he agens operae. Given his comprehensive picure of he economy, for each year, a model soluion defines a wide range of indicaors of economic performance. Povery and inequaliy analysis, as in oher CGE models, can be performed in several ways. he simples bu leas desirable mehod uses an elasiciy calculaion for povery given changes in per-capia household consumpion. Represenaive-household or surveybased microsimulaion approaches are preferable. he former assume fixed disribuions of income or consumpion wihin each household group, providing welfare esimaions direcly from he CGE model resuls. he laer can be eiher op-down, feeding CGE simulaion resuls o a household model, or inegraed, wih he household model buil direcly ino MAMS. 3

5 In essence, he curren model srucure is recursive: he decisions of economic agens depend on he pas and he presen, no he fuure, i.e., for he mos par, forward-looking behavior is no assumed. 2 However, when he model is solved in single-pass mode, nonrecursive feaures may be (and have been) incorporaed; for example, he governmen may selec fixed growh raes over ime (or differen degrees of fron- or back-loading) for differen governmen services so ha MDG arges are achieved in Such decisions are forward-looking since hey depend on fuure values ouside of direc conrol of he governmen (such as household consumpion per capia). 3 Poenially, when he model is solved in single-pass mode, seleced aspecs of privae producer and consumer behavior could also be forward-looking, incorporaing variable values from he fuure. he disaggregaion of he model is daa-driven and flexible in mos areas: subjec o compuer memory consrains, i can handle any number (one or larger) of primary facors, households, producion aciviies, and commodiies. 4 he applicabiliy of he model o specific policy issues depends in par on he degree of disaggregaion. For example, he analysis of issues relaed o povery requires a relaively deailed disaggregaion of household income sources (from facor endowmens and he producion aciviies in which hey are employed) and consumpion. If povery and inequaliy is analyzed using a represenaive-household or inegraed micro-simulaion approach, hen he household secor mus also be disaggregaed (highly disaggregaed for he inegraed micro-simulaion case). For many analyical purposes, i is also preferable o disaggregae non-governmen producion ino muliple secors. In he res of his documen, we describe he differen pars of our model, making frequen reference o he accompanying ables: ables 1-2 (noaion and equaions for he 2 As a resul of his absence of non-recursive feaures, he wihin-period module, including he subse of he MDG equaions ha only refer o he curren period, can be solved recursively, one period a a ime, wih updaing of seleced parameers beween each soluion. his updaing is described in he beween-period module and in a second subse of he MDG equaions wih lagged relaionships. 3 Solving he model in he single-pass mode has he addiional advanage of being compuaionally more efficien. On he oher hand, especially during he developmenal sage, i is ofen easier o solve and debug he model when i is run in he muli-pass mode. 4 Mechanically, he model can accommodae one or more enerprises, i.e., non-consuming domesic nongovernmen insiuions ha earn capial rens and allocae hese rens o oher insiuions (domesic or foreign he owners of he enerprises) afer paying axes and saving. However, his would require addiional changes in he pars of he model ha view oher insiuions as he direc owners of capial socks ha evolve over ime as a funcion of depreciaion and new invesmens by hese insiuions. 4

6 core CGE model) and 3-4 (noaion and equaions for he MDG Module) presen he formal model; able 5 summarizes he closure rules for he macro balances. hroughou his paper, he following noaional convenions apply: endogenous variables are wrien in upper case Lain leers; if he variable is fixed, a bar is placed above he name. Parameers have Greek or lower-case Lain leers. Subscrips refer o se indices. A 0 superscrip is used o refer o base-year variable values. Oherwise, superscrips are exponens (i.e., no par of he name of he variable or parameer ha is a he lower level). In he presence of he 0 superscrip, he ime subscrip () has been suppressed. Core CGE Model: Wihin-Period Module In essence, he wihin-period module defines a one-period, saic CGE model. 5 As shown in able 2, i is divided ino blocks covering prices, producion and rade, domesic insiuions, invesmens, and sysem consrains and macro variables. he price sysem of he model is exensive, especially for commodiies. he price block (Equaions 1-11) defines prices ha can be expressed as funcions of oher endogenous variables (as opposed o being free variables ha perform marke-clearing funcions). Among hese prices, i is worh noing ha ransacions coss (he cos of moving he commodiy beween he border and he demanders or suppliers, or beween domesic demanders and suppliers) are accouned for in he definiions of demander (domesic-currency) impor prices, supplier (domesic-currency) expor prices, and demander prices for domesic oupu sold domesically (Equaions 1, 2, and 4). Whereas he ransformaion of oupu beween expors and domesic sales ypically is imperfec, he model allows for he special case of perfec ransformabiliy wih zero expors as one possible oucome. For his case, expor and domesic supplier prices are idenical if expors are non-zero. If expors are zero, he domesic supplier prices may (and are likely o) exceed he expor prices (Equaion 3). Various aggregaive prices for composie supplies, for produced 5 Apar from he fac ha variables are ime indexed, mos of he wihin-period module is similar o he sandard, saic CGE model described in Lofgren e al. (2002). his documen provides more deail on model feaures and references o he CGE modeling lieraure. 5

7 commodiies, and value-added are derived from relaionships ha define oal revenue or coss as he sum of disaggregaed receips or paymens (equaions 5-7 and 9). he price of he aggregaive inermediae commodiy for any aciviy depends on is commodiy composiion and he prices of he commodiies involved (Equaion 8). he model is homogeneous of degree zero in prices, wih he CPI serving as he model numéraire (Equaion 10). 6 Alernaive, he price index for non-radables may serve as numéraire (Equaion 11). he producion and rade block (Equaions 12-29) includes he firs-order condiions for profi-maximizing producion and ransformaion decisions as well as cosminimizing domesic demand decisions. Given available echnology and marke prices (aken as given in a perfecly compeiive seing), producers maximize profis. he echnology is defined by a nesed, wo-level srucure. A he op, wo alernaives are possible, eiher a Leonief aggregaion of value-added and an aggregae inermediae or a CES aggregaion of he same wo variables (Equaions 12-15). A he boom, hese are linked o a CES aggregaion of primary facors (a value-added funcion) and a Leonief aggregaion of inermediae inpus (Equaions 16-18). Given ha he naional accouns rarely aribue value-added o governmen capial, he CES value-added funcion is limied o labor. 7 Each aciviy produces one or more oupus wih fixed yield coefficiens (Equaion 19). Any commodiy may be produced and markeed by more han one aciviy. A CES approach, assuming profi-maximizing producer behavior, is used o aggregae marke sales of any commodiy from differen aciviies (Equaions 20-21). Producion is ransformed ino expors and domesic sales on he basis of a CE (Consan Elasiciy of ransformaion) funcion. he profi-maximizing, opimal raio beween he quaniies of expors and domesic sales is posiively relaed o he raio beween he corresponding supply prices (Equaions 22-23). A less complex relaionship applies o producion wihou expors or wihou domesic sales (Equaion 24). For any 6 he compuer code permis he user o choose eiher he CPI or he price index for non-radables as numéraire. As long as he model is homogeneous of degree zero in prices, his choice has no impac on he equilibrium values of real variables. his homogeneiy condiion is no me under he macro closures where he savings or he domesic borrowing variables of he governmen are fixed. In hese cases, i is implicily assumed ha he fixed variables are indexed o he numéraire. 7 Neverheless, he model accouns for he fac ha governmen capial socks indeed are needed in he producion of governmen services: in he invesmen block, governmen invesmens are deermined on he basis of capial demands (linked o he level of governmen service producion) and capial socks. 6

8 expored commodiy, wo alernaives are possible for expor demand, eiher exogenous prices (in foreign currency) combined wih an infiniely elasic demand or price-sensiive expor demands (defined by consan-elasiciy funcions) wih he foreign currency prices deermined by domesic condiions and he exchange rae. (Equaion 25 applies o he consan-elasiciy case.) Domesic demanders are assumed o minimize he cos of imperfecly subsiuable impors and commodiies from domesic producion according o an Armingon (CES aggregaion) funcion (Equaions 26-27). For commodiies wih only one supply source he supply from his source equals he composie supply (Equaion 28). he ransacions (rade and ranspor) demand for any service commodiy is he sum of demands arising from domesic sales, expors, and impors, each of which is he produc of he quaniy raded and a fixed inpu coefficien (showing he quaniy of he service commodiy per uni of rade; Equaion 29). he domesic insiuion block (Equaions 30-45) accouns for he receips and expendiures of all domesic insiuions, boh governmen and non-governmen (households) as well as seleced paymen flows o and from he res of he world. he equaions are srucured o accommodae daabases wih any number of households, one governmen, and one eniy represening he res of he world. he paymens in his block are highly inerrelaed since insiuions ofen are boh a he receiving and paying ends. Firs, facor incomes are defined as a funcion of domesic wages (which may vary across aciviies) and employmen levels, augmened by facor incomes from he res of he world (Equaion 30) and allocaed across differen insiuions (domesic and foreign) in value shares ha depend on facor endowmen shares (Equaions 31-32). Domesic nongovernmen insiuions: (i) earn ne ineres incomes, defined as he difference beween ne ineres earnings from loans o he governmen and ne ineres paymens o he res of he world on borrowing from abroad (Equaion 33); (ii) ransfer fixed shares of heir incomes (ne of direc axes and savings) o oher insiuions (domesic or foreign) (Equaion 34); and (iii) earn oal gross incomes defined as he sum of facor incomes, ne ineres incomes, and ransfers from oher insiuions (wih separae reamens depending on wheher he sending insiuion is he governmen, he res of he world, or anoher domesic non-governmen insiuion, and on wheher he receiving insiuion is 7

9 a household or non-household) (Equaion 35); (iv) pay direc axes according o raes ha are fixed unless adjused as par of he governmen closure rule; cf. discussion below (Equaion 36); and (v) save ou of incomes ne of direc axes according o marginal (and average) raes ha are endogenous, depending on changes in per-capia incomes (if he elasiciy of savings wih respec o per-capia income is differen from uniy). Alernaively, for any given insiuion, he savings rae may be adjused as par of he governmen closure (discussed below) (Equaions 37-38). For households, incomes ne of direc axes, savings, and ransfers o oher insiuions (defined in Equaion 39) are allocaed across differen commodiies according o LES (Linear Expendiure Sysem) demand funcions, defined in per-capia form wih separae equaions for demands from he marke and from own-producion (Equaions 40-41). For he remaining domesic insiuion, he governmen, curren incomes come from axes (which are disaggregaed ino a wide range of caegories), facor endowmens (he governmen may own various non-labor facors), and ransfers from oher domesic insiuions and he res of he world (Equaion 42). he (re)curren expendiures of he governmen are divided ino consumpion, ransfers o domesic insiuions (CPIindexed) and he res of he world (fixed in foreign currency), and ineres paymens on domesic and foreign deb (Equaions 43). For each period excep he firs, real governmen consumpion, disaggregaed by commodiy, is defined as he level in he previous year imes a growh facor ha consiss of muliple erms (Equaion 44). For he base case, hese erms are all exogenous; in simulaions wih oher rules for deermining governmen consumpion (including simulaions argeing MDGs), one of hese may be (parly) endogenous. 8 Finally, governmen savings is simply he difference beween curren revenues and curren expendiures (Equaion 45). he invesmen block (Equaions 46-55) defines he ransformaion of savings ino differen ypes of invesmens, including adjusmens for financial ransacions (some of which involve he res of he world) and foreign direc invesmen. he prices of new 8 RQG is flexed if he absorpion share of oal governmen consumpion is fixed. RQGC c, is flexed when some arge influenced by his specific governmen service (c) is fixed for year. For he mos sraighforward case, rqgadj c, c, is 1 when c c and zero oherwise. However, if he analys wans one or more kind of governmen consumpion o grow in andem wih anoher, more han one c may have a value of 1 for any given c. However, each c is linked o only one c. 8

10 capial socks depend on heir composiion and marke prices (Equaion 46). Governmen fixed invesmen spending is defined on he basis of hese prices and real governmen fixed invesmen demand (he deerminaion of which is defined below) (Equaion 47). his fixed invesmen value is financed by some combinaion of governmen savings (ne of spending on sock changes), new governmen bonds, and Cenral Bank borrowing, foreign borrowing, and foreign grans (which is a caegory separae from governmen ransfers from he res of he world) (Equaion 48). According o one possible closure, governmen borrowing is flexible, assuring ha his equaliy holds. (If so, he oher erms would be exogenous or deermined via oher mechanisms.) Governmen bond borrowing and Cenral Bank borrowing is allocaed across seleced non-governmen insiuions on he basis of heir savings shares (Equaions 49-50). 9 he fixed invesmen value of each domesic non-governmen insiuion is defined as is savings, ne of spending on sock changes and lending o he governmen, and augmened by borrowing and grans from he res of he world. For he res of he world, he fixed invesmen value is simply he value of foreign direc invesmen (FDI; fixed in foreign currency) imes he exchange rae; he FDI erm is invariably fixed a zero for domesic insiuions (Equaion 51). For each nongovernmen insiuion, invesmens in differen capial socks are deermined by oal fixed invesmen values, he prices of capial goods, and exogenous value shares of differen capial socks; he value share is uniy if he daabase only specifies a single privae capial ype (Equaion 52). 10 Governmen invesmen demand by capial sock is deermined by he difference beween he anicipaed capial demand nex year (drawing on producion growh from las year) and he capial sock ha would remain if no invesmens were made; if he demand is posiive, hen he equaion will hold as an 9 he savings shares are adjused by a disorion erm (gbdis i ) ha reflecs deviaions beween household shares for governmen borrowing and savings. Implicily, he burden of Cenral Bank borrowing (which is anamoun o money prining) is fel by oher agens since i exracs real purchasing power from hem by reducing he value of he old money ha hey hold. In he absence of an explici reamen of money in his model, his burden is here allocaed across households on he basis of heir savings shares. he governmen is assumed o pay no ineres on is deb o he Cenral Bank (even if ineres is paid, Cenral Bank profis end o be recycled o he governmen). Given his, his deb sock is no moniored. 10 ypically, he model will only have one privae capial sock, i.e. he value of he share parameer is uniy for his capial ype. If he model has more han one privae capial sock, he allocaion beween he differen socks may be endogenized, possibly deviaing from he base-level allocaion in response o changes in relaive profi raes. 9

11 equaliy (Equaions 53-54). 11 Finally, oal invesmen demand by commodiy source is defined given gross changes in capial socks (boh privae and governmen) and he capial composiion parameer (Equaion 55). he sysem consrain and macro block (Equaions 56-62) explicily capures he over-all resource consrains under which he economy operaes as well as he deerminans of FP (oal facor produciviy) in he differen producion aciviies. For each marke facor (all facors excep governmen capial socks), he supply is defined as he sum of insiuional endowmens (Equaion 56). In he markes for he same se of facors, quaniies demanded and supplied are se equal (Equaion 57). Each marke is cleared by he flexible, facor-specific wage variable (WF), which, a a more disaggregaed level, can differ across aciviies by an aciviy-, facor-, and ime-specific wage disorion (or differenial) erm (WFDIS ; cf. equaions 17 and 30). In he special case of no wage differenials, his erm is fixed a uniy. Alernaively, in some cases i may be desirable o impose an exogenous ime pah for he employmen of specific facors in seleced aciviies (drawing on oher pieces of informaion, for example daa on he expeced evoluion of secors based on he exploiaion of naural resources). If so, he user only has o flex he wage disorion variable (WFDIS) and fix he employmen variable (QF) for he relevan combinaion of facors, aciviies, and ime periods. his can be done wihou changing he closure rule for oher aciviies. Oher alernaives for he facor marke may be added, including closures wih explici unemploymen. For composie commodiies, he supply is also se equal o he sum of demands (Equaion 58). As noed above, he composie supplies sem from wo sources, impors and domesic supplies o domesic markes, each of which has is own marke clearing variable, he impor quaniy (QM) and he supplier price (PDS), respecively. he balance of paymens consrain (Equaion 59) imposes equaliy beween foreign exchange uses (spending on impors, facor incomes and ransfers o he res of he world, and ineres paymens on foreign debs) and sources (expor revenues, ransfers, facor 11 A mixed-complemenary formulaion is used wih a lower limi of zero for he governmen invesmen variable (DKGOV) and governmen invesmen defined as being larger han or equal o zero. his reamen assures ha, if DKGOV is posiive, hen invesmen will be equal o anicipaed demand whereas, if DKGOV is zero, hen i may be larger han a negaive invesmen demand level (which would reflec he excepional case of a rae of producion decline in excess of he depreciaion rae). Equaion 54 ransfers he value of DKGOV o DKINS for he governmen, a variable ha is used elsewhere in he model across all capial socks. 10

12 incomes, borrowing, grans, and FDI). 12 Finally, his block includes hree macro variables, real GDP a marke prices and he real rade-gdp raio (boh of which appear in oher model equaions), and real GDP a facor cos (which, as will be noed below, may be used as a fixed arge in he calibraion of FP growh for he base run; Equaions 60-62). Core CGE Model: Beween-Period Module he equaions in he beween-period module updae household populaions and insiuional socks of asses and liabiliies and FP for seleced aciviies. Invariably he equaions in his module include lagged relaionships. As shown in able 2, he equaions in his module do no apply o he firs year, for which he values of he variables defined in his module are fixed. As we will see in he MDG module, we assume ha each household group is endowed wih an unchanged share of he economywide oal of every labor facor. he populaion of each household in any year is defined as is populaion in he preceding year imes he growh facor of is labor force, muliplied by a populaion scaling facor (Equaion 63). As a resul, if he household has a relaively large (small) share of he labor ypes ha grow mos rapidly, hen is populaion will also grow more (less) rapidly. As long as he model has more han one household, he resuling growh raes for each household group will deviae from is naural growh, indicaing ha, implicily, pars of he populaion migrae beween household groups. he populaion scaling facor assures ha he sum of he represenaive household populaions is equal o he exogenous populaion oal (Equaion 64). In effec his means ha, if he aggregae labor force paricipaion rae goes up (down), hen his change will be imposed across all household groups. For he differen asses and liabiliies held by households as well as for oher aspecs of heir behavior (such as consumpion paerns), he general assumpion is ha he 12 Implicily, an addiional sysem consrain, he savings-invesmen balance, also holds: by channeling domesic savings and he erms ha make up foreign savings o invesmen, he model equaions assure ha oal savings and oal invesmen are equal. 11

13 differen household groups reain heir original characerisics subjec o adjusmens needed o assure ha he sums across he differen household equal known oals. Accordingly, for he caegory of (non-labor) facors wih exogenous oal household socks (land may be an example), he endowmen of each household is defined as he produc of an exogenous per-capia endowmen, populaion, and a facor-specific scaling facor (Equaion 65). he scaling facor is adjused o assure ha he oal across all households equals an exogenous oal (Equaion 66). For capial, he sock of each insiuion (households and ohers) is defined as he sum of is old, (poenially) redisribued capial sock, new invesmens, and exogenous adjusmens (which may reflec he impac of naural disasers or insiuional changes, removing pars of he capial sock from producion) (Equaion 67). For non-households, he old, redisribued sock is simply wha remains of is non-depreciaed sock of las year. For households, he non-depreciaed sock is adjused upwards for populaion growh and muliplied by a facor-specific scaling facor (Equaion 68). he oal redisribued capial sock across all household groups is equal o he oal, nondepreciaed sock (Equaion 69). he scaling facor will adjus o assure ha his consrain is saisfied. Excep for he absence of depreciaion, idenical relaionships hold for foreign deb (Equaions 70-72) and governmen bonds (Equaions 73-75). For foreign deb, he reamen is poenially more complex since he model allows for he possibiliy of non-paid ineres (which is added o he deb) and deb relief. Finally, he oal facor produciviy of each aciviy is defined as he produc of a rend erm, changes due o capial accumulaion, and changes due o changes in economic openness (defined by he real rade-gdp raio). he effecs of capial accumulaion and changes in openness depend on he values of exogenous, consan elasiciies if hey are se a zero, he effec is zero and only he rend erm will maer (Equaion 76). he rend erm is ypically exogenous. However, as par of he model calibraion, i may be endogenized in a seing where real GDP a facor cos is fixed in every ime period (Equaion 77). 13 he rade-gdp raio, he mos common indicaor of economic openness 13 When developing he model base run, he rend erm may be exogenous. If so, he analys needs o monior overall GDP growh and, if needed adjus he exogenous growh erm (CALFPG). he esimaes of iniial capial socks and depreciaion raes may also have o be revisied. Alernaively, he rend erm may be endogenized while real GDP (a facor cos) is fixed in each year. If so, he analys 12

14 (in erms of oucome, no policy sance) is defined in real erms (o avoid he impac of nominal changes, for example due o exchange rae depreciaion). he impac of changes in his raio is lagged in order o avoid large sudden changes. he fac ha he elasiciy parameers are disaggregaed (by aciviy for rade and by aciviy and funcion for capial) make i possible o specify differen channels and magniudes for he produciviy effecs of rade and differen ypes of governmen invesmens. MDG Module he MDG module (Equaions 78-91) is a core componen of he model. I specifies he mechanisms ha deermine he values for he indicaors relaed o he differen MDGs and educaional behavior as well as he size and disaggregaion (by educaional achievemen) of he labor force. he res of he economy, which was presened in he preceding secions, influences he evoluion of he MDGs and he educaional secor hrough variables relaed o household consumpion, he provision of differen ypes of MDG-relaed services, labor wages, and capial socks in infrasrucure. In is urn, he MDG module influences he res of he economy hrough is impac on he size and composiion of he labor force. In addiion, he evoluion of one se of MDGs can influence oher MDGs. he noaion and he equaions of he MDG module are presened in ables 3 and 4. he educaional componen, which is disaggregaed by cycle (wih hree cycles as a ypical level of disaggregaion), consiss of Equaions Wihin any cycle, he model endogenizes he following aspecs of suden behavior (or oucomes): he shares of he enrolled ha graduae from heir curren grade, drop ou, or repea he grade nex year (referred o as grd, dropou, and rep). Noe ha he erm graduae hroughou his paper and he model no only refers o sudens who successfully finish a given educaion cycle, bu is also used o refer o sudens who successfully complee a grade (i.e., pass) and coninue o should review he resuling overall growh rae for he rend erm and, if needed, adjus he real GDP levels ha are imposed. For non-base runs, rend FP growh is ypically fixed, permiing real GDP growh o be influenced by facor accumulaion and endogenous FP changes. 13

15 a higher grade wihin he cycle. he sum of hese shares is uniy i.e., during he school year, a suden mus eiher graduae, drop ou, or become a repeaer (his applies o each grade and for each cycle as a whole); he shares among he graduaes from heir curren grade (grd) who graduae from heir curren cycle (grdcyc) or coninue o a higher grade wihin his cycle (concyc). I.e., in erms of shares: grdcyc + concyc grd; he shares among cycle graduaes who exi he school sysem (grdexi) or coninue o nex cycle (grdcon). he sum of hese shares is also uniy. For graduaes from he las cycle, he share of hose who exi is uniy; and he share of he cohor of he 1 s year in primary school ha eners school (g1enry). Equaions define he share variables ha idenify differen aspecs of suden behavior. For each cycle, a logisic funcion (Equaion 78) defines he shares for 1 s year in-cohor enry, for graduaes from he curren grade, and for graduaes who decide o coninue o nex cycle (i.e. g1enry, grd, and grdcon, he elemens of he se BLOG). he logisic funcional form was seleced since i makes i possible o impose exreme (for educaion i is a maximum) values for he funcion and o incorporae exraneous informaion abou elasiciies and condiions under which arge values are achieved. Anoher advanage is ha i allows for segmens of increasing and decreasing marginal reurns o improvemens in he deerminans of educaional behavior. he only endogenous variable in he logisic funcion (SHREDIN), is defined in a consanelasiciy formulaion (Equaion 79) as a funcion of: (i) educaional qualiy; (ii) wage incenives, defined as relaive wage gains from coninued schooling (i.e., he relaive wage gain ha sudens can achieve if hey complee a cycle ha is sufficienly high o enable hem o climb o he nex higher level in he labor marke); (iii) he under-five moraliy rae (a proxy for he healh saus of he school populaion); (iv) he size of he infrasrucure capial sock; and (v) household consumpion per capia. he parameers in Equaions are seleced as follows: he parameer exed shows he exreme (maximum) value o which he behavior share should converge (here one) as he value of he inermediae variable approaches infiniy; 14

16 he parameer α ed is calibraed so ha, under base-year condiions, he behavioral share replicaes he base-year value; he parameers β ed and φ ed are calibraed so ha he wo equaions: (i) replicae he base-year elasiciies of he behavioral share (SHRED) wih respec o he argumens of he consan-elasiciy funcion; and (ii) achieve a behavioral arge (e.g. a share very close o one for g1enry) under a se of values for he argumens of he consan-elasiciy funcion ha have been idenified by oher sudies; and he value of he parameer γ ed deermines how he base-year poin on he logisic funcion is posiioned relaive o he inflecion poin (where he curve swiches from increasing o decreasing marginal reurns as he deerminans of educaional behavior improve). Equaion 79 is calibraed so ha, in he base year (under base-year 0 condiions), SHRedinb, c, SHRedbc,. (Noe ha hese wo erms ener he denominaor of he second erm in equaion 78.) Separae equaions define wo of he deerminans of he CE funcion. Educaional qualiy (EDUQUAL) is defined as he raio beween real services per suden (oal services divided by oal enrollmen) in he curren year and in he base year; i.e., in he base-year, educaional qualiy is indexed o one (Equaion 80). Average real household consumpion per capia (QHPC) is defined as oal household consumpion a base-year prices divided by oal populaion (Equaion 81). Drawing on he shares defined in he preceding equaions, he shares for repeaers, dropous, and cycle graduaes exiing from he school sysem (rep, dropou, and grdexi; elemens in he se BRES) are defined residually (Equaion 82). he formulaion considers he fac ha, as noed above, seleced shares have o sum o uniy. If more han one variable in BRES has o be adjused in relaion o one or more elemens in BLOG (as is he case for he adjusmen of shares for repeaers and dropous in response o changes in he share of graduaes), hen all adjused variables are scaled up or down by he same facor. 14 he share of graduaes from a cycle (grdcyc) is defined as he share for he oal number of graduaes in he cycle (grd) divided by he number of years in he cycle 14 he equaion is formulaed so ha i works for cases wih one or more han one erm in any of he sums over relaed shares (defined by he mappings MBB and MBB2) in eiher of he ses BRES and BLOG. 15

17 whereas he residual share is assigned o graduaes wihin a cycle (concyc) (Equaions 83-84). We use he ne compleion rae as our MDG 2 indicaor. I is defined as he produc of he relevan 1s-year primary school enry rae (g1enry) and he graduaion raes (grd) over ime for he cohor ha graduae from primary school in he curren year (Equaion 85). 15 Drawing on he above informaion, we can define he number of enrolled sudens by cycle and year. he number of old enrolled sudens in any cycle (i.e., hose who were enrolled in he same cycle las year) is defined as he sum of hose who: (i) coninue wihin he cycle afer successful compleion of an earlier grade; and (ii) repea he grade hey were in las year (Equaion 86). he number of new enrolled sudens is defined as he sum of: (i) graduaes from he relevan earlier cycle las year who chose o coninue; (ii) cohor enrans (only for he 1 s primary cycle); and (iii) oher, non-cohor enrans enering any cycle in he educaional sysem (Equaion 87). 16 he oal number of enrolled sudens in a cycle is he sum of old and new sudens (Equaion 88). Drawing on hese enrollmen variables, insiuional labor endowmens are defined as he sum of he following componens (Equaion 89): (i) remaining labor from he preceding year; (ii) new labor force enrans among sudens who exied from he school sysem in he previous year (wih separae erms for graduaes and dropous); (iii) new labor force enrans from he non-suden populaion who reach he age a which hey, o he exen ha hey seek work, become par of he labor force. Depending on heir highes compleed grade, he new labor force enrans are allocaed o a specific labor caegory. he reamen underlying MDGs 4, 5, 7a and 7b is similar bu less complex. For hese, a logisic funcion direcly defines he MDG indicaors as a funcion of an inermediae variable ha is defined in a relaed CE funcion (Equaions 90-91). he values for he parameers exmdg, α mdg, β mdg, and φ mdg are defined following he same principles as he corresponding parameers in he logisic and CE funcions for 15 In oher words, in order for 100% of he cohor o complee he primary cycle in ime, i is necessary ha all of hem ener a he ime of heir firs year and afer ha all manage o graduae in each year (i.e., successfully complee each grade) up o he final year of he cycle. Given ha we do no generae separae graduaion raes for sudens in he relevan cohor (as opposed o sudens ouside his cohor), we assume ha he raes for in-cohor sudens are idenical o he over-all raes for sudens in he cycle. 16 his caegory includes non-cohor enrans o he 1 s primary year of primary school (a leas during a ransiional period of primary school expansion). I may also include immigrans from oher counries. 16

18 educaion. he argumens of he CE funcion are similar excep for ha he relevan service supply is expressed in per-capia form (no per enrolled suden). Wihin-Period Rules for Macro Balances Like oher economywide models, MAMS includes hree macroeconomic balances: for he governmen, he res of he world (he balance of paymens), and savingsinvesmens (loanable funds). In he compuer code, he user chooses among a se of preprogrammed alernaive closure rules for hese balances. (he se can easily be expanded.) he choices made have no influence on he soluion for he base year bu will almos invariably influence he resuls for oher years and across differen simulaions. he preprogrammed alernaives are summarized in able For he governmen balance (Equaions 42, 43, 45, and 48), under he firs closure, governmen savings (he difference beween curren governmen revenues and curren governmen expendiures) is a flexible residual while all ax raes are fixed. Flexible domesic governmen borrowing covers he gap in he governmen capial accoun (beween governmen invesmen coss and financing from oher sources: governmen savings, foreign borrowing and foreign grans). he second closure (GOV-2) differs in ha domesic governmen borrowing is fixed a some exogenous level (defined by year and simulaion) while he direc ax raes of domesic non-governmen insiuions are adjused o assure ha governmen savings suffice o cover he gap in he governmen capial accoun. According o he direc ax adjusmen rule, he raes for seleced insiuions are adjused endogenously by he same number of percenage poins. Insead of relying on domesic sources of financing, he hird governmen closure (GOV-3) assumes ha foreign grans cover he gap in he governmen capial accoun in a seing where direc ax raes and domesic governmen borrowing are fixed. he fourh closure (GOV-4) combines elemens of he second and hird closure: boh direc ax raes and foreign grans are flexible while governmen savings is fixed. his closure may be used 17 For a discussion of macro closures in he conex of he sandard CGE model, see Lofgren e al. (2002, pp ). able 5 includes he alernaives ha are likely o be used mos frequenly. he GAMS code includes addiional opions, iner alia, for he closures where direc ax and savings raes are adjused for seleced insiuions. hese opions involve scaling of raes ha oherwise would have prevailed insead of uniform percenage poin changes. 17

19 in a seing where direc ax raes are adjused in response o an increase in governmen recurren spending (perhaps wih he objecive of achieving some MDG arge) a he same ime as foreign grans respond o a relaed increase in governmen capial spending. he fifh governmen closure (GOV-5) is idenical o he hird excep for ha, insead of foreign grans, foreign borrowing covers he gap in he governmen capial accoun. Under all of he above rules, i is assumed ha governmen consumpion is deermined according o some oher rule (i.e., adjusmens in governmen consumpion are no par of he mechanisms for achieving governmen balance). hree alernaive rules for deermining governmen consumpion are specified (cf. equaion 54): fixed real quaniy by commodiy and year; flexible absorpion share; his is he rule ha was assumed in he preceding model presenaion; 2. fixed absorpion share and flexible scaling of exogenous consumpion quaniies by a facor ha is uniform across all commodiies; i.e., fix he variable indicaing he absorpion share of governmen consumpion and flex he variable QCSHRABSADJ ; and 3. for seleced commodiies and ime periods, flexible growh raes combined wih fixed arges for MDG indicaors relaed o he governmen commodiy (service) (i.e., flex he variable RQGC c, for seleced c and ); for remaining commodiies, fixed real quaniy by commodiy and year and flexible absorpion share (same as 1). For he balance of paymens (Equaion 59), which is expressed in foreign currency, hree closures are specified. he firs closure (ROW-1) has a flexible real exchange rae whereas all iems on he capial accoun, including foreign grans, are fixed. Given his, foreign savings (he curren accoun defici) is implicily fixed. o exemplify how his works: if, ceeris paribus, he balance of paymens is in defici, hen a depreciaion of he real exchange rae eliminaes his defici by (i) reducing spending on impors (a fall in impor quaniies a fixed world prices); and (ii) increasing earnings from expors (an increase in expor quaniies a fixed world prices). he oher wo res-of-world closures are designed o work wih specific governmen closures. If, for he governmen balance, 18 In addiion o he equaions in ables 2 and 4, he complee compuer model includes an equaion ha defines he absorpion share of governmen consumpion, a variable ha is fixed under rule 2. 18

20 he hird or fourh closure is used (GOV-3 or GOV-4), hen he second res-of-world closure (ROW-2) should be acivaed: i combines a flexible exchange rae wih flexible foreign grans (where he laer in effec is deermined o balance he governmen accouns); similarly, if for he governmen, he fifh closure is used (GOV-5), hen he hird res-of-world closure (ROW-3), which assumes flexible foreign borrowing, should be used. In he savings-invesmen balance (which is implici in he model), governmen invesmen spending is deermined by he demand for capial by he differen governmen service aciviies whereas he deerminaion of governmen savings depends on he closure rule adoped for he governmen balance. Hence, he alernaive closures for he savings-invesmen balance focus on he non-governmen componens of invesmen and savings. he closures are eiher invesmen-driven (he value of savings adjuss) or savings-driven (he value of invesmen adjuss). he firs closure (SI-1) is invesmen driven: privae invesmen is a fixed share of oal absorpion (which may vary over ime). 19 In order o assure ha oal savings and invesmen values are equal, he savings raes of seleced non-governmen insiuions are adjused by a uniform number of percenage poins (he variable DMPS is flexed; Equaion 37). he second closure (SI-2) makes he opposie assumpions: he variable for savings adjusmen (DMPS) is fixed while he privae invesmen absorpion share is flexible. he las closure (SI-3) is idenical o he firs excep for ha he absorpion share ha is fixed defines oal invesmen. 19 he complee compuer model includes equaions ha define he absorpion shares of privae and oal invesmen (no included in ables 2 or 4). hese absorpion variables are fixed or flexible depending on he macro closure. 19

21 REFERENCES Bourguignon, François, Maurizio Bussolo, Luiz A. Pereira da Silva, Hans immer and Dominique van der Mensbrugghe MAMS MAquee for MDG Simulaions: a simple Macro-Micro Linkage Model for Counry-Specific Modeling of he Millennium Developmen Goals or MDGs. Mimeo. World Bank. Lofgren, Hans, Rebecca Lee Harris, and Sherman Robinson, wih assisance from Moaaz El-Said and Marcelle homas A Sandard Compuable General Equilibrium (CGE) Model in GAMS. Microcompuers in Policy Research, Vol. 5. Washingon, D.C.: IFPRI (hp:// 20

22 able 1: Ses, parameers, and variables for core CGE modules of MAMS model SES Symbol Explanaion Symbol Explanaion a A Aciviies f, f ' F facors a ACES ( A) a ALEO ( A) aciviies wih CES funcion beween Value Added and Inermediae inpus aciviies wih Leonief fn beween Value Added and Inermediae inpus c C Commodiies f FEXOG( F) c CD( C ) commodiies wih domesic sales of domesic oupu f FCAP( F) capial facors f FCAPGOV ( FCAP) governmen capial facors facors wih exogenous growh raes f FLABN ( F) non-labor facors c CDN ( C ) commodiies no in CD h H( INSDNG ) households (incl. NGOs) c CE( C ) expored commodiies i INS insiuions (domesic and res of world) c CEN( C ) commodiies no in CE i INSD( INS ) domesic insiuions c CECEN ( C) expored commodiies wihou CE funcion i INSDNG( INSD ) c CM ( C ) impored commodiies i INSNG( INS ) c CMN( C ) commodiies no in CM ( f, a) MFA c C ( C) ransacion service commodiies domesic non-governmen insiuions non-governmen insiuions mapping showing ha disaggregaed facor f is used in aciviy a ime periods PARAMEERS LAIN LEERS capcomp c, f cws c quaniy of commodiy c per uni of new capial f weigh of commodiy c in he CPI pwse c, depr f depreciaion rae for facor f qe c, dws domesic sales price weighs qfachho, c fdebrelief i, foreign deb relief for domesic insiuion i world price for expor subsiues (FCU) qds c,, i quaniy of sock change f qfacinsadj i, f, expor demand for c if pwe pwse (world price for subs) oal household sock of exogenous, non-labor facors exogenous facor sock adjusmen 21

23 fdi i, finra i, finradue i, fprd fa,, gbdis i gfcfshr f,, i ginra i, ica ca, icd c, c', ice c, c ', icm c, c ', ifa f, a ina a iva a mps01 i foreign direc invesmen by insiuion i (res of world) (FCU) ineres rae on foreign deb for domesic insiuion i (paid) ineres rae on foreign deb for domesic insiuion i (due) produciviy of facor f in aciviy a disorion facor for gov borrowing from insiuion i share of gross fixed capial formaion for insiuion i in capial facor f ineres rae on governmen bonds for domesic insiuion i quaniy of c as inermediae inpu per uni of aggregae inermediae in aciviy a rade inpu of c per uni of commodiy c produced & sold domesically rade inpu of c per uni of commodiy c expored rade inpu of c per uni of commodiy c impored quaniy of capial f per uni of governmen aciviy a quaniy of aggregae inermediae inpu per uni of aciviy a quaniy of value-added per uni of aciviy a 0-1 parameer wih 1 for insiuions wih poenially flexed direc ax raes qfpc i, f, rqgadj c, c', shii ii,' per-capia quaniy of exogenous-supply facor f by insiuion i and year parameer linking governmen consumpion growh across commodiies share of ne income of i o i (i INSDNG) a a, ax rae for aciviy a e c, expor ax rae f f, direc ax rae for facor f fp01 a, fpelasqg a, f, fpelasrd a fprdw, ' ins01 i ins i, 0-1 parameer for aciviies wih endogenous FP growh elas'y of FP for a w.r.. o governmen capial cap sock f elasiciy of FP for a w.r.. o GDP rade share weigh of period in fp-rade link in 0-1 parameer wih 1 for insiuions wih poenially flexed direc ax raes exogenous componen in direc ax rae for domesic insiuion i m c, impor ariff rae q c, rae of sales ax rnsfr i, i ', popo oal populaion by year rnsfr f, i', pwe c, expor world price of c (FCU) rnsfrpc i, i ', pwm c, impor world price of c (FCU) va a, exogenous ransfer from insiuion i o insiuion i exogenous ransfer from insiuion i o facor f per-capia ransfers from insiuion i' o hhd insiuion i rae of value-added ax for aciviy a 22

24 PARAMEERS GREEK LEERS α shif parameer for op level CES a δ CES value-added funcion share va a, funcion f a parameer for facor f in aciviy a per capia household subsisence α shif parameer for domesic ac γ h c a, c, h consumpion of home commodiy c commodiy aggregaion funcion from aciviy a α exogenous componen of efficiency vag a, γ per capia household subsisence m, (FP) for aciviy a ch cons of markeed commodiy c α q c Armingon funcion shif parameer ρ aa CES op level funcion exponen α c CE funcion shif parameer ρ domesic commodiy aggregaion acc funcion exponen β h a, c, h β m ch, δ a a δ ac a marginal share of household consumpion on home commodiy c from aciviy a marginal share of household consumpion spending on markeed commodiy c share parameer for op level CES funcion share parameer for domesic commodiy aggregaion funcion ρ q c Armingon funcion exponen ρ sav i δ Armingon funcion share parameer θ, q c δ c CE funcion share parameer elasiciy of savings rae wih respec o per-capia income for insiuion (household) h ρ c CE funcion exponen ρ vaa CES value-added funcion exponen ac yield of oupu c per uni of aciviy a 23

25 VARIABLES α va a, efficiency parameer in he CES PQ c, composie commodiy price value-added funcion α va2 a, endogenous FP rend erm by a PVA a, CALFPG Calibraion facor for FP growh PX c, CBBOR i, CBBORO governmen Cenral Bank borrowing (defici moneizaion) governmen Cenral Bank a, borrowing (defici moneizaion) CPI consumer price index QD c, DGBOND i, DGBONDO f, change in holding of governmen bonds for domesic insiuion i oal change in holding of governmen bonds value-added price (facor income per uni of aciviy) aggregae producer price for commodiy PXAC ac,, price of commodiy c from aciviy a QA quaniy (level) of aciviy quaniy sold domesically of domesically produced c QE c, quaniy of expors of commodiy c QF f, a, DKGOV gross governmen invesmen in f QFACINS i, f, DKINS i, f, DMPS DPI DINS gross change in capial sock (invesmen in) f for insiuion i uniform poin change in savings rae of seleced domesic insiuions producer price index for nonraded oupu uniform poin change in direc ax rae of seleced domesic insiuions QFCAPRED i, f, quaniy demanded of facor f by aciviy a real endowmen of facor f for insiuion i sock of redisribued capial by ins - f - QFS f, quaniy supplied of facor f QFSCAL f, QG c, QH EG governmen expendiures,, EH h, EXR FBOR i, i, ch consumpion spending for household exchange rae (LCU per uni of QINA a, FCU) foreign borrowing for domesic insiuion i QHA ach,,, QIN ca,, FDEB foreign deb for domesic ins i QINV c, FDEBRED i, FDEBSCAL redefined foreign deb sock for household i scaling facor for foreign deb socks o mee aggregae consrain scaling facor for consrain on oal facor sock quaniy of governmen consumpion of commodiy c quaniy consumed by household h of markeed commodiy c quaniy consumed of home commodiy c from ac a by hhd h quaniy of aggregae inermediae inpu used by aciviy a quaniy of commodiy c as inermediae inpu o aciviy a quaniy of invesmen demand for commodiy c QM c, quaniy of impors of commodiy c QQ c, quaniy of goods supplied o domesic marke (composie supply) 24