1

Core methodology II: Core methodology II:

MAMS: Basic features, MDG block, MAMS: Basic features, MDG block, dynamics and closure rulesdynamics and closure rules

Marco V. SanchezMarco V. Sanchez

(UN(UN--DESA/DPAD)DESA/DPAD)

Presentation prepared for the inception and training workshop ofPresentation prepared for the inception and training workshop ofthe project the project ““Assessing Development Strategies to Achieve the Assessing Development Strategies to Achieve the MDGs in Asia and the Pacific, Bangkok, 20MDGs in Asia and the Pacific, Bangkok, 20--22 August, 2008.22 August, 2008.

UNDP UNUNDP UN--DESA UNDESA UN--ESCAPESCAP

1. MAMS: What? Who?•• MAMS = MAMS = MaMaquettequette for for MMdg dg SSimulationsimulations•• DynamicDynamic--recursive CGE (Computable General Equilibrium) model, recursive CGE (Computable General Equilibrium) model,

extended to link government services and MDG and education extended to link government services and MDG and education outcomesoutcomes

•• A SAM (Social Accounting Matrix) defines accounting consistency A SAM (Social Accounting Matrix) defines accounting consistency and organizes much of database of MAMS.and organizes much of database of MAMS.

•• Initially developed at the World Bank to analyze MDG strategies Initially developed at the World Bank to analyze MDG strategies (Ethiopia)(Ethiopia)

•• Development of model evolved as lessons were learned from Development of model evolved as lessons were learned from application to 19 Latin American and Caribbean countries in application to 19 Latin American and Caribbean countries in UNDP/UNUNDP/UN--DESA/World Bank project.DESA/World Bank project.

•• For more details, see Lofgren Hans and Carolina DiazFor more details, see Lofgren Hans and Carolina Diaz--Bonilla Bonilla (2008) (2008) ““MAMS: An EconomyMAMS: An Economy--wide Model for Analysis of MDG wide Model for Analysis of MDG Country Strategies Country Strategies –– an application to Latin America and the an application to Latin America and the Caribbean.Caribbean.”” Forthcoming as chapter 3 of a volume on Forthcoming as chapter 3 of a volume on Public Public Policies for Human Development. Feasible Financing Strategies foPolicies for Human Development. Feasible Financing Strategies for r Achieving the Achieving the MDGsMDGs in Latin America and the Caribbeanin Latin America and the Caribbean, edited by , edited by Rob Rob VosVos, Enrique , Enrique GanuzaGanuza, Hans Lofgren, Marco V. , Hans Lofgren, Marco V. SSááncheznchez, and , and Carolina DiazCarolina Diaz--Bonilla. The study reflects outcomes of a joint project Bonilla. The study reflects outcomes of a joint project of UNDP, UN/DESA, UN/ECLAC and the World Bank. of UNDP, UN/DESA, UN/ECLAC and the World Bank.

2. Model Structure2. Model Structure

A.A. ““StandardStandard”” CGE modelCGE modelB.B. DynamicDynamic--recursive modulerecursive moduleC.C. MDG Module: Education outcomes and other MDG Module: Education outcomes and other

MDGsMDGsD.D. Macroeconomic closure rules and factor Macroeconomic closure rules and factor

market adjustmentmarket adjustment

A. A. ““StandardStandard”” CGE modelCGE model•• Not really a Not really a ““standardstandard”” model, but one often used model, but one often used developed at developed at

IFPRI based on conventional practices in trade policy modelling IFPRI based on conventional practices in trade policy modelling ((Dervis Dervis et al., et al., 1982; Robinson, 1989; Lofgren 1982; Robinson, 1989; Lofgren et al.et al., 2002). , 2002).

•• A A ““standardstandard”” CGE model CGE model provides the starting point (baseprovides the starting point (base--year year solution) and withinsolution) and within--period solutions (for all years).period solutions (for all years).–– Computable Computable system of multiple equations solvable system of multiple equations solvable

numericallynumerically–– General General economyeconomy--widewide–– Equilibrium Equilibrium

•• optimizing agents find their best solutions subject to their optimizing agents find their best solutions subject to their budget constraintsbudget constraints

•• macroeconomic balance through alternative closure rulesmacroeconomic balance through alternative closure rules•• quantities demanded = quantities supplied in factor and quantities demanded = quantities supplied in factor and

commodity marketscommodity markets•• neoneo--classical in many ways, but many classical in many ways, but many ““structuraliststructuralist”” featuresfeatures

–– A A ““realreal”” model: only relative prices matter; no explicit modelling model: only relative prices matter; no explicit modelling of inflation or the monetary sector.of inflation or the monetary sector.

Aggregate payments in CGE framework

Activities

Com’ty Markets

Factor Markets

Rest of the World

Households Government Sav./Inv.

FactorCosts

Wages& Rents

IntermediateInput Cost

DomesticSales

PrivateConsumption

Taxes

Domestic Private Savings

GovernmentConsumption

Gov. Savings

InvestmentDemand

ImportsExports Foreign Savings

Transfers

Foreign Transfers

B. DynamicB. Dynamic--recursive modulerecursive module•• DynamicDynamic--recursive recursive the solution in any time period depends on the solution in any time period depends on

current and past periods, not the future.current and past periods, not the future.–– Static moduleStatic module: : ““StandardStandard”” CGE model provides withinCGE model provides within--period period

equilibrium solutionsequilibrium solutions•• Initial SAM values are replicated for first withinInitial SAM values are replicated for first within--period period

equilibrium solution (that is, the base year).equilibrium solution (that is, the base year).•• New New SAMsSAMs are generated via following withinare generated via following within--period period

equilibrium solutions equilibrium solutions –– Dynamic moduleDynamic module: takes the immediate past within: takes the immediate past within--period period

equilibrium solution as given and provides a new withinequilibrium solution as given and provides a new within--period period equilibrium solution. equilibrium solution. •• InterInter--temporal linkages established through lagged variables temporal linkages established through lagged variables

and updating exogenous variables and parameters that are and updating exogenous variables and parameters that are either fixed or absent in the baseeither fixed or absent in the base--year solution.year solution.

–– This dynamicThis dynamic--recursive adjustment is solved recursively from the recursive adjustment is solved recursively from the base year to 2015 (or even longer if needed).base year to 2015 (or even longer if needed).

DynamicsDynamics•• Updating of stocks of factors and debtsUpdating of stocks of factors and debts

–– exogenous population growth and factor depreciation ratesexogenous population growth and factor depreciation rates–– endogenous for different types of labor (see later) and capital,endogenous for different types of labor (see later) and capital, and and

exogenous for other factors (i.e. land if available)exogenous for other factors (i.e. land if available)–– endogenous for domestic and foreign debts (depending on endogenous for domestic and foreign debts (depending on

closure rules!; see later)closure rules!; see later)•• TFP (Total Factor Productivity)TFP (Total Factor Productivity)

–– endogenous part depends on tradeendogenous part depends on trade--toto--GDP ratio and growth in GDP ratio and growth in government infrastructure stocksgovernment infrastructure stocks

–– exogenous part captures what is not explained in model (more exogenous part captures what is not explained in model (more skilled labor in the long run, beyond 2015; institutions, new skilled labor in the long run, beyond 2015; institutions, new technologies, and so on)technologies, and so on)

–– it can be adapted if empirical evidence is availableit can be adapted if empirical evidence is available•• GDP growth is determined by: GDP growth is determined by:

–– growth in economygrowth in economy--wide TFP wide TFP –– growth in factor employment (mostly endogenous)growth in factor employment (mostly endogenous)

C. MDG moduleC. MDG module

•• DynamicDynamic--recursive model is extended to capture the recursive model is extended to capture the generation of MDG outcomes.generation of MDG outcomes.–– MDG 1: poverty (partly modelled outside of MAMS)MDG 1: poverty (partly modelled outside of MAMS)–– MDG 2: primary school completionMDG 2: primary school completion–– MDG 4: underMDG 4: under--five mortality ratefive mortality rate–– MDG 5: maternal mortality rateMDG 5: maternal mortality rate–– MDG 7a: water accessMDG 7a: water access–– MDG 7b: sanitation accessMDG 7b: sanitation access

•• Inclusion of (MDGInclusion of (MDG--related) related) social servicessocial services and their and their impact on the rest of the economy impact on the rest of the economy →→ key addition to key addition to ““standardstandard””, dynamic CGE framework., dynamic CGE framework.

•• Social servicesSocial services may be produced by the government may be produced by the government and the private sector.and the private sector.

Social service deliverySocial service delivery•• Social servicesSocial services (education, health, water & sanitation) are (education, health, water & sanitation) are

produced using labor, capital, and intermediates produced using labor, capital, and intermediates –– fixed coefficients for capital, intermediate inputs, and fixed coefficients for capital, intermediate inputs, and

aggregate laboraggregate labor–– flexible coefficients for disaggregated laborflexible coefficients for disaggregated labor

•• Private providers are assumed to be Private providers are assumed to be ““profit maximizersprofit maximizers””•• Government demand (consumption and investment) is Government demand (consumption and investment) is

classified by function: classified by function: social servicessocial services, other infrastructure , other infrastructure and other government servicesand other government services Key policy tool under Key policy tool under government controlgovernment control

•• Government spending is financed by domestic taxes, Government spending is financed by domestic taxes, domestic borrowing, foreign borrowing, and foreign grantsdomestic borrowing, foreign borrowing, and foreign grants

financing is the other key policy tool under government financing is the other key policy tool under government control. See closure rules nextcontrol. See closure rules next

•• Model tracks government domestic and foreign debt stocks Model tracks government domestic and foreign debt stocks (including foreign debt relief) and related interest payments.(including foreign debt relief) and related interest payments.

Government recurrent revenue

, ,

,

, ; , ;, , ; , , ;

, , ; , ;

,

h h a a a a a

c c c c c c

c c c gov row gov,f

direct tax actrates,

household incomes

government

revenue

TINS YI ta tva ,PA PVA QAYG f tm pwm QM te pwe QE

tq PQ QQ trnsfr EXR YIF

= f

⎛ ⎞⎜ ⎟

= ⎜ ⎟⎜ ⎟⎝ ⎠

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦

,

ivity and VA tax rates, activity and VA prices, activity levels

import tariff export tax rates, import rates, export prices (FCU), prices (FCU),

import quantities export quantities

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤ ⎡⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

, ,sales tax transfers from government

rates, composite rest of world incomesupply prices (FCU), from and quantities exchange rate factor f

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥⎢⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦

⎥⎥⎥⎥

Government recurrent expenditures

,, ; ;

, ;,

c c h gov

h h

gov gov

=f

government trans-consumption fers to

govern- of c, house-ment price of c holds

recurrentexpen-diture

PQ QG trnsfr

EG f dintrat GDEBTfintrat , FDEBT EXR

+

⎛ ⎞⎜ ⎟

= ⎜ ⎟⎜ ⎟⎝ ⎠

⎡ ⎤ ⎡⎢ ⎥

⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎣ ⎦ ⎣⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

interest on domestic and foreign debt: debtlevels and interestrates; exchange rate

+

⎡ ⎤⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎦⎢ ⎥⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦

Real government consumption demand

( ),, , 1- -- -

--1

,

,

c tc t c t

govern govern growth in ment con ment con government

= fsumption sumption consump of c in t of c in t tion of c in t

QG f QG GRWQG−=

⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦

Important! Important! →→ in a baseline scenario, MAMS in a baseline scenario, MAMS assumes that growth in government assumes that growth in government consumption by commodity is fixed consumption by commodity is fixed –– it it becomes a tool to ensure that becomes a tool to ensure that ““business business stays as usualstays as usual””

Government savings

govern-govern-govern ment re-ment re-ment currentcurrentsavings expen-revenue ditures

GSAV YG EG

= −

= −

⎡ ⎤⎡ ⎤⎡ ⎤ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦

Government investment demand

,

, ,, , ,

,, 1

- + :

fcap agov

gov fcap tgov fcap t agov t

fcap tagov t

government expected government deminvestment and for fcap in t 1 demand in t capi

for capital fcap

ifaQFINS

DKINS f QAdepr

QA −

⎛ ⎞⎛ ⎞⎜ ⎟

= − ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎜ ⎟

⎝ ⎠

⎡ ⎤⎢ ⎥ =⎢ ⎥⎣ ⎦

- ; - -

governmentstock of fcap

tal input coefficient, in t depactivity level in t and t 1 reciation rate

⎡ ⎤⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥ −⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦

Price of new capital stock

( ), ;

,

fcap c fcap c

quantities of price of prices

commodities new cap- of com-

c per unit of ital stock modities

new capital fcap c

stock f

f

PK f capcomp PQ

=

=

⎡⎡ ⎤ ⎤⎡ ⎤ ⎡ ⎤⎢⎢ ⎥ ⎥⎢ ⎥ ⎢ ⎥⎢⎢ ⎥ ⎥⎢ ⎥ ⎢ ⎥⎢⎢ ⎥ ⎥⎣ ⎦ ⎣ ⎦⎣⎣ ⎦ ⎦

Government investment value

, , , , , ,f t gov f t t c t c gov t tf FCAPGOV c C

government fixed government spending on total change in holdings investment value savings stock changes of government bonds

PK DKINS GSAV PQ qdst GBORTOT∈ ∈

= − +

⋅ = − ⋅ +

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣

∑ ∑

( ), , tt gov t gov tGovernment Central Bank foreign borrowing and

borrowing (deficit monetization) foreign grants (in LCU)

GBORMSTOT FBOR FGRANT EXR

+ +

⎤⎦

+ + + ⋅

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

Non-government investment value

[ ]

( )

, , , , , ,

, ,, ,

i t i t c t c i t i tc C

i t i ti t i t t

non-government fixed stock change in holdings ofsavings

investment value changes government bonds

Gove

INVVAL INSSAV PQ qdst GBOR

GBORMS FBOR FGRANT fdi EXR

∈

= − −

−

= − ⋅ −

− + + + ⋅

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ ⎣ ⎦

∑

rnment Central foreign borrowing, grants, Bank borrowing and direct investment (in LCU)

+⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦

Investment demand by commodity (investment by origin or source)

,, ,

;c fcapc

gov fcap insng fcap

invest- quantities of gross investmentsment commodities c in c

demand per unit of for com- new capital modity c stock fcap

f

capcompQINV f

DKINS , DKINS

,=

⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

apital stocks fcap by government

and non-govern-ment institutions

⎡ ⎡ ⎤⎤⎢ ⎢ ⎥⎥⎢ ⎢ ⎥⎥⎢ ⎢ ⎥⎥⎣ ⎣ ⎦⎦

MDG MDG ““productionproduction””

•• Together with other Together with other determinantsdeterminants, government social , government social services determine the "production" of MDGservices determine the "production" of MDG--related related services.services.

•• DeterminantsDeterminants: What does it take to get all children in : What does it take to get all children in school? What factors influence child and maternal school? What factors influence child and maternal mortality, on the one hand, and water & sanitation mortality, on the one hand, and water & sanitation coverage, on the other? What interdependencies between coverage, on the other? What interdependencies between MDG achievements and other public infrastructure? Etc.MDG achievements and other public infrastructure? Etc.

•• See separate presentationSee separate presentation

Determinants of MDG outcomes (reduced form)Determinants of MDG outcomes (reduced form)

44XXXXXXXX22––Primary Primary schoolingschooling

7a,7b7a,7bXXXXXX44--UnderUnder--fivefivemortalitymortality

7a,7b7a,7bXXXXXX55--Maternal Maternal mortalitymortality

XXXXXX7a7a--WaterWater

XXXXXX7b7b--SanitationSanitation

Other Other MDGsMDGs

Public Public infrainfra--

structurestructure

WageWageincenincen--tivestives

ConsumpConsump--tion pertion percapitacapita

ServiceServiceper capita per capita or studentor student

MDGMDG

MDG MDG ““productionproduction””•• MDGsMDGs are modelled as being are modelled as being ““producedproduced”” by a combination by a combination

of determinants (table in previous slide) using a (reduced) of determinants (table in previous slide) using a (reduced) functional form that permits:functional form that permits:–– Imposition of limits (maximum or minimum) given by Imposition of limits (maximum or minimum) given by

logic or country experienceslogic or country experiences–– Replication of baseReplication of base--year values and year values and elasticitieselasticities–– Calibration of a reference time path for achieving Calibration of a reference time path for achieving MDGsMDGs–– Diminishing marginal returns to the inputsDiminishing marginal returns to the inputs

•• TwoTwo--level function: level function: 1.1. ConstantConstant--elasticity (CE) function at the bottom of nest: Z elasticity (CE) function at the bottom of nest: Z

= = f(Xf(X))2.2. Logistic function at the top of nest: MDG = Logistic function at the top of nest: MDG = g(Zg(Z))

EducationEducation•• Service measured per student in each teaching cycle Service measured per student in each teaching cycle

(primary, secondary, tertiary)(primary, secondary, tertiary)

•• Model tracks evolution of enrollment in each cycleModel tracks evolution of enrollment in each cycle

•• Educational outcomes as functions of a set of determinants: Educational outcomes as functions of a set of determinants:

–– for each cycle for each cycle →→ rates of entry, pass, repeat, and drop rates of entry, pass, repeat, and drop outout

–– between cycles between cycles →→ share that continuesshare that continues

•• MDG 2 computed as product of 1MDG 2 computed as product of 1stst grade entry rate and grade entry rate and primary cycle pass rates for the relevant series of years for primary cycle pass rates for the relevant series of years for the cyclethe cycle

–– net primary completion rate rather than just the enrolment net primary completion rate rather than just the enrolment raterate

–– it makes MDG 2 more difficult to achieveit makes MDG 2 more difficult to achieve

Educational quality

( )-

;

,

cedu cedu cedu

real enrollindex of educational f services in ment inquality at cycle cedu cycle cedu cycle cedu

EDUQUAL f QQ QENR

=

=

⎡ ⎤⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦

Enrollment by cycle (level)

( ),

, 1 , , 1

', 1 , , 1

, , 1

:

, ,

, ,

, cedu t

educedu t behav cedu t

educedu t behav cedu t

edubehav cedu t t

continuing old students e

enrollmentin cycle fceduin t

QENR f

QENR SHR

QENR SHR

SHR popg1

− −

− −

−

−

=

=

⎛ ⎞⎜ ⎟⎜ ⎟⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

- -

)

: ' - ;

- (

nrollment in cedu in t 1;student behavior in t 1 (shares that repeat or pass continue in cedu

new students in cedu in t enrollmentin preceding cycle cedu in t 1student behavior in t 1

+

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

+

shares thatgraduate continue to cedu) and in t (share of cohort entering 1st grade)

+

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦

CE function: student behavior (bottom of nest)

, 4

-

;

; ;

; ;cedu flab

behav cedu mdg

fcapgovinf

intermediate variable forshare of students or population with behavior behav (pass, enter from previous cycle newentrant

EDUQUAL WF

ZEDU CE QHPC MDGVAL

QFINS

⎛ ⎞⎜ ⎟

= ⎜ ⎟⎜ ⎟⎝ ⎠

; - -

;

[ -])

education quality; wage incentivesper capita household consumptionstudent health (proxied by MDG4);

only for prim infrastructure capital stockary for cycle cedu

CE

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ = ⎢⎢ ⎥ ⎢⎢ ⎥ ⎢⎢ ⎥ ⎢⎣ ⎦⎣ ⎦

⎥⎥⎥⎥

MDG determinants

( )

,

, ,

, , , ,

, ,

, , , ,

, ,

, ,

, ,

b c edu qual

b c w prem b c w prem

b c mdg4mdg4 t

edu

b c t b c c t

edu edu

f labs t f labt t

f labn t f labs t

edu

i f ti INS

edu

educeZEDU

WF WFMDGVAL

WF WF

QFINS

EDUQUAL

ϕ

ϕ

ϕ ϕϕ

α −

− −

− −

− −

∈

⋅

= ⋅

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞⎜ ⎟⎝ ⎠

⋅ ⋅ ⋅

∑, ,

, ,

=

:

b c f

b c qhpcedut

f FCAPGOVINF

intermediate variable for student share with behavior b in cycle c

influence of education quality (service pexogenoustrend value

QHPCϕ∈

⋅

⋅

⎡ ⎤⎣ ⎦

⎡ ⎤⎣ ⎦

∏

)-

-

er student); wage premia (for c secondary and c tertiary, resp. ;student health (proxied by MDG4); level of infrastructure; and per capita household consumption

≤ ≥⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦

Logistic function: student behavior (top of nest)

( ), , -

; [ ])

behav cedu behav cedu

share of students or popintermediate

ulation with behavior behav behavi

(pass, enter from previous LOGcycle new entrant only forprimary for cycle cedu

SHREDU LOG ZEDU

=

=

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ,behav cedu

or variable ZEDU

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

( )

( ), ,

,, , ,

, , , ,1

b c t

b cb c t b c

b c b c b c t

edued

edu edu

logistic function of intermediatestudent share with behavior variable ZEDUbehavior b in cycle c

SHREDU extEXP ZEDU

αγ β

=

= ++ + ⋅

⎡ ⎤⎡ ⎤⎢ ⎥⎣ ⎦ ⎣ ⎦

Student behaviour logistic functionStudent behaviour logistic function

-- αα and and ββ are constant parameters calibrated so thatare constant parameters calibrated so that-- under baseunder base--year conditions, the leftyear conditions, the left--hand side variables will hand side variables will replicate basereplicate base--year valuesyear values-- under conditions derived from supporting studies, the leftunder conditions derived from supporting studies, the left--hand hand side variables will take on values indicative of or compatible wside variables will take on values indicative of or compatible with ith MDG achievementMDG achievement

-- γγ determines distance of inflection point (where the curve switchdetermines distance of inflection point (where the curve switches es from increasing to decreasing marginal returns) from basefrom increasing to decreasing marginal returns) from base--year pointyear point--extedextedb,cb,c: : extreme (max or min) value to which the behavioural share extreme (max or min) value to which the behavioural share should converge as the value of should converge as the value of ZEDUZEDU approaches infiniteapproaches infinite

-- for example, 100% for MDG 2for example, 100% for MDG 2

Advantages of the logistic functionAdvantages of the logistic function

•• It makes it possible to impose extreme values for It makes it possible to impose extreme values for the function and to incorporate extraneous the function and to incorporate extraneous information about information about elasticitieselasticities and conditions and conditions under which target values are achieved.under which target values are achieved.

•• It allows for segments of increasing and It allows for segments of increasing and decreasing marginal returns to improvements in decreasing marginal returns to improvements in the determinates of educational behaviour (or the determinates of educational behaviour (or health or W&S for the other health or W&S for the other MDGsMDGs; as explained ; as explained next).next).

Example: Logistic student behavior

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8

ZEDU

SHR

EDU

(pas

s,pr

imar

y)

Student behavior: residual indicatorsStudent behavior: residual indicators

( ), ',

-

behav cedu behav cedu

shares w ith student share w ith related residual behavior behav (repeater,dropout, exiting graduate, passing student continuing w ithin cycle) in cedu

SH RED U f SH RED U

f

=

⎡ ⎤⎢ ⎥⎢ ⎥

=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

behavior behav' (passing, graduate w ho continues tonext cycle, passing student graduatingfrom cycle)

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

ZEDU and SHREDU are first defined for students with ZEDU and SHREDU are first defined for students with behaviour passing, entering cycle, and entering the system. behaviour passing, entering cycle, and entering the system. How about the other types of behaviour?How about the other types of behaviour?

Relationships that Relationships that MUSTMUST hold:hold:•• (1) rep + dropout + grd = 1 (for each cycle (1) rep + dropout + grd = 1 (for each cycle -- and for each grade and for each grade

within each cycle)within each cycle)–– each student in each grade for each cycle has 1 of 3 options: each student in each grade for each cycle has 1 of 3 options:

repeat, dropout, or graduaterepeat, dropout, or graduate

•• (2) grd = grdcyc + contcyc(2) grd = grdcyc + contcyc–– graduates from any grade in any cycle are allocated between graduates from any grade in any cycle are allocated between

two options: 'grdcyc' (graduates from last grade) or 'contcyc' two options: 'grdcyc' (graduates from last grade) or 'contcyc' (graduates from grades other than the last). (graduates from grades other than the last).

•• Simplifying assumption: the share of 'grdcyc' in the total numbeSimplifying assumption: the share of 'grdcyc' in the total number of r of graduates is equal to the share of the last year in the total nugraduates is equal to the share of the last year in the total number of mber of years in the cycle. This could be refined.years in the cycle. This could be refined.–– given (2) can rewrite (1) as: rep + dropout + (grdcyc + contcycgiven (2) can rewrite (1) as: rep + dropout + (grdcyc + contcyc) )

= 1= 1

•• (3) grdcont + grdexit = 1 (for each cycle)(3) grdcont + grdexit = 1 (for each cycle)–– graduates from any graduates from any cycle cycle have two options: either continue to have two options: either continue to

next cycle or exit the school systemnext cycle or exit the school system

MDG 2: primary school completionMDG 2: primary school completion

( ), , , '-

mdg2 t behav cedu t

primary shares for 1st school net grade entry and = PRODcompletion pass for relevant rate in t preceding years t'

MDGVAL PROD SHREDU=

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

Once all shares (Once all shares (SHREDUsSHREDUs) have been calculated for the ) have been calculated for the primary cycle, MAMS computes the value for MDG 2primary cycle, MAMS computes the value for MDG 2

Education behaviour feeds back into the Education behaviour feeds back into the labour marketlabour market

, ;

, h flab

cedu

labor force labor force; population particip in labor force age not ation rate enrolled in school

QFINS

labpartrat f poplabQENR

f−

⎛ ⎞⎜ ⎟

= ⎜ ⎟⎜ ⎟⎝ ⎠⎡ ⎤⎡ ⎤ = ⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦

Labour endowment by type

, ,

, ,, , 1

,,

,

- -

-

,,

, ,h flab tbehav cedu t

h flab tcedu t

flab tflab t

endow endowment ment of labor in t 1,flab for household h in t

QFINS f

SHREDUQFINS

shrlabentDEPR

shrlabent2

f

−=

⎛ ⎞⎛ ⎞⎜ ⎟⎛ ⎞ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎡ ⎤⎢ ⎥

=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

:

- -

,

new entrantseducational behavior (shares graduating from cycle and exiting, dropping out); labor rate of force entry shares (amongretire students and non students ment reaching labor a

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ge)

⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦

Other MDG indicators(bottom of nest)

- --

, ;

;

cmdg

mdgmdg

fcapgovinf

inter service level, total populmediate ation; per capita variable household consumpfor MDG indicator (4, 5, 7a or 7b)

CE

QQ poptot

QHPCZMDG CE

MDGVAL

QFINS

⎛ ⎞⎜ ⎟⎜ ⎟= ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

⎡ ⎤⎢ ⎥

=⎢ ⎥⎢ ⎥⎣ ⎦

tion; other MDG indicators (7a and 7b influencing 4 and 5); infrastructure capital stock

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

,

,

, '

,,

, ,

|( , )

','

mdg cmdg

mdg f

mdg mdg

c tmdg t mdg

t

m

i f ti INSf FCAPGOVINF

m

c Ccmdg CMDGcmdg c MCM

mmdg t

mdg MDGSTD

mceQQ

poptot

QFINS

ZMDG

MDGVAL

ϕ

ϕ

ϕ

α

∈∈

∈∈∈

∈

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞⋅ ⎜ ⎟

⎝ ⎠

⎛ ⎞⎜⎜⎝

= ⋅

⋅

∑∏

∑∏

∏ ," "

:

;

mdg hhdconspcmt

influence of real value for services per capita; intermediate variable exogenous

level of infrastructure; water and sanitation MDGsfor MDGs 4 and 5 parameter

househo

QHPCϕ

= ⋅

⋅⎟⎟⎠

⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ ld consumption per capita

⎡ ⎤⎢ ⎥⎣ ⎦

Other MDG indicators (top of nest)

( )--

mdg mdg

value for MDG inter(4 = under five mortality rate; mediate5 = maternal mortality rate; LOG behavior 7 = share of population with variaaccess to basic water and sanitation

MDGVAL LOG ZMDG

=

=

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ mdg

ble ZMDG

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

( )

( )

,

,

,1

mdg

mdg mdg mdg t

mdg t

mdg t mdg

logistic function of intermediateMDG MDG value value

mdg

EXP

ZMDG

mdgmdg

MDGVALmdg ZMDG

extα

βγ

=

++

⋅=

⎡ ⎤⎡ ⎤⎣ ⎦ ⎣ ⎦

+

•• αα,, ββ, and , and γγ as already defined (for MDG 2).as already defined (for MDG 2).•• extmdgextmdg: : extreme (max or min) value to which the extreme (max or min) value to which the

behavioural share should converge as the value of behavioural share should converge as the value of ZMDGZMDG approaches infiniteapproaches infinite

-- international extreme values (MDGs 4&5) or international extreme values (MDGs 4&5) or physical extreme values (MDGs 7a&7b): e.g., physical extreme values (MDGs 7a&7b): e.g., minimum values for health MDGs (4&5) from minimum values for health MDGs (4&5) from NorwayNorway

D. Macro closures and market D. Macro closures and market clearing rulesclearing rules

•• Macro closuresMacro closures: mechanisms for clearing : mechanisms for clearing (assuring that receipts = outlays) of:(assuring that receipts = outlays) of:

1.1. Balance of Payments Balance of Payments →→ real exchange ratereal exchange rate2.2. SavingsSavings--Investment Balance Investment Balance →→ private private

investmentinvestment3.3. Government budget Government budget →→ next slidenext slide

•• Labour market clearing mechanismsLabour market clearing mechanisms(below)(below)

Government ClosuresGovernment Closures

•• The selection of variable clearing for the The selection of variable clearing for the government budget is an important part of the government budget is an important part of the BAU scenario and many counterfactual BAU scenario and many counterfactual scenariosscenarios

•• Common options:Common options:–– domestic tax rates (with options)domestic tax rates (with options)–– foreign grantsforeign grants–– domestic borrowing (government bonds or via domestic borrowing (government bonds or via

deficit monetization)deficit monetization)–– foreign borrowingforeign borrowing

Government recurrent revenue

, ,

,

, ; , ;, , ; , , ;

, , ; , ;

,

h h a a a a a

c c c c c c

c c c gov row gov,f

direct tax actrates,

household incomes

government

revenue

TINS YI ta tva ,PA PVA QAYG f tm pwm QM te pwe QE

tq PQ QQ trnsfr EXR YIF

= f

⎛ ⎞⎜ ⎟

= ⎜ ⎟⎜ ⎟⎝ ⎠

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦

,

ivity and VA tax rates, activity

and VA prices, activity levels

import tariff export tax rates, import rates, export prices (FCU), prices (FCU),

import quantities export quantities

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤ ⎡⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

, ,sales tax transfers from government

rates, composite rest of world incomesupply prices (FCU), from and quantities exchange rate factor f

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥⎢⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦

⎥⎥⎥⎥

Government investment value

, , , , , ,f t gov f t t c t c gov t tf FCAPGOV c C

government fixed government spending on total change in holdings investment value savings stock changes of government bonds

PK DKINS GSAV PQ qdst GBORTOT∈ ∈

= − +

⋅ = − ⋅ +

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣

∑ ∑

( ), , tt gov t gov tGovernment Central Bank foreign borrowing and

borrowing (deficit monetization) foreign grants (in LCU)

GBORMSTOT FBOR FGRANT EXR

+ +

⎤⎦

+ + + ⋅

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

FactorFactor--market clearingmarket clearing

•• Factors. Two alternatives:Factors. Two alternatives:1.1. exogenous unemployment: wage clearsexogenous unemployment: wage clears2.2. endogenous unemployment. Two regimes:endogenous unemployment. Two regimes:

•• unemployment above minimum rate: unemployment above minimum rate: unemployment rate clears (influencing reservation unemployment rate clears (influencing reservation and market wage)and market wage)

•• unemployment at minimum rate (= full unemployment at minimum rate (= full employment): wage clearsemployment): wage clears

( ), ,1f a f i fa A i INS

total quantity 1 - unem- sum of all employed ployment institutional en-of factor f rate dowments of f

QF UERAT QFINS∈ ∈

= − ⋅

⎡ ⎤ ⎡ ⎤ ⎡ ⎤= ⋅⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

∑ ∑

Equilibrium condition

Factor market with endogenous unemploymentFactor market with endogenous unemployment

0

1

2

3

4

5

85 90 95

100 - unemployment rate (%)

Wag

e SupplyDemand

UpwardUpward--sloping sloping →→ workers request higher wages workers request higher wages as the labor market gets tighter, but the as the labor market gets tighter, but the unemployment rate clears the market and a unemployment rate clears the market and a reservation wage is paidreservation wage is paid

Full employment Full employment (at the minimum (at the minimum unemployment rate unemployment rate of 5%), wages clear of 5%), wages clear the marketthe market

Reservation wage

( )- - -

-

, ,

, ,

f f

reserv unem conhouseholdation ployment sumerper capita rate for pricewage for consumption factor f indexfactor f

WFRES f QHPC UERAT CPI

f

=

⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥= ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦⎣ ⎦

Complementary slackness relation for wages and unemployment (constraints)

f f

f f

reservationwage for

wage forfactor f

factor f

unemploy minimum ment rate unemployment for factor f rate for factor f

WF WFRES

UERAT ueratmin

−

≥

⎡ ⎤⎡ ⎤ ≥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦

≥

⎡ ⎤ ⎡ ⎤≥⎢ ⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

( )( ) 0

f f

f f

Complementary slackness relationship:1. If wage > reservation wage, then unemployment rate = its minimum.2. If unemployment rate > its minimum, then wage = res

WF WFRES

UERAT ueratmin

− ⋅

− =

ervation wage.

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

3. Scenario analysis in MAMS3. Scenario analysis in MAMS•• BusinessBusiness--asas--usual scenario:usual scenario:

–– Purpose: a plausible benchmark for comparisonsPurpose: a plausible benchmark for comparisons–– GDP growth and government consumption calibrated to trend GDP growth and government consumption calibrated to trend

from last 5from last 5--15 years;15 years;•• government spending is fixed.government spending is fixed.

–– Balanced and sustainable evolution of macro aggregates; many Balanced and sustainable evolution of macro aggregates; many of which may have unchanged GDP shares. of which may have unchanged GDP shares.

–– MDG targets may not necessarily be achieved.MDG targets may not necessarily be achieved.•• MDG indicators are flexible.MDG indicators are flexible.•• Is the country Is the country ““on trackon track”” under current policies?under current policies?

•• Alternative (counterAlternative (counter--factual) scenarios:factual) scenarios:–– Change one or more parameters (policy tools or parameters Change one or more parameters (policy tools or parameters

beyond government control, e.g. aid, world prices, productivity)beyond government control, e.g. aid, world prices, productivity)..–– MDG scenariosMDG scenarios: an indicator that represents a policy target is : an indicator that represents a policy target is

fixed (ex: a health MDG) and a policy tool (ex: government fixed (ex: a health MDG) and a policy tool (ex: government health services) becomes flexible.health services) becomes flexible.

•• MDG targets are achieved assuming unlimited government MDG targets are achieved assuming unlimited government spending and financing through alternative mechanisms.spending and financing through alternative mechanisms.

Argentina: Government consumption

0

100

200

300

400

500

600

700

800

900

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

BAU scenario MDG scenario

Argentina: MDG 2 (primary completion rate)

50

60

70

80

90

100

110

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

Target BAU scenario MDG scenario

4. Concluding remarks4. Concluding remarks

•• MAMS has evolved into a flexible framework for MAMS has evolved into a flexible framework for analysis of public policy in the mediumanalysis of public policy in the medium-- to longto long--run: run: –– Aggregated versions with limited data needs can be Aggregated versions with limited data needs can be

used for simple macro analysisused for simple macro analysis–– Disaggregated version with stronger data demands Disaggregated version with stronger data demands

can address a wider range of issues relevant to can address a wider range of issues relevant to development strategies, including human development strategies, including human development and the MDGs in particular.development and the MDGs in particular.

•• Some caveats need to be considered, though.Some caveats need to be considered, though.

4. Concluding remarks4. Concluding remarks

•• MAMS gives stylized picture of economy, but, as MAMS gives stylized picture of economy, but, as with any model, the results are sensitive to with any model, the results are sensitive to model assumptions and parameter estimatesmodel assumptions and parameter estimates

•• Always imperfect instrument, but provides Always imperfect instrument, but provides integrated and consistent pictureintegrated and consistent picture–– Better costing instrumentBetter costing instrument–– Improved identification of Improved identification of ““on trackon track”” vs. vs. ““off trackoff track””–– Link macroeconomic and social policiesLink macroeconomic and social policies

•• Need to avoid its use as Need to avoid its use as ““black boxblack box””, but see as , but see as instrument to help policy dialogueinstrument to help policy dialogue

Key referencesKey references•• Dervis, K., J. de Melo and S. Robinson (1982), Dervis, K., J. de Melo and S. Robinson (1982), General equilibrium General equilibrium

models for development policymodels for development policy. Cambridge: Cambridge University . Cambridge: Cambridge University Press.Press.

•• Lofgren, Hans and Carolina DiazLofgren, Hans and Carolina Diaz--Bonilla (2008, forthcoming), Bonilla (2008, forthcoming), ““MAMS: An economyMAMS: An economy--wide model for the analysis of MDG country wide model for the analysis of MDG country strategies strategies –– An application to Latin America and the CaribbeanAn application to Latin America and the Caribbean””, in: , in: Vos, Rob, Enrique Ganuza, Hans Lofgren, Marco V. Sanchez and Vos, Rob, Enrique Ganuza, Hans Lofgren, Marco V. Sanchez and Carolina DiazCarolina Diaz--BonillaBonilla (eds) (eds) Public Policies for Human Development. Public Policies for Human Development. Feasible Financing Strategies for Achieving the MDGs in Latin Feasible Financing Strategies for Achieving the MDGs in Latin America and the CaribbeanAmerica and the Caribbean, New York and Washington, D.C.: , New York and Washington, D.C.: UNDP, UN/DESA, World Bank, and UNUNDP, UN/DESA, World Bank, and UN--ECLAC (forthcoming).ECLAC (forthcoming).

•• Lofgren, Hans, Rebecca Lee Harris, and Sherman Robinson, with Lofgren, Hans, Rebecca Lee Harris, and Sherman Robinson, with assistance from Moataz Elassistance from Moataz El--Said and Marcelle Thomas (2002), Said and Marcelle Thomas (2002), A A Standard Computable General Equilibrium (CGE) Model in GAMSStandard Computable General Equilibrium (CGE) Model in GAMS. . Microcomputers in Policy Research, Vol. 5. Washington, D.C.: IFPMicrocomputers in Policy Research, Vol. 5. Washington, D.C.: IFPRI RI ((http://www.ifpri.org/pubs/microcom/micro5.htmhttp://www.ifpri.org/pubs/microcom/micro5.htm).).

•• Robinson, S. (1989) Robinson, S. (1989) ‘‘Multisector ModelsMultisector Models’’, in H. Chenery and T.N , in H. Chenery and T.N Srinivasan (eds) Srinivasan (eds) Handbook of Development EconomicsHandbook of Development Economics, vol. 2, pp. , vol. 2, pp. 885885--947. Amsterdam; New York and Oxford: Elsevier Science, 947. Amsterdam; New York and Oxford: Elsevier Science, North Holland.North Holland.