The Social Accounting Matrix (SAM): What is it? How is it 

adapted for MAMS?

Inception workshop on “Strengthening Macroeconomic and Social Policy Coherence through Integrated Macro‐Micro Modelling”, Manila, 

2‐3 October, 2012.

Martín Cicowiez(CEDLAS‐UNLP)

Marco V. Sánchez(UN‐DESA/DPAD)

Outline

• Introduction: what is a SAM?

• SAM‐based calibration

• A SAM for MAMS

• Steps in Building a SAM for MAMS

• Some numbers from Philippines’ 2006 SAM

What is a SAM?

• A SAM is a consistent and complete data system that captures the interdependence that exists within a socio‐economic system– it portrays both the input‐output and national and external accounts in a consistent framework

• Originated from the pioneering work on national accounts by Meade and Stone (1940)– first SAM developed by Nobel Laureate Richard Stone for the UK in 1962; work on developing countries started in the 1970s

Features of a SAM

• A SAM is a square matrix with identical row and column accounts– each cell shows payment from its column account to its row account

• Accounting consistency means that column totals = row totals– budget constraint; supply=demand

• A SAM says nothing about the behavioral and technical relationships that generated its values.

Uses of a SAM

• A SAM describes the economic structure.• The SAM construction process puts together data from disparate sources– usually, need for reconciliation – in fact,  SAM building helps to check data consistency

• A SAM can be key data source for economy‐wide models– SAM multiplier models and CGE models– in MAMS, the SAM provides the bulk of the data used to define base‐year parameter values

Main Account Types in a SAM

• Activities: each activity produces one or more commodities using factor services and intermediates.

• Commodities: supplied by activities and/or via imports; demanded for exports and domestic final and intermediate use.

• Factors: services produced by stocks– labor, capital, land, other natural resources

• Institutions: entities that own factors, consume and invest, receive or pay taxes and transfers– households, enterprises, government, rest of world

• Others: taxes, interest, saving, capital, and investment.

A Standard MacroSAMact com fac hhd gov row tax-dom tax-imp sav-inv total

act prod

com io cons cons exp inv

fac va incf

hhd va-h trns trns

gov va-g trns trns itax+dtax mtax

row imp incf trns trns

tax-dom atax ctax dtax

tax-imp mtax

sav-inv sav sav sav

total

A Standard MacroSAM ‐‐ accountsaccount explanationact production activitiescom commoditiesfac factorshhd households (domestic non‐government)gov governmentrow rest of worldtax‐dom domestic taxestax‐imp import taxessav‐inv savings‐investment (consolidated)

A Standard MacroSAM ‐‐ Cellsitem explanationprod production (output)cons consumptionexp exportsimp importsio intermediate consumptionva value added (=GDP at factor cost)va‐g value added paid to governmentva‐h value added paid to householdsinv investmentsav savingsdtax direct taxesitax domestic indirect taxesmtax import taxes (tariffs)trns transfersincf factor income

A Standard MacroSAM: Numerical Exampleact com fac hhd gov row tax s‐i total

act 975 975com 499 332 43 163 121 1,157fac 458 3 460hhd 398 15 32 445gov 39 2 61 101row 156 23 1 0 181tax 19 25 17 61s‐i 95 43 ‐18 121total 975 1,157 460 445 101 181 61 121

SAM‐Based CGE Model Calibration

• A typical CGE model is calibrated using a SAM.

• SAM‐based calibration– on the basis of a dataset for a base period given by the SAM, the parameters of the model are estimated in a manner that enables the model solution to precisely replicate the SAM

• (in the absence of shocks)

Calibration Examples• According to the Standard MacroSAM

– Average propensity to save (aps)• household savings = 95

• household income = 445 

• aps = 95/445 = 0.21

– Average propensity to consume (apc)• household consumption = 332

• household income = 445 

• apc = 332/445 = 0.75

– Effective commodity tax rate (tax‐com)• commodity tax payments = 25

• total supply of commodities  =  1,157

• tax‐com = (35/1,157)*100 = 2.2%

• These would all be base‐year parameter values that would appear in the model equations; unless they are changed exogenously after byr

Calibration Example; Cobb‐Douglas

• According to the SAM – specific activity,– production value = Ush 100

– labor payment = Ush 40

– capital payment = Ush 60

– intermediate consumption = 0 

100Q 60K

40L

1 rwpLK LKQ

1 LK

Calibration Example – cont.

• The cost minimization problem consist in finding the input combination that minimizes a firm’s production cost, given quantity of output. Analytically,

LK LKqKrLw ..min

01 KL KLwL LL

01 KL KLrQK K L

0 KL KLq L

Calibration Example – cont.

• From the First Order Conditions,

60.0pQrK

K 40.0pQwL

L

60.01001601

xx

K 40.01001401

xx

L

SAM‐Based Model Calibration

• Main disadvantage– high dependence on data for one year; results may be misleading, especially if the year is exceptional or there are data errors

• make sure the SAM is good! 

• Main advantage– makes it possible to develop a model that can address relatively detailed policy‐relevant issues without asking for non‐existent data and/or carrying out complicated estimations

• Implications– careful judgment has to be applied; draw on model for insights, not for exact numbers.

A SAM for MAMS

• Minimum account disaggregation– activities/commodities: government, private– factors: labor, private capital– institutions: household, government, rest of world

• Accounts of each institution– current (= named after the institution)– capital

• Other institution‐related accounts– taxes but also interest payments

• One investment account per capital stock

A SAM for MAMSa‐prv

a‐gov

c‐prv

c‐gov

f‐lab

f‐capprv

hhd

gov

row

tax‐dom

tax‐imp

int‐d

omint‐row

cap‐hhd

cap‐gov

cap‐row

inv‐prv

inv‐gov

dstk

total

a‐prv proda‐gov prodc‐prv io io con exp inv inv dstkc‐gov conf‐lab va vaf‐capprv vahhd va‐h va‐h trns trns intdgov va‐g trns trns itax+dtax mtaxrow imp trns trns intrtax‐dom atax ctax incf itaxtax‐imp mtaxint‐dom intdint‐row intr‐h intr‐gcap‐hhd sav borrcap‐gov sav borr borrcap‐row savinv‐prv inv‐p inv‐pinv‐gov inv‐gdstk dstk‐h dstk‐gtotal

Cells in SAM for MAMSitem explanationprod production of gov/priv commoditycons gov/hhd consumption of gov/priv commodityexp exports of private commodityimp imports of private commodityio intermediate use of private commodity by gov/priv activityva value added from gov/priv activity va‐g/va‐h value added to gov/hhd from capital/labor and capitalincf factor income to capital/RoW from RoW/capitalsav gov/hhd/RoW savingsborr borrowinginv investment use of private commodity for gov/priv capitalinv‐g investment in gov capital financed by govinv‐p investment in priv capital financed by hhd or RoWdstk stock change for priv commoditydstk‐g/dstk‐h stock change financed by gov/hhddtax/itax direct/indirect domestic taxesmtax import taxes (tariffs)trns transfers to gov/hhd/RoW from gov/hhd/RoWintd domestic interest to hhd from govintr RoW interest (total)intr‐g/intr‐h RoW interest from gov/hhd

SAM for MAMS: Non‐Standard Accounts

• The MDG version of MAMS focuses on human development. Then, need to disaggregate government accounts (activity, commodity, investment) into – education (primary, secondary, tertiary)– health– water and sanitation

• In addition, other government sectors are usually singled out– public infrastructure (roads, bridges, airports, and so on) ‐‐ provide productivity‐raising services

– other government (public administration and other services)

SAM for MAMS: Non‐Standard Accounts – cont.

• The labor factor is disaggregated by educational achievement into– less than completed secondary 

– completed secondary but not tertiary

– completed tertiary 

• Typically, payments to capital from government activities do not appear in IO tables ‐‐may only reflect depreciation.

SAM for MAMS: Non‐Standard Accounts – cont.

• Private activity and commodity into – agriculture  ‐‐ can be split further– industry  ‐‐ can be split further– services

• split further to single out MDG‐related services provided by the private sector

• Private capital into– private capital (defined more narrowly)– agricultural land– natural resources

• Household and related capital account into rural/urban or by income characteristics if needed.

Steps in the SAM Building Process

1. Construction of a MacroSAM– national accounts, government budget, and the 

balance of payments

2. Disaggregation of the MacroSAM into a matrix with a large sectoral breakdown (MicroSAM) suitable for the calibration of MAMS

– use data in MacroSAM as control totals

– disaggregate accounts for activities, commodities, factors, institutions

3. Adaptation of the MicroSAM to make it suitable for the calibration of MAMS.

Macro Indicators Derived from Philippines 2006 SAM

Macro Aggregate % of GDP

Private consumption 75.7

Investment 14.2

Stock variation 0.8

Government consumption 9.7

Exports 41.5

Imports 41.9

GDP market prices 100

Exports and imports sharesSector EXPshr EXP‐OUTshr IMPshr IMP‐DEMshrAgriculture 2.3 7.0 2.7 8.8Industry 81.2 100.0 75.4 100.0Water and Sanitation 0.0 0.0 0.0 0.0Construction 0.3 2.1 0.4 2.9Other infrastructure, government 0.0 0.0 0.0 0.0Primary education, private 0.0 0.8 0.1 2.8Secondary education, private 0.0 0.9 0.0 2.9Tertiary education, private 0.0 0.9 0.0 3.0Health, private 0.0 1.0 0.2 4.6Primary education, government 0.0 0.0 0.0 0.0Secondary education government 0.0 0.0 0.0 0.0Tertiary education, government 0.0 0.0 0.0 0.0Health, government 0.0 0.0 0.0 0.0Other government services 0.1 0.8 0.1 0.4Other private services 16.0 15.4 21.2 20.6Total 100.0 36.6 100.0 38.4

Value added sector and factor compositionSector VAshr f‐labn f‐labs f‐labt f‐cap totalAgriculture 14.3 27.0 8.3 1.1 63.6 100.0Industry 27.4 7.9 13.9 4.5 73.7 100.0Water and Sanitation 0.3 1.4 11.8 17.9 68.8 100.0Construction 1.9 22.0 21.1 3.3 53.5 100.0Other infrastructure, government 1.2 22.0 21.1 3.3 53.5 100.0Primary education, private 1.1 0.4 2.5 65.2 31.8 100.0Secondary education, private 0.5 0.4 2.5 65.2 31.8 100.0Tertiary education, private 0.2 0.4 2.5 65.2 31.8 100.0Health, private 1.1 2.1 10.9 39.1 47.9 100.0Primary education, government 1.8 0.6 3.7 95.7 0.0 100.0Secondary education government 0.8 0.6 3.7 95.7 0.0 100.0Tertiary education, government 0.4 0.6 3.7 95.7 0.0 100.0Health, government 0.5 4.0 20.9 75.1 0.0 100.0Other government services 5.8 5.4 27.9 59.4 7.3 100.0Other private services 42.7 3.0 8.4 13.6 75.1 100.0total 100f‐labn: unskilled labour factor (workers who have not completed secundary)f‐labs: semi‐skilled labour factor (workers who have completed secundary)f‐labt: skilled labour factor (workers who have completed tertiary)f‐cap: factor capital