SOCIAL ACCOUNTING MATRICES AND THEIR USE IN ECONOMICS MODELLING Finn Tarp Department of Economics University of Copenhagen

SOCIAL ACCOUNTING MATRICES AND THEIR USE IN ECONOMICS MODELLING

Finn TarpDepartment of EconomicsUniversity of Copenhagen

http://www.econ.ku.dk/ftarp/

Workshop at CIEM, Hanoi, 16 January 2009

2

Outline

• Introduction• SAM: an overview from a macro perspective• SAM: going back to the micro foundations• Vietnam SAMs• Conclusion

SAM from a macro perspective Overview – the basic idea The individual cells Macroeconomic accounting identities

in a SAM context

GOODSAGENT

SS-I ROW

GOODS C I E*X

AGENTS

GDP

S-I SE*CUR

R

ROW E*M

Simple Open Economy Real SAM

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Accnt.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Additional variables

Sh = Private Savings

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Accnt.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Additional variables

Sg = Government Savings

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Accnt.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Additional variables

T = Tax Payments

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Accnt.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Additional variables

Sf = Foreign Savings

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Acc.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Additional variables

G = Government Spending

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Acc.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Accounting Identities:

Mat. Bal. Y + Z = C + G + I + X

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Acc.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Accounting Identities:

Income C + T + Sh = Y

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Acc.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Accounting Identities:

Govt. Budget G + Sg = T

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Acc.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Accounting Identities:

Saving-Investment I = Sh + Sg + Sf

Social Accounting Matrices (SAMs)

Expenditures

Receipts

1 2 3 4 5 Total

1. Suppliers

- C G I X Demand

2. Households

Y - - - - Income

3. Government

- T - - -Receipts

4. Capital Acc.

- Sh Sg - Sf Savings

5. Rest of World

Z - - - - Imports

Total Suppl

yExpendi-ture

Expenditure

Invest-ment

ROW

Accounting Identities:

Trade Balance X + Sf = Z

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Back to the microfoundations - Input-output: a three sector economy

• Input-output concept simple. Consider the production of the ith sector.

• We may isolate (1) flows xij from that industry to other industries; (2) the quantity of that production that goes to final demand, ci, and (3) total output, xi.

• Put in a transactions tableau

Economic Activities

Inputs to Agriculture

Inputs to Manu-

facturing

Inputs to Transport

Final Demand

Total Output

Agriculture 5 15 2 68 90

Manufacturing 10 20 10 40 80

Transportation 10 15 5 0 30

Labor 25 30 5 0 60

or

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The Leontief coefficients

Leontief, the innovator of input-output analysis, uses a special production function which depends linearly on the total output variables xi. Using Leontief coefficients aij, we may

manipulate our transactions information into what is known as an input-output table:

:

or

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Next step

Rewriting finally yields

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One more step

denote the total output vector, the final demand vector, the unit matrix and the input-output matrix, respectively.

Introducing matrix notation, we can see how a solution may be obtained. Let

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Key result

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Input-output analysis: discussion

• No supply constraints• No substitution (input coefficients are constant) (marginal input

coefficients = average) – what happens in the growth process?• External economies are ruled out, constant returns to scale

assumed• If sectoral linkages weak, the IO is of limited value• What about the optimal choice of technique? -> Linear

programming …• What about feedback effects from income-expenditure behaviour

etc.? -> SAM modelling …

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Macro policy and IO production structure relations are important

But so is wider economic structure and economic interactions between sectors and institutions of the economy, on the one hand, and between the domestic economy and the rest of the world (ROW), on the other

We want to understand these interactions to formulate appropriate policy recommendations - we need a framework (or accounting device) in which to organize our structural and institutional data

The next step: Why Build SAMs?

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What is a SAM?

A Social Accounting Matrix (SAM) is a square matrix that builds on the input-output table - but the SAM goes further

A SAM considers not only production linkages, but tracks income-expenditure feedbacks (institutions are introduced)

Each “transactor” (such as factors of production, households, enterprises, the government and the ROW) has a row and a column – double entry national income accounting (row totals therefore equal to corresponding column total)

A SAM is a consistent data system that provides a snapshot of the economy in a given year

Note that the SAM reconciles data from different sources and we often talk about the SAM as consisting of two corresponding layers: the Macro-SAM and the Micro-SAM

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What is a Macroeconomic SAM?

The Macro-SAM is the upper (aggregate) layer of the SAM

Try to visualize (open a door and look into an office or library)

Technically: the Macroeconomic SAM is an extension (or matrix representation) of basic national income identities:

Y + M = C + G + I + E (GNP) C + T + Sh = Y (Income) G + Sg = T (Govt. Budget) I = Sh + Sg + Sf (Savings-Investment) E + Sf = M (Trade Balance)

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Schematic Macroeconomic SAM

Expenditures

Receipts 1 2 3 4 5 Total

1. Suppliers - C G I E Demand

2. Households Y - - - - Income

3. Government - T - - - Receipts

4. Capital Acct. - Sh Sg - Sf Savings

5. Rest of World M - - - - Imports

Total Supply Expenditure Expenditure Investment ROW

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Generic Macro-SAM

Receipts

Expenditures

1. Activ-ties

2. Commo-dities

3.Factors 4.PrivateHouse-holds

5.Enterprises

6.Recur-rent State

7.Investment/Savings

8.Rest ofWorld

9.Total

1.Marketed production

Home cons.

Total domestic sales

2.Intermediateconsumption

Marketing margins

Private marketed sons.

State cons.

Invest-ment

ExportsTotal comm.demand

3. Value addedValue added

4.

Wages, salaries,enterprise profits

Dist.Profits, social security

Social Security, other current transfers

Net foreign transfers

Private house-hold Income

5.Gross profits

Entrpr. subsidies

Net foreign transfers

Enterp. Income

6.

Value added and otherproduction taxes

Commodity taxes

Factor taxes

Income taxes

Enterpr. taxes

Net foreign transfers

State Revenue

7.Household savings

Retained earnings

State savings

Total savings

8. ImportsEnterpr. Remitt.

Imports, remitt.

9.Total domestic payments

Total commodity supply

Total factor payments

Allocation private household income

Total entr. payments

Allocation of state revenue

Total invest-ment

Total foreign exchan-ge

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What is a Microeconomic SAM?

The Micro-SAM is the lower (disaggregated) layer of the SAM Try to visualize (being inside an office or library - look around) Technically: each of the 81 (=9x9) cells in the macro-SAM are

disaggregated so as to capture detailed interdependencies between institutions and sectors

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Additional remarks

SAMs are an economy-wide accounting device that captures the many interdependencies among sectors and institutions in the economy

As such SAMs are useful in their own right through inspection – descriptive analyses of the structure of the economy (at various levels of aggregation!)

And the SAMs become the basis for detailed multiplier analyses that go well beyond traditional input-output multiplier analysis

Finally, the SAMs form the informational basis for the building and calibration of (applied) computable general equilibrium (CGE) models. CGE models are important analytical tools for policy support. They

take explicit account of the importance of price-mediated resource allocation, the hallmark of a market economy – used to analyse issues such as the distribution of the benefits of growth and economic reform, including increased international economic integration

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Multiplier Analysis

The SAM accounts can give detailed information about direct and indirect income and expenditure linkages in the economy. For the economywide SAM, one uses the basic multiplier calculation

Svv Svx

Sxv Sxx

M = (I – A)-1

where M is the square matrix of multipliers for exogenous demand changes on endogenous accounts, and A is the coefficients (expenditure) matrix of endogenous accounts (note: mij = income multiplier for i arising from j)

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Multisectoral models: the SAM (Ghatak Table 11.1)

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Multisectoral models: Separating the accounts (Ghatak Table 11.2)

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The SAM multiplier (Ghatak Table 11.3 first part)

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The SAM multiplier (Ghatak Table 11.3 second part)

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SAM multipliers - discussion

• Fixed coefficients, no substitution• No supply constraints, demand driven (fixed price response

to exogenous change)• To capture substitution in supply and demand and price

adjustments -> CGE (but beyond scope here....)

CIEM Seminar,

Hanoi 28

October 2004

Introduction - Vietnam

Institutional background and acknowledgments The CIEM-NIAS project CIEM-DoE research collaboration GSO, Danida etc.

The 1999 and the first 2000 Vietnam Social Accounting Matrices (SAMs) (published in 2001 and 2002)

Some economic analyses carried out A reference to the international conference on

“Vietnam’s international economic integration - Opportunities and challenges" held in March 2004

http://eurasia.nias.ku.dk/ciemnias http://www.ciem.org.vn

SAM revision and updating an ongoing process

CIEM Seminar,

Hanoi 28

October 2004

Macro policy is important But so is economic structure and economic

interactions betweens sectors and institutions of the economy, on the one hand, and between Vietnam and the rest of the world (ROW), on the other

We want to understand these interactions to formulate appropriate policy recommendations - we need a framework (or accounting device) in which to organize our structural and institutional data

Why Build SAMs? A recap

Table 3.1: Dimensions of the SAM

1.Activi-ties (112)

2.Com-modi-ties (114)

3.Fac-tors (14)

4.Hou-seholds (16)

5.En-terpri-ses (3)

6.Re-current State (1+7)

7.In-vest-ment/Saving (1)

8. ROW (1)

Total

1 (112)

  112 x 114

  112 x 16

        112 x 1

2 (114)

114 x 112

114 x 114

  114 x 16

  114 x 8

114 x 1

114 x 1

114 x 1

3 (14) 14 x 112

              14 x 1

4 (16)     16 x 14

  16 x 3 16 x 8   16 x 1 16 x 1

5 (3)     3 x 14         3 x 1 3 x 1

6 (1+7)

8 x 112

8 x 114

8 x 14 8 x 16 8 x 3     8 x 1 8 x 1

7 (1)       1 x 16 1 x 3 1 x 8     1 x 1

8 (1)   1 x 114

    1 x 3 1 x 8     1x 1

Total 1 x 112

1 x 114

1 x 14 1 x 16 1 x 3 1 x 8 1 x 1 1 x 1

CIEM Seminar,

Hanoi 28

October 2004

The New 2000 Vietnam Micro-SAM - An Overview

In sum, a 269x269 matrix 112/114 domestic production

activities/commodities 14 factors of production 16 household types 3 types of enterprises (private, public, and foreign) 1 state 7 taxes 1 consolidated capital (investment/savings) account 1 balance of payments (with details on 194

international trading partners for the 114 commodities)

CIEM Seminar,

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October 2004

Labour Force Disaggregation

12 labour categories:

Skilled

Unskilled

M. Skilled

Rural

FemaleMale

Factors

Skilled

Unskilled

M. Skilled

Skilled

Unskilled

M. Skilled

Skilled

Unskilled

M. Skilled

Urban

FemaleMale

CIEM Seminar,

Hanoi 28

October 2004

Household Disaggregation

16 types:

Rural Urban

Household

Self-empl non-farmer

Wage-earnersSelf-empl. farmers

Non-employed

Male Female Male Female

Self-empl non-farmer

Wage-earnersSelf-empl. farmers

Non-employed

CIEM Seminar,

Hanoi 28

October 2004

Tax disaggregation (7 categories)

Value added tax (VAT)Production tax (PTAX) Special consumption sales tax (STAX) Import tariffs (TARIFF) Factor taxes (FTAX) (divided into land

and capital factor taxes) Enterprise taxes (ETAX) Household taxes (HTAX)

On 2003 Vietnam SAM:Construction & Description

SAM Construction Methodology• Unbalanced Macro SAM (Primary Data Sources)• Balanced Macro SAM (Statistical Balancing)• Unbalanced Micro SAM (Primary Data & Macro

SAM Totals)• Balanced Micro SAM (Statistical Balancing)

2003 Vietnam SAM accounts (274)• Goods Accounts: Activities (112), Commodities

(112), Trade Margins (3) & Transportation Margins (3)

• Factor Accounts: Land (1), Labor (12) & Capital (1)• Institutional Current Accounts: Enterprises (1),

Households (16), Government (7) & Rest of World (1)

• Institutional Capital Accounts: Private (2), Government (2) & Aggregate (1)

CIEM Seminar,

Hanoi 28

October 2004

Final Remarks (1)

SAMs are an economy-wide accounting device that captures the many interdependencies among sectors and institutions in the economy

As such SAMs are useful in their own right through inspection – descriptive analyses of the structure of the economy (at various levels of aggregation!)

And the SAMs become the basis for detailed multiplier analyses that go well beyond traditional input-output multiplier analysis

CIEM Seminar,

Hanoi 28

October 2004

Final Remarks (2)

Finally, the SAMs form the informational basis for the building and calibration of (applied) computable general equilibrium (CGE) models. CGE models are important analytical tools for policy support.

They take explicit account of the importance of price-mediated resource allocation, the hallmark of a market economy, and are therefore well suited to analyse issues such as the distribution of the benefits of growth and economic reform, including increased international economic integration

A word on future SAM work, f.ex. General updating, VHLSS and new national accounts SME and household surveys Regionalization Environmental issues

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Conclusions

• Is planning a good idea?• How has planning been imlemented in the past?• What role for planning in the future?• What is the role of SAMs?