How to Read a Social Accounting Matrix (SAM)
A Practical Guide Using Pakistan SAM 2007-08
Economic & Finance Models · Chapter 1 · Section 1.1
Introduction
A Social Accounting Matrix (SAM) is a comprehensive data framework that captures all economic transactions in an economy for a single year. This guide explains how to read and interpret a SAM using Pakistan's 2007-08 SAM as an example.
The Golden Rule of Reading SAMs
Cell T(i, j) = Payment FROM column j TO row i
Simply: "Column pays Row"
This means:
- Reading across a row → all income sources of that account
- Reading down a column → all expenditure uses of that account
Critical Rule: For every account, Row Total = Column Total (income equals expenditure)
Structure of Pakistan SAM 2007-08
The Pakistan SAM has 9 main accounts:
| Account | Description |
|---|---|
| Activities | Production sectors |
| Commodities | Goods and services |
| Land | Factor of production |
| Labor | Factor of production |
| Capital | Factor of production |
| Household | Consumers |
| Government | Public sector |
| S-I | Savings-Investment |
| ROW | Rest of World (foreign trade) |
Reading Specific Cells: Key Examples
Production and Consumption Flows
Cell: Activities Row, Commodities Column = "Supply Matrix"
- Reading: Commodities pays Activities
- Meaning: Shows which activities produce which commodities
Cell: Commodities Row, Activities Column = "Intermediate Consumption"
- Reading: Activities pays Commodities
- Meaning: Activities buy commodities as production inputs
Factor Payments
Cell: Labor Row, Activities Column = "VA by Labor"
- Reading: Activities pays Labor
- Meaning: Wages paid by production sectors
Cell: Household Row, Labor Column = "Factor Income → HH"
- Reading: Labor pays Household
- Meaning: Workers receive wage income
Household Transactions
Cell: Commodities Row, Household Column = "Private Consumption"
- Reading: Household pays Commodities
- Meaning: Households buy goods and services
Cell: Government Row, Household Column = "Direct Taxes"
- Reading: Household pays Government
- Meaning: Households pay income taxes
Trade Flows
Cell: Commodities Row, ROW Column = "Imports"
- Reading: ROW pays Commodities
- Meaning: Foreign goods enter domestic market
Cell: ROW Row, Commodities Column = "Exports"
- Reading: Commodities pays ROW
- Meaning: Domestic goods sold abroad
Reading a Complete Row: Household Income
Reading the Household Row across shows all household income sources:
| From Account | Transaction | Meaning |
|---|---|---|
| Land | Factor Income | Land rent |
| Labor | Factor Income | Wages |
| Capital | Factor Income | Profits, dividends |
| Government | Govt Transfers | Welfare payments |
| ROW | Remittances | Money from abroad |
Row Total = Total Household Income
Reading a Complete Column: Household Expenditure
Reading the Household Column down shows how households spend:
| To Account | Transaction | Meaning |
|---|---|---|
| Commodities | Private Consumption | Buying goods/services |
| Government | Direct Taxes | Income tax |
| S-I | HH Savings | Savings |
Column Total = Total Household Expenditure
Must equal Row Total (income = expenditure)
Tracing Economic Flows: A Textile Factory Example
Follow money through the economy:
- Factory produces cloth → Activities → Commodities (Supply Matrix)
- Factory buys cotton → Commodities ← Activities (Intermediate Consumption)
- Factory pays workers → Labor ← Activities (VA by Labor)
- Workers receive wages → Household ← Labor (Factor Income)
- Workers buy food → Commodities ← Household (Private Consumption)
- Workers pay taxes → Government ← Household (Direct Taxes)
This shows the circular flow of income: production → factor income → household spending → more production.
Key Blocks in the Pakistan SAM
1. Production Block
- Activities ↔ Commodities
- Shows production technology and input use
2. Factor Income Block
- Factors (Land, Labor, Capital) ← Activities
- Shows factor payments (wages, rents, profits)
3. Household Income Block
- Household ← Factors (wages, rents, profits)
- Household ← Government (transfers)
- Household ← ROW (remittances)
4. Final Demand Block
- Commodities ← Household (consumption)
- Commodities ← Government (public spending)
- Commodities ← S-I (investment)
- Commodities ← ROW (exports)
5. Government Revenue Block
- Government ← Commodities (sales tax, import tax)
- Government ← Household (income tax)
- Government ← Capital (state enterprise income)
- Government ← ROW (foreign grants)
6. Trade Block
- Imports: Commodities ← ROW
- Exports: ROW ← Commodities
Understanding What Each Cell Tells You
| Cell Location | What It Shows | Example |
|---|---|---|
| (Labor, Activities) | Wage bill by sector | Agriculture pays wages |
| (Household, Labor) | Labor income to households | Workers receive wages |
| (Commodities, Household) | Consumer spending | Households buy goods |
| (Government, Commodities) | Indirect taxes | Sales tax collected |
| (Commodities, ROW) | Imports | Foreign goods purchased |
| (ROW, Commodities) | Exports | Domestic goods sold abroad |
Common Interpretation Mistakes
❌ Wrong: "Cell (Labor, Activities) = labor employed" ✓ Correct: "Cell (Labor, Activities) = payments FROM Activities TO Labor (wage bill)"
❌ Wrong: Reading row as expenditure ✓ Correct: Row = income sources, Column = expenditure uses
❌ Wrong: Ignoring that Row Total must equal Column Total ✓ Correct: Always verify accounting balance
Detailed Cell-by-Cell Explanation
Row 1: Activities (Production Sectors)
Reading Activities Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Activities | — | Activities don't pay themselves |
| Commodities | Supply Matrix | Production output — Activities produce commodities |
| Factors | — | Factors don't buy from activities |
| Household | — | Households don't buy directly from activities |
| Government | — | Government doesn't buy directly from activities |
| S-I | — | Investment doesn't buy from activities directly |
| ROW | — | Foreign sector doesn't buy from activities directly |
Row Total = Gross Output (total value of production)
Row 2: Commodities (Goods & Services)
Reading Commodities Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Activities | Intermediate Consumption | Activities buy commodities as inputs (e.g., steel for car manufacturing) |
| Commodities | — | Commodities don't buy from themselves |
| Factors | — | Factors don't consume commodities directly |
| Household | Private Consumption | Households buy commodities for consumption |
| Government | Public Consumption | Government purchases goods/services |
| S-I | Fixed Investment | Investment demand for capital goods |
| ROW | Exports | Commodities sold to foreign buyers |
Row Total = Aggregate Demand (total demand for commodities)
Key Insight: This row shows the demand side — who buys the commodities produced.
Row 3: Land (Factor of Production)
Reading Land Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Activities | VA by Land | Activities pay rent for using land (e.g., agricultural land rent) |
| All others | — | Land receives income only from Activities |
Row Total = Land Income (total rent earned by the land factor)
Row 4: Labor (Factor of Production)
Reading Labor Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Activities | VA by Labor | Activities pay wages to workers (labor compensation) |
| All others | — | Labor receives income only from Activities |
Row Total = Labor Income (total wages earned)
Row 5: Capital (Factor of Production)
Reading Capital Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Activities | VA by Capital | Activities pay return to capital (profits, interest, dividends) |
| All others | — | Capital receives income only from Activities |
Row Total = Capital Income (total return to capital)
Row 6: Household (Consumers)
Reading Household Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Activities | — | Households don't receive from activities directly |
| Commodities | — | Households don't receive from commodities |
| Factors (Land/Labor/Capital) | Factor Income → HH | Households own factors and receive factor income |
| Government | Govt Transfers | Social security, subsidies, welfare payments |
| S-I | — | No payment |
| ROW | Remittances | Money sent from Pakistanis working abroad |
Row Total = HH Income (total household income from all sources)
Key Insight: Shows all sources of household income — primarily factor income (wages, rents, profits), plus government transfers and remittances.
Row 7: Government (Public Sector)
Reading Government Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Activities | — | Government doesn't receive from activities directly |
| Commodities | Sales/Import Tax | Indirect taxes (VAT, sales tax, customs duties) |
| Capital factor | Capital → Govt | Income from state-owned enterprises |
| Household | Direct Taxes | Personal income tax from households |
| ROW | Foreign Grants | International aid, donor assistance |
Row Total = Govt Revenue (total government revenue from all sources)
Key Insight: Government revenue comes from taxes (direct and indirect), state enterprise profits, and foreign aid.
Row 8: S-I (Savings-Investment Account)
Reading S-I Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Household | HH Savings | Household savings (income not consumed or taxed) |
| Government | Govt Savings | Government budget surplus (positive) or deficit (negative) |
| ROW | Foreign Savings | Net capital inflow from abroad |
Row Total = Total Investment (total investment financing available)
Key Insight: This row collects all savings in the economy — from households, government, and foreign sources. In Pakistan 2007-08: Household PKR 2,168bn + Government −PKR 777bn + Foreign PKR 868bn = PKR 2,259bn total investment.
Row 9: ROW (Rest of World)
Reading ROW Row Across:
| Column | Cell Content | Interpretation |
|---|---|---|
| Commodities | Imports | Pakistan buys goods from abroad |
| Capital factor | Dividend Repatriation | Profits sent back to foreign investors |
| Government | Govt Payments Abroad | Debt service, foreign aid given |
Row Total = FX Outflow (total foreign exchange leaving Pakistan)
Reading the Columns (Expenditure Side)
Column 1: Activities (Production Costs)
Reading Activities Column Down:
| Row | Cell Content | Interpretation |
|---|---|---|
| Commodities | Intermediate Consumption | Activities buy inputs (raw materials, energy, services) |
| Land | VA by Land | Activities pay land rent |
| Labor | VA by Labor | Activities pay wages |
| Capital | VA by Capital | Activities pay capital returns |
Column Total = Cost of Production
Formula: Cost = Intermediate Inputs + Land Rent + Wages + Capital Returns
Column 2: Commodities (Supply Sources)
Reading Commodities Column Down:
| Row | Cell Content | Interpretation |
|---|---|---|
| Activities | Supply Matrix | Domestic production supplies commodities |
| Government | Sales/Import Tax | Taxes added to commodity prices |
| ROW | Imports | Foreign supply of commodities |
Column Total = Aggregate Supply (domestic production + imports + taxes)
Column 3: Factors — Land, Labor, Capital (Factor Expenditure)
Reading Factors Column Down:
| Row | Cell Content | Interpretation |
|---|---|---|
| Household | Factor Income → HH | Factor income flows to households (who own the factors) |
| Government | Capital → Govt | Some capital income goes to government (state enterprises) |
| ROW | Dividend Repatriation | Some capital income goes to foreign owners |
Column Total = Factor Expenditure (how factor income is distributed)
Column 4: Household (Household Spending)
Reading Household Column Down:
| Row | Cell Content | Interpretation |
|---|---|---|
| Commodities | Private Consumption | Households buy goods and services |
| Government | Direct Taxes | Households pay income tax |
| S-I | HH Savings | Households save part of income |
Column Total = HH Expenditure
Formula: Expenditure = Consumption + Taxes + Savings
Column 5: Government (Government Spending)
Reading Government Column Down:
| Row | Cell Content | Interpretation |
|---|---|---|
| Commodities | Public Consumption | Government buys goods/services (healthcare, education, defense) |
| Household | Govt Transfers | Social security, subsidies, welfare payments |
| S-I | Govt Savings | Government budget surplus (or negative if deficit) |
| ROW | Govt Payments Abroad | Debt service, foreign commitments |
Column Total = Govt Expenditure
Column 6: S-I (Investment Expenditure)
Reading S-I Column Down:
| Row | Cell Content | Interpretation |
|---|---|---|
| Commodities | Fixed Investment | Investment purchases (machinery, buildings, infrastructure) |
| (Change in Stocks) | Inventory | Stock accumulation |
Key Insight: Savings collected in the S-I row are spent on capital goods from the commodities account.
Column 7: ROW (Foreign Exchange Sources)
Reading ROW Column Down:
| Row | Cell Content | Interpretation |
|---|---|---|
| Commodities | Exports | Pakistan sells goods abroad (brings in foreign exchange) |
| Household | Remittances | Pakistanis abroad send money home |
| Government | Foreign Grants | International aid received |
| S-I | Foreign Savings | Net capital inflow (foreign investment) |
Column Total = Foreign exchange sources for Pakistan
Row and Column Totals at a Glance
Row Totals (What Each Account Earns)
| Account | Row Total Represents |
|---|---|
| Activities | Gross Output — total production value |
| Commodities | Aggregate Demand — total demand for goods/services |
| Land | Land Income — total rent earned |
| Labor | Labor Income — total wages earned |
| Capital | Capital Income — total capital returns |
| Household | HH Income — total household income |
| Government | Govt Revenue — total government revenue |
| S-I | Total Investment — total investment financing |
| ROW | FX Outflow — foreign exchange leaving Pakistan |
Column Totals (What Each Account Spends)
| Account | Column Total Represents |
|---|---|
| Activities | Cost of Production — total production costs |
| Commodities | Aggregate Supply — total commodity supply |
| Factors | Factor Expenditure — factor income distribution |
| Household | HH Expenditure — how households spend |
| Government | Govt Expenditure — government spending |
| S-I | Investment Uses — where investment goes |
| ROW | FX Inflow — foreign exchange sources |
The Balance Condition
For each account: Row Total = Column Total
| Account | What Must Balance |
|---|---|
| Household | Income (factors + transfers + remittances) = Consumption + Taxes + Savings |
| Government | Revenue (taxes + state enterprises + aid) = Public consumption + Transfers + Budget balance |
| Commodities | Demand (intermediate + final + exports) = Domestic production + Imports + Taxes |
| S-I | Savings (HH + Govt + Foreign) = Fixed Investment + Stock Changes |
Key Economic Insights from Pakistan SAM 2007-08
1. Production Structure
- Activities produce commodities using intermediate inputs, land, labor, and capital
- Value Added = Labor + Capital + Land payments per sector
2. Income Distribution
- Households earn from three factors: land rent, wages, capital income
- Government transfers and remittances are significant secondary sources
- Remittances (PKR 763bn) play a critical role in rural household budgets
3. Expenditure Patterns
- Households split income across consumption, taxes, and savings
- Government spends on public goods, transfers, and external commitments
- Investment financing = domestic savings (households + government) + foreign savings
4. External Sector
- Pakistan imports commodities and exports predominantly manufactured goods
- Receives large remittances from the diaspora
- Foreign savings (PKR 868bn) financed the investment gap left by the fiscal deficit
5. Circular Flow
The SAM captures the complete circular flow of income in one consistent matrix:
Activities → produce → Commodities
Commodities → intermediate inputs → back to Activities
Activities → wages → Labor → → Households
Activities → land rent → Land ──→ Households
Activities → profits → Capital ──→ Households
Households → consumption → Commodities → demand → Activities
Households → taxes → Government → public spending → Commodities
Government deficit + Household savings + Foreign savings → S-I → Fixed Investment → Commodities
ROW → exports → Commodities → Imports → ROW
Every payment in this flow appears exactly twice in the SAM — once as income, once as expenditure. That is the double-entry principle applied to an entire economy.
Simple takeaway: Once you understand that every cell is a payment from a column account to a row account, you can read any SAM — the logic is identical regardless of the size or country.
Also available in the CS Book — Economic & Finance Models