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Chapter 8Aggregate Accounts,

Budget Constraints, and Model Consistency

© Pierre-Richard Agénor

The World Bank

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Production, Income, and Expenditure A Consistency Accounting Matrix National Income Identities and Budget

Constraints A Three-Good Model with Banks An Intertemporal Framework

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Production, Income, and Expenditure

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Production: Goods, services carried out by domestic agents; firms, self-employed workers, financial institutions, and the government.

Income: Wages and salaries, firms' operating surpluses, property income, and imputed compensation.

Expenditure: Outlays on durable and nondurable final consumption goods and investment.

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Linked by three macroeconomic relationships: Production and income: total value of production

must equal the value of income (excluding transfers) generated domestically.

Income, expenditure, and savings: for any economic agent, income earned plus transfers must be equal to expenditure plus savings.

Savings and asset accumulation: savings plus borrowing must equal asset acquisition for any economic agent.

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A Consistency Accounting Matrix Current account transactions Capital account transactions

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Five sets of accounts incorporated in the consistency framework:

The national accounts. The accounts of the nonfinancial private sector. The government accounts. The balance sheets of the financial sector. The balance of payments.

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Current Account Transactions

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See Table 8.1 Rows: sources of finance for each sector. Columns: uses of finance for each sector.

Ex Post: each sector’s deficit must be financed,

sum of rows = sum of columns.

Ex Ante: sectoral balances are constraints.

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National Accounts Row 1 & Column A, National Accounts:

consolidated current-period activities of all production units; incorporated enterprises (financial and

nonfinancial); informal sector firms; producers of government services; production by households for own

consumption.

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National Accounts Row 1, allocation of goods, services produced

domestically, Y, or imported, J, between: government consumption, Cg; private consumption, Cp; exports, X; government and private sector investment, Ig

and Ip, with I = Ig + Ip.

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National Accounts Column A, GDP at current market prices, Y,

decomposed into types of income generated through sale (plus own consumption) of domestic output;

net indirect taxes: indirect taxes, TI, less

subsidies, SUB; operating surplus of government enterprises, OSg; wages and salaries, W, and profits, ; incomes of the self-employed and own-account

producers, Ys.

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National Accounts GDP at factor costs, Yfc: sum of employee

compensation (wages, salaries and incomes of own-account producers) and operating surpluses of all enterprises.

Value added at factor cost, Vfc: by convention, accrues to households or government.

Value added at Market Price: Vfc + net indirect taxes.

Total amount of goods and services available for final use: sum of value added at market prices and imports.

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Current Government Transactions

Row 2 & Column B: Government savings, Sg, given by,

Sg = Tg - G,

Tg = TI - SUB + OSg + TD + NTgf,

G = Cg + NTpg + INTpg + INTfg .

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Row 2: Sources of government revenues, Tg, as, net indirect taxes, TI - SUB; operating surpluses of government-owned

enterprises, OSg; direct taxes on the nonfinancial private sector, TD;

net transfers to government from external sector, NTgf.

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Current Government Transactions

Row 2 & Column B: Column B: government expenditures, G, as

government consumption of goods and services, Cg;

net transfers to the nonfinancial private sector, NTpg;

interest paid to the private sector on domestic public debt, INTpg;

interest payments on public foreign debt, INTfg.

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Row 3 & Column C: Financial system: pure intermediary. There is no

independent revenues, expenditure accounts.

Financial Sector

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Row 4 & Column D: Private saving, Sp: total private sector income, Yp,

minus total current expenditures of the private sector, CCp:

Sp = Yp - CCp

with

Yp = W + + s + NTp + INTpg + NTpf + NFPpf,

CCp = Cp + TD + INTfp + Sp.

Nonfinancial Private Sector

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Row 4 & Column D: Row 4: private sector revenues, Yp, as,

factor income, including wages and salaries, W, profits, , and incomes of the self-employed, s;

net transfers received from the government, NTp; interest payments received on government debt

holdings, INTpg; net transfers, NTpf, plus net factor payments from

abroad, NFPpf.

Nonfinancial Private Sector

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Nonfinancial private sector

Row 4 & Column D: Column D: private sector expenditures, CCp, as,

private consumption, Cp; payment of direct taxes, TD; interest payments on private external debt, INTfp.

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External Sector

Row 5 & Column E: Current Account Balance, CA: - (savings by foreign

residents);

CA = X + (NTgf + NTpf) + NFPpf - J - INTfg

- INTfp

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External Sector

Row 5 & Column E: Row 5: sources of income to foreign residents;

value of imports of goods and services, J; public and private sector interest payments on

their respective external debts, INTfg and INTfp. Column E: sources of income from foreign

residents; exports of goods and services, X; net current transfers to the government and

private sectors, NTgf and NTpf; net factor payments to the private sector,

NFPpf.

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Capital Account Transactions

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Financing of asset acquisition by government, private nonfinancial sector, and external sector.

Government

Row 6 & Column F: Row 6: sources of financing:

government savings, Sg; net borrowing from the financial system,Lgb; net borrowing from the private sector, Bp; net foreign borrowing, FBg.

Column F: gross fixed capital investment by the government, Ig.

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Financial Sector

Row 7 & Column G: Row 7: financial system liabilities, M;

new domestic currency issues, demand deposits, time deposits.

Column G: financial system assets; loans to the government, Lgb, loans to the private sector, Lpb, net foreign assets, R*.

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Nonfinancial Private Sector

Row 8 & Column H: Row 8: private sector asset acquisition financing;

private sector savings, Sp, net borrowing from the financial system, Lpb, net borrowing from abroad, FBp.

Column H: private sector asset acquisitions; private investment, I p; physical assets, inventories

and working capital, plus intangible nonfinancial assets;

net lending to the government, Bp; increases in holdings of monetary assets, M, that is,

liabilities issued by the financial sector.

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External Sector

Row 9 & Column I: Row 9: savings by foreign residents, CA (deficit),

and acquisition of net foreign exchange reserves by the financial system, R*.

Column I: net foreign borrowing of the government, FBg, and the private sector, FBp.

Rise (fall) in either the current account deficit or foreign exchange reserves must be accompanied by a rise (fall) in foreign savings (borrowing from abroad).

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Savings-Investment Balance

Row 10 & Column J:

Total domestic savings finances total investment; Row 10: total domestic savings; government

saving, Sg, private saving, Sp, plus foreign saving (CA).

Column J: Total investment; government investment, Ig, plus private investment, I p.

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National Income Identitiesand Budget Constraints

Gross domestic product and absorption The government budget constraint The private sector budget constraint The balance sheet of the financial system The savings-investment balance

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Gross Domestic Product and Absorption Two approaches for estimating GDP:

expenditure approach and value added approach

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Set row 1 = column A,

Cg + Cp + X + Ig + Ip =

W + + s + OSg + (TI - SUB) + J (1)

GDP at market prices, Y:

Y = C + I + X - J, (2)

with, C = Cp + Cg, and I = Ip and Ig. GDP at factor cost, Yfc:

Yfc = W + + s + OSg (3)

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Y = Yfc + (TI - SUB),

Y: GDP at market price equals Yfc: GDP at factor prices, plus indirect taxes net of subsidies.

J - X = A - Y = I - (Y - C) = I - S,

J - X: net imports, equals A-Y: domestic absorption over output, equals I-S: investment over savings.

Reduction in trade deficit requires decrease (increase) in absorption (domestic savings).

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The Government Budget Constraint Government Revenues/Expenditures,

Row 2 = Column B,

TI - SUB + OSg + TD + NTgf = Cg + NTpg +

(INTpg + INTfg) + Sg (6)

or, Tg - G = Sg (7).

Current public revenues equal current expenditures plus current savings.

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Government savings and borrowing, Row 6 = Column F,

Sg + Lgb + Bp + FBg = Ig (8)

Government savings plus net domestic and foreign borrowing equals physical assets acquired.

Substitute (Tg – G) for Sg in (8):

G + Ig - Tg = Lgb + Bp + FBg (9)

with,

G + Ig - Tg : overall fiscal deficit,

Lgb + Bp + FBg: sources of deficit financing.

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The Private Sector Budget Constraint Private Sector Income/Expenditures

Row 4 = Column D,

W + + s + NTpg + INTpg + NTpf + NFPpf = Cp + TD + INTfp + Sp

or

Yp = CCp + Sp (10)with

CCp = Cp + TD + INTfp

Yp = W + + s + NTpg + INTpg + NTpf + NFPpf

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Private Sector Saving/Borrowing Row 8 = Column H:

Sp + Lpb + FBp = Ip + Bp + M (11)

Substituting (Yp – CCp) for Sp in (11)

Private sector budget constraint:

Yp - CCp

+ Lpb + FBp = Ip + Bp + M

Private sector income plus borrowing net of expenditures equals asset acquisitions; money, physical investment, and lending to the government.

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The External Sector Budget ConstraintExternal sector income/expenditures Row 5 = Column E,

J + INTfg + INTfp = X + NTgf + NTpf + NFPpf + CA .

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External sector saving/borrowing Row 9 = Column I,

CAD = FBg + FBp - R*

CA deficit financing via, increasing net foreign borrowing; drawing down reserves.

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External sector budget constraint:

J - X = F - R*,

with,

J: J + INTfg + INTfp ;

X: X + NTgf + NTpf + NFPpf ; gross payments by domestic economy, J; sum

of imports and all interest payments on external debt;

gross receipts to the domestic economy, X; exports plus net transfers;

and net factor payments from abroad.

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The Balance Sheet of the Financial System Pure Intermediary: not budget constraint per se,

but rather a balance sheet accounting identity. Row 7 = Column G,

L + R* = M,

with

L = Lgb + Lpb, R* = M - L

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Increases (decreases) in domestic credit (L), with money demand unchanged, result in decreases (increases) in foreign reserves.

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The Savings-Investment Balance Add budget constraints of the government and

private sectors to yield:

S + L + F = I + M.

Given that

F = J - X + R*,

Then

S + L + (J - X) + R* = I + M

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Savings-investment balance: With

L + R* = M,

we have,

I = S + (J - X)

Domestic investment, I, financed by domestic savings, S, and foreign saving, J - X, (e.g. the current account deficit, CA).

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A Three-Good Model with Banks

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Open-economy macroeconomic model Accounting relationships integrated with behavioral

equations to analyze transmission process of macroeconomic policy and exogenous shocks.

5 agents: households, producers, commercial banks, the government, and the central bank.

All households, firms, banks are identical in endowments and behavior.

Exchange rate fixed. Economy produces two goods: home good and

exportable good. Fixed capital stock and perfect labor mobility.

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Households Supply labor inelasticaly. Consume both home and importable goods. Four types of financial assets: domestic money,

bank deposits, domestic bonds, and foreign bonds.

Financial assets are imperfect substitutes. Consumption decisions: two stage process.

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Stage 1: Consumption determined by,

C = (1 - s)(Y - T), 0 < s < 1, (20)

Y: net factor income,

T: lump-sum taxes,

s: marginal propensity to save.

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Stage 2: consumption of imported goods (CI) and home goods (CN) by,

CI = (1 - )C, (21)

: share of home goods in private expenditures.

PNCN = EC (22)

Using (20), (22) rewritten as,

CN = zC = z(1 - s)(Y - T) (23)

z E/PN: real exchange rate.

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Asset Demand Equations: Money Demand: Md = Md(ib,Y) (24)

Demand for Bank Deposits: Dp = Dp(id,ib,Y)(25)

- +

+ - +

Demand for Foreign Bonds:

B* = (i* + a - ib ), > 0, (26)

i* : interest rate spread of foreign minus domestic bonds,

a : expected nominal exchange rate devaluation,

: degree of substitutability, or capital mobility in fixed income markets.

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Uncovered Interest Parity Condition:

ib = i* + a

holds, when , e.g. perfect capital mobility.

Using (24), (25), and (26), demand function for domestic bonds, B given by,

B = W - Md - Dp - B*.

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Firms and the Labor MarketWorking capital needs financed via commercial

banks.

Total Production Costs: Labor costs (only) plus interest payments on bank

loans.

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Maximization problem written as:

max Yh - h Nh - iLLh, (27)

h: as exportable (h = X) and non-tradable goods (h = N)

Yh: output of good h,

Nh: quantity of labor employed in sector h,

h : product wage in sector h,

Lh: bank loans obtained by firm operating in sector h, iL: nominal bank lending rate.

Yh

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Output-employment relationship,

Nh = Yh , > 1, (28)

decreasing returns to labor. Firm’s financial constraint:

Lh h Nh , (29)

bank loans must cover labor cost.

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Output supply inversely related to the effective product wage h(1+iL).

Labor demand [(30) into (28)]:

Nhd = Nh

d[h(1+iL)], Nhd < 0 (31)

Maximizing (27) subject to (28) and (29) yields,

h(1+iL)

1/(-1)

{ }Yhs = 1

(30)

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Firm’s demand for credit:

Lhd = whNh

d = Lhd[wh,iL]. (32)

Wage increase both raises labor costs and lowers demand for labor.

-?

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Wage determination Wages are perfectly flexible. Zero unemployment: perfect labor mobility

across sectors. Exportable/nontradable sector wages related by,

N = zX (33)

Equilibrium real wage negatively related to the real exchange rate and the bank lending rate,

X = WX(z,iL) (34)--

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Output of exportables (home goods) is positively (negatively) related to the real exchange rate.

Demand for credit, Ld, in terms of exportables,

Sectoral supply equations: Substituting (33) and (34) into (30) yields,

YXs = YX

s(z,iL), YNs = YN

s(z,iL) (35)- -+ -

Ld = LXd + z-1LN

d = Ld(z,iL)- -

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Commercial Bank Bank assets: credit extended to firms, Ls, and

reserves held at the central bank, RR. Bank liabilities: deposits held by households, Dp.

Dp = Ls + RR

RR = Dp,

: coefficient of reserve requirements.

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Supply of credit:

Ls = (1 - )Dp

Under zero-profit conditions, lending/deposit rates,

iL = id / (1 - )

Credit supply given by,

Ls = (1 - )Dp[(1- )iL,ib,Y].

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Government and the Central Bank Government:

levies lump-sum taxes on households; consumes home goods, in quantity GN .

Central Bank: ensures the costless conversion of domestic

currency holdings into foreign currency at the prevailing fixed exchange rate, E;

lends only to the government; does not engage in sterilized intervention.

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Real money supply, Ms, given by

Ms = Lg +R* ,

R*: foreign currency reserves.

Lg : credit to the government (exogenously determined).

R*: determined by the balance of payments; capital and current accounts,

R* = YXs - CI - B*,

substituting,

R* = YXs - (1 - )C + (ib - i* - a).

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Credit Market

Equilibrium condition:

Ls = Ld

Equilibrium bank lending rate:

Money Market:

Equilibrium condition:

Ms = Md(ib,Y)

Solving for ib yields,

iL = iL(z,ib). ?+

Equilibrium Conditions.

ib iL z, ambiguous, why?

real depreciation causes increase in output and demand for bank deposits, lowering lending rate.

and raises demand for loans, causing an increase in lending rate to maintain credit market equilibrium.

ib = ib(z,iL;Ms)- - -

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Can be solved for the equilibrium real exchange rate as,

z = (iL;T,GN).

The market for home goods Equilibrium condition of the market for home goods,

CN + GN - YNs = 0.

- + -

Thus, an increase in bank lending, or government spending on home goods requires an appreciation of the real exchange rates, z falls.

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Extensions:

Model can be applied to variety of macroeconomic issues:

Effects of changes in government spending on the real exchange rate, domestic interest rates, and capital flows.

Study terms of trade shocks: Unlike a dependent-economy framework, the production structure adopted here allows a distinction between the terms of trade and the real exchange rate (Figure 8.4).

Credit market imperfections, introduced through mark-up pricing by banks (see Agénor and Aizenman, 1999).

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Figure 8.4aDeveloping Countries: Non-oil Commodity Prices, 1980-94

(1990 = 100)

Sources: International Monetary Fund and The Economist.

Jan80 Jan82 Jan84 Jan86 Jan88 Jan90 Jan92 Jan94

70

80

90

100

110

120

130

140 In U.S. dollars

The Economist index

IMF index

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Figure 8.4bDeveloping Countries: Non-oil Commodity Prices, 1980-94

(1990 = 100)

Sources: International Monetary Fund and The Economist.

1/ Deflated by the price of exports of manufactured goods by industrial countries.

Jan80 Jan82 Jan84 Jan86 Jan88 Jan90 Jan92 Jan94

70

80

90

100

110

120

130

140

150

160

170

180 In real terms 1/

IMF index

The Economist index

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Production of importables and imported intermediate inputs can also be integrated in the analysis.

Two Limitations Behavioral functions for consumption and asset

demand functions are postulated rather than derived from microeconomic considerations.

The static nature of the model implies that the stock budget constraints that the various agents faced are not explicitly accounted for.

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An Intertemporal Framework

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Intertemporal model: addresses limitations of three-good model presented earlier; explicitly derives behavioral rules from an

optimization framework; accounts for agents’ flow and stock budget

constraints in a dynamic setting, ensuring across periods.

Useful in understanding current account deficits.

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Basic Structure: Two-period model. No financial assets. Only one good. Assumes perfect foresight, optimal behavior of

individual agents, and perfect capital mobility. Output is supply determined with full employment

assumed.

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GNP, Y, given as,

Y = Q + Z,

Q: GDP;

Z: net factor payments from abroad.

Y + R = C + Sp + T

thus GNP, Y, plus net unilateral transfers from

abroad, R, can be used for consumption, savings

and taxes.

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Current Account Surplus, CA, defined in three equivalent ways: exports minus imports of goods and services plus

unilateral transfers and net factor payments from abroad (income transfers, for short),

CA = X - J + Z + R,

national income minus domestic absorption,

CA = Y - (C + I + G) + R,

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national saving minus domestic investment,

CA = S - I, with

S = Sp + Sg .

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Model: Two periods; present (t = 1) and future (t = 2). Single household with utility function U(C1,C2),

Supply Side of Model:

Y10 and Y2

0

initial endowments (income) for each agent in periods 1 and 2.

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Intertemporal investment decisions: output in the second period Y2, is linked to the endowment Y2

0 through the following relationship:

Y2=Y20 + I1

, 0 < < 1

with

I1 = Y1

0 - C1

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Return on marginal project, 1+r: Ratio of return to cost;

-C2/C1 = 1 + r.

Production possibility frontier (PPF): Figure 8.5,

slope given by -(1+r).

In autarchy, household's PPF = consumption possibility frontier.

Equilibrium at tangency between PPF and consumer indifference curves.

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Figure 8.5The Two-Period Intertemporal Model

Source: Lee and Szenberg (1994, p. 994).

V

R

E

U

H

U

C1W1

DW1

1

2

C1RC1

A

C2R

C2A

Y2

C2

Slope: -(1+i)

Slope: -(1+i*)

Y20

Y 10

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Household (country) maximization problem:

max U(C1,C2),

subject to production constraint,

F(C1-Y10,C2 - Y2

0) = 0

C1, C2

Solution found at F1/F2 = UC1/UC2,

F1/F2 = 1 + r,

UC1/UC2 = 1 + .

= r.

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In autarchy, savings must necessarily equal investment .

serves as the ex post discount rate and the autarchy interest rate, i.

~

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Financial Openness: If world interest rate, i*, is lower than the autarchy

interest rate i, it is optimal to run a current account deficit (capital account surplus).

Maximize the present value of profits, PV, given by,

PV = I1 /(1 + i)* - I1

With financial openness, i domestic converges to i* foreign.

Firms will increase investment, I1, until the rate of return on the marginal project, r, equals the world interest rate.

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Figure 8.5 shows the effect of financial openness on investment levels demonstrating with isovalue lines and the tranformation function.

Isovalue line: maximum level of wealth, W1,

H + Y2/(1 +i*) = Y10 + Y2

0/(1 + i*) + PVm

W1

Household’s intertemporal budget constraint

C1 + C2/(1 +i*) = Y10 + Y2

0/(1 + i*) + PVm

W1

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First period budget constraint,

C1 = Y10 + L1 - I1

Second-period budget constraint,

C2 = Y20 + I1

- (1 + i*)L1

L1: first period borrowing

-(1 + i*)L1: gross repayment in second period.

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Current Account Period 1, CA, (surplus)

CA1 = Y10 - C1 - I1

e.g. domestic savings minus investment

and

also equal to the trade balance, TB1.

Period 2, CA,

CA2 = Y2 - C2 - i*L1

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Intertemporal solvency: Discounted sum of first period and second period

trade accounts equal zero:

TB1 + TB2/(1 + i*) = 0.

Current account

CA1 + (CA2 - L1)/(1 + i*) = 0.

Homothetic utility function: given i, ratio of consumption in two periods is independent of wealth level.

See Figure 8.5.