Chapter 8
Aggregate Accounts,
Budget Constraints, and
Model Consistency
© Pierre-Richard Agénor
The World Bank
1





Production, Income, and Expenditure
A Consistency Accounting Matrix
National Income Identities and Budget
Constraints
A Three-Good Model with Banks
An Intertemporal Framework
2
Production, Income,
and Expenditure
3



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.
4
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.
5
A Consistency Accounting Matrix


Current account transactions
Capital account transactions
6

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.
7
Current Account Transactions
8


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.
9
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.
10
National Accounts
 Row 1, allocation of goods, services produced
domestically, Y, or imported, J, between:
g
 government consumption, C ;
p
 private consumption, C ;
 exports, X;
g
 government and private sector investment, I
and Ip, with I = Ig + Ip.
11
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.

12
National Accounts
 GDP at factor costs, Yfc: sum of employee
compensation (wages, salaries and incomes of ownaccount 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.
13
Current Government Transactions
Row 2 & Column B:
g
 Government savings, S , given by,
Sg = Tg - G,
Tg = TI - SUB + OSg + TD + NTgf,
G = Cg + NTpg + INTpg + INTfg .
14

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.
15
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;
fg
 interest payments on public foreign debt, INT .
16
Financial Sector
Row 3 & Column C:
 Financial system: pure intermediary. There is no
independent revenues, expenditure accounts.
17
Nonfinancial Private Sector
Row 4 & Column D:
p
p
 Private saving, S : total private sector income, Y ,
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.
18
Nonfinancial Private Sector
Row 4 & Column D:
p
 Row 4: private sector revenues, Y , as,
 factor income, including wages and salaries, W,
profits, , and incomes of the self-employed, s;
p
 net transfers received from the government, NT ;
 interest payments received on government debt
holdings, INTpg;
pf
 net transfers, NT , plus net factor payments from
abroad, NFPpf.
19
Nonfinancial private sector
Row 4 & Column D:
p
 Column D: private sector expenditures, CC , as,
p
 private consumption, C ;
 payment of direct taxes, TD;
fp
 interest payments on private external debt, INT .
20
External Sector
Row 5 & Column E:
 Current Account Balance, CA: - (savings by foreign
residents);
CA = X + (NTgf + NTpf) + NFPpf - J - INTfg
- INTfp
21
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,
22
NFPpf.
Capital Account Transactions
23
Financing of asset acquisition by government,
private nonfinancial sector, and external sector.
Government
Row 6 & Column F:


Row 6: sources of financing:
g
 government savings, S ;
gb
 net borrowing from the financial system,L ;
p
 net borrowing from the private sector, B ;
g
 net foreign borrowing, FB .
Column F: gross fixed capital investment by the
government, Ig.
24
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;
gb
 loans to the government, L ,
pb
 loans to the private sector, L ,
*
 net foreign assets, R .
25
Nonfinancial Private Sector
Row 8 & Column H:
 Row 8: private sector asset acquisition financing;
p
 private sector savings, S ,
pb
 net borrowing from the financial system, L ,
p
 net borrowing from abroad, FB .
 Column H: private sector asset acquisitions;
p
 private investment, I ; physical assets, inventories
and working capital, plus intangible nonfinancial
assets;
p
 net lending to the government, B ;
 increases in holdings of monetary assets, M, that
is, liabilities issued by the financial sector.
26
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).
27
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.
28
National Income Identities
and 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
29
Gross Domestic Product and Absorption

Two approaches for estimating GDP:
expenditure approach and value added
approach
30

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)
31
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).
32
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.
33

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,
34
Lgb + Bp + FBg: sources of deficit financing.
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
35
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.
36
The External Sector Budget Constraint
External sector income/expenditures
 Row 5 = Column E,
J + INTfg + INTfp = X + NTgf + NTpf + NFPpf
+ CA .
37
External sector saving/borrowing
 Row 9 = Column I,
CAD = FBg + FBp - R*

CA deficit financing via,
 increasing net foreign borrowing;
 drawing down reserves.
38
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.
39
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
40

Increases (decreases) in domestic credit (L), with
money demand unchanged, result in decreases
(increases) in foreign reserves.
41
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
42
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).
43
A Three-Good Model with
Banks
44
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.
45
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.
46

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.
47

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.
48


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.
49

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*.
50
Firms and the Labor Market
Working capital needs financed via commercial
banks.
Total Production Costs:
 Labor costs (only) plus interest payments on bank
loans.
51

Maximization problem written as:
max Yh - h Nh - iLLh, (27)
Yh
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.
52

Output-employment relationship,
Nh = Yh ,  > 1,

(28)
decreasing returns to labor.
Firm’s financial constraint:
L h  h N h ,
(29)
bank loans must cover labor cost.
53

Maximizing (27) subject to (28) and (29) yields,
Yhs


=
{
1
h(1+iL)
1/(-1)
}
(30)
Output supply inversely related to the effective
product wage h(1+iL).
Labor demand [(30) into (28)]:
Nhd = Nhd[h(1+iL)], Nhd < 0 (31)
54

Firm’s demand for credit:
?
-
Lhd = whNhd = Lhd[wh,iL]. (32)

Wage increase both raises labor costs and lowers
demand for labor.
55
Wage determination
 Wages are perfectly flexible.
 Zero unemployment: perfect labor mobility
across sectors.
 Exportable/nontradable sector wages related by,

N = zX (33)

Equilibrium real wage negatively related to the real
exchange rate and the bank lending rate,
-X = WX(z,iL) (34)
56
Sectoral supply equations:
 Substituting (33) and (34) into (30) yields,
YXs = YXs(z,iL), YNs = YNs(z,iL) (35)
+ -


-
Output of exportables (home goods) is positively
(negatively) related to the real exchange rate.
Demand for credit, Ld, in terms of exportables,
Ld =
LXd +
z-1LNd =
d
L (z,i
L)
57
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.
58

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].
59
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.
60

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).
61
Equilibrium Conditions.
Money Market:
Equilibrium condition:
Ms = Md(ib,Y)
Solving for ib yields,
- - -s
ib = ib(z,iL;M )
Credit Market
Equilibrium condition:
Ls = Ld
Equilibrium bank lending
rate:
?+
iL = iL(z,ib).
 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
62
market equilibrium.
The market for home goods
 Equilibrium condition of the market for home goods,
CN + GN - YNs = 0.

Can be solved for the equilibrium real exchange rate
as,
- + -
z = (iL;T,GN).

Thus, an increase in bank lending, or government
spending on home goods requires an appreciation
of the real exchange rates, z falls.
63
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 dependenteconomy 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).
64
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66



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.
67
An Intertemporal Framework
68


Intertemporal model: addresses limitations of threegood 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.
69
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.
70

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.
71

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,
72

national saving minus domestic investment,
CA = S - I,
with
S = Sp + Sg .
73
Model:
 Two periods; present (t = 1) and future (t = 2).
 Single household with utility function U(C1,C2),

Supply Side of Model:
Y10 and Y20
initial endowments (income) for each agent in periods
1 and 2.
74

Intertemporal investment decisions: output in the
second period Y2, is linked to the endowment Y20
through the following relationship:
Y2=Y20 + I1,
0<<1
with
I1 = Y10 - C1
75
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.

76
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
Household (country) maximization problem:
max U(C1,C2),
C 1, C 2
subject to production constraint,
F(C1-Y10,C2 - Y20) = 0

Solution found at F1/F2 = UC1/UC2,
 F1/F2 = 1 + r,
 UC1/UC2 = 1 + .
  = r.
78


In autarchy, savings must necessarily equal
investment .
~ serves as the ex post discount rate and the
autarchy interest rate, i.
79
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.
80


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 + Y20/(1 + i*) + PVm
 W1

Household’s intertemporal budget constraint
C1 + C2/(1 +i*) = Y10 + Y20/(1 + i*) + PVm
 W1
81

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.
82
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
83
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.
84
See Figure 8.5.