Interrelations Among Macroeconomic Accounts

Interrelations Among Interrelations Among Macroeconomic AccountsMacroeconomic Accounts

Thorvaldur GylfasonThorvaldur GylfasonLivingstone, ZambiaLivingstone, Zambia

10-21 April 200610-21 April 2006

OutlineOutline

Monetary approach to balance of balance of paymentspayments

Accounting relationshipsTrace linkageslinkages among

oBalance of payments accountsoNational income accountsoFiscal accountsoMonetary accounts

Proceed from linkages to financial programmingfinancial programming Numerical examples

What is money?What is money?

Liabilities of banking systembanking system to the public That is, the private sector and public enterprises

M = C + TM = C + T C = currency, T = deposits

The broader the definition of deposits ...Demand deposits, time and savings deposits, etc.,

... the broader the corresponding definition of moneyM1, M2, M3, etc.

1

Overview of banking system

C entra l Bank C om m ercia l Banks

Banking System(M onetary Survey)

O ther F inancia l Institu tions

Financia l System

Balance sheet of Central Bank

AssetsLiabilitie

s

DG C

DB B

RC

DG = domestic credit to government

DB = domestic credit to commercial banks

RC = foreign reserves in Central Bank

C = currency

B = commercial bank deposits in Central Bank

Balance sheet of Commercial Banks

AssetsLiabilitie

s

DP DB

RB T

B

DP = domestic credit to private sector

RB = foreign reserves in commercial banks

B = commercial bank deposits in Central Bank

DB = domestic credit from Central Bank to commercial banks

T = time deposits

DG + DP + DB + RB + RC + B = C + T + B + DB

Adding up the two balance sheets

D R

MHence, M = D + R

Balance sheet of banking system

Monetary Survey

AssetsLiabilitie

s

D M

R

D = DG + DP = net domestic credit from banking system (net domestic assets)

R = RC + RB = foreign reserves (net foreign assets)

M = money supply

A fresh view of money

The monetary survey implies the following new definition of money:

M = D + RM = D + Rwhere M is broad money (M2), which equals narrow

money (M1) + quasi-money One of the most useful equations in economics Money is, by definition, equal to the sum of

domestic credit from the banking system (net domestic assets) and foreign exchange reserves in the banking system (net foreign assets)

An alternative derivation of monetary survey

PublicPublic sector G – T = G – T = B + B + DDGG + + DDFF

Private Private sector I – S = I – S = DDPP - - M - M - BB

External External sector X – Z = X – Z = R - R - DDFF

Now, add them up



Private Private sector I – S = I – S = DDPP - - M - M - BB

External External sector X – Z = X – Z = R - R - DDFF

G – T + I – S + X – Z = 0,

so left-hand sides sum to

zero


PublicPublic sector G – T = G – T = BB + + DDGG + + DDFF

PrivatePrivate sector I – S = I – S = DDPP - - M - M - BB

ExternalExternal sector X – Z = X – Z = R - R - DDFF















PrivatePrivate sector I – S = I – S = DDPP - - MM - - BB

ExternalExternal sector X – Z = X – Z = RR - - DDFF

So, adding them up, we get: 0 = D - M + R because DDGG + D + DPP = D = D

Hence,

M = D + RM = D + R

Monetary approach to balance of payments

The monetary survey (M = D + RM = D + R) has three key implications:

Money is endogenousendogenous If RR increases, then MM increases Important in open economies

Domestic creditDomestic credit affects money If RR increases, may want to reduce DD to contain MM

R = R = M - M - DD Here R = X – Z + FR = X – Z + F Monetary approach to balance of payments


The monetary approach to the balance of payments (R = R = M - M - DD) has the following implications:

Need to Forecast M

And then Determine D

In order to Meet target for R

DD is determined as a residual given both MM and R*R*R*R* = reserve target, e.g., 3 months of imports

Essence of Essence of

financial financial

programmingprogramming


Domestic credit is a policy variable that involves both monetary and fiscal policy

Can reduce* domestic credit (DD) To private sectorTo public sector

• By reducing government spending• By increasing taxes

Monetary and fiscal policy are closely related through domestic credit

*Or rather slow down*Or rather slow down

LinkagesLinkages

Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF

2

LinkagesLinkages


National accountsNational accountsY = E + X – Z

LinkagesLinkages



Fiscal accountsFiscal accountsG – T = B + DG + DF

LinkagesLinkages


Monetary accountsMonetary accountsM = D + R= DG + DP + R



Linkages: ReservesLinkages: Reserves





Linkages: Current accountLinkages: Current account





Linkages: Foreign creditLinkages: Foreign credit





Linkages: Credit to governmentLinkages: Credit to government





LinkagesLinkages





Private sector accountsPrivate sector accountsI – S = DP – M – B

Linkages: Linkages: BondsBonds






Linkages: Linkages: MoneyMoney






Linkages: Linkages: Private creditPrivate credit






ModelModel

Express accounting linkages in terms of simple algebra

Use model to describe how nominal income and reserves depend on domestic creditDemonstrate how BOP target translates into

prescription for fiscal and monetary policy Financial programming in action

3

List of variablesList of variables

M = moneyD = domestic creditR = foreign reservesR = R-R-1 = balance

of paymentsP = price levelY = real incomev = velocity

X = real exportsPx = price of exports

Z = real importsPz = price of imports

F = capital inflowm = propensity to

import

Two behavioral

parameters: m and v

List of relationshipsList of relationships

M = D + R (monetary survey)

M = (1/v)PY (money demand)

R = (1/v)PY – D (M schedule)

R = PxX – PzZ + F (balance of

payments)

PzZ = mPY (import demand)

R = PxX – mPY + F + R-1 (B schedule)Estimate m and v by

regression analysis

The M scheduleThe M schedule

Reserves (R)

GNP (PY)

M schedule

1

v

R = (1/v)PY – D

D up

An increase in reserves increases demand for money, and hence also income

PY = v(R + D)

PY is nominal income

The B scheduleThe B schedule

Reserves (R)

GNP (PY)

B schedule

1

m

R = PxX – mPY + F + R-1

F up, e down

An increase in income encourages imports, so that reserves decline

Solution to modelSolution to model

Two equations in two unknowns1) R = (1/v)PY – D 2) R = PxX – mPY + F + R-1

Solution for R and PY

FXPRDmv

vPY x

11

Dmv

mvFXPR

mvR x

11

11

Multipliers: AlgebraMultipliers: Algebra

mv

v

dD

dPY

1 mv

v

XdP

dPY

x

1

mv

mv

dD

dR

1 mvXdP

dR

x

1

1

Multipliers: NumbersMultipliers: Numbers

22

4

4)4/1(1

4

dD

dPY

2

1

4)4/1(1

4)4/1(

dD

dR

Suppose m = ¼ and v = 4

Credit multiplier

Half of credit

expansion

leaks abroad

through balance of

payments

Macroeconomic equilibriumMacroeconomic equilibrium

GNP (PY)

M schedule

Equilibrium

B schedule

Reserves (R)

D up

F up, e down

Economic modelsEconomic models

Exogenousvariables

Endogenousvariables

Model

Change in domestic credit or the exchange rate

Financial programming model

Foreign reserves and nominal income

Experiment: Export boomExperiment: Export boom

M schedule

B schedule

Reserves (R)

GNP (PY)

A

Export boomExport boom

GNP (PY)

M

BB’

A

C

Exports increase

Reserves (R)

Export boomExport boom

GNP (PY)

M

BB’

A

C

Reserves (R)

An increase in exports increases both reserves and nominal income

An interpretationAn interpretation

Exogenousvariables

Endogenousvariables

Model

Export boom orcapital inflow

Financial programming model

Foreign reserves and nominal income increase

Another experiment: Another experiment: Domestic credit expansionDomestic credit expansion

GNP

M

B

D upM’

A

C

An increase in D increases PY, but reduces R.

Reserves (R)

D up M up PY up PzZ up R down

Domestic credit contractionDomestic credit contraction

GNP (PY)

M

B

D down

M’

A

When D falls, M also falls, so that PY goes down and PzZ also decreases. Therefore, R increases. Here, an improvement in the reserve position is accompanied by a decrease in income.

R*

C

Reserves (R)

Too low reserves

Domestic credit contraction Domestic credit contraction accompanied by devaluationaccompanied by devaluation

GNP (PY)

M

B

F up, e down

D down

B’

M’

A

C

When D falls, M also falls, so that PY goes down and PzZ also decreases. Therefore, R increases. Further, a devaluation strengthens the reserve position and helps reverse the decline in income.

R*

Reserves (R)

Comparative statics: Comparative statics: An overviewAn overview

D PxX F e

R - + + - -

PY + + + - +

= inflation= inflation

Experiment: Experiment: Inflation goes upInflation goes up

M

B schedule

Reserves (R)

GNP (PY)

M’

A

C

An increase in inflation () increases v, so the M schedule becomes flatter. Hence, R goes down and PY increases in the short run.

up

Experiment: Experiment: Inflation goes upInflation goes up

M

B schedule

Reserves (R)

GNP (PY)

M’

A

C

An increase in inflation () makes domestic currency appreciate in real terms, so the B schedule shifts left. Hence, R goes farther down and PY can rise or fall in the short run.

up

B’

up eP/P* up X down B shifts left

History and targetsHistory and targets Record history, establish targetsRecord history, establish targets

ForecastingForecasting Make forecasts for balance of payments, Make forecasts for balance of payments,

output and inflation, moneyoutput and inflation, money

Policy decisionsPolicy decisions Set domestic credit at a level that is Set domestic credit at a level that is

consistent with forecasts as well as consistent with forecasts as well as foreign reserve targetforeign reserve target

Numerical examplesNumerical examples 3

1)1)Make forecasts, set reserve target R*Make forecasts, set reserve target R*– E.g., reserves at 3 months of importsE.g., reserves at 3 months of imports

2)2) Compute permissible imports from BOPCompute permissible imports from BOP– More imports will jeopardize reserve More imports will jeopardize reserve

targettarget

3)3) Infer permissible increase in nominal Infer permissible increase in nominal income from import equationincome from import equation

4)4) Infer monetary expansion consistent with Infer monetary expansion consistent with increase in nominal incomeincrease in nominal income

5)5) Derive domestic credit as a residual: D = M Derive domestic credit as a residual: D = M – R*– R*

Financial programming Financial programming step by stepstep by step

Known at beginning of program period:Known at beginning of program period: MM-1-1 = 70, D = 70, D-1-1 = 60, R = 60, R-1-1 = 10 = 10

Recall: Recall: M = D + RM = D + R

XX-1-1 = 30, Z = 30, Z-1-1 = 50, F = 50, F-1-1 = 15 (all nominal) = 15 (all nominal)

Recall: Recall: R = X – Z + FR = X – Z + F

So,So,RR-1-1 = 30 – 50 + 15 = -5, so R = 30 – 50 + 15 = -5, so R-2-2 = 15 = 15Current account deficit, overall deficitCurrent account deficit, overall deficit

RR-1-1/Z/Z-1-1 = 10/50 = 0.2 = 10/50 = 0.2Equivalent to 2.4 (= 0.2Equivalent to 2.4 (= 0.2••12) months of 12) months of

importsimportsWeak reserve positionWeak reserve position

HistoryHistory

X grows by a third, so X = 40X grows by a third, so X = 40

F grows by 40%, so F = 25F grows by 40%, so F = 25

Suppose R* is set at 15 (Suppose R* is set at 15 (R* = 5)R* = 5)Z = X + F + RZ = X + F + R-1-1 – R* – R*

= 40 + 25 + 10 – 15 = 60= 40 + 25 + 10 – 15 = 60

Level of imports is consistent with R*Level of imports is consistent with R*RR**/Z = 15/60 = 0.25/Z = 15/60 = 0.25Equivalent to 3 (= 0.25Equivalent to 3 (= 0.25••12) months of 12) months of

importsimports

Forecast for balance Forecast for balance of paymentsof payments

BOP BOP fore-fore-castscasts

Increase in Z from 50 to 60, i.e., by Increase in Z from 50 to 60, i.e., by 20%, is consistent with R20%, is consistent with R** equivalent equivalent to 3 months of importsto 3 months of imports

Now, recall that Z depends on PY Now, recall that Z depends on PY where P is price level and Y is outputwhere P is price level and Y is output

Hence, if income elasticity of import Hence, if income elasticity of import demand is 1, PY can increase by demand is 1, PY can increase by 20% 20% E.g., 5% growth and 15% inflationE.g., 5% growth and 15% inflation

Forecast for real Forecast for real sectorsector

If PY can increase by 20%, then, if If PY can increase by 20%, then, if income elasticity of money demand is income elasticity of money demand is 2/3, M can increase by 14% 2/3, M can increase by 14%

Hence, M can expand from 70 to 80Hence, M can expand from 70 to 80

Alternatively, by quantity theory of Alternatively, by quantity theory of moneymoneyMV = PYMV = PY

Constant velocity means that Constant velocity means that

%%M = %M = %PY = %PY = %P + %P + %YYIf so, income elasticity of money demand is

1

Forecast for Forecast for moneymoney

˜

Recall M = D + M = D +

RR

Having set reserve target at R* = 15 Having set reserve target at R* = 15 and forecast M at 80, we can now and forecast M at 80, we can now compute level of credit that is compute level of credit that is consistent with our reserve target, consistent with our reserve target, based on M = D + Rbased on M = D + R

So, D = 80 – 15 = 65, up from 60So, D = 80 – 15 = 65, up from 60D/DD/D-1-1 = 5/60 = 8% = 5/60 = 8%Quite restrictive, given that PY rises by Quite restrictive, given that PY rises by

20%20%Implies substantial reduction in domestic Implies substantial reduction in domestic

credit in real termscredit in real terms

Determination of creditDetermination of credit

Financial programming Financial programming step by step: Recapstep by step: Recap

Sequence of stepsSequence of steps

R*R* ZZ YY MM DD

Z = X + F + RZ = X + F + R-1-1 – R – R**

Z = mPYZ = mPY

MV = PYMV = PY

D = M – RD = M – R**

ConclusionConclusionThese slides will be posted on my

website: www.hi.is/~gylfason

The EndThe End The four mains sets of macroeconomic

accounts are closely intertwined These interrelations form the analytical

basis of financial programmingFund economists understand that countries

differ, and they seek to help tailor financial programs to the needs of individual countries

Even so, certain fundamental principles and relationships apply everywhere

Documents

Interrelations Among Macroeconomic Accounts