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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
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
G – T + I – S + X – Z = 0,
so left-hand sides sum to
zero
An alternative derivation of monetary survey
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
An alternative derivation of monetary survey
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
An alternative derivation of monetary survey
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
An alternative derivation of monetary survey
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
An alternative derivation of monetary survey
PublicPublic sector G – T = G – T = B + B + DDGG + + 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
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
Monetary approach to balance of payments
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
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
National accountsNational accountsY = E + X – Z
LinkagesLinkages
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
LinkagesLinkages
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Linkages: ReservesLinkages: Reserves
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Linkages: Current accountLinkages: Current account
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Linkages: Foreign creditLinkages: Foreign credit
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Linkages: Credit to governmentLinkages: Credit to government
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
LinkagesLinkages
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Private sector accountsPrivate sector accountsI – S = DP – M – B
Linkages: Linkages: BondsBonds
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Private sector accountsPrivate sector accountsI – S = DP – M – B
Linkages: Linkages: MoneyMoney
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Private sector accountsPrivate sector accountsI – S = DP – M – B
Linkages: Linkages: Private creditPrivate credit
Balance of paymentsBalance of paymentsR = X – Z + F = X – Z + DF
Monetary accountsMonetary accountsM = D + R= DG + DP + R
National accountsNational accountsY = E + X – Z
Fiscal accountsFiscal accountsG – T = B + DG + DF
Private sector accountsPrivate sector accountsI – S = DP – M – B
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