financial programming thorvaldur gylfason an introduction
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Financial ProgrammingFinancial Programming
Thorvaldur GylfasonThorvaldur Gylfason
An IntroductionAn Introduction
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 Analytical model
Financial programming in action
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, 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 - - M - M - BB
ExternalExternal sector X – Z = X – Z = R - R - 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 slow down*Or 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 exampleNumerical example 4
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 = 800, D = 800, D-1-1 = 700, R = 700, R-1-1 = 100 = 100
Recall: Recall: M = D + RM = D + R
PPxxXX-1-1 = 750, Z = 750, Z-1-1 = 800, F = 800, F-1-1 = 50 = 50
Recall: Recall: R = PR = PxxX – PX – PzzZ + FZ + F
So,So,RR-1-1 = 750 – 800 + 50 = 0 = 750 – 800 + 50 = 0Current account deficit, overall balanceCurrent account deficit, overall balance
RR-1-1/P/PzzZZ-1-1 = 100/800 = 0.125 = 100/800 = 0.125Equivalent to 1.5 (= 0.125Equivalent to 1.5 (= 0.125••12) months of 12) months of
importsimportsWeak reserve positionWeak reserve position
HistoryHistory 1.5 months = 6 1.5 months = 6
weeksweeks
PPxxX grows by a third, so PX grows by a third, so PxxX = 1,000X = 1,000
F doubles, so F = 100F doubles, so F = 100
Suppose R* is set at 240. ThenSuppose R* is set at 240. ThenPPzzZ = PZ = PxxX + F + RX + F + R-1-1 – R* – R*
= 1,000 + 100 + 100 – 240 = 960= 1,000 + 100 + 100 – 240 = 960
Level of imports is consistent with R*Level of imports is consistent with R*RR**/P/PzzZ = 240/960 = 0.25Z = 240/960 = 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 PIncrease in PzzZ from 800 to 960, i.e., Z from 800 to 960, i.e., by 20%, is consistent with Rby 20%, is consistent with R** equivalent to 3 months of importsequivalent to 3 months of imports
Now, recall that PNow, recall that PzzZ depends on PY 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 1, M can also increase by 20% 1, M can also increase by 20%
Recall quantity theory of moneyRecall quantity theory of moneyMV = PYMV = PY
Constant velocity means that Constant velocity means that
%%M = %M = %PY = %PY = %P + %P + %YY
Hence, M can expand from 800 to 960Hence, M can expand from 800 to 960
Forecast for Forecast for moneymoney
˜
Recall M = D + M = D +
RR
Having set reserve target at R* = 240 Having set reserve target at R* = 240 and forecast M at 960, we can now and forecast M at 960, 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 = 960 – 240 = 720, up from 700So, D = 960 – 240 = 720, up from 700D/DD/D-1-1 = 20/700 = 2.9% = 20/700 = 2.9%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
PPxxX grows by a third, so PX grows by a third, so PxxX = 1,000X = 1,000
F doubles, so F = 100, as beforeF doubles, so F = 100, as before
R* is now set at 200, not 240. ThenR* is now set at 200, not 240. ThenPPzzZ = PZ = PxxX + F + RX + F + R-1-1 – R* – R*
= 1,000 + 100 + 100 – 200 = 1,000= 1,000 + 100 + 100 – 200 = 1,000
Level of imports is consistent with R*Level of imports is consistent with R*RR**/P/PzzZ = 200/1000 = 0.2Z = 200/1000 = 0.2Equivalent to 2.4 (= 0.2Equivalent to 2.4 (= 0.2••12) months of 12) months of
importsimports
Forecast for balance Forecast for balance of paymentsof payments
BOP BOP fore-fore-castscasts
So try again
Increase in PIncrease in PzzZ from 800 to 1,000, i.e., Z from 800 to 1,000, i.e., by 25%, is consistent with Rby 25%, is consistent with R** equivalent to 2.4 months of importsequivalent to 2.4 months of imports
Now, recall that PNow, recall that PzzZ depends on PY 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 25% 25% E.g., 5% growth and 20% inflation, E.g., 5% growth and 20% inflation,
roughlyroughly
Forecast for real Forecast for real sectorsector
If PY can increase by 25%, then, if If PY can increase by 25%, then, if income elasticity of money demand is income elasticity of money demand is 1, M can also increase by 25% 1, M can also increase by 25%
However, if income elasticity of However, if income elasticity of money demand is 0.8, M can money demand is 0.8, M can increase by only 20% as beforeincrease by only 20% as before
Hence, if the income elasticity is 1, M Hence, if the income elasticity is 1, M can expand from 800 to 1,000can expand from 800 to 1,000
Forecast for Forecast for moneymoney Recall M = D + M = D +
RR
Having set reserve target at R* = 200 Having set reserve target at R* = 200 and forecast M at 1,000, we can now and forecast M at 1,000, 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 = 1,000 – 200 = 800, up from 700So, D = 1,000 – 200 = 800, up from 700D/DD/D-1-1 = 100/700 = 14% = 100/700 = 14%Still restrictive, given that PY rises by Still restrictive, given that PY rises by
25%, but less restrictive than before 25%, but less restrictive than before
Determination of creditDetermination of credit
Known at beginning of program period:Known at beginning of program period: MM-1-1 = 800, D = 800, D-1-1 = 700, R = 700, R-1-1 = 100 = 100
Recall: Recall: M = D + RM = D + R
XX-1-1 = 500, Z = 500, Z-1-1 = 600, F = 600, F-1-1 = 50 = 50
Recall: Recall: R = PR = PxxX – PX – PzzZ + FZ + F
So,So,RR-1-1 = 500 – 600 + 50 = -50 = 500 – 600 + 50 = -50Current account deficit (-100), smaller overall Current account deficit (-100), smaller overall
deficitdeficit
RR-1-1/P/PzzZZ-1-1 = 100/600 = 0.167 = 100/600 = 0.167Equivalent to 2 (= 0.167*12) months of Equivalent to 2 (= 0.167*12) months of
importsimportsWeak reserve positionWeak reserve position
HistoryHistory Once more
PPxxX grows by 40%, so PX grows by 40%, so PxxX = 700X = 700
F doubles, so F = 100F doubles, so F = 100
Suppose R* is set at 180. ThenSuppose R* is set at 180. ThenPPzzZ = PZ = PxxX + F + RX + F + R-1-1 – R* – R*
= 700 + 100 + 100 – 180 = 720= 700 + 100 + 100 – 180 = 720
Level of imports is consistent with R*Level of imports is consistent with R*RR**/P/PzzZ = 180/720 = 0.25Z = 180/720 = 0.25Equivalent to 3 (= 0.25*12) months of Equivalent to 3 (= 0.25*12) months of
importsimports
Forecast for balance Forecast for balance of paymentsof payments
BOP BOP fore-fore-castscasts
Increase in PIncrease in PzzZ from 600 to 720, i.e., Z from 600 to 720, i.e., by 20%, is consistent with Rby 20%, is consistent with R** equivalent to 3 months of importsequivalent to 3 months of imports
But PBut PzzZ depends on PY 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 1, M can also increase by 20% 1, M can also increase by 20%
Hence, M can expand from 800 to 960Hence, M can expand from 800 to 960
Forecast for Forecast for moneymoney Recall M = D + M = D +
RR
Having set reserve target at R* = 180 Having set reserve target at R* = 180 and forecast M at 960, we can now and forecast M at 960, we can now compute level of credit that is compute level of credit that is consistent with our reserve targetconsistent with our reserve target
So, D = 960 – 180 = 780, up from 700So, D = 960 – 180 = 780, up from 700D/DD/D-1-1 = 80/700 = 11% = 80/700 = 11%Quite restrictive, given that PY rises by Quite restrictive, given that PY rises by
25%25%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
PPzzZ = PZ = PxxX + F + RX + 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 Financial programming is an oral
tradition that spans the entire history of the IMF
When expressed in simple algebra, financial programming is not to be taken literally as a one-size-fits-all modelFund 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