Financial Programming
An Introduction
Thorvaldur Gylfason
Outline
 Monetary approach to balance of payments
 Accounting relationships
Trace linkages among
o Balance of payments accounts
o National income accounts
o Fiscal accounts
o Monetary accounts
Proceed from linkages to financial programming
 Analytical model
Financial programming in action
What is money?
 Liabilities of banking system to the public
 That is, the private sector and public enterprises
 M=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 money
 M1, M2, etc.
Overview of banking
system
Financial System
Banking System
(Monetary Survey)
Central Bank
Other Financial Institutions
Commercial Banks
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
Central Bank
Assets
Liabilities
DG
C
DB
B
RC
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
Balance sheet of
Commercial Banks
Assets
Liabilities
DP
DB
RB
T
B
Adding up the two
balance sheets
D
R
DG + DP + DB + R B + RC + B
= C + T + B + DB
M
Balance sheet of
banking system
D = DG + DP =
net domestic
credit from
banking system
(net domestic
assets)
RC
RB
R=
+
=
foreign reserves
(net foreign
assets)
M = money supply
Assets
Liabilities
D
M
R
A fresh view of money
The monetary survey implies the following new
definition of money:
M=D+R
where 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
 Public sector
 G – T = B + DG + DF
 Private sector
 I – S = DP - M - B
 External sector
 X – Z = R - DF
An alternative derivation of
monetary survey
 Public sector
 G – T = B + DG + DF
 Private sector
 I – S = DP - M - B
 External sector
 X – Z = R - DF
An alternative derivation of
monetary survey
 Public sector
 G – T = B + DG + DF
 Private sector
 I – S = DP - M - B
 External sector
 X – Z = R - DF
An alternative derivation of
monetary survey
 Public sector
 G – T = B + DG + DF
 Private sector
 I – S = DP - M - B
 External sector
 X – Z = R - DF
An alternative derivation of
monetary survey
 Public sector
 G – T = B + DG + DF
 Private sector
 I – S = DP - M - B
 External sector
 X – Z = R - DF
An alternative derivation of
monetary survey
 Public sector
 G – T = B + DG + DF
 Private sector
 I – S = DP - M - B
 External sector
 X – Z = R - DF
An alternative derivation of
monetary survey
 Public sector
 G – T = B + DG + DF
 Private sector
 I – S = DP - M - B
 External sector
 X – Z = R - DF
So, adding them up, we get: 0 = D - M + R
because DG + DP = D
Monetary approach to
balance of payments
The monetary survey (M = D + R) has three key
implications:
 Money is endogenous
 If R increases, then M increases
 Important in open economies
 Domestic credit affects money
 If R increases, may want to reduce D to contain M
 R = M - D
 Here R = X – Z + F
 Monetary approach to balance of payments
Monetary approach to
balance of payments
The monetary approach to the balance of payments
(R = M - D) has the following implications
Need to
 Forecast M
 And then
 Determine D
 In order to
 Meet target for R
 D is determined as a residual given both M and R*
 R* = reserve target, e.g., 3 months of imports
Monetary approach to
balance of payments
 Domestic credit is a policy variable that
involves both monetary and fiscal policy
 Can reduce* domestic credit (D)
To private sector
To public sector
• By reducing government spending
• By increasing taxes
 Monetary and fiscal policy are closely
related through domestic credit
Linkages
Balance of payments
R = X – Z + F
= X – Z + DF
Linkages
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Linkages
Balance of payments
R = X – Z + F
= X – Z + DF
Fiscal accounts
G – T = B + DG + DF
National accounts
Y=E+X–Z
Linkages
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages: Reserves
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages: Current account
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages: Foreign credit
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages: Credit to
government
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages
Private sector accounts
I – S = DP – M – B
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages:
Bonds
Private sector accounts
I – S = DP – M – B
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages:
Money
Private sector accounts
I – S = DP – M – B
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Linkages:
Private credit
Private sector accounts
I – S = DP – M – B
Balance of payments
R = X – Z + F
= X – Z + DF
National accounts
Y=E+X–Z
Fiscal accounts
G – T = B + DG + DF
Monetary accounts
M = D + R
= DG + DP + R
Model
 Express accounting linkages in terms of
simple algebra
 Use model to describe how nominal
income and reserves depend on domestic
credit
Demonstrate how BOP target translates into
prescription for fiscal and monetary policy
Financial programming in action
List of variables
M = money
D = domestic credit
R = foreign reserves
R = R-R-1 = balance of
payments
P = price level
Y = real income
v = velocity
X = real exports
Px = price of exports
Z = real imports
Pz = price of imports
F = capital inflow
m = propensity to
import
List of relationships
M=D+R
M = (1/v)PY
R = (1/v)PY – D
R = PxX – PzZ + F
PzZ = mPY
R = PxX – mPY + F + R-1
(monetary survey)
(money demand)
(M schedule)
(balance of payments)
(import demand)
(B schedule)
The M schedule
Reserves (R)
M schedule
1
v
D up
R = (1/v)PY – D
PY = v(R + D)
An increase in reserves
increases demand for money,
and hence also income
PY is nominal income
GNP (PY)
The B schedule
Reserves (R)
R = PxX – mPY + F + R-1
An increase in income encourages
imports, so that reserves decline
m
1
F up, e down
B schedule
GNP (PY)
Solution to model
Two equations in two unknowns
1) R = (1/v)PY – D
2) R = PxX – mPY + F + R-1
Solution for R and PY
 v 
PY  
D  R1  PxX  F 
 1  mv 
 1 
 mv 
R
R1  PxX  F   
D
 1  mv 
 1  mv 
Multipliers: Algebra
dPY
v

dD 1  mv
dPY
v

dPxX 1  mv
dR
mv

dD
1  mv
dR
1

dPxX 1  mv
Multipliers: Numbers
Suppose m = ¼ and v = 4
dPY
4
4

 2
dD 1  (1 / 4)4 2
dR
(1 / 4)4
1


dD
1  (1 / 4)4
2
Macroeconomic equilibrium
Reserves (R)
M schedule
D up
Equilibrium
F up, e down
B schedule
GNP (PY)
Economic models
Exogenous
variables
Change in
domestic
credit or the
exchange rate
Model
Financial
programming
model
Endogenous
variables
Foreign reserves
and nominal
income
Experiment: Export boom
Reserves (R)
M schedule
A
B schedule
GNP (PY)
Export boom
Reserves (R)
M
C
A
Exports increase
B’
B
GNP (PY)
Export boom
Reserves (R)
M
C
An increase in exports
increases both reserves
and nominal income
A
B’
B
GNP (PY)
An interpretation
Exogenous
variables
Export boom or
capital inflow
Model
Financial
programming
model
Endogenous
variables
Foreign reserves
and nominal
income increase
Another experiment:
Domestic credit expansion
Reserves (R)
An increase in D
increases PY, but
reduces R.
M
M’
D up
D up
M up
PY up
PzZ up
R down
A
C
B
GNP
Domestic credit contraction
Reserves (R)
M’
M
C
D down
R*
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.
B
GNP (PY)
Domestic credit contraction
accompanied by devaluation
Reserves (R)
M
M’
C
R*
F up, e down
A
D down
B’
B
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.
GNP (PY)
Comparative statics:
An overview
D
PxX
F
e
p
R
-
+
+
-
-
PY
+
+
+
-
+
Experiment:
Inflation goes up
Reserves (R)
M
p up
A
C
An increase in
inflation (p)
increases v, so the
M’ M schedule
becomes flatter.
Hence, R goes
down and PY
increases in the
short run.
B schedule
GNP (PY)
Experiment:
Inflation goes up
Reserves (R)
p up
eP/P* up
p up
A
C
B’
X down
B shifts left
An increase in
inflation (p) makes
M
domestic currency
M’ appreciate in real
terms, so the B
schedule shifts left.
Hence, R goes
farther down and
PY can rise or fall
B schedule
in the short run.
GNP (PY)
Numerical example
History and targets
 Record history, establish targets
Forecasting
 Make forecasts for balance of payments,
output and inflation, money
Policy decisions
 Set domestic credit at a level that is consistent
with forecasts as well as foreign reserve target
Financial programming step
by step
1) Make forecasts, set reserve target R*
2)
3)
4)
5)
– E.g., reserves at 3 months of imports
Compute permissible imports from BOP
– More imports will jeopardize reserve target
Infer permissible increase in nominal income from
import equation
Infer monetary expansion consistent with
increase in nominal income
Derive domestic credit as a residual: D = M – R*
History
Known at beginning of program period:
 M-1 = 800, D-1 = 700, R-1 = 100
Recall: M = D + R
 PxX-1 = 750, Z-1 = 800, F-1 = 50
Recall: R = PxX – PzZ + F
So, R-1 = 750 – 800 + 50 = 0
Current account deficit, overall balance
 R-1/PzZ-1 = 100/800 = 0.125
Equivalent to 1.5 (= 0.125•12) months of imports
Weak reserve position
Forecast for balance of
payments
PxX grows by a third, so PxX = 1,000
F doubles, so F = 100
Suppose R* is set at 240. Then
PzZ = PxX + F + R-1 – R*
= 1,000 + 100 + 100 – 240 = 960
Level of imports is consistent with R*
R*/PzZ = 240/960 = 0.25
Equivalent to 3 (= 0.25•12) months of imports
Forecast for real
sector
Increase in PzZ from 800 to 960, i.e., by
20%, is consistent with R* equivalent to 3
months of imports
Now, recall that PzZ depends on PY
where P is price level and Y is output
Hence, if income elasticity of import
demand is 1, PY can increase by 20%
E.g., 5% growth and 15% inflation
Forecast for
money
If PY can increase by 20%, then, if income
elasticity of money demand is 1, M can also
increase by 20%
Recall quantity theory of money
MV = PY
Constant velocity means that
%M = %PY =
˜ %P + %Y
Hence, M can expand from 800 to 960
Determination of credit
Having set reserve target at R* = 240 and
forecast M at 960, we can now compute
level of credit that is consistent with our
reserve target, based on M = D + R
So, D = 960 – 240 = 720, up from 700
D/D-1 = 20/700 = 2.9%
Quite restrictive, given that PY rises by 20%
Implies substantial reduction in domestic credit
in real terms
Forecast for balance of
payments
PxX grows by a third, so PxX = 1,000
F doubles, so F = 100, as before
R* is now set at 200, not 240. Then
PzZ = PxX + F + R-1 – R*
= 1,000 + 100 + 100 – 200 = 1,000
Level of imports is consistent with R*
R*/PzZ = 200/1000 = 0.2
Equivalent to 2.4 (= 0.2•12) months of imports
Forecast for real
sector
Increase in PzZ from 800 to 1,000, i.e., by
25%, is consistent with R* equivalent to
2.4 months of imports
Now, recall that PzZ depends on PY
where P is price level and Y is output
Hence, if income elasticity of import
demand is 1, PY can increase by 25%
E.g., 5% growth and 20% inflation, roughly
Forecast for
money
If PY can increase by 25%, then, if income
elasticity of money demand is 1, M can also
increase by 25%
However, if income elasticity of money
demand is 0.8, M can increase by only
20% as before
Hence, if the income elasticity is 1, M can
expand from 800 to 1,000
Determination of credit
Having set reserve target at R* = 200 and
forecast M at 1,000, we can now compute
level of credit that is consistent with our
reserve target, based on M = D + R
So, D = 1,000 – 200 = 800, up from 700
D/D-1 = 100/700 = 14%
Still restrictive, given that PY rises by 25%, but
less restrictive than before
History
Known at beginning of program period:
 M-1 = 800, D-1 = 700, R-1 = 100
Recall: M = D + R
 X-1 = 500, Z-1 = 600, F-1 = 50
Recall: R = PxX – PzZ + F
So, R-1 = 500 – 600 + 50 = -50
Current account deficit (-100), smaller overall deficit
 R-1/PzZ-1 = 100/600 = 0.167
Equivalent to 2 (= 0.167*12) months of imports
Weak reserve position
Forecast for balance of
payments
PxX grows by 40%, so PxX = 700
F doubles, so F = 100
Suppose R* is set at 180. Then
PzZ = PxX + F + R-1 – R*
= 700 + 100 + 100 – 180 = 720
Level of imports is consistent with R*
R*/PzZ = 180/720 = 0.25
Equivalent to 3 (= 0.25*12) months of imports
Forecast for real
sector
Increase in PzZ from 600 to 720, i.e., by
20%, is consistent with R* equivalent to 3
months of imports
But PzZ depends on PY
where P is price level and Y is output
Hence, if income elasticity of import
demand is 1, PY can increase by 20%
E.g., 5% growth and 15% inflation
Forecast for
money
If PY can increase by 20%, then, if income
elasticity of money demand is 1, M can also
increase by 20%
Hence, M can expand from 800 to 960
Determination of credit
Having set reserve target at R* = 180 and
forecast M at 960, we can now compute
level of credit that is consistent with our
reserve target
So, D = 960 – 180 = 780, up from 700
D/D-1 = 80/700 = 11%
Quite restrictive, given that PY rises by 25%
Implies substantial reduction in domestic credit
in real terms
Financial programming step
by step: Recap
Sequence of steps
PzZ = PxX + F + R-1 – R* MV = PY
R*
Z
Y
Z = mPY
M
D
D = M – R*
Conclusion
These slides will be posted on my website:
www.hi.is/~gylfason
 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 model
Fund 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