financial programming thorvaldur gylfason an introduction

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.

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

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

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

MHence, M = D + R

Balance sheet of banking system

Monetary Survey

AssetsLiabilitie

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

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

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 slow down*Or slow down

LinkagesLinkages

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

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

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

R = (1/v)PY – D

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

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

mvFXPR

Multipliers: AlgebraMultipliers: Algebra

1 mvXdP

Multipliers: NumbersMultipliers: Numbers

4)4/1(1

4)4/1(

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)

F up, e down

Economic modelsEconomic models

Exogenousvariables

Endogenousvariables

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)

Export boomExport boom

GNP (PY)

Exports increase

Reserves (R)

Export boomExport boom

GNP (PY)

Reserves (R)

An increase in exports increases both reserves and nominal income

An interpretationAn interpretation

Exogenousvariables

Endogenousvariables

Export boom orcapital inflow

Financial programming model

Foreign reserves and nominal income increase

Another experiment: Another experiment: Domestic credit expansionDomestic credit expansion

D upM’

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)

D down

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.

Reserves (R)

Too low reserves

Domestic credit contraction Domestic credit contraction accompanied by devaluationaccompanied by devaluation

GNP (PY)

F up, e down

D down

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.

Reserves (R)

Comparative statics: Comparative statics: An overviewAn overview

D PxX F e

R - + + - -

PY + + + - +

= inflation= inflation

Experiment: Experiment: Inflation goes upInflation goes up

B schedule

Reserves (R)

GNP (PY)

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

Experiment: Experiment: Inflation goes upInflation goes up

B schedule

Reserves (R)

GNP (PY)

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 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 +

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

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

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

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 +

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

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

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

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

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 +

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

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

financial programming thorvaldur gylfason an introduction

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