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Chapter 9 Policy Tools for

Macroeconomic Analysis

© Pierre-Richard Agénor

The World Bank

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Assessing Business Cycle Regularities Assessing the Effects of External Shocks Financial Programming

The Polak Model An Extended Framework

The World Bank RMSM Model The Merged Model and RMSM-X Three-Gap Models Lags and Behavioral Functions

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Assessing Business Cycle Regularities

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Little attention paid to developing countries in recent past:

Why? Limited data quality and frequency. Cycle-spotting problematic; prone to sudden

crises.

5

Analysis of macroeconomic fluctuations beneficial: Helps specify applied macroeconomic models that

capture some of the most important correlations. Unconditional correlations can provide insight to

the type of shocks that dominate fluctuations in some macroeconomic aggregates

Design of stabilization programs; insight gained in assessing pattern of leads and lags between aggregate time series and economic activity.

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Four Step Process Step 1: choose a measure of real activity Step 2: decompose all series into trend and cyclical

components. Step 3: assess comovement of series with

measure of real activity (output). Step 4: determine phase shift of series with respect

to output.

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Step 1: choosing a measure of real activity Real GDP often chosen. Can be inappropriate:

Agricultural output, frequently contingent on non-macroeconomic variables (e.g. weather conditions) comprises a large percentage of GDP.

Nonagricultural output may be a preferable measure in select developing countries.

Figure 9.1.

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Figure 9.1aStructure of Output

(Value added, in percent of GDP)

Source: World Bank.

Agriculture Industry Services

Benin

Burundi

Cameroon

Côte d'Ivoire

Ethiopia

Ghana

Kenya

Malawi

Nigeria

Tanzania

Zambia

Zimbabwe

0 20 40 60 80 100

Africa

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

Bangladesh

India

Indonesia

Korea

Malaysia

Nepal

Pakistan

Philippines

Sri Lanka

Thailand

0 20 40 60 80 100

Asia

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Argentina

Bolivia

Brazil

Chile

Colombia

Costa Rica

Ecuador

Jamaica

Mexico

Peru

Uruguay

Venezuela

0 20 40 60 80 100

Latin America

Figure 9.1bStructure of Output

(Value added, in percent of GDP)

Source: World Bank.

Agriculture Industry Services

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

19801995

Algeria

Egypt

Jordan

Mauritania

Morocco

Oman

Syria

Tunisia

Turkey

Yemen

0 20 40 60 80 100

Middle East and North Africa

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Step 2: nonstationary and stationary components Augmented Dickey-Fuller (ADF) test

Most techniques rely on stationary (cyclical) data.

ADF: test for unit roots.

xt = + t + ( - 1)xt-1 + h xt-h + ut

ut : error term;k 0; For xt to be stationary, - 1 should be negative

and significantly different from zero.

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Step 2: nonstationary and stationary components. Given

xt = xt* + xtc,

xt* : trend component

xtc : cyclical component

Hodrick-Prescott (HP) filter can be used to estimate and filter the trend component, xt

*. Criticism of HP filter:

removes potentially valuable information and may impart spurious cyclical patterns to data;

assumes independent relationship between trend and cyclical components.

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Step 3: assessing the comovements Contemporaneous correlation coefficient, (0),

between filtered components of yt (series) and xt (output):

Procyclical if (0) is positive. Countercyclical if (0) is negative. Acyclical if (0) is zero.

With 10% significance threshold, series yt is;

Strongly contemporaneously correlated:

.3 (0)< 1. Weakly contemporaneously correlated:

.1 (0)< .3.

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Contemporaneously uncorrelated:

0 (0)< .1.

Step 4: determining the phase shift Phase shift of yt relative to output: cross-

correlation coefficients, (j), j {+/-1,+-2,…}: yt leads the cycle by j period(s) if (j)is

maximum for a negative j; yt lags the cycle if (j) is maximum for a

positive j; yt is synchronous if (j) is maximum for j = 0.

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Table 9.1: results for Kenya and Venezuela, private consumption, investment and private sector

credit are procyclical but less volatile than output; fiscal stance is countercyclical in Kenya,

procyclical in Venezuela; trade ratio is countercyclical in Venezuela; broad money seems to lag movements in activity; terms of trade is countercyclical in Venezuela; inflation is countercyclical.

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Assessing the Effects of External Shocks

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McCarthy, Neary, and Zanalda (1994)

Step 1: estimate impact of three components on BOP, expressed as a percentage of output.

Terms of trade, interest rate effect, changes in global demand.

Terms of trade shock: measured as the market value of the net import effect.

Interest rate effect: change in world interest rates multiplied by stock of interest rate sensitive external debt.

Changes in global demand: deviation of growth of world export volumes from estimated trend multiplied by initial export volume.

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McCarthy, Neary, and Zanalda (1994) Step 2: estimate economy’s response to shocks.

Level of demand: adjustment in imports from reduction in aggregate demand; difference between expected import volumes using historical import elasticity of GDP using trend growth versus actual GDP growth.

Expenditure-switching measures: captured by changes in export performance and the degree of import intensity.

Step 3: calculate additional net external financing as the difference between the effect of all shocks and the economy’s responses.

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Financial Programming

The Polak Model An Extended Framework

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The Polak Model

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Considers small open economy, with fixed exchange rate.

Four Equations:

Ms = L + R (4)

Ms: money supply, L: domestic credit, R : official foreign exchange reserves

R = X - Y + F, 0 < < 1, (5)

F: capital inflows

Md = v-1Y, v > 0, (6)

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v: income velocity of money

Ms = Md (7)

Polak focus: Determine effects of changes in domestic credit on

foreign exchange reserves.

Using (4), (6), and (7),

R = v-1Y - L . Reserves will only increase when nominal money

demanded exceeds change in domestic credit.

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Polak model structure:

Target Variables: R.

Endogenous Variables: M, Y, J = Y.Exogenous Variables: X, F.

Policy Instruments: L.

Parameters: v, .

23

Polak example: Consider increase in L at period t = 0, by L0 ,

Ms rises by L0, by (4), Md rises by L0 , by (7),

nominal income, Y, must rise, by vL0, by (6),

thus, imports rise by Y = vL0,

reserves fall -vL0 on impact,

Ms then increases only (1 - v)L0 .

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Consider increase in L at period t = 0 by L0 ,

cumulated fall in reserves at end of period 1:

Rt=1 = -vL0 - v(1 - v)L0,

over an infinite time horizon (t ):

Rt = -L0 ,

in long run, initial expansion in money supply via increase in domestic credit is completely offset by the reduction in official reserves.

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Given a targeted level of reserves,

L = v-1Yp - R

R: targeted reserves,

Yp: projected level of nominal income

L: required change in credit, allows policy makers to estimate a credit ceiling.

Domestic credit expansion levels crucial in obtaining BOP objective:

note: exports, capital flows and income velocity of money treated as exogenous variables.

~

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Monetary Approach to the Balance of Payments (MABP):

Assumptions: stable demand for money, purchasing power parity, continuous stock equilibrium in money markets

Results in an instantaneous absorption by reserves of credit change, unlike Polak which assumes a more gradual absorption.

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Limitations of the Polak Model: Assumes that changes in domestic credit have no

effect on domestic money demand; in many developing countries the bank credit-supply side link is a critical feature of the economy.

Assumes a stable money demand function; in practice money demand tends to be unstable as a result of volatile inflation expectations.

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An Extended Framework

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Khan, Haque, and Montiel (1990) Distinguishes between real and nominal output and

the sources of credit growth.

Extended framework equations: Consider single good economy where,

Y = Py

Y: nominal income, P: overall price index, and y: real output.

Y = Py-1 + P-1y

30

Price changes: function of domestic price changes, PD and exchange rate adjusted foreign prices changes by,

P = PD + (1 - )(E + P*), 0 < <1 Domestic credit

L = Lp + Lg, Lp : private sector credit

Lg : government credit

Lp : f(demand for working capital), proportional to changes in nominal output:

Lp = Y;

31

Money supply identity:

M = L + R;with

R = ER*

R = X - J + F

X: Exports (exogenous); J: Imports in nominal terms,

J = EQJ,

QJ : import volume; E : nominal exchange rate

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Changes in import volume, related to the change in

output and the relative price of foreign goods,

QJ = y + [PD - (E + P*)]

> 0: import elasticity to relative price changes.

Nominal value of imports:

J = J-1 + (QJ-1 - E-1)E

+ E-1[y + (PD - P*)] (16)

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With relatively small QJ-1, a devaluation in the nominal exchange rate (E > 0) will lower the nominal value of imports, improve the trade balance and increase

official reserves. Income velocity: constant as in Polak model, money

market assumed to be in flow equilibrium. Government Budget Constraint: G - T = L + Fg,

budget deficit is financed by foreign borrowing or

changes in central bank credit.

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Structure of Extended Framework:

Target variables: R, PD

Endogenous variables: Y, Lp, M, P, J, G-T

Exogenous variables: y, P*, X, F = Fp + Fg

Policy instruments: Lg, E

Predetermined: y-1, P-1, QJ-1

Parameters: v, , , , .

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Target variable equations:

R = (v-1 - )y - 1 PD = (20)

with

= (v-1 - )[y-1(1 - )(E + P*) + P-1y] -Lg.

R + PD = X + F - J-1 + (QJ-1 - E-1)E

+ P* - E-1y (21)

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Positive and programming mode solutions Positive Mode: for given values of exogenous

variables and policy instruments, determine simultaneously the target variables.

Programming Mode: R, PD are targets and equations are solved for

the policy instruments, Lg, E.

~ ~

See Figure 9.2 for graphical representation of (20) and (21) in R-PD space as the MM and BB curves respectively.

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Figure 9.2The Extended Financial Programming Model

R

PD

R~

~PD

E

E'

B

B

M

M

Source: Adapted from Khan, Montiel, and Haque (1990, p. 161).

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Programming Mode Given the objective of lowering inflation and

increasing official reserves, policymakers can, reduce Lg, shift MM curve left in Figure 9.2, or depreciate the nominal exchange rate, shift MM

left and BB right in Figure 9.2.

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The World Bank RMSM Model

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Revised Minimum Standard Model: Precursor to the RMSM-X model. Developed in the early 1970s. Objective: make explicit the link between medium-

term growth and its financing.

41

Five relationships (prices taken as given):

I = y/ (22)

: incremental capital-output ratio (ICOR). Imports:

J = y, 0 < < 1 (23)

Cp = (1 - s)(y - T), (24) 0 < s < 1: marginal propensity to save.

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Balance-of-payments identity:

R = X - J + F (25)

National income identity:

y-1 + y = Cp + G + I + (X - J) (26)

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The structure of RMSM:

Target Variables: R, y.

Endogenous Variables: I, Cp, J.

Exogenous Variables: X .

Policy Instruments: G, T, F

Predetermined: y-1

Parameters: , s, .

44

Target equations:

(s + )y-1 + (1 - s)T - (X + G)y =

-1 - (s + )(27)

(28)

Substituting (23) in (25),

R = X - (y-1 + y) + F.

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Solutions:

Positive or Policy Mode Recursive: first equation can be used to determine

second equation. See Figure 9.3: for given values of exogenous

variables and policy instruments, equilibrium is found at the interception of the horizontal YY curve and the BB curve, equations (27) and (28) respectively.

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Figure 9.3The RMSM Model in the Positive Mode

y

E

B

B

Y Y

R

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Programming Mode: Trade-gap mode: Given X-J, calculates F in (25). Saving-gap mode: Given X-J and F, calculates

required level of savings, y/ in (22). Total consumption assumed to be a residual of

national income identity (26),

Cp = y-1 + y - y/ - X - m(y-1 + y) - G

~

Limitation: priori expectation that private consumption will be consistent with national accounts identity unrealistic.

However, possible to use trade sap and saving gap as potentially binding constraints.

48

Two-Gap Mode: Determine financing requirements for alternative

target rates of output growth and official reserves. Determine feasibility of particular growth rate given

alternative financing scenarios.

Saving Constraint: Begin with national income accounting identity,

I = (y - T - Cp) + (T - G) + (J - X) (30)

(y - T - Cp): private sector savings;

(T - G) : public sector savings;

(J - X ): foreign savings.

49

Saving Constraint: Substituting out for Cp and J - X,

I S + F (31) with,

S = s(y-1 + y) + [(1 - s)T - G] - R.~ ~

Figure 9.4: graphs inequality in I-F space.

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Figure 9.4The RMSM Model in Two-Gap Mode

Zone IV

Zone I

Zone II

Zone III

I

F

45º

ST

T

S

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Substitute (23) into (32),

y = (X - R + F)/ - y-1. (33)

Trade constraint: substitute (33) into (22),

I T + F/ (34)with,

T = (X - R)/ - y-1/

J - X = F - R. (32)~

Trade Constraint: Rewrite (25) as,

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Step 2: given target output, determine required investment,

IR = y/~

RMSM: Two Gap Mode Binding constraint: constraint yielding lowest level

of investment. Suppose foreign financing is binding constraint.

Other variables solved for using iterative process:

Step 1: Specify values for a) parameters, , s, and ; b) predetermined variable, y-1; c) exogenous variables, X and F; d) policy instruments, T and G; e) policy targets, y and R.

~ ~

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Step 3: Determine the levels of investment, IS and IT implied by the saving constraint (31),

Imin = min(IS , IT).

Step 4: If Imin IR, no constraint is binding.

4a: If Imin IR, and if savings constraint is binding

either increase taxes, T, and/or reduce G, and/or reduce R, until constraint is relaxed or you have exhausted policy instrument options.

~

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4b: If Imin IR and if trade constraint is binding reduce R, until constraint is relaxed or

further policy or target variable changes unfeasible.

~

4c: If Imin IR and both constraints are binding: reduce R and/or adjust T and G.

~

y = Imin ~

Step 5: If adjustments in step four do not still satisfy constraints, lower desired level of output by,

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Step 6: determine required level of imports as

JR = (y-1 + y)

Step 7: now, given JR, X, and F, recalculate target level of reserves as,

R[1] = X - JR + F,

redo iterations in step 3-8 until R[1] R. ~ ~

~

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Step 8: Once convergence has been achieved, model yields inter-related consistent values of the levels of investment, the change in output, imports, and the change in official reserves.

Step 9: Use equation (24) along with the new value

of output and the value of taxes to estimate private

consumption, Cp.

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Three criticisms: Difficulty identifying binding constraint a priori.

Assumes imports as essential for investment and growth; however, saving gap can also be closed by combination of reducing imports or increasing exports, thereby freeing foreign exchange necessary for investment.

Incomplete; essentially a growth-oriented model with emphasis on a small number of real variables and no financial side.

Relative prices and induced substitution effects among production factors (and their possible impact on exports, for instance) are neglected.

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The Merged Model and RMSM-X

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Combines extended model and RMSM model. As in extended model, relative prices affect imports

and domestic absorption.

Equations: Changes in real output,

y = I/(1 + P),

Y = Py-1 + P-1y,

P = PD + (1 - )E,

P* = 0

The Merged IMF-World Bank Model

60

Domestic credit

L = Lp + Lg, with

Lp = Y.

Money supply identity

M = L + R, with

R = ER*

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Balance of payments:

R = X - J + F, with

F = (1 + E)F*,

X: exogenous.

Nominal imports:

J = J-1 + (QJ-1 - E-1)E + E-1(y + PD).

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Money demand:

Md = v-1Y.

Flow equilibrium of the money market:

Ms = Md

63

Government budget constraint:

G - T = Lg + Fg.

Private Sector Budget Constraint:

(Y - Cp - T) - I = Md - Lp - Fp

Cp = (1-s)(y - T), private sector budget constraint implies,

I = s(Y-1 + Y - T) + Lp + Fp - Md. (47)

64

Structure of the merged model:

Target Variables: R,PD, y

Endogenous Variables: Y, Lp, M, P, J, G-T

Exogenous Variables: X, F = Fp + Fg

Policy Instruments: Dg, E, G or T

Predetermined: y-1, P-1

Parameters: , , , , .

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Target equations: merged model

- + (-1 - )y PD =

y-1

- (1 - )-1E

R + (y-1PD + y) =

R = X - J-1 - (QJ-1 - E-1)E

- E-1(y + PD) + F

Figure 9.5.

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Figure 9.5The Merged IMF-World Bank Model

y

E

M

M

Y

Y

RPD

B

B

A

E'A'

R~~PD

y~

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Expanded version of the RMSM model (see World Bank, 1997b):

Conceptual basis: merged IMF-World Bank model described earlier (adds to the RMSM model a price sector, a monetary sector, and government accounts, along the lines of the financial programming approach.

In practice, RMSM-X models fairly detailed; General RMSM-X model characteristics: often consist

of four economic sectors: the public sector, the private sector, the consolidated banking system, and the external sector.

The RMSM-X Framework

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Budget constraints associated with each sector. National accounts derived via aggregation of the

sectoral budget constraints serve to close the RMSM-X model.

Two types of financial assets, money and foreign assets in standard model, some versions include (particularly for middle-income countries) domestic bonds.

Money demand function frequently follows Polak model; constant income velocity of money.

69

Some models disaggregate banking system structure: here Ms is not equal to the sum of central bank credit and official reserves; rather obtained as the product of the monetary base and a constant money multiplier.

Prices: assume domestic and foreign goods are imperfect substitutes, so that substitution effects can be analyzed on the demand side.

Imports: several categories with the demand a function of the real exchange rate and either real GDP or (e.g. imports of capital goods) gross domestic investment.

70

Consumption: generally assumed to depend only on disposable income---thereby excluding consumption-smoothing effects.

Model closures: Public sector closure: values for all variables

except public sector expenditure and domestic borrowing specified; latter two variables then determined by model.

Private sector closure: values for government expenditure and revenue are specified, and the model estimates private sector variables.

71

Marginal economic agent: In both approaches, likely disbursements from

external donors provide estimate of external financing.

External borrowing requirements determined separately, through the balance-of-payments identity.

Gap financed by marginal economic agent. In public sector closure, central government is

marginal borrower and foreign commercial banks are assumed to be the marginal foreign creditor.

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Policy closure as availability mode: all external financing identified in advance and imports are adjusted to equilibrate BOP.

Programming Mode: targeted values given; RMSM-X then solved for mix of fiscal,

monetary and exchange rate policies consistent with targeted values.

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Programming mode: solution sequence Step 1: set targets for inflation rate, potential GDP

growth rate (evaluated at full employment), real exchange rate, real interest rate, and international reserves (specified in months of imports).

Step 2: Calculate investment requirements, given estimates of ICOR and the actual growth rate of output.

Step 3: Calculate the demand-side relationships based on the projections of the exogenous variables.

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Step 4: Estimate likely availability of foreign borrowing. Calculate reserve requirements for exogenously determined import target. Determine additional foreign borrowing required.

Step 5: Determine growth rate of money supply, given inflation targets, output growth, estimates of velocity and the money multiplier. Estimate, residually, amount of domestic credit supplied by the central bank or banking system, given the reserve accumulation target.

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Step 6: Close the model by determining the following residuals in the relevant markets: consumption of goods and services, that is, public (private) consumption in the public (private) sector closure; borrowing from the foreign external sector; and credit allocated by the banking system (or, in more specific cases, central bank credit to the nonfinancial public enterprises).

Limitations Retains limitations of the two models that underlie

it. IMF framework rudimentary; static nature

problematic for short-term projections, given the importance of lags.

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Missing important features of developing countries: effect of debt financing of fiscal deficit on

domestic interest rates as well as the endogeneity of private capital flows ignored;

short-run link between production and bank credit ignored, obviating a critical channel through which monetary policy can affect the real economy.

Supply-side problems: Not account for the complementarity between

public investment and private investment. Fixed-coefficient production function (the ICOR

relationship) remains subject to a number of analytical and practical difficulties.

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Easterly (1999) found that the assumed linear relationship between growth and investment is significantly rejected by the data.

ICOR rules out capital-labor substitutability and is unable to account for observed fluctuations in real wages.

Relative prices (and the real exchange rate) influence the allocation of resources only through the demand side, not the supply side.

No role to expectations. No explicit role for the labor market, unable to

account for fluctuations in unemployment.

78

Three-Gap Models

79

Two gap RMSM approach extended to three-gap framework by Bacha (1990).

Addition of fiscal gap links foreign exchange availability directly to the rate of growth of productive capacity and only indirectly to the actual level of real output.

80

Equations: ICOR relationship:

I = y/,

81

Setting up the foreign exchange constraint:

JK = I,

XN = X - (J - JK),

XN: level of exports net of noncapital imports.

FN : F minus changes in foreign exchange reserves, R.

OS : net factor serves to rest of world (external debt services and other transfers)

82

Standard BOP identity,

R = (X - J) - OS + F.

Substitute, FN = F - R, and X = XN + J - JK, rearrange,

FN - OS + (XN - JK) = 0.

Solve for JK, then substitute I = JK/ ,

I = (XN + H)/with

H = FN - OS .

83

Suppose (non-capital) imports are invariant and there is an upper bound on exports, XN, based on external

demand. First gap: foreign exchange constraint,

I (XN + H)/~

84

Setting up the saving constraint: Using (58), basic national income identity is written as,

I = (y - Cp - G) + H,

equivalently,

I = Sp + (T - G) + H

with

Sp = y - T - C,

decomposes financing of investment into domestic and public sector savings.

85

Setting up the fiscal constraint: Suppose:

money money is only asset available; foreign capital inflows serve to finance

government’s budget deficit.

Second gap: saving constraint

I Sp + (T - G) + H~

Cp: assume exogenous.

Sp = y - Cp

with y bounded from above by full capacity output.

~ ~

86

Private sector budget constraint can be written as

Sp - Ip = M/P. Assume constant real money balances. M/P: measures both seigniorage and inflation tax. Revenue generated as function of inflation rate,

P/P and propensity to hoard, ,

M/P = h(, ).

Budget constraint of the consolidate public sector:

Ig = h(, ) + (T - G) + H.

87

Suppose: private and public investment are complements:

Ip Ig,

: ratio of private to public investment in capital stock.

Ig + Ig = I,

(1 + ) Ig = I

Third gap: fiscal constraint

I (1 + )[h(, ) + (T - G) + H]

88

Model without fiscal constraint Consider changes in level of foreign financing, H, in

presence of foreign exchange and savings constraints.

Figure 9.6: Foreign exchange and saving constraint graphed in

I-H space as FF and SS respectively. Slope of SS is unity, whereas slope of FF is 1/.

Three cases considered: Case 1: if net foreign inflows H are equal to H*

(where FF and SS curve intersect), both constraints are binding and investment is equal to I*.

89

Figure 9.6The Three-Gap Model

Source: Adapted from Bacha (1990, p. 291).

F

F

S

S

G

G

I

0 H* H

I*

(1+)[h(,) + (T-G)]

S + (T-G) ~p

X/~

90

Case 2: if H is less than H*, only FF binds. Investment determined by foreign exchange

availability. Economy suffers from excess capacity with

actual output given by,

y = Cp + G + (1 - )Ic + XN

Ic: foreign exchange constrained investment.

~

91

Case 3: if H exceeds H*, the economy will be constrained by domestic saving:

Output at full capacity; actual value of adjusted exports will be less than

maximum value, given by foreign demand; domestic demand ‘squeezes’ exports to

XN = y - Cp - G + (1 - )Ic

Ic :saving-constrained level of investment

~

92

Minding the Fiscal Gap

Adding the fiscal gap leads to the following adjustments:

In Figure 9.6, add GG curve with slope 1 + and vertical intercept, (1 + )[h(, ) + (T - G)].

Curves GG and SS have same slope. Relative heights depend on the values of and . As

long as Ip is positive, the private sector budget constraint, implies that,

Sp > h(, ).

Larger values of and raise the height of GG relative to SS.

~

93

Fiscal constraint incorporated in a variety of ways.

Two possibilities: Inflation as an endogenous variable: Fiscal constraint

serves limited purpose of determining inflation rate, , necessary for a given level of total investment.

Inflation as an exogenous policy variable: GG serves as an independent constraint; if fiscal constraint does not bind, is slack variable

and Ip is determined residually; if fiscal constraint does bind, a rise in H will

increase capacity growth. Output will rise, economy will move to full capacity with lower net exports.

94

The 1-2-3 Model

95

Developed at the World Bank by Devarajan et al. (1997),

CGE (computable general equilibrium) models. 1-2-3 captures features of CGE models: highly

disaggregated models (on both the demand and the supply side) designed to study issues such as the allocational and distributional effects of domestic and external shocks (see Bandara, 1991).

Demand side: typically consider several households. Price rigidities common.

96

Macroeconomic dimension of CGE models: Closure rules for ensuring identity between

aggregate savings and investment. Classical rule:investment endogenous and

determined by aggregate saving. Keynesian rule:investment exogenous and real

wages adjust to establish saving, investment identity.

Johansen rule: endogenous public or private consumption equates total saving to exogenous investment.

97

The Minimal setup: Small open economy. Two representative agents: a producer and a

household. Economy produces two goods: home good and

exportable good, the price of which is fixed on world markets.

Household consumes an imported good.

Assume: demand for exportables perfectly elastic; zero access to capital markets; external equilibrium

at, X - J = 0.

98

Production possibility frontier (PPF): Defines the maximum achievable combinations of

exportables and nontradables that the economy can supply, given by,

Y = F(YX, Yns ;) (71)

with Y assumed fixed (e.g. full employment to all production factors).

99

Using a constant elasticity of transformation (CET) function:

Y = [YX + (1 - )YN

]1/ ,

with

0 < < 1, 1 < < +. Elasticity of transformation, ,

1 - 1 =

100

Efficient ratio of exportables to nonexportables in output as:

YX/Yns = h1(PX , PN ) (72)

PN : price of home goods;PX : price of exportables.

Price of aggregate output:

PY = g1(PX , PN ). (74)

Thus

PYY PXYXs + PNYN

S (75)

101

Household consumption function,

Qs = q(Ynd, J; ) (76)

Qs = [YN + (1 - )J]1/ ,

0 < < 1, - < < 1

1 1 -

= : elasticity of substitution.

102

Desired ratio of imported, home goods,

J/Ynd = h2(PJ , PN ). (77)

Aggregate supply of the composite good and import, nontradables demand related by,

PQQs PJ J + PNYNd . (80)

Household total income, V,

V = PYY (81)

103

With all income spent on composite goods,

V PQQd (83)

Equilibrium conditions Demand and supply of nontradables:

Yns = Yn

d (84)

Demand and supply of composite goods:

Qs = Qd (85)

104

Balanced trade:

PJ J - PXYX = 0 (86)

Constraints not independent as in Walras’ Law. Model satisfies all three identities in the following equation:

PN(Yns - Yn

d) + PQ (Qs - Qd) + PJ J - PXYX = 0

105

Figure 9.7: illustration of the model. World prices are normalized to unity, PX

* = PJ*.

Balance of trade constraint shown as 45-degree line in quadrant 1.

PPF (71) and CPF shown as mirror images with balanced foreign trade.

Absorption (maximizing (76)) occurs at point of tangency between isoabsorption curve and consumption possibility frontier.

106

Figure 9.7Equilibrium in the 1-2-3 Model

Source: Adapted from Devarajan et al. (1997, p. 164).

C

A

J

XNYd

Market for home goods

NY s

Trade balance

NP /PX

NP /PJ

NQ = q(J,Y ;s d

45º

BX = J

107

Adverse Terms-of-Trade Shock

Suppose import prices, PJ*, increase.

Figure 9.8: PN/PJ remains constant; imports decline; new equilibrium at lower utility, consumption of both

imports and home goods have declined (e.g. income and substitution effect);

value of import rises, exports must rise; real exchange rate must depreciate.

108

Figure 9.8An Adverse Terms-of-Trade Shock in the 1-2-3 Model

Source: Adapted from Devarajan et al. (1997, p. 167).

C

A

J

XNY d

Market for home goods

NY s

Trade balance

NP /PX

NP /PJ

NQ = q(J,Y ;s d

45º

C' B'

B

A'

X = J

109

Real exchange rate, depreciate?

Contingent on the elasticity of substitution between imports and home goods, .

If 0, isoabsorption curves are L-shaped, real exchange rate will depreciate

If , isoabsorption curves are flat; tangency with new CPF will occur to the left of initial equilibrium consumption point, C. Demand for home goods rises and the real exchange rate appreciates.

110

Income and substitution effects: If < 1, the income effect dominates. Reduction in

output of nontradables and an increase in output of exportables.

Real depreciation: If > 1, substitution effect dominates. Real exchange

rate appreciates If = 1, there is no change in either real exchange

rate or production.

111

Investment, Saving, and the Government

Two extensions: government sector and investment Government imposes tariff on imported goods at rate,

0 < J < 1,

PJ = (1 + J)EPJ*

112

Sales price of composite good, cost of living index, differs from PQ , by sales tax, 0 < s < 1,

PS , = (1 + s)PQ

and,

PQQs PJ J + PSYNd .

113

Houshold income, V,

V = PYY + PQNTgg + E ·NTf

h

NTgg : net transfers from government.

NTfh : net transfers from abroad.

Share of household income used on composite good,

PSQhd = (1 -sh - V)V,

sh : household savings rate.

114

Government sector: Government revenues:

T = J EPJ*J + S PQQd + V V

Government savings:

Sg = T - PQG - PQNTgh

Aggregate savings:

S = Sg + sVV

115

Market-clearing conditions: External balance:

PZ*Z - PX

*X - NTfh = 0.

Equality between saving and investment:

PsI = S

116

Lags and Behavioral Functions

117

Accounting for lags: critical for establishing short-term projections.

Two types of lags: Inside lags: legal and institutional delays involved

in implementing a change in policy. Outside lags: delay involved between

implementation of a policy and its effects on the target variables.

118

Endogeneity of lags: often affected by private agents’ expectations

about the sustainability of the various policies; highly credible policy; with low probability of

reversal may have relatively short lag. Behavioral functions often difficult to estimate in

countries undergoing comprehensive reform programs or large shifts in policy.

In this case, use of relatively sophisticated econometric techniques such as the error correction framework may not be enough to detect stable relationships.