Chapter 9
Policy Tools for
Macroeconomic Analysis
© Pierre-Richard Agénor
The World Bank
1
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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
2
Assessing Business Cycle
Regularities
3


Little attention paid to developing countries in recent
past:
Why?
 Limited data quality and frequency.
 Cycle-spotting problematic; prone to sudden
crises.
4
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.
5
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.
6
Step 1: choosing a measure of real activity
 Real GDP often chosen.
 Can be inappropriate:
 Agricultural output, frequently contingent on nonmacroeconomic 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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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.
10
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.
11
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.

12
Contemporaneously uncorrelated:
0  (0)< .1.
Step 4: determining the phase shift
 Phase shift of yt relative to output: crosscorrelation 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.

13
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.
14
Assessing the Effects of
External Shocks
15
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.
16
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.
17
Financial
Programming


The Polak Model
An Extended Framework
18
The Polak Model
19


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-1Y, v > 0, (6)
20
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-1Y - L .

Reserves will only increase when nominal money
demanded exceeds change in domestic credit.
21
Polak model structure:
Target Variables: R.
Endogenous Variables: M, Y, J = Y.
Exogenous Variables: X, F.
Policy Instruments: L.
Parameters: v, .
22
Polak example:
 Consider increase in L at period t = 0, by L0 ,
s
 M rises by L0, by (4),
d
 M rises by L0 , by (7),
 nominal income, Y, must rise, by vL0, by (6),
 thus, imports rise by Y = vL0,
 reserves fall -vL0 on impact,
s
 M then increases only (1 - v)L0 .
23
Consider increase in L at period t = 0 by L0 ,
 cumulated fall in reserves at end of period 1:
Rt=1 = -vL0 - v(1 - v)L0,

over an infinite time horizon (t  ):
Rt   = -L0 ,

in long run, initial expansion in money supply via
increase in domestic credit is completely offset by
the reduction in official reserves.
24

Domestic credit expansion levels crucial in
obtaining BOP objective:
 note: exports, capital flows and income velocity
of money treated as exogenous variables.

Given a targeted level of reserves,
L =
v-1Yp
~
- R
R: targeted reserves,
Yp: projected level of nominal income
L: required change in credit, allows policy makers
to estimate a credit ceiling.
25
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.
26
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.
27
An Extended Framework
28
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-1y
29

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;
30

Money supply identity:
M = L + R;
with
R = ER*
R = X - J + F
X: Exports (exogenous); J: Imports in nominal terms,
J = EQJ,
QJ : import volume; E : nominal exchange rate
31

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)
32

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.

33
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, , , , .
34

Target variable equations:
R = (v-1 - )y - 1 PD = 
(20)
with
 = (v-1 - )[y-1(1 - )(E + P*) + P-1y]
-Lg.
R + PD = X + F - J-1 + (QJ-1 - E-1)E
+ P* - E-1y
(21)
35
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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Programming Mode
 Given the objective of lowering inflation and
increasing official reserves, policymakers can,
g
 reduce L , shift MM curve left in Figure 9.2, or
 depreciate the nominal exchange rate, shift MM
left and BB right in Figure 9.2.
38
The World Bank RMSM
Model
39
Revised Minimum Standard Model:
 Precursor to the RMSM-X model.
 Developed in the early 1970s.
 Objective: make explicit the link between mediumterm growth and its financing.
40
Five relationships (prices taken as given):

I = y/
(22)
 : incremental capital-output ratio (ICOR).
 Imports:
J = y, 0 <  < 1

Cp = (1 - s)(y - T),
(23)
(24)
0 < s < 1: marginal propensity to save.
41

Balance-of-payments identity:
R = X - J + F

(25)
National income identity:
y-1 + y = Cp + G + I + (X - J)
(26)
42
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, .
43

Target equations:
(s + )y-1 + (1 - s)T - (X + G)
y =
-1 - (s + )
(27)

Substituting (23) in (25),
R = X - (y-1 + y) + F. (28)
44
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.
45
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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.
47
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.
48
Saving Constraint:
p
 Substituting out for C 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.
49
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Trade Constraint:
 Rewrite (25) as,
~
J - X = F - R. (32)

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/
51
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.

Step 2: given target output, determine required
investment,
~
IR = y/
52


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.
53
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.


Step 5: If adjustments in step four do not still satisfy
constraints, lower desired level of output by,
y = Imin
~
54

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.
55

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.
56
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.
57
The Merged Model
and RMSM-X
58
The Merged IMF-World Bank Model
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-1y,
P = PD + (1 - )E,
P* = 0
59

Domestic credit
L = Lp + Lg,
with
Lp = Y.

Money supply identity
M = L + R,
with
R = ER*
60

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).
61

Money demand:
Md = v-1Y.

Flow equilibrium of the money market:
Ms = Md
62

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)
63
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: , , , , .
64
Target equations: merged model
PD =
- + (-1 - )y
y-1
- (1 - )-1E
R + (y-1PD + y) = 
R = X - J-1 - (QJ-1 - E-1)E
- E-1(y + PD) + F

Figure 9.5.
65
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.
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
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
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
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
66
The RMSM-X Framework



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.
67




Budget constraints associated with each sector.
National accounts derived via aggregation of the
sectoral budget constraints serve to close the RMSMX 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.
68



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.
69



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.
70




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.
71


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.
72
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.
73


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.
74



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.
75



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
76
analytical and practical difficulties.
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.





77
Three-Gap Models
78


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.
79
Equations:
 ICOR relationship:
I = y/,
80

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)
81

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 .
82

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)/
83
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.
84

Cp: assume exogenous.
~
~
p
S =y

- Cp
with y bounded from above by full capacity output.
Second gap: saving constraint
~
I  Sp + (T - G) + H
Setting up the fiscal constraint:
 Suppose:
 money money is only asset available;
 foreign capital inflows serve to finance
government’s budget deficit.
85

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.
86

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]
87
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* .
88
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.
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89

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.
90

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
91
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.
92



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
93
exports.
The 1-2-3 Model
94
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.

95
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.
96
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.
97
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).
98

Using a constant elasticity of transformation
(CET) function:
Y = [YX + (1 - )YN]1/ ,
with
0 <  < 1,

1 <  < +.
Elasticity of transformation, ,
1
=
-1
99
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 + PNYNS (75)
100

Household consumption function,
Qs = q(Ynd, J; )
(76)
Qs = [YN + (1 -  )J]1/ ,
0 <  < 1, -  <  < 1
1
=
1-
: elasticity of substitution.
101

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)
102

With all income spent on composite goods,
V  PQQd

Equilibrium conditions
Demand and supply of nontradables:
Yns = Ynd

(83)
(84)
Demand and supply of composite goods:
Qs = Qd
(85)
103

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 - Ynd) + PQ (Qs - Qd) + PJ J - PXYX
=0
104
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.
105
F
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.
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d
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(
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,
Y
;


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P
/
P
J
N
d
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4
5
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.
(
1
9
9
7
,
p
.
1
6
4
)
.
106
Adverse Terms-of-Trade Shock
Suppose import prices, PJ*, increase.
Figure 9.8:
N
 P /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.

107
F
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e
9
.
8
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s
d
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=
q
(
J
,
Y
;


N
B
B
'
C
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/
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J
N
d
Y
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4
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.
(
1
9
9
7
,
p
.
1
6
7
)
.
108
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.
109
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.
110
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*
111

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 .
112

Houshold income, V,
V = PYY + PQNTgg + E ·NTfh
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.
113
Government sector:
 Government revenues:
T = J EPJ*J + S PQQd + V V

Government savings:
Sg = T - PQG - PQNTgh

Aggregate savings:
S = Sg + sVV
114
Market-clearing conditions:
 External balance:
PZ*Z - PX*X - NTfh = 0.

Equality between saving and investment:
PsI = S
115
Lags and Behavioral
Functions
116


Accounting for lags: critical for establishing shortterm 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.
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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.
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