3. Macroeconomic Structural Equations
In this section we provide the structural equations of Indonesian macroeconomics system considered as an open-economy model, where some external factors related to the economic transactions such as
export and import, are taken into account, see McCallum and Nelson 2001. The equations are then formulated into standard linear rational expectations models and solved by undetermined coefficient
method.
Most of the variables involve in the model are presented in log-linearized form. Formally, let V
t
be the vector of variables and V their steady-state, then the vector of log-deviations of V
t
is defined as : log
log .
t t
v V
V =
− 17
In the next part we describe the structural equations, endogenous and exogenous variables which involve in the model.
3.1. Structural Equations
There are thirteen equations considered in the model. 1. Output gap
.
t t
t
y y
y =
−
18 Output gap
t
y
is the deviation between actual output y
t
and potential output
t
y
. 2. Potential output
.
y t
t t
y q
e γ
= +
19 Potential output is influenced by the competitiveness reflected by the real exchange rate q
t
and the technological shock
y t
e . 3. Price
1
.
t t
t
p p
p
−
= Δ +
20 We follow the common definition about the inflation rate
Δp
t
, i.e., the difference of the price in the current and last periods.
4. Real exchange rate .
q t
t t
t
q s
p e
= − +
21 Here, s
t
is the nominal exchange rate and the shock process
q t
e constitutes the law of one price under normalized international price.
5. Uncovered interest parity UIP
1
,
s t
t t t
t
R E s
s e
+
= − +
22 where R
t
is the nominal interest rate and the shock process
s t
e reflects the premium risk premium with non-constant variance and possibly inter-correlated.
6. Real interest rate
1 1
.
t t
t t
t t
R E
E p
λ λ
+ +
= +
− Δ
23 7. Consumption-saving
1 1
2 1
1
1 .
c t t
t t
t t
B E c B c
B c h
e β
β λ
+ −
= −
− − +
24 The coefficients involve in this equation are the discount factors. The shock process
c t
e describes the stochastic shock relates to the household preferences on the current and forthcoming
consumption level c
t
and c
t+1
. The forthcoming consumption depends on the real interest rate. Or, in other words, the intertemporal substitution factor is considered as an indicator which affects the
consumption level. 8. Export
2 1
.
x t
t t
t
x b q
b y e
∗
= +
+ 25
The export level is given by x
t
. The coefficients b
1
and b
2
are, respectively, the substitution elasticity coefficients between real exchange rate q
t
and international output
t
y , which are exogenously considered.
9. Net export
3 4
1 .
t t
t t
x x
b y b
q = −
+ −
26 The net export level is given by
t
x
. Here, b
4
−1 can be seen as the substitution elasticity coefficient between goods and labors in the production processes.
10. Aggregate supply AS
1 1
1 2
.
p t
t t
t t
t
p y
p E p
e α
− +
Δ = + Δ
+ Δ +
27 The aggregate supply equation follows that of Fuhrer-Moore, where the current inflation rate is
determined by the average of the last rate and the expectation for the next period. The shock process
p t
e
is assumed to have zero mean and constant variance. 11. Aggregate expenditure
1 2
3
.
t t
t t
y c
x g
η η
η
= +
+
28 The aggregate expenditure exhibits the simplification of
1 2
3 4
t t
t t
t
y c
x g
I
η η
η η
= +
+ +
, where I
t
denotes the invest level. By the equation, it does not mean that invest and import are excluded from the model. Note that the invest has been taken into account in the consumption-saving equation 24,
where h denotes the elasticity coefficient between invest level and the real interest rate. Furthermore, the import is exclusively considered as the material input to the production of home-country goods,
since most of the import consists of capital and material goods. 12. Monetary policy MP rule
1 3
1 1
2 3
1 3
1 4
3 1
4
1 1
1 1
.
R t
t t
t t
t t
t t
R E
p E y
R E
e μ
μ μ
μ μ
μ μ
ψ
− −
− −
= − +
Δ + −
+ +
− +
29 The monetary authority is assumed obey the above equation in launching a monetary policy,
where the nominal interest rate in the current period influenced by the backward expectation of the inflation rate and the output gap.
13. Weight on inflation rate and output
1
.
t t
t t
p y
y
ψ
−
= Δ + −
30 The above open-economy macroeconomics model involves 24 endogenous variables and 9
exogenous variables. Endogenous variables consist of non-predetermined 14 variables:
1
, ,
, ,
, ,
, ,
, ,
, ,
, .
t t
t t
t t
t t
t t
t t
t t
t
y y
y R
q s
c x
p p
E p x
λ ψ
+
Δ Δ
and predetermined 10 variables:
1 1
1 1
1 1
1 1
1 1
1
, ,
, ,
, ,
, ,
, .
t t
t t
t t
t t
t t
t t
t t
t
c R
y E
E y E y
p p
E p
E p
ψ
− −
− −
− −
− −
− +
−
Δ Δ
Δ Exogenous variables consist of government expenditure, international output, and all the
shocks: ,
, ,
, ,
, ,
, .
q y
c R
s p
x t
t t
t t
t t
t t
e e
e e
e y
e g
e
∗
3.2. State Space Representation
Kategori