72 to construct for Indonesia, we will outline several variants of SSMM that have been
adopted by some countries in the following subsections
6
.
3.3.1 Batini-Haldane Model BH
In this subsection, we will examine the basic model of Batini-Haldane 1999, hereafter BH that is employed at the Bank of England and discuss the relative merits of this small
scale model. The model comprises six equations as follows:
t t
t t
t t
t t
t t
q E
i y
E y
y y
1 4
1 3
1 2
1 1
ε α
π α
α α
+ +
− +
+ =
−
+ +
−
1
t t
t t
t
i y
p m
2 2
1
ε β
β +
+ =
− 2
t f
t t
t t
t
i i
e E
e
3 1
ε
+ −
+ =
+
3
2 1
1 −
+ =
t t
d t
w w
p
4
t t
t t
t t
t t
t t
t
y y
p w
p E
w E
p w
4 1
1 1
1 1
1
ε γ
γ γ
+ −
+ −
− +
− =
−
− −
+ +
5
t d
t t
e p
p 1
θ θ
− +
=
6
Excluding the policy rule, which we will discuss later, the model consists of both the behavioural equations and the identities, whereby the former can be estimated or
calibrated. All variables, except interest rates, are in logarithms. Equally important to note is that in the simulations, all behavioral relationships are expressed as deviations
from equilibrium.
6
There are other SSMMs that are not discussed in this thesis, for example: Vincent 2002 on small-scale model of the US economy, and Arreaza et al 2003 on Venezuelan economy.
73 We will discuss in detail each equation found in the BH small scale
macroeconomic model. Equation 1 is a typical IS curve with the usual expected signs such as the negative relation between the ex-ante real interest rate and real output
3
α , y
t
, and the positive relation between the real exchange rate—
t
q =
t f
t t
p p
e −
+ with e
t
being the nominal exchange rate that represents the domestic currency price of foreign currency—and real output
4
α .
7
In the BH model, the short-term real interest rate is used instead of the long real interest rate
8
. In order to determine whether it is more appropriate to employ the long- or short-term real interest rate, we
should analyze and judge the responsiveness and sensitivity of expenditures to either real interest rate as well as looking at the debt instruments used in practice.
A distinguishing feature of this IS specification is the existence of a lead term in addition to the usual model whereby output depends on its own lag because of adjustment
costs. The lead term is motivated by the McCallum and Nelson 1999 optimizing IS-LM specification for monetary policy and business cycle analysis. They consider a dynamic,
optimizing general equilibrium macro-model of the Sidrauski-Brock type that corresponds to the traditional IS-LM functions. Their work has shown that this IS
specification is different from the conventional one in that an additional variable reflecting the expected next-period income is included. The modified IS specification
yields a dynamic, forward-looking aspect to the economy’s saving behavior. This is an
7
The representation of the exchange rate found in Batini and Haldane 1999 is the converse of this, i.e. e
t
being the nominal exchange rate that represents the foreign currency price of domestic currency. Thus we would expect a negative relation between the real exchange rate and the real output in this case. We employ
this definition to be consistent with the Indonesian SSMM in Chapters 4 and 5.
8
We could include a long-term interest rate by linking long- and short-term interest rates through an arbitrage condition, as in the Fuhrer and Moore 1995a model.
74 important modification since we acknowledge the forward-looking behaviour of
economic agents in the decision-making process, thus enabling monetary policy to work more effectively by recognizing these responses
9
. Finally,
t
1
ε is the demand shock or innovation in the IS specification, such as shocks to foreign output and fiscal policies.
Equation 2 is an LM curve with the conventional arguments that depicts real money balances as being dependent on a nominal interest rate and real output. McCallum
and Nelson 1999 show that this conventional LM function can be derived as the reduced form of an optimizing stochastic general equilibrium model. The innovation
element
t
2
ε is named “velocity” shocks. Altogether, the IS-LM specification in this model, based on McCallum and Nelson 1999, provides a model of aggregate demand
behavior that is rather tractable and also usable with a variety of aggregate supply specifications from full price flexibility to sticky prices. McCallum and Nelson 1999
also argued that traditional IS-LM specifications need to be modified especially for the conduct of monetary policy by adding a forward-looking element.
Equation 3 is an uncovered interest parity condition for the open economy, expressing the dynamic relationship between the exchange rate and the spread between
domestic and foreign interest rates, without the exchange risk premium being made explicit. It depends on the expected level of the nominal exchange rate and the interest
rate disparity between domestic and foreign nominal interest rates. The shock,
t
3
ε , comprises foreign interest rate shocks and possible disturbances in the foreign exchange
9
This is to be contrasted with the traditional IS specification, unless we believe that income per capita is expected to be constant in the future.
75 market, including exchange risk premium shocks and arbitrage elements. Equations 4
and 5 define the model’s supply side that takes a similar form to the staggered wage contract models
10
. The former specifies a constant markup equation of domestic output prices over the weighted average of the current and preceding period’s contract wages.
The latter is the wage-contract equation that specifies wage contracts for two periods. The current real contract wage is a weighted average of the real contract wage of the other
period’s contract wages of labourers, i.e. the wages in the preceding period and the wages expected in the next period. This specification does not necessitate lag symmetry and
allows for flexible mixed specifications See Fuhrer and Moore 1995b; Blake 1996; Blake and Westaway 1996. Fuhrer 1997 found that this flexible mixed specification is
preferred empirically. This will allow for a varying degree of forward-looking behaviour in the wage-bargaining process which is suitable for empirical testing and simulation.
The sum of lead-lag weights are restricted to be unity to preserve price homogeneity in the wage-price system that translates into a vertical long-run Phillips curve. Also present
in the wage bargaining equation is the output gap term that measures the tightness in the labour market. The innovation term
t
4
ε captures the shocks to the natural rate of output and other types of supply shocks.
Equation 5 has great theoretical and empirical appeal. For example, Duesenberry 1949 argued that wage relativities were a key consideration when wage-
bargaining activities are initiated. The empirical attraction of this wage-price specification is that it generates inflation persistence Batini and Haldane 1999 which is
10
Refer to Fuhrer and Moore 1995a for detailed treatments and Buiter and Jewitt 1981 for an early formulation.
76 absent in the Taylor 1980 specification as found by Fuhrer and Moore 1995a and
Fuhrer 1997. Lastly, Equation 6 defines the consumption price index that comprises the prices of domestic goods and imported foreign goods. The weights of these two
components sum up to 1. Note that the equation implies full and immediate pass-through of import prices into consumption prices. Batini and Haldane 1999 come up with the
following reduced-form Phillips curve specification using equations 4-6 as follows:
[ ]
t t
t t
t t
t t
t t
c E
c y
y E
5 1
1 1
1 1
1 1
ε χ
χ μ
χ π
χ π
χ π
+ Δ
− Δ
− +
+ +
− +
=
+ −
− +
7
where
t t
t
p e
c −
= real exchange rate,
1 2
φ μ
− =
, Δ is the backward difference operator, and
[ ]
1 1
4 5
t t
t t
t t
t t
w E
w p
E p
− −
− −
− +
= χ
ε ε
whereby this composite error term includes expectation errors made by wage bargainers.
The transmission of monetary impulses in this model is very different from the closed economy case. We will look in particular at the transmission of policies through
the channel of money supply and interest rates. As we know, there is a conventional real interest rate channel that works through the output gap and thereof onto inflation. In
addition, there is a real exchange rate effect that operates through two distinct channels, namely: an indirect output gap route running through net exports and thence onto
inflation; and secondly, direct price effects via the cost of imported consumption goods and wages and hence, via domestic output prices. Under certain specifications of tastes
and technology, the system of equations 1–6 can be derived as the linear reduced-form
77 rational expectations macromodel of a fully optimizing general equilibrium model
McCallum and Nelson 1999.
3.3.2 Small Model of the Australian Macroeconomy
