84 foundations for the behaviour of economic agents. In addition, the choice of parameters
in some equations seemed rather arbitrary and some of them were kept or dropped just for the sake of accommodating stylized facts as close as possible. As the authors have
pointed out, rational expectations do not play a role in the model. This might be a drawback, given the wide acceptance of the concept of rational expectations in theoretical
and empirical macroeconomic modelling. Lastly, the absence of any explicit role for monetary quantities inhibits the examination of the transmission mechanism of monetary
policy. Although it has been argued that there was no stable long-run relationship between money, income, and interest rates, there might be a good case to introduce at
least a simple Taylor rule or a modified version of it
16
.
3.3.3 Simple Model of the Brazilian Economy
The third variant of SSMMs that we are going to discuss in this subsection is a simple model of the Brazilian economy. This model was built ultimately to address the issue of
inflation targeting in Brazil. In particular, the Central Bank of Brazil CBB developed the model to study the transmission mechanism of monetary policy after Brazil’s Real
Plan, that is, the switch in the exchange rate regime to a floating system. As opposed to the RBA model discussed in the previous subsection, de Freitas and Muinhos 1999
developed a small scale model based on the BH approach with embedded theoretical microeconomic foundations in it. The main difference with the BH model is the
modifications they introduce so that only three equations are estimated as opposed to six
16
The authors argued that instead of augmenting the model with a policy reaction function such as a Taylor rule, they simply illustrate the model’s properties with dynamic simulations and track their responses to
shocks. For Australian models with a policy reaction function, refer to de Brouwer and O’Regan 1997; Lowe and Ellis 1997; Shuetrim and Thompson 1999.
85 structural equations in BH plus the policy rule. They also focus mostly on studying the
monetary policy transmission with respect to output and inflation. Thus the main aim of their study is to concentrate on the optimality of the policy rules employed by the central
bank
17
. The discussion in this subsection is particularly useful to show an example of yet another variant in the class of SSMMs and it also provides a good starting point to
understand how the BH model has been modified to suit other countries.
In early 1999, Brazil switched her exchange rate regime from a fixed exchange rate system to a floating regime with the implementation of the so-called “Real Plan”.
Following that, in June 1999, Brazil joined some other countries such as the United Kingdom UK and Sweden in formally adopting an inflation targeting regime. The main
aspect of this new monetary arrangement is to pay attention to expected future inflation when deciding on the current interest rate as an instrument. Thus, the forward-looking
element is inherent due to the fact that most transmission mechanisms of monetary policy indicate that the interest rate affects inflation with a lag working through aggregate
demand
18
. In other words, the decision on interest rates made today by the central bank will determine expected future inflation so that it is crucial to include forward-looking
behavior of agents in this setting.
In their paper, de Freitas and Muinhos 1999 estimated an IS curve and a Phillips equation for Brazil that were used to simulate the effects of different interest rates rules in
relation to the variability of inflation and the output gap. Their benchmark is the optimal
17
To be precise, their focus is on comparing monetary policy rules with interest rates as the main tool of policy. They compare the policy rule that minimizes the loss function with Taylor-type rules.
18
Refer to King 1997, Ball 1999, and Svensson 1998.
86 interest rate rule that is obtained from the Bank’s minimization of a loss function which
essentially is the weighted average of the variance of inflation and output gap see Appendix 2 of their paper. de Freitas and Muinhos 1999 leveraged on the BH model to
come up with a simplified three-equation model in studying the monetary transmission mechanism
19
:
1 1
2 1
3 1
1 4
1 t
t t
t t
t t
t
y y
r g
y y
c β
β β
β ε
∗ ∗
− −
− −
−
− =
+ +
− + Δ
+ 13
t t
t t
t t
t
e e
y y
η α
α π
α π
+ −
+ −
+ =
− ∗
− −
− 1
3 1
1 2
1 1
14
t t
t
e e
υ +
=
−1
15
Equation 13 is an open economy IS curve with the output gap y - y depending on its
own lags, on the lag of the real interest rate, r, on the lag of the first-difference of the real exchange rate
c Δ
, on the lag of the fiscal deficit denoted by g, and on a demand shock ε . Equation 14 is an open economy Phillips curve with inflation π depending on a lag
of itself, on a lag of the output gap, on the change in the nominal exchange rate,
e
, and on a shock
η . Finally, Equation 15 is the exchange rate process that is assumed to follow a random walk. It can be seen clearly that exchange rate affects inflation directly
through the price of imports and indirectly through its effects on the output gap as shown by Equations 13 and 14. The model consists of aggregate supply and demand as given
by the Phillips curve and the IS curve respectively. Furthermore, the transmission mechanism from the interest rate to inflation occurs through aggregate demand only, i.e.
through the IS equation and it takes two periods for the interest rate decision by the CBB
19
Excluding the policy rule.
87 to have an effect on inflation. An important point worth noting is that the random walk
process for the exchange rate precludes the conventional uncovered interest parity UIP channel, whereby a home country appreciation follows an increase in the world interest
rates, ceteris paribus. Wadhwani 1999 argued that although UIP is more attractive in modeling the exchange rate due to its theoretical appeal, predictions of future exchange
rates using random walk specifications usually outperform UIP predictions. Given the three-equation model structure, it is straightforward to see that the choice of interest rate
by the central bank will affect inflation from two periods ahead. Hence, a policy rule is required for the central bank to make the decision. de Freitas and Muinhos 1999
consider Taylor-type rules and optimal rules to close the model
20
.
Estimation of the CBB model used quarterly data whereby inflation is measured by the general price index, the output proxy is GDP, and thus the output gap is GDP
minus potential output. The Hodrick-Prescott filter is used to estimate potential output. The nominal exchange rate is the period average of the ask prices, the nominal interest
rate is the Selic rate
21
, and the fiscal variable is the federal government primary deficit as of GDP. The sample period is 1992:Q4 to 1999:Q1 for the IS equation and 1995:Q1
to 1999:Q2 for the Phillips curve. The equations were estimated using OLS. The IS curve does not contain the real exchange rate term or a fiscal term in their final estimated
results
22
. In addition, dummy variables were introduced for the “Real Plan” and third quarter of 1998.
20
Refer to section 3.4 for the discussion of policy rules in SSMMS.
21
The equivalent of the US Fed funds rate.
22
The authors might have dropped them due to insignificance.
88 de Freitas and Muinhos 1999 imposed a long-run vertical Phillips curve that
translates into the restriction that the sum of the coefficients of lagged inflation and nominal exchange rate changes is 1 in Equation 14. This means that any devaluation in
the exchange rate will be completely passed through to prices in the long run and it has a contemporaneous pass-through effect of 20 in the short run. As mentioned earlier, the
effect of interest rate changes on inflation takes two quarters to realize. A one percentage point increase in the real interest rate will negatively affect the output gap by 0.39
percentage points. Similarly, a decrease of 1 in the output gap reduces inflation by 0.31 percentage points. The final result from these effects is that an increase of 1 percentage
point in the interest rate will reduce inflation by 0.12 percentage points in the short run. As for the long run, the ultimate effect of a 1 percentage point increase in interest rate
would be a 0.6 reduction in inflation
23
.
The CBB model shows that even with a super small scale model, an SSMM can aid in providing recommendations and guidance to the central bank in making its
decisions. However, some caveats also need to be added. First, the relatively short sample period as mentioned beforehand posed the problem of having too few degrees of
freedom as the authors mentioned. This is especially so when they decided to use quarterly data for such a short period. In addition to that, there are some variables
dropped in their final estimation results such as the real exchange rate and the fiscal term that might appear to be important from an economic point of view. Second, their random
walk exchange rate process lacks theoretical content. It also does not take into account
23
Taking into account the autoregressive coefficient in the Phillips equation, which is 0.80, we have 0.12 1 – 0.80 = 0.6 as the long run elasticity.
89 the effects of the interest rate on the exchange rate, which is inappropriate since the
interest rate is the central bank’s main tool of monetary policy.
All in all, the CBB model and the BH model in general has shown the usefulness of a small-scale macroeconomic model for analyzing the major
macroeconomic variables of a country and for performing dynamic simulations to understand the monetary transmission mechanism. The CBB model has provided us with
indirect evidence that using a reasonably small macroeconomic model which embodies important macroeconomic variables and having just a simple monetary policy rule could
still lead to some very important insights regarding the conduct of monetary policy by central banks. In building a good SSMM, an appropriate balance of relevant theoretical
content with important stylized facts needs to be struck in order to yield a robust SSMM that can produce meaningful policy simulation results. In the next subsection, we discuss
several types of policy rules that are required for the conduct of policy simulations.
3.4 Policy Rules in SSMMs
