134 The first two deterministic exercises are carried out under the assumption that our
stochastic equations hold exactly over the forecast period. In reality, we would expect to see the same sort of errors occurring in the future as we have seen in history. Random
errors are therefore added to each equation with the condition that the average value of the chosen random errors is zero. We have also ignored the fact that some of the
coefficients in our equations are estimated, rather than fixed at known values. We may like to reflect this uncertainty about our coefficients in some way in the results from our
model.
Up until now we have thought of our model as producing point forecasts for each of our endogenous variables at each period. As soon as we add uncertainty to the model,
we should think instead of our model as predicting a whole distribution of outcomes for each variable. In a non-linear model such as the Indonesian SSMM, the mean of the
distribution need not match up to the deterministic solution of the model. Our goal is to summarize these distributions using appropriate statistics—this is the essence of
stochastic simulation. We will perform a stochastic simulation to evaluate the
performance of alternative monetary policy rules in macroeconomic stabilization of the Indonesian economy. This is our third and most important exercise.
5.4.2 Model-Consistent Expectations
In our Indonesian SSMM, we have several forward-looking variables in some of the equations. In general, future values of endogenous variables may influence the decisions
made in the current period. Consequently, the treatment of expectations in econometric
135 models should be given careful consideration. Although the way that individuals form
expectations is obviously complex, if the model being considered accurately captures the structure of the problem, we might expect the expectations of individuals to be broadly
consistent with the outcomes predicted by the model. In the absence of any other information, we may choose to make this relationship hold exactly. Expectations of this
form are often referred to as model-consistent expectations.
Specifically, our Indonesian SSMM involves certain expectations of future periods such as those found in the IS equation lead of the non-oil output gap, inflation
equation expected inflation, the UIP identity expected exchange rate, and the Taylor rule expected inflation. Model-consistent expectations will be applied to the two
behavioural equations and the policy rule when we perform the deterministic simulations. If we assume that there is no uncertainty in the model, imposing model-consistent
expectations simply involves replacing any expectations that appear in the model with the future values predicted by the model. As discussed earlier in the estimation context, this
effectively amounts to the assumption of perfect foresight on the part of economic agents.
When it comes to performing stochastic simulations with the SSMM, however, we used the actual future values of output and inflation as the corresponding
expectations. This is a much simpler computational alternative to the use of rational expectations, which would require a complicated procedure like the following: firstly, an
initial guess needs to be made as to a path for expectations over the forecast period for example, by calculating a solution for the expectations in the deterministic case.
136 Secondly, a large number of stochastic repetitions of the model is run holding these
expectations constant, and calculating the mean paths of the endogenous variables over the entire set of outcomes. Finally, the mean paths of the endogenous variables are
checked to see if they are equal to the current guess of expectations within some tolerance; if not, the procedure is repeated.
5
The UIP identity in the Indonesian SSMM is given as
t f
t t
t t
t
i i
e E
e
4 1
ε +
+ −
=
+
, where the exchange risk premium is captured by the error term instead of being modelled
explicitly. Although the UIP condition cannot be verified directly, since neither market expectations of the spot rate nor the currency risk premium are observable, economic
models typically assume that this relationship holds and that if markets are efficient and investors are risk-neutral, then the excess return on domestic assets, defined as the
interest differential net of the observed exchange rate movement, should be “unforecastable”.
6
1 +
t t
e E
is defined as the market’s one-step-ahead expectations for the spot exchange rate made at time t. Thus, we must use survey data or forecasts as a proxy
for this expectation. The former is not available at the quarterly frequency and, even if it is, the survey will just be based on the RupiahUS exchange rate. We therefore resort to
using forecasts of the exchange rate as a proxy for the market’s expectation of the future exchange rate. Brigden et al. 1997 argued that although forecasts of next period’s spot
exchange rate might well be biased and inefficient, all that matters is that interest rate
5
An alternative will be to perform numerical optimization techniques for solving the equilibrium conditions. We will not pursue this matter further in this thesis and interested readers are referred to Clarida
et al 1999, Fuhrer and Moore 1995, Leitemo and Roisland 2000, McCallum and Nelson 1999, Rotemberg and Woodford 1999, and Svensson 1997.
6
For some influential works on exchange rate issues and particularly on UIP, refer to Cumby and Obstfeld 1981, Fisher et al. 1990, Meese and Rogoff 1983.
137 differentials feed through one-for-one to exchange rate movements. We confirmed that
for the UIP relationship in the Indonesian economy, using forecasts of the exchange rate works well see the baseline simulation results below. We employ an ARIMA 1,1,1
model to obtain the forecasts of the exchange rate and subsequently take this to be the market’s expectations of next period’s exchange rate.
Finally, we need to specify the terminal condition that affects the way the model is going to be solved when one or more equations in the model contain future values of
the endogenous variables. The terminal condition is needed to specify how the values of the endogenous variables are determined for leads that extend past the end of the forecast
period. We use a constant difference specification for the terminal values. In this specification, terminal values are determined endogenously by adding the condition that
the values of the endogenous variables follow a linear trend over the post-forecast period, with a slope given by the difference between the last two forecasted values. This option
may be a good choice if the model is in logarithmic form and tends to converge to a steady state.
5.4.3 Solution Algorithms
