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
There are two types of algorithm available in solving our SSMM. The first is the Gauss- Seidel algorithm, which is an iterative algorithm whereby at each iteration, we solve each
equation in the model for the value of its associated endogenous variable, treating all other endogenous variables as fixed. This algorithm requires little working memory and
has fairly low computational costs, but requires the equation system to have certain
138 stability properties for it to converge. Although it is easy to construct models that do not
satisfy these properties, in practice, the algorithm generally performs well on most econometric models.
The alternative to the Gauss-Seidel method is the Newton-Raphson algorithm. The Newton-Raphson method is also an iterative method whereby at each iteration, we
take a linear approximation to the model, and then solve the linear system to find the solution of the model. Although this algorithm can handle more complicated models than
the Gauss-Seidel method, it requires considerably more working memory. Consequently, we eschew this algorithm and employ the Gauss-Seidel algorithm for all the simulation
exercises in our thesis.
The use of the Gauss-Seidel algorithm is also appropriate for another reason: the Indonesian SSMM requires iterative forward solution, which the method is able to handle
well. Specifically, the solution of the model for a given period involves both past and future values of the endogenous variables. To arrive at the solutions, it is not possible to
solve the model recursively in one single pass but instead, the equations from all the periods across which the model is going to be solved must be treated as a simultaneous
system that requires terminal as well as initial conditions.
The econometric software that we use, Eviews 5.0, applies a Gauss-Seidel iterative scheme across all the observations of the sample. This involves looping
repeatedly through every observation in the forecast sample, at each observation solving
139 the model while treating the past and future values as fixed. The loop is repeated until
changes in the values of the endogenous variables between successive iterations become less than a specified tolerance. This method is often referred to as the Fair-Taylor
method.
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5.4.4 Baseline Simulation Results
