The Settings of Stochastic Simulations

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5.6 Alternative Monetary Policy Rules

In this section, we perform stochastic simulations of our Indonesian SSMM. This technique is particularly useful for deriving the implications for output and inflation of different monetary policy rules, namely the Taylor rule and the McCallum rule. Following this, we sketch the trade-off frontier between output and inflation variability in the Indonesian economy for alternative specifications of the Taylor rule.

5.6.1 The Settings of Stochastic Simulations

Before we proceed with the stochastic analysis of policy rules, we will briefly outline the basic setup of our stochastic simulations. In a stochastic simulation, the model is solved repeatedly for different draws of the stochastic components of the model. We include coefficient uncertainty in the model, such that a new set of coefficients is drawn before each repetition, using the estimated coefficient variability from the SSMM whenever possible. 13 This technique provides a method of incorporating uncertainty surrounding the true values of the coefficients into our results. During each replication, random errors are generated for each equation according to the residual uncertainty, as described further below. Similarly, shocks to the exogenous variables are calibrated to have the same variances as in the historical data. At the end of each replication, the statistics for the endogenous variables are updated. When a comparison is being made with an alternative scenario, the same set of random residuals and exogenous variable shocks are applied to both scenarios during each replication. We set the number of replications in our 13 Note that coefficient uncertainty is ignored in nonlinear equations. 159 stochastic simulation to be 1000 so that the sampling variation in the statistics that we obtain is relatively small. In generating the innovations of the stochastic equations, we use the values of the standard deviations calculated from the behavioural equations in our model. The exception is exchange rate innovations in the UIP equation, which are assumed to be zero. To simulate the distributions of the random error components, we use a Monte Carlo approach as follows. At each replication of a stochastic simulation, a set of independent random numbers is drawn from the standard normal distribution, and then these numbers are scaled to match the actual variance-covariance matrix of the system. 14 This ensures that the correlations of the random draws match the correlations of the observed equation residuals. The model is solved many times with pseudo-random numbers substituted for the unknown errors at each repetition. Finally, we employ the same Gauss-Seidel algorithm to solve the model as in the deterministic case.

5.6.2 A Quest for Best Monetary Policy Response