Deterministic versus Stochastic Simulations

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5.4.1 Deterministic versus Stochastic Simulations

There are two types of simulations namely, deterministic and stochastic. In the deterministic setting, the inputs to the model are fixed at known values, and a single path is calculated for the output variables. In a stochastic environment, uncertainty is incorporated into the model by adding a random element to the coefficients, the equation residuals, or the exogenous variables. As the first exercise in assessing our model, we would like to examine the ability of our model to provide one-period-ahead forecasts of our endogenous variables. One way to do so is to look at the predictions of our model against the historical data, using actual values for both the exogenous and the lagged endogenous variables of the model. We refer to this as a static-deterministic simulation. An alternative way of evaluating our model is to examine how the model performs when it is used to forecast many periods into the future. To do so, we must use our forecasts from previous periods, not actual historical data, when assigning values to the lagged endogenous terms in our model—a method we refer to as a dynamic-deterministic forecast. The second set of exercises in our simulations is to use our model to trace the movements of the endogenous variables under different economic scenarios. To produce such forecasts, we change the path of one exogenous variable or parameter at a time while holding the rest constant. In the next section, we carry out three scenario analyses pertaining to the effects of a foreign income shock, the credibility of the central bank in inflation targeting and the choice between a headline inflation or core inflation target. 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