119 Unit root tests are carried out on all the variables employed and the results are
shown in the Data Appendix. Where they are found to be integrated of order one i.e. I1, their changes are used in the estimation of the SSMM, except in the case of the LM
equation. The LM equation is specified and estimated in log levels because the variables in it are found to be cointegrated. The other exception to this rule is made for the non-oil
and oil output series, both of which are taken as deviations from their potential, which is measured by the Hodrick-Prescott filter, as done in most of the other SSMM studies cited
in Chapter 3.
5.2 Estimation Methods
This section deals with the estimation of the parameters in our model. We will discuss the issues underlying the choice of estimation method and justify our choice for the
Indonesian SSMM. By way of doing this, we begin with a review of the techniques that are available for estimating simultaneous equation models.
5.2.1 Single Equation versus System Methods
A small-scale scale macroeconomic model attempts to explain the workings of an economy that is written as an interdependent system of equations describing some
hypothesized behavioural relationships among economic variables. Consequently, a system of simultaneous equations appears quite naturally when estimating economic
models. However, the use of simultaneous equations methods to estimate the unknown parameters of an interdependent system of equations such as an SSMM still generates
120 considerable controversy and there is often disagreement over which are the best
techniques to employ in practice.
Some critical issues are worth mentioning here. In building an economic model, the model builder must distinguish between endogenous variables which are determined
by the system and exogenous variables which are determined outside the system. It is widely assumed that movements in the latter variables are autonomous or in other words,
they are unexplained causes of movements in the former variables. If in any system of equations each of the endogenous variables can be expressed as a function of the
exogenous variables, then the usual ordinary least squares OLS method warrants consideration and implementation. The main task here is to validly determine and
distinguish what are the endogenous and the exogenous variables in the system and then subsequently derive the reduced form equations. However, even if reduced form
equations can be found, such equations have no structural interpretation and thus they will not be useful for policy analysis and inference.
Our Indonesian SSMM has equations containing more than one endogenous variable. These so-called “structural” equations have interesting causal interpretations
and form the basis for policy analysis and dynamic simulations. However, in doing so, we need a representation in which the postulated changes in explanatory variables are
easily described—a concept that naturally leads to the degree of autonomy of an equation Rothenberg 1990. The analysis of policy changes in our SSMM will be greatly
simplified if our equations possess considerable autonomy whereby a policy change or a
121 kind of shock to a variable changes one equation and leaves the other equations
unchanged. Rothenberg 1990 made the observation that structural parameters in a simultaneous equation model cannot be well estimated using OLS because the logic of
interdependent systems suggests that structural errors are likely to be correlated with all the endogenous variation. In this case, the usual least-squares techniques often turn out to
have poor statistical properties in the face of simultaneity. However, if the correlation is small as compared with the sample variables, the resulting bias will also be small.
Moreover, alternative estimation methods that have been developed often produce implausible and questionable estimates which render OLS still preferable.
All this boils down to a choice between estimating the Indonesian SSMM using a limited information method such as OLS or two-stage least squares TSLS that can be
applied to one equation at a time, and system or full information maximum likelihood FIML methods that require a complete specification and joint estimation of all
equations. The main difference between these two methods is one of statistical efficiency. It is generally accepted that the more that is known about the process being studied, the
more precise the estimates that one can obtain of the unknown parameters with the available data. In a simultaneous equation model, information about the variables
appearing in one equation can be used to get better estimates of the coefficients in other equations—the essence of full information estimation methods. Thus, in a small and
theoretically sound model with restrictions across equations, it is worth exploiting the efficiency gains.
122 However, a trade-off does exist. Although full information methods are more
efficient, they are prone to specification errors and are also subject to higher computational burden, although this is not a problem with the present computer
technology. In particular, if we misspecify one of the equations in the system and estimate the parameters using single equation methods, only the misspecified equation
will be poorly estimated. If we employ system estimation techniques, however, the poor estimates for the misspecified equation may contaminate estimates for the other
equations.
5.2.2 Estimation Methods for Indonesian SSMM
