RDP 7901: Estimation and Statistical Evaluation of an Economic Model 3. The RBA76 Project: Some Econometric Issues

L.A. Moore

July 1979

The RBA76 model of the Australian economy was discussed at a Conference in Applied Economic Research at the Reserve Bank in December 1977.3 The model is a non-linear model specified in continuous time with a discrete approximation for estimation, and estimated by a full information maximum likelihood following Wymer (1976). Since appropriate formal evaluation criteria are not available for this type of model, reliance is placed on a series of tests rather than a single test statistic, in line with the approach of Dhrymes et al (1972). The criteria used in the project have been as follows: sign and significance of parameter estimates; informal goodness-of-fit measures; linear dynamic control simulation and counterfactual simulation (graphical analysis and RMSPE); eigensystem analysis and estimation of the model over different observation periods. This set of criteria can be expanded to include non-linear dynamic control simulation and counterfactual simulation, stochastic simulation, forward simulation, simulation of various size shocks and from different starting periods and analysis of autocorrelation. The likelihood ratio test is not used because of the small sample size. It may not be practical or appropriate to use all of these criteria all of the time, but most or all of them should be used at some stage in a model building project. The application of most of these criteria is reported in sections 4 and 5.

Comments and suggestions from the Conference and elsewhere indicated that the main econometric issues for the RBA76 project are as follows:

  • alternative estimation techniques;
  • linearisation approximations and non-linear simulations;
  • seasonal adjustment;
  • the shape of the likelihood surface;
  • autocorrelation in residuals;
  • the prewhitening filter;
  • use of averaged data;
  • restrictions on the model.

Some aspects of the RBA76 methodology have been examined as part of the IMPACT Project, and several conference participants also reported empirical work on the mid-1977 version of RBA76. The results of this and other work are as follows:

  • autocorrelation functions (Bacon and Johnston (1977)) and the sign reversal test (Giles (1977)) both indicate autocorrelation in some equations. The similarity of the autocorrelation functions of the model estimated with and without prewhitened data indicate that the filter to remove the serial correlation introduced with the discrete approximation is having little impact on the residuals. However, both of these measures were calculated with the reduced form residuals of the model, and tests using the more appropriate structural form residuals may provide different results.
  • 2SLS estimates of the model (using the full set of predetermined variables) are close to OLS estimates, and the residuals of the 2SLS model are similar to those for the model estimated with FIML (Bacon and Johnston (1977)).
  • preliminary results of a comparison by G. Taylor (1979) of the XIIQ and Wymer seasonal adjustment methods at the primary and secondary stage indicate that the different adjustment methods and stages have little effect on the parameter estimates.
  • alternative linearisation approximations are evaluated against the first order Taylor series approximation and in terms of their impact on OLS estimates and equation residuals (Walters (1978)).
  • unconstrained and constrained[21] OLS estimates of the model are obtained by Perrazelli (1977) as a test of restrictions in RBA76: there is a significant difference between the two sets of estimates for only two equations.
  • for evaluation of two models in his undergraduate thesis at Sydney University, Trevor (1978) defines additional informal goodness-of-fit measures and a measure of the non-contemporaneous serial correlation within and across the residuals of the structural equations.
  • a study of parameter stability and simulation characteristics of RBA76 and the RBF1 forecasting model is reported in J. Taylor (1979): the models were re-estimated over a number of different sample periods and it was found that for both models there was considerable paramete volatility with changing estimation period, and that policy implications of the models can be sensitive to the estimation period.

In this paper, simulations of the non-linear version of the model are given, the procedure of data averaging is examined and the shape of the likelihood surface is discussed. Since previous work on these issues has related to the mid-77 version of the model, this study uses a late-77 version of RBA76. For this model, the linearisation approximations and the pre-whitening filter are examined, and OLS estimates are given. The testing of restrictions is not examined in the current study because of the overlap with specification issues and the inappropriateness of t1 likelihood ratio test. The issue of autocorrelation in residuals is also not pursued any further in this paper: although the tests indicat that the residuals of many of the equations in RBA76 are auto-correlated, there is conflict as to whether this should be accounted for by estimation with autocorrelation adjustment,[22] or whether further attempts should be made to trace the source of mis-specificatic The model used as a basis for the analysis in this paper is Model II from Section 7 of Jonson et al (1977), with some modifications.[23]

Footnotes

Cross equation parameter estimates from FIML are required for constrained OLS estimation. [21]

This procedure would require more than the available core of the present computing system, if the model is estimated as a whole. [22]

The model was re-estimated with revised data and a term for the miscellaneous items in the money supply identity was added. The main parameter estimate to change was that representing the effect of the bond rate on money demand: the model was re-estimated with this parameter constrained. This version of the model was also used as the benchmark model in Jonson, Evans and Moore (1978). [23]