Observer Based Control with Nonlinear Macroeconometric Models

R. D. Herbert
Macquarie University, Sydney
ric@mpce.mq.edu.au

Abstract

This paper is concerned with the use of low order linear models to develop controls for large nonlinear macroeconometric models. This contrasts with the usual approach to this class of problems of using nonlinear optimization with the nonlinear model, or Linearization of the model and the use of linear quadratic control techniques.

The use of output injection from the nonlinear model into the low order model allows it to learn about the nonlinear model's behavior. The low order model acts as an observer of the larger nonlinear model and is used as the basis of developing control policies for the nonlinear model. As the observer is linear, then linear control techniques can be used with the model. Such an approach is less computationally intensive than nonlinear optimization, especially with a low order observer. It also saves explicit linearizing of the nonlinear model. Further, as the observer learns the behavior of the nonlinear model, then it need not be as concerned with many of the issues, such as the solution of forward looking behavior of economic actors, that are of concern to the nonlinear model.

There is the issue as to whether the learning via output injection interferes with the process of developing control policies. For linear models and accurate observers, these processes can be shown to be separate. In this paper the issue is examined by building an observer using a similar theoretical basis to the nonlinear model; by estimating the observer so that its response is similar, for the variables of interest, to the nonlinear model; and by considering the observer's robustness to model uncertainty.

Two implementations of the observer based approach are given in a counterfactual policy analysis exercise. In the first, the low order linear model is used to develop policies for the nonlinear model using linear quadratic techniques, at the same time as it learns through output injection. The second implementation starts with the use of nonlinear optimization to develop a set of optimal policies for the nonlinear model over the entire time horizon. Shocks to the nonlinear model will cause deviations from these optimal policies, and the observer based approach is used to generate variations in these policies to offset the shocks.

The technique is applied using the Murphy Model of the Australian economy. The aim is to examine if policies could have been developed for the Murphy Model so that GNP and inflation would have followed smooth trajectories rather than their historical values, and, if so, what are the implications for other key economic variables.