Stabilisation policy and the time-forms of lagged responses

Abstract

In an earlier article (chapter 16) I used a number of dynamic process models to illustrate the operation of certain types of stabilisation policy. In setting up the models I assumed that each lagged response was of the particular time-form known as an exponential lag. I pointed out (pp. 136-7) that other time-forms would probably give better representations of the real responses in an economic system, but did not introduce these more realistic lag forms into the models owing to the difficulty of solving the high- order differential equations to which they would have led. Since then the National Physical Laboratory and Short Brothers and Harland, Ltd, have allowed me to use their electronic simulators, by means of which the time responses of quite complex systems with a variety of lag forms can be found very rapidly. In addition, I have become more familiar with the frequency-response method of analysis based on the Nyquist stability criterion. This is a graphical method which not only enables considerable information to be obtained about the dynamic properties of a system without solving the differential equation of the system, but also gives valuable insight into the ways in which the dynamic properties would be altered if the relationships and lag forms in the system were modified or additional relationships included. A study, using frequency-response analysis and electronic simulators, of the properties of models in which the lags are given more realistic time- forms has shown that the problem of stabilisation is more complex than appeared to be the case when attention was confined to the simpler lag forms used in my earlier article.

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