On the Derivation of the “Efficient” Phillips Curve

Abstract

I IKTRODVCTIONIt will be argued in this paper that for policy purposes the measure of inflation-unemployment trade-off provided by the conrentional Phillips curve is inadequate. A n alternative relationship, which we call the "efficient Phillips curve", is suggested to account for the complex concept of the infIatioii-uiieniploynient trade-off. The efficient Pldlips curve takes into account the inter-relationships between inflation and unemployment that arise in blie macroeconomy, the preferences of the policy maker in terms of these two objective variables ( I ' and U ) as well as his choice of the instruments (or the instrument mix) used. The efficient Phillips cnrve is derived using the tlicory of optimal control and, unlike the conventional Phillips curve, i t is based 011 the "e5cient frontier" of the econometric model. The slope of the efficient Phillips curve will of course vary, inter a h , with the structure of the model. I n the present case, two versions of the National Institute's (XIESR, 1979) macroeconometric model ("NIESR model") are dcployed, which differ solely, but crucially, in the form of wage equation that appears in the model. Efficient Phillips curves are first derived analytically for static approximations t o each of the two versions of the N E S R model ; subsequently, numerical derivations are obtained which usc the full dj-naniic rcrsions of the model to compare their policy properties. *Nnnuscript received 10.3.82; 6nnl version received 29.4.82. tFirinncia1 support from the S.S.R.C. is gratefully acknowledged. The author3 would like to thank P. -4reSti9, 11. J. Artis, K. Cuthbertson and B. Rustem for helpful comments on M earlier draft. The usual disclaimer applies. 151

Policy Trade-Offs in the NIESR Model: Exercises Using Optimal Control

“…Again it is informative to conduct sensitivity analysis by varying these desired values and recomputing the implied optimal solutions. The sensitivity of the optimisation as the weights on objectives are changed approximates the effects of changes in the desired values of objectives, and so we do not explore changes in the latter here (see Henry, Karakitsos and Savage [1982]).…”

“…(if) Changes in indirect taxes Dynamic analysis of an earlier version of the 1~l~tg®~~l Institute model (l~®d~~ IV, NIESR [1979]) concluded that optimising using only average indirect tax rates in pursuit of inflation and unemployment objectives could simultaneously reduce both. The policy recommendation f~®~ix~~ from this conclusion appears to be that the average rate of indirect tax be reduced to ~e~°®9 or even that indirect taxes be replaced by subsidies (see, for example, Artis and Karakitsos [1983] and Bray [1982]).…”

“…From these counter arguments it follows that a significant trade-off may exist in the short to medium term between unemployment and inflation, which may be exploitable by aggregate demand policy. In the rest of this article we use control-theoretic methods to illustrate what these are in the case of the current version of the National Institute model (NIESR, 1983).…”

Optimal Control of Econometric Models. Problems Developments and an Application With a Model of the Italian Economy(*)

“…Therefore, the results obtained depend on the specification of the objective function which in turn, determines the optimal policy instruments mix. Different specifications of the objective function in all likelihood would yield different slopes and lines (see Henry et al 1982).…”