Mis-Specification and Cyclical Models: The Real Wage and the Phillips Curve

Abstract

This paper discusses some misinterpretations that can arise when cyclical data are incorrectly assumed to be generated by movements between equilibria. One example is the cyclical behaviour of the real wage, an issue discussed by Grossman (1973) and others. In Section II a small dynamic model is examined which can give a procyclical pattern of the real wage even though it has a negative equilibrium relation between employment and the real wage. This suggests that predicting the cyclical pattern of the real wage from the equilibrium relations of a model can give incorrect results. The theoretical model is used to reinterpret the empirical evidence on the cyclical pattern of the real wage (Bodkin, 1969). Another area of possible dynamic mis-specification is the Phillips Curve literature. Two important studies, Cagan (1968) and Desai (1975), which use unconventional estimation techniques, are examined using a dynamic model. The conclusion is that the methods of these two studies do not guarantee against a confusion of equilibrium and cyclical relations. The discussions of the Phillips Curve and the movement of the real wage provide potential applications of the econometric tests for mis-specification developed by Hendry (1974). Section I presents some properties of a cyclical dynamic system which simplify the economic analysis of Section II. These results can also be applied to other discussions of cyclical data and dynamic mis-specification. For example, the analysis by Tobin (1970) of the cyclical relation between changes in the money supply and nominal income, and that by Grossman (1974) of cyclical rotations about the Phillips Curve, can be simplified using Section I.