پویایی های بازار کار نئوکلاسیک، آشفتگی و منحنی فیلیپس دستمزد واقعی

The relationship between wage inflation and unemployment has been extensively investigated since the early work of Phillips [Phillips, A.W., 1958. The relation between unemployment and the rate of change of money wage rates in the U.K. 1861–1957. Economica 25, 283–299] and Lipsey [Lipsey, R.G., 1960. The relation between unemployment and the rate of change of money wage rates in the U.K. 1861–1957: a further analysis. Economica 27, 1–31], and it is still a matter of debate. In this paper we study the dynamics of a standard neoclassical labour market under the simplest Walrasian adjustment rule. We show that when consumption and leisure are sufficiently low substitutes, the unique Walrasian equilibrium of the economy can be destabilised, and regular or even chaotic fluctuations of wages and employment appear. This leads to an interesting resurrection of a real wage Phillips curve as a long-term phenomenon.

The relation between wage inflation and unemployment, extensively discussed since the early work of Phillips (1958) and Lipsey (1960), is presently a matter of renewed interest.1 In this paper we consider a model describing the dynamics of the labour market under standard neoclassical assumptions. The labour market, demand and supply side, is described by a Cobb–Douglas technology and by a CES individual utility function. The current labour demand and supply are assumed to adjust to their optimal counterparts following a continuous-time adjustment, and the wage adjusts on the current excess demand for labour according to the usual “Walrasian” rule. Our main finding is that a robust cyclical and even chaotic behaviour of prices and quantities may occur even in a simple micro-founded economic model characterised by the simplest adjustment mechanism when the substitution between consumption and leisure is sufficiently weak. Furthermore, stickiness in the labour demand of the firm, as well as flexibility in the labour supply, can lead to the following interesting phenomena: (a) a real wage Phillips curve necessarily re-emerges as a long-term phenomenon2 and (b) in the chaotic case a “trapping” region emerges in which the Walrasian equilibrium (WE from now on), viewed as the “center of mass” around which the system evolves, completely loses its “predictive ability”.3 In our model the points belonging to the Phillips’ curve are just the realisation of a single trajectory of the underlying (fully deterministic) process rather than a set of different equilibrium points among which the policy maker could choose as in the traditional view of the curve. In a related paper by Chichilnisky et al. (1995), their re-discovery of the Phillips curve from complex dynamics is obtained by a less general framework, compared to the one adopted here, because they assume a discontinuous production function with a special discrete-time formulation. The plan of the paper is as follows. In Section 2, we present the model. Some theoretical results are reported in Section 3, while the numerical simulations are reported in Section 4. Concluding remarks follow.

This paper has shown that regular fluctuations and chaotic behaviour of wages and employment may be a robust outcome of a market economy when consumption and leisure are low substitutes. In particular when the unique Walrasian equilibrium of this economy is destabilised, then the economic variables evolve toward a stable attracting region in which motion is cyclical or chaotic. In this region the wage always moves in opposite direction to the unemployment. This is an evident “resurrection” of the Phillips curve that appears as a true long run phenomenon and not only a transitory disequilibrium phenomenon for a wage adjustment process converging to the equilibrium as postulated by the neoclassical interpretation of the Phillips curve. We pointed out, however, that such a curve is a totally useless policy tool. Moreover, a further interesting point is that, although many Walrasian systems can be forced to show complex dynamics by suitable complications of the adjustment process, this work has shown that chaos is a feature of a neoclassical economy under the simplest (i.e. linear) adjustment rule. Thus, our result, which, interestingly, is based on a simple neoclassical framework, intends to be a further contribution to the literature on chaotic economic dynamics (Rosser, 1999).