Symbolic Dynamics and Control in a Matching Labor Market Model

In this paper we apply the techniques of symbolic dynamics and chaos control to the analysis of a labor market model which shows chaotic behavior and large volatility in employment flows. The possibility that chaotic dynamics may arise in modern labor markets had been totally strange to economics until recently. In an interesting paper Bhattacharya and Bunzel [2] have found that the discrete time version of the Pissarides-Mortensen matching model, as formulated in Ljungqvist and Sargent [23], can easily lead to chaotic dynamics under standard sets of parameter values. This paper explores this version of the model with two main objectives in mind: (i) to clarify some open questions raised by Bhattacharya and Bunzel by providing a rigorous proof of the existence of chaotic dynamics in the model; and (ii) to show that this type of dynamics can be easily controlled by linear feedback techniques – the OGY method – without producing modifications to the original model, apart from locally changing its type of stability. These techniques may be of significant importance for the study of economic theory and policy, in particular, if complexity becomes more frequently encountered in the models developed to properly describe the behavior of modern economies, and the view of purely exogenous shocks as explaining cycles and volatility looses its large predominance in contemporary economics.