In this paper we apply the techniques of symbolic dynamics to the analysis of a labor market which shows large volatility in employment flows. In a recent paper, Bhattacharya and Bunzel cite{BB} have found that the discrete time version of the Pissar
ides-Mortensen matching model can easily lead to chaotic dynamics under standard sets of parameter values. To conclude about the existence of chaotic dynamics in the numerical examples presented in the paper, the Li-Yorke theorem or the Mitra sufficient condition were applied which seems questionable because they may lead to misleading conclusions. Moreover, in a more recent version of the paper, Bhattacharya and Bunzel cite{BB1} present new results in which chaos is completely removed from the dynamics of the model. Our paper explores the matching model so interestingly developed by the authors with the following objectives in mind: (i) to show that chaotic dynamics may still be present in the model for standard parameter values; (ii) to clarify some open questions raised by the authors in cite{BB}, by providing a rigorous proof of the existence of chaotic dynamics in the model through the computation of topological entropy in a symbolic dynamics setting.
There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King (1997), Clarida et al. (1999), Svensson (1999) a
nd Woodford (2003). In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper (which allows for convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy. We emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle--path stability, for different sets of parameter values we may have saddle stability, totally unstable equilibria and chaotic attractors; (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem intuitively correct. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility (but this is sensitive to the values given to the parameters of the model); and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility.
