2D Chaos in the Interaction of Inflation and Unemployment: Moving Averages and the Modeling of High Frequency Macrodynamics

The paper argues that applicable macro is high frequency macro and the data generating process is therefore to be modeled in continuous time. It exemplifies this with a misuse of a 2D period model of monetarist type which becomes extremely overshooting, allowing for routes to “chaos,” when iterated at low frequencies. Instead of such low frequency procedures, we augment the model by a Keynesian feedback chain (the real rate of interest channel) to introduce local instability into the model. We also introduce heterogeneous opinion dynamics into it. The implied 4D dynamics are made bounded thereby, but seem to allow only complex limit cycles, with no transition towards strange attractors anymore. 1. Introduction The next several sections examine the behavior of a variety of models that differ mainly in how they model real and nominal stickiness. … They are formulated in continuous time to avoid the need to use the uninterpretable “one period” delays that plague the discrete time models in this literature [1, p.318]. This quotation can be considered as introducing the objective of this paper in a very pronounced way. We intend to demonstrate in addition to this interpretational riddle that macrodynamic period models are devoid of empirical content if their qualitative features differ from the ones of their continuous time analog. We will use Soliman’s [2] period model in order to demonstrate this from a different angle compared to how it was done in Flaschel and Proa？o [3], but could have used equally well more recent approaches by Brianzoni et al. [4] or Roa et al. [5], and indeed many other papers as well. We have chosen the Soliman paper here, since it makes use of a monetarist baseline model—with an estimated wage Phillips curve—a model type which is known to provide strong point attractors, and so we want to compare it with a Keynesian extension of it. A basic empirical fact in the macrodynamic literature is, see Flaschel and Proa？o [3], that the actual data generating process in macroeconomics (which is generally based on the use of annualized data) is by and large a daily one (and that the data collection frequency is now also much less than a year in the real markets of the economy). This suggests that empirically oriented or estimated macromodels should be iterated with a very short period length as far as actual processes are concerned and will then in general provide the same qualitative answer as their continuous-time analogues. Concerning expectation formation, the data collection process is however of importance and may give rise to certain