Internal rationalityuyuyuy, heterogeneity and complexity in the New Keynesian model

This paper studies the dynamic behaviour of a workhorse New Keynesian model in which households and firms can be fully rational or internally rational. First, we derive the model with a fixed proportion n of agents fully rational and a fixed proportion (1-n) of agents internally rational, in a similar manner to Massaro (2013). In this model, we establish two propositions. First, a decrease in the proportion of fully rational agents does not destabilise the system if the rational expectations determinacy condition for the monetary rule holds. Second, the rational expectations determinacy condition is identical to the stability condition for the model in which all agents are internally rational. We then extend the model to include predictor selection along the lines of Branch and McGough (2010). In this model, we establish two further propositions. First, the rational expectations determinacy condition ensures local determinacy and stability as the cost of being fully rational becomes infinitely negative. Second, if the model starts from a position of indeterminacy, an increase in the fixed cost of being fully rational can lead to the loss of local stability via a Hopf bifurcation. A rational route to randomness follows from this, which we explore numerically. Taken as a whole, these results indicate that complex dynamics in the internally rational New Keynesian model are closely associated with monetary policy failures. Finally, we consider the robustness of our results to changes in the monetary policy rule.