On expectations, heterogeneity and the Phillips curve Three essays in New Keynesian economics

The Great Recession and the following monetary policy easing have given rise to a 'new normal' in the U.S and Europe where the interest rate have been 'low for long'. Yet, no substantial changes in inflation have been observed, neither during the downturn nor during the following unexpectedly slow recovery.
Inflation remaining consistently below target and the Great Recession depth have challenged conventional macroeconomic modelling in the form of the New Keynesian model and its main feature: the New Keynesian Phillips curve. In this context, nominal rates are stuck at the effective lower bound so real interest rates are entirely determined by inflation expectations. As a result, expectations have become increasingly more important for central banks as well as for economists.
The goal of this dissertation is to discuss various deviations from the standard hypothesises used in the classic New Keynesian model in order to address the recent macroeconomic events and some known shortcomings of the canonical model. This thesis focuses on three assumptions, the rational expectation hypothesis, the representative agent hypothesis and the New Keynesian Phillips curve.