Mind the output gap: the disconnect of growth and inflation during recessions and convex Phillips curves in the euro area

We develop a theoretical model that features a business cycle-dependent relation between out- put, price inflation and inflation expectations, augmenting the model by Svensson (1997) with a nonlinear Phillips curve that reflects the rationale underlying the capacity constraint theory (Macklem (1997)). The theoretical model motivates our empirical assessment for the euro area, based on a regime-switching Phillips curve and a regime-switching monetary structural VAR, employing different filter-based, semi-structural model-based and Bayesian factor model-implied output gaps. The analysis confirms the presence of a pronounced convex relationship between inflation and the output gap, meaning that the coefficient in the Phillips curve on the output gap recurringly increases during times of expansion and abates during recessions. The regime switching VAR reveals the business cycle dependence of macroeconomic responses to monetary policy shocks: Expansionary monetary policy induces less pressure on inflation at times of weak as opposed to strong growth; thereby rationalizing relatively stronger expansionary policy, including unconventional volume-based policy such as the Expanded Asset Purchase Programme (EAPP) of the ECB, during times of deep recession.