The Taylor principle and (in-)determinacy in a New Keynesian model with hiring frictions and skill loss

We introduce skill decay during unemployment into Blanchard and Gali's (2008) New-Keynesian model with hiring frictions and real-wage rigidity. Plausible values of quarterly skill decay and real-wage rigidity turn the long-run marginal cost-unemployment relationship positive in a "European" labour market with little hiring but not in a fluid "American" one. If the marginal cost-unemployment relationship is positive, determinacy requires a passive response to inflation in the central bank's interest feedback rule if the rule features only inflation. Targeting steady state output or unemployment helps to restore determinacy. Under indeterminacy, an adverse sunspot shock increases unemployment extremely persistently.