Are State and Time dependent models really different?

Yes, but only for large monetary shocks. In particular, we show that in a broad class of models where shocks have continuous paths, the propagation of a monetary impulse is independent of the nature of the sticky price friction when shocks are small. The propagation of large shocks instead depends on the nature of the friction: the impulse response of inflation to monetary shocks is independent of the shock size in time-dependent models, while it is non-linear in state-dependent models. We use data on exchange rate devaluations and inflation for a panel of countries over 1974-2014 to test for the presence of state dependent decision rules. We present some evidence of a non-linear effect of exchange rate changes on prices in a sample of flexible-exchange rate countries with low inflation. We discuss the dimensions in which this finding is robust and the ones in which it is not.