We propose and estimate a model where unemployment fluctuations result from self-fulfilling changes in expected inflation (sunspot shocks) affecting nominal wage bargaining. Since the estimated parameters fall near the locus of Hopf bifurcations, country-specific expected inflation shocks can replicate the strong persistence and heterogeneity observed in European unemployment rates. They also generate positive comovements in macroeconomic variables and a large relative volatility of consumption. All these features, hardly accounted for by standard sunspot-driven models, are explained here by the fact that liquidity constrained workers, facing earnings uncertainty in the context of imperfect unemployment insurance, choose to consume their current income.