Revisiting the effects of long-term unemployment on inflation: the role of non-linearities

We demonstrate that it is necessary to control for state dependence in the Phillips curve in order to be able to appropriately identify separate slopes for short and long-term unemployment rates. Whereas several existing studies have typically concluded that long-term unemployment is largely immaterial for price pressures, our evidence suggests that the effect of long-term unemployment on inflation is highly state dependent. In particular, reductions in long-term unemployment are found to be significantly inflationary when aggregate unemployment is low, displaying a larger and more immediate peak effect on inflation than short-term unemployment. The explanation for our finding is a direct consequence of allowing for non-linearity in the Phillips curve together with short and long-term unemployment gaps that enter the specification separately. Variation in long-term unemployment typically arises following large recessionary shocks and the Phillips curve also tends to be flatter in deep recessions. It therefore follows that the comovement between long-term unemployment and inflation will be understated in linear regressions. In order to address this, we adopt a flexible methodology that combines non-linearity and heterogeneity in the unemployment duration distribution, enabling us to control for this confounding effect of state dependence on the identification of separate Phillips-curve slopes for short and long-term unemployment. Our results would caution against underweighting long-term unemployment in the inflation-relevant measure of economic slack, especially when unemployment is low.