Long-term unemployment and convexity in the Phillips curve

The notion that the long-term unemployed are relatively detached from the labour market and therefore exert only little downward pressure on wage inflation has regained significant traction recently. This paper investigates whether the conclusion that long-term unemployment is only weakly related to inflation depends on the assumption of linearity in the Phillips curve. Specifically, once convexity is allowed for during the estimation process, long-term unemployment appears to have a significant negative influence on wage inflation, whereas in a linear Phillips curve model it is only the short-term unemployment rate that matters for wage dynamics. The intuition is simple; by the time the long-term unemployment rate rises during a recession, the economy may have already transitioned into a relatively flat region of the Phillips curve, generating the misperception that the marginal effect of long-term unemployment on wage inflation is smaller than that of short-term unemployment. Linear models which do not capture state dependence in the slope of the Phillips curve would therefore bias downwards the estimated importance of long-term unemployment in explaining wage dynamics if the true Phillips curve is convex.