Long-term unemployment, hysteresis and missing deflation: reconsidering the New-Keynesian approach by means of an 'old' Phillips curve

A recent explanation of hysteresis in unemployment, refers to long-term unemployed as a cause of downward wage rigidity, since they are detached from the labour market and therefore are no good inflation fighters. Therefore, the debate on the Phillips curve has regained significant traction to explain the missing inflation matter. Based on the above-mentioned interpretation of hysteresis some scholars tried to provide a new estimation of the NAIRU incorporating short-term unemployed uniquely or taking into account the relative weight of unemployment duration. This essay is situated within this line of inquiry as it investigates whether the conclusion that long-term unemployment is less relevant for the inflation path, than the short one, depends on the assumption of linearity in the Phillips curve. The thesis we want to test is whether the lower effect of long-term unemployment on wage dynamics comes from not considering the convexity of the Phillips curve. Indeed, the phenomenon of long-term unemployment spreads in correspondence to a very high total unemployment rate, when the Phillips curve is flat. By contrast, no appreciable differences between short and long-term unemployment in affecting nominal wage would appear when convexity is considered. Using panel data of 25 OECD countries for the 1970-2016 period, we test the difference between short and long-term unemployment rate coefficients in a linear version of the Phillips curve and verify that there is no statistical difference between them. Then, we impose a convex shape to the relationship and test the relevance of the very high incidence of long-term unemployment in nominal wage inflation. Our findings indicate that once convexity in the Phillips curve is proved, no relevant difference between long and short-term unemployed in wage-setting exists.