How do Beveridge and Phillips curves in the euro area behave under the stress of the world economic crisis?

In this paper, the authors present a new concept of the 'modified output gap' based on the New Keynesian Phillips curve and on the Beveridge curve. In the first part of the paper, both mentioned curves are derived analytically. In doing so, we identify key parameters for the shift of the Beveridge curve (up- or downwards) and prove that - fulfilling a minimum of assumptions - the New Keynesian Phillips curve is (also) a falling convex relationship between the inflation rate and the unemployment rate in the tradition of Phillips (1958). Inserting the Phillips curve into the Beveridge curve reveals the explicit positive relationship between the vacancy ratio and the inflation rate. In the second part of the paper, we put all three relationships under an empirical 'stress test' using panel data from eleven of the EA 12 countries for three different samples during the world economic crisis: In all cases, the parameter estimates confirm the presumed existence of the three functions.