The paper estimates the NAIRU from a Phillips curve relationship in the state-space framework. To identify the inflation-unemployment trade-off we account for a time-varying inflation trend to control for the part of inflation that is not affected by the cyclical component of unemployment. In addition we use shifts in the relative volatility of shocks to unemployment and inflation to address the simultaneity problem in Phillips curve estimations. Applying the method of Rigobon and Sack (2003) allows for a data driven identification of the contemporaneous coefficients on the unemployment gap in the Phillips curve and yields more precise estimates of the structural coefficients in the Phillips curve. This tightens the economic relation on the basis of which the NAIRU is derived.Keywords: non-accelerating inflation rate of unemployment, state-space estimation, identification through heteroskedasticity, trend inflation JEL classification: E24, E31, E32
Non-technical summaryEstimations of the so-called NAIRU -the unemployment rate which is associated with a stable inflation rate -typically yield less satisfactory results for Germany. Partly, this is reflected in a statistically insignificant (or only weakly significant) relation between inflation and unemployment; partly, estimations only allow for very imprecise statements about the level of the NAIRU. This paper aims at improving estimations of the NAIRU with a view to both weaknesses.Our first contribution is to better measure the relevant inflation rate by incorporating a time-varying inflation trend into the Phillips curve. Allowing the first difference of the actual inflation rate to be influenced by the cyclical component of the unemployment rate neglects the fact that inflation might contain a trend component which is unaffected by cyclical variation in the unemployment rate, but rather influenced by inflation expectations and/or the inflation target of monetary policy. Therefore we model trend inflation as an additional unobserved variable and relate the cyclical component of unemployment to the cyclical component of inflation.Second, since observations of the unemployment and inflation rate are (short-run) equilibrium points the Phillips curve is often identified by explicitly or implicitly imposing the restriction that there is no contemporaneous effect (or none at all) from the inflation rate on unemployment. In contrast, we take potential contemporaneous effects into account in a state-space system. To identify the Phillips curve we follow Rigobon and Sack's (2003, 2004) method of identification through heteroskedasticity.We evaluate the effect of both modifications, first, by their impact on the size and significance of the coefficients on the unemployment gap in the Phillips curve. A larger absolute value of the sum of coefficients and smaller standard errors would point to an economically more meaningful relationship between the unemployment gap and the inflation gap. Second, the contributions of filter uncertainty and parameter uncertainty ...