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Estimating the natural rate of unemployment in euro-area countries with co-integrated systems

2011; Taylor & Francis; Volume: 44; Issue: 10 Linguagem: Inglês

10.1080/00036846.2010.539548

1466-4283

Sven Schreiber,

Italy: Economic History and Contemporary Issues

Abstract Given that for France, Germany, Italy and the Netherlands the unemployment rates are best classified as I(1), we apply permanent-transitory decompositions based on co-integrated Vector Autoregressions (VAR) with relevant variables (labour productivity, wages, tax wedges, foreign relative prices) to estimate the time-varying natural unemployment rates. In general all variables seem to matter, and the results are quite different from published Organization for Economic Co-operation and Development (OECD) Nairus. Our implied unemployment gaps are better than the OECD gaps in predicting unemployment changes and inflation gaps, but they are (except for Italy) as bad as the OECD gaps for forecasting inflation changes. Acknowledgements Work on this project started during a visit of the author at the Deutsche Bundesbank, and the hospitality I enjoyed there is gratefully acknowledged. This article has benefitted from comments by anonymous referees and by seminar participants at the Bundesbank, at Humboldt University Berlin, at the ESEM and VfS meetings and at DIW Berlin; I wish to thank especially Dieter Nautz, Ragnar Nymoen, Christian Schumacher and Harald Uhlig for useful suggestions. Notes 1 Sometimes even a double random walk specification is used (i.e. random walk with stochastic drift, where the drift itself is again a random walk), see for example Laubach (Citation2001). However, such an I(2) specification would imply that unemployment changes themselves are nonstationary and therefore would seem quite extreme. 2 It must be acknowledged, however, that there is also a recent literature using more complex multivariate unobserved-components models to estimate potential output and/or the Nairu where a priori smoothness restrictions are not always needed; see for example Apel and Jansson (Citation1999), using Sweden for illustration, Proietti et al. (Citation2007), dealing with aggregate euro-area data, and Basistha and Startz (Citation2008), for the US. But with these complex models technical problems like nonconvergence of the algorithms are common. Our approach does not require iterative numerical algorithms because closed-form algebraic formulas are available. 3 See Appendix A for additional unit root test results. 4 The empirical results in this article have been produced with gretl 1.8.x (Cottrell and Lucchetti (Citation2009), for tests and estimates of co-integration restrictions and tests on α), gretl scripts and functions written by the authors (for the common-trends tests, tests and α⊥ and the decompositions) and with JMulTi (for some rank and stability tests as well as unit root tests with breaks, see Krätzig (Citation2004)). Some of the custom gretl codes are publicly available as packages from the official gretl function package server; the remaining ones are available from the author. 5 However, the shift will be restricted to the stationary directions by forcing its coefficient to be of the form α iτi , where only the part τi is unrestricted. Put differently, a broken trend in y i, t will be ruled out a priori. Another way of formulating that restriction is to replace y i,t −1 and β i by and in the VECM. 6 The nominal (hourly) wage inflation displays roughly the analogous behaviour, albeit with more short-term volatility. The inflation of imported raw materials (in local currency) is virtually identical for all four countries, since the price volatility dwarfs any exchange rate discrepancies. Also, it is clearly stationary. The inflation series of noncommodity imports is much more volatile than the domestic inflation series and contains a less pronounced downward tendency over the longer run (All those series and results are not shown to save space). 7 Or more precisely but also more involved: the wedge between total labour costs deflated by some producer price index and the after-tax wage income deflated by the consumer price index. 8 This reasoning does not negate the fact that inefficiencies of the public insurance schemes represent an excess burden. Pension contributions, for example, surely imply a tax component since an individual could get higher (risk-adjusted) rates of return on the world capital market. However, the resulting loss in each period is an order of magnitude smaller than the total contribution value. 9 The lag truncation determines the lag window that is used to calculate the estimated long-run variance of the time series in the nonparametric correction of the test statistic for auto-correlated series. It is a well-known problem that the choice of that bandwidth parameter often affects the results substantially in real-world samples. Typically, too small a lag truncation value implies an oversized test, whereas a value that is too large reduces power considerably. Unfortunately, in contrast to the uni-variate case, in a multivariate setting the literature does not provide a data-based procedure to choose an optimal bandwidth. 10 Only the p-value of the exclusion test of the German external price wedge fxDE,t is too high compared to conventional significance levels. 11 See, for example, Claar (Citation2006) for an assessment of equilibrium unemployment measures based on inflation forecasts.