Is the Phillips Curve of Germany Spurious?

A simple plot of seasonal adjusted quarterly data between the change of nominal wage rates and the unemployment rate for the German economy shows a picture similar to that by which Phillips was inspired to his famous discovery, that there is a long-term tendency of a negative, non-linear relationship coupled with minor deviations from this tendency, which form so-called loops. At first sight, the Phillips Curve of Germany comprises clusters of data points and movements between these clusters. In spite of the striking differences of these phenomena, a model with one regression equation is sufficient to explain the loops, the movements between the loops and the long-term tendency of the German Phillips Curve. It might well be that the German Phillips Curve and the corresponding regressions are spurious, but an allegedly missing co-integration of wage rate changes and unemployment rate is not the argument that could be drawn on to sustain this scepticism. On the contrary, both variables are co-integrated. To get a more detailed insight into the relationship, the two variables are split into a trend and a cyclical component by the help of the HP-filter. The results of regression analyses applied to the separated components support Phillips’ hypothesis of a negative relationship between wage rate changes and the unemployment rate.Wages, Unemployment, Phillips Curve

Clusters and Loops of the German Phillips Curve

A preliminary regression analysis of different versions of the Phillips Curve on the basis of yearly data of the German economy from 1952 to 2004 leads to the conclusion that the original finding might still be of empirical relevance. A simple plot of seasonal adjusted quarterly data between the change of nominal wage rates and the unemployment rate shows a picture similar to that by which Phillips was inspired to his famous discovery: A long-term tendency of a negative, non-linear relationship coupled with minor deviations from this tendency forming sometimes so called loops. At fist sight, the Phillips Curve of Germany comprises clusters of data points and movements between these clusters. The clusters can be analysed and – together with the rest of data – dissolved into 12 (left or right turning) loops and 9 movements between these loops during the period from 1971Q1 to 2009Q4. In spite of the striking differences of these phenomena, a model with one regression equation is sufficient to explain the loops, the movements between the loops and the long-term tendency of the German Phillips Curve. This empirical finding contradicts several aspects with the ruling dogma of a Phillips Curve that broke down in the ‘70s and with the allegedly better fit of its replacements by augmented and modified Phillips Curves.Wages, inflation, unemployment, Phillips curve

Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type, II

The class of finitely presented algebras A over a field K with a set of generators x_{1},...,x_{n} and defined by homogeneous relations of the form x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{sigma(i_l)}, where l geq 2 is a given integer and sigma runs through a subgroup H of Sym_n, is considered. It is shown that the underlying monoid S_{n,l}(H)= <x_1,x_2,...,x_n|x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{\sigma (i_l)}, sigma in H, i_1,...,i_l in {1,...,n}> is cancellative if and only if H is semiregular and abelian. In this case S_{n,l}(H) is a submonoid of its universal group G. If, furthermore, H is transitive then the periodic elements T(G) of G form a finite abelian subgroup, G is periodic-by-cyclic and it is a central localization of S_{n,l}(H), and the Jacobson radical of the algebra A is determined by the Jacobson radical of the group algebra K[T(G)]. Finally, it is shown that if H is an arbitrary group that is transitive then K[S_{n,l}(H)] is a Noetherian PI-algebra of Gelfand-Kirillov dimension one; if furthermore H is abelian then often K[G] is a principal ideal ring. In case H is not transitive then K[S_{n,l}(H)] is of exponential growth.Comment: 8 page

The Contribution of Alternative NAIRU-curves to the Explanation of Inflation

The Non-Accelerating Inflation Rate of Unemployment (NAIRU) is a major concept in (monetary) economics in predicting changes in the inflation rate. As the inflation neutral unemployment rate is an unobserved and, in the long run, a changing variable, several questions arise about its adequate estimation. The following study determines four different possible NAIRU-curves for the German economy during the period of 1973Q1-2010Q2 by the use of a State-Space-Model. With the help of the Ordinary-Least-Square (OLS) and the Maximum-Likelihood (ML) method, these curves are implemented and utilized in regression models which are trimmed to satisfactorily explain inflation changes. It turns out that besides the NAIRU, several other variables like the changes in the unemployment rate or the labor productivity are necessary to forecast changes in the inflation rate accurately. Among the four regression models, the one applying the NAIRU with the lowest variance and with a high theoretic plausibility has the worst record, while the equation with a NAIRU fluctuating more than the unemployment rate explains the inflation rate best.Non-Accelerating Inflation Rate of Unemployment; NAIRU

Estimating Thermal Material Properties Using Step-Heating Thermography Methods in a Solar Loading Thermography Setup

This work investigates solar loading thermography applications using active thermography algorithms. It is shown that active thermography methods, such as step-heating thermography, present good correlation with a solar loading setup. Solar loading thermography is an approach that has recently gained scientific attention and is advantageous because it is particularly easy to set up and can measure large-scale objects, as the sun is the primary heat source. This work also introduces the concept of using a pyranometer as a reference for the evaluation algorithms by providing a direct solar irradiance measurement. Furthermore, a recently introduced method of estimating thermal effusivity is evaluated on ambient-derived thermograms

Estimating Thermal Material Properties Using Solar Loading Lock-in Thermography

This work investigates the application of lock-in thermography approach for solar loading thermography applications. In conventional lock-in thermography, a specimen is subjected to a periodically changing heat flux. This heat flux usually enters the specimen in one of three ways: by a point source, a line source or an extended source (area source). Calculations based on area sources are particularly well suited to adapt to solar loading thermography, because most natural heat sources and heat sinks can be approximated to be homogenously extended over a certain region of interest. This is of particular interest because natural heat phenomena cover a large area, which makes this method suitable for measuring large-scale samples. This work investigates how the extended source approximation formulas for determining thermally thick and thermally thin material properties can be used in a naturally excited setup, shows possible error sources, and gives quantitative results for estimating thermal effusivity of a retaining wall structure. It shows that this method can be used on large-scale structures that are subject to natural outside heating phenomena