In this paper we follow an empirical approach to examine the implications of the Fisher hypothesis, namely cointegration linking interest rates and inflation, and stationarity of the real interest rate implying in turn homogeneity of the potential equilibrium relation. The considered sample is an unbalanced panel and comprises monthly time series data from more than 100 economies covering at most a period of about 45 years. In total more than 31000 observations enter our empirical analysis. From cross sectional error correction and dynamic OLS regressions we find that the presumed dynamic relation is hardly homogeneous over the cross section. Therefore, building on cross sectional parameter homogeneity nonstationary panel data models are provided merely as a complement to cross section specific analyses. Apart from standard between regressions we exploit the cross section dimension to infer on parameter homogeneity over particular economic states. For this purpose we rely on semiparametric implementations of so-called functional coefficient models. The latter are suitable to relate key model parameters on economic states, as e.g. periods of higher vs. lower inflation or inflation risk. From the latter approach we find that time or state invariance of key model parameters is not supported empirically. Moreover the evidence in favor of cointegration is weak over periods of high inflation. The Fisher coefficient turns out to be remarkably stable and is, over most considered states, significantly less than unity.