This paper focuses on the analysis of persistence in the unemployment and inflation rates in a group of 38 OECD countries as well as on the relationship between the two variables. For this purpose, fractional integration is used. The results indicate that the two individual variables are highly persistent, especially the unemployment rate, and evidence of mean reversion is only found in the cases of Colombia and Costa Rica for unemployment and in Norway for inflation. Conducting the analysis on the difference between the two variables, the order of integration is significantly smaller in a number of cases, and reversion to the mean takes place in the cases of Austria, Switzerland, Costa Rica, Israel, and Turkey. Policy recommendations derived from the results are presented in the concluding section of the article.