The article explores how tests can be used to study the convergence of prices and inflation rates. By using these tests in different ways, researchers can tell if prices are getting closer or have already reached a balance. They also look at whether this convergence happens in relative prices or just in inflation rates. The study suggests that a specific test can be more powerful for certain types of data, like those with strong patterns over time. The tests were applied to consumer price data in Italian cities from 1970 to 2003.