We consider how unit root and stationarity tests can be used to study the convergence properties of prices and rates of inflation. Special attention is paid to the issue of whether a mean should be extracted in carrying out unit root and stationarity tests and whether there is an advantage to adopting a new (Dickey-Fuller) unit root test based on deviations from the last observation. The asymptotic distribution of the new test statistic is given and Monte Carlo simulation experiments show that the test yields considerable power gains for highly persistent autoregressive processes with relatively large initial conditions, the case of primary interest for analysing convergence. We argue that the joint use of unit root and stationarity tests in levels and first differences allows the researcher to distinguish between series that are converging and series that have already converged, and we set out a strategy to establish whether convergence occurs in relative prices or just in rates of inflation. The tests are applied to the monthly series of the Consumer Price Index in the Italian regional capitals over the period 1970-2003. It is found that all pairwise contrasts of inflation rates have converged or are in the process of converging. Only 24% of price level contrasts appear to be converging, but a multivariate test provides strong evidence of overall convergence.

Convergences of Prices and Rates of Inflation

We consider how unit‐root and stationarity tests can be used to study the convergence of prices and rates of inflation. We show how the joint use of these tests in levels and first differences allows the researcher to distinguish between series that are converging and series that have already converged, and we set out a strategy to establish whether convergence occurs in relative prices or just in rates of inflation. Special attention is paid to the issue of whether a mean should be extracted in carrying out tests in first differences and whether there is an advantage to adopting a (Dickey–Fuller) unit‐root test based on deviations from the last observation. The asymptotic distribution of this last test statistic is given and Monte Carlo simulation experiments show that the test yields considerable power gains for highly persistent autoregressive processes with ‘relatively large’ initial conditions. The tests are applied to the monthly series of the consumer price index in the Italian regional capitals over the period 1970–2003.

Convergence of Prices and Rates of Inflation

We study the evolution of price level dispersion in Europe by combining time-series information on harmonized indices of consumer prices (HICPs) with occasional observations of absolute price levels. We find that European price levels converged over much of the last 40 to 50 years. In the United States, our benchmark, price level dispersion is more or less stable. A back-of-the-envelope calculation suggests that indirect tax rate harmonization, convergence of nontraded input costs, and convergence of traded input costs (in the form of exchange rate stability and increased openness) are all important in explaining European price level convergence.

https://www.jstor.org/stable/info/25483499

A Short History of Price Level Convergence in Europe

Evidence is provided on the PPP hypothesis using a sample of 50 Spanish cities for a long time period through the application of panel data unit root tests. Although results suggest non-rejection of the PPP, short-run deviations – as measured by half-lives – indicate that real factors might be causing a slow rate of convergence to a common price index, even in highly integrated economies.

http://www-sre.wu-wien.ac.at/ersa/ersaconfs/ersa03/cdrom/papers/273.pdf

Evidence on the purchasing power parity in a panel of cities

https://www.shsu.edu/~eco_hkn/JMACRO2337.pdf

J. Devereux

Papers

What can US city price data tell us about purchasing power parity