Relative price convergence among US cities: Does the choice of numeraire city matter?

Using annual consumer price index (CPI) data for 17 US cities between 1918 and 2007, this paper examines the implications of the choice of numeraire city for the behavior of relative prices across cities. A common factor representation of relative price is used to understand the nature of the dynamic behavior of relative prices. This paper finds overwhelming evidence of convergence in relative prices with Atlanta, Chicago, and Los Angeles as the numeraire city. Further, with Boston, Cincinnati, Houston, San Francisco, Seattle, and St. Louis, the lack of convergence in relative prices is found to be driven by the nonstationarity of the common factor. In contrast, with New York, Philadelphia, and Portland, while the common factor is stationary, the idiosyncratic components are unit root processes. This paper further investigates the implications of the choice of numeraire city by estimating the half-life with different numeraire cities, after correcting for the small-sample and the time aggregation bias. These half-life estimates are smaller than those reported in previous studies and they vary depending on the choice of numeraire city. The relative price volatility seems to hold some promise for explaining why the choice of numeraire city matters for the unit root results or the half-life estimates.