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Unbiased estimation of the half-life to price index convergence among U.S. cities.

Article Excerpt
AN ADVANTAGE OF examining real exchange rates (relative prices) between cities within a single country is that some of the plausible explanations for slow convergence or for the complete breakdown of international purchasing power parity (PPP), such as nominal exchange rate movements, trade barriers, and differences in CPI baskets, do not hold. Thus, by studying the behavior of intranational city prices we can hope to gain a better understanding of deviations from PPP. This is the primary motivation behind the relatively recent literature that examines the PPP hypothesis using aggregate price data for cities within the same country. (1) An examination of city level or regional price index convergence is also useful in its own right, as persistent deviations of relative prices across regions create the possibility of persistent regional differences in real interest rates and wage rates within a country resulting in misallocation of productive resources. (2)

Previous studies based on the U.S. city-level aggregate CPI data either provide little support for PPP (Culver and Papell 1999) or present evidence of slow convergence (Cecchetti et al. 2002). Both these studies use panel unit root tests. Use of the panel techniques to test for convergence and to estimate half-life is appealing because such methods combine cross-sections with time series to increase the number of observations, potentially increasing the power of the tests and the precision of half-life estimates.

However, Choi et al. (2006) recently emphasize that estimating half-life from panel data may introduce three potential sources of bias. First, if the dynamic behavior of price indices across cities exhibits sufficient heterogeneity (i.e., the autoregressive coefficients are significantly different across cities), then panel estimation of a common autoregressive coefficient will be biased upward and so will be the implied half-life. Second, in small samples, the estimation of a dynamic regression with a constant leads to a downward bias. Nickell (1981) discusses this small-sample bias in the panel context and, therefore, it is known as the "Nickell bias." Finally, the annual CPI data are averages of goods and services prices recorded monthly, rather than point-in-time sampled prices. This time-averaging (also referred to as time aggregation) process introduces a moving average structure into the regression error when city prices are modeled as autoregressive processes. Failure to account for this imparts an additional upward bias in the estimation of the autoregressive coefficient and the implied half-life. Because the magnitude of half-life is very sensitive to the value of...