Price level convergence across cities? Evidence from panel unit root tests

Abstract

This article empirically tests for convergence in Consumer Price Indices (CPIs) across 17 major cities in the United States over the period 1918 to 2008. Although the conventional panel unit root tests generally fail to reject the null hypothesis of nonstationarity, the panel LM tests of Im et al. (2005), by taking the presence of structural breaks into account, find overwhelming evidence in support of the hypothesis of price convergence The main finding is confirmed even when we consider both the structural changes and the cross-sectional dependence by using the recent advanced panel unit root approach of Bai and Carrion-i-Silvestre (2009).

Acknowledgements

The authors are grateful to Junsoo Lee, Jushan Bai and Josep L. Carrion-i-Silverstre for making available the GAUSS codes used in this article. Any remaining errors are our own responsibility.

Notes

¹Perron (1989) shows that the presence of structural changes is likely to cause nonrejection of the unit root null hypothesis if they are not appropriately taken into account.

²According to Bai and Carrion-i-Silvestre (2009), and are the mean and variance of the individual MSB _i (λ _i ) statistic, respectively.

³Originally, there are 19 cities, including Washington, DC and Baltimore, in Cecchetti et al. (2002). However, the Bureau of Labor Statistics no longer provides separate data for these two cities since 1996. Thus, these two cities are excluded from our analysis.

⁴Specifically, Im et al. (2005) test with heterogenous breaks allows alternative cities to have different number of breaks by deciding the optimal number of breaks for each city using a general-to-specific search procedure. Basically, the searching procedure is performed as follows. Starting with two-break minimum unit root test, we examine the significance of the t-statistic of each estimated break coefficient at 10% significance level in an asymptotic normal distribution (with critical value as 1.645). If less than two breaks is significant, we repeat the procedure using the one-break minimum LM unit root test. If no break is significant, then the no-break LM unit root test statistic is reported.