Research - Unit Root Tests

Median-Unbiased Estimation in DF-GLS Regressions and the PPP Puzzle

with Murray C.J., and D.H. Papell, Applied Economics, 45(4), 455-464, 2013.      Using median-unbiased estimation based on Augmented-Dickey-Fuller (ADF) regressions, recent research has questioned the validity of Rogoff’s “remarkable consensus” of 3-5 year half-lives of deviations from PPP. The confidence intervals of these half-life estimates, however, are extremely wide, with lower bounds of about one year and upper bounds of infinity. We extend median-unbiased estimation to the DF-GLS regression of Elliott, Rothenberg, and Stock (1996). We find that combining median-unbiased estimation with this regression has the potential to tighten confidence intervals for the half-lives. Using long horizon real exchange rate data, we find that the typical lower bound of the confidence intervals for median-unbiased half-lives is just under 3 years. Thus, while previous confidence intervals for median-unbiased half-lives are consistent with virtually anything, our tighter confidence intervals are inconsistent with economic models with nominal rigidities as candidates for explaining the observed behavior of real exchange rates and move us away from solving the PPP puzzle.

Convergence of Euro Area Inflation Rates

with D.H. Papell, Journal of International Money and Finance, 31(6), 1440-1458, 2012     We study the behavior of inflation rates among the 12 initial Euro countries in order to test whether and when the group convergence initially dictated by the Maastricht treaty and now by the ECB, occurs. We also assess the impact of events such as the advent of the Euro and the 2008 financial crisis. Due to the small size of the estimation sample, we propose a new procedure that increases the power of panel unit root tests when used to study group-wise convergence. Applying this new procedure to Euro area inflation, we find strong and lasting evidence of convergence among the inflation rates soon after the implementation of the Maastricht treaty and a dramatic decrease in the persistence of the differential after the occurrence of the single currency. After the 2008 crisis, Euro area inflation rates follow the ECB’s price stability benchmark, although Greece reports relatively higher inflation.

Panel Unit Root with Good Power in Small Samples

Econometric Reviews, 28(4), 295-313, 2009     We propose a new pooled panel unit root test allowing for serial and contemporaneous correlation. The new test combines Elliott, Rothenberg and Stock’s (1996) local-to-unity transformation with a pooled panel ADF test. As initially advocated by O’Connell (1998), the new test accounts for contemporaneous correlation by estimating the residual covariance matrix. Monte Carlo simulations demonstrate significantly better finite sample power properties of the new test over a wide range of existing panel unit root tests accounting for cross-sectional correlation. Furthermore, enhanced performances are particularly noticeable when the series are highly persistent and the panels are relatively small. An application to the real exchange rate convergence illustrates the impact of such improvements. Analyzing the post Bretton Woods period, the new test provides strong and reliable rejections of the unit root among the real exchange rates of industrialized countries.

State of the Art Unit Root Tests and Purchasing Power Parity

With C.J. Murray and D.H. Papell, Journal of Money Credit and Banking, 37,361-369, 2005     Although the question of whether Purchasing Power Parity (PPP) holds in the long run has been extensively studied, the answer is still controversial. Some of the strongest evidence is provided by Taylor (2002), who concludes that long-run PPP held over the twentieth century. We argue that this conclusion is quite sensitive to the use of suboptimal lag selection in unit root tests. Using superior lag selection methods, we find that long run PPP held for the real exchange rates of only 9 out of the 16 industrialized countries in Taylor’s sample with the U.S. dollar as the base currency.