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Prepared by Rodolphe Blavy and Luciana Juvenal. We would like to thank the staff of the Banco de Mexico for their helpful comments, Steven Phillips for his contributions at various stages of this paper, and Roberto Benelli, Roberto Garcia-Saltos, David Robinson, Lucio Sarno, and seminar participants at the IMF and at the LACEA conference. We also thank Modupeh Williams for excellent editorial assistance.
There is now an established literature on nonlinear behavior of sectoral real exchange rates for developed markets (see Obstfeld and Taylor, 1997; Sarno, Taylor and Chowdhury, 2004; Imbs and others, 2003; and Juvenal and Taylor, 2007),
An important contribution of our paper is methodological: to use recently developed testing techniques to confirm whether the autoregressive process outside the threshold band is different from the random walk observed inside the band.
Heckscher (1916) first pointed out at the possibility of nonlinearities in relative prices in the presence of trade frictions. In the case of Mexico, Gonzalez and Rivadeneyra (2004) investigate the LOOP between Mexican cities and provide empirical evidence that transactions costs (including tariff and non-tariff barriers) explain departures from the LOOP.
As noted in Hansen (1997), the conventional tests have asymptotic nonstandard distributions, approximated using a bootstrap procedure.
A forthcoming working paper discusses the econometric methodology in greater detail.
The data sources for the CPI indices are the Bank of Mexico, the U.S. Bureau of Labor Statistics and Statistics Canada. Monthly nominal exchange rates are period averages taken from the International Financial Statistics (IFS) of the International Monetary Fund (IMF).
To gauge the sensitivity of empirical results to underlying assumptions and variable definitions, we conduct three robustness checks. First, we consider the possibility of long-run trends in the measured price differentials arising from aggregation issues in price indices or from the presence of nontradable components (Harrod-Balassa-Samuelson effect). We also test the sensitivity of the results to (i) allowing for a different mean over the 1994–12 to 1995–12 period (corresponding to the Tequila Crisis), and (ii) restricting the estimation period to 1996–2006. Overall, our baseline findings are robust to these checks.
One possible alternative explanation for finding that thresholds are lower between the U.S. and Canada than between Mexico and the U.S. may be that goods are more homogenous between the first two countries. More generally, the comparability of the sectors may vary across country pairs. First, wealth effects may be at play. The relatively large income differences between Mexico and the U.S. and Canada affects the specific goods sampled in each CPI category. This may complicate the analysis, with the composition between luxury, middle, and ordinary products varying across countries. Second, statistical differences exist in the compilation of price level data, notably in adjustments for quality changes. A solution to this problem is to look at more disaggregated price indices and SRERs. Preliminary work on this is reported in Box 1.
Previous studies computed the half-life of the SETAR model in the outer regime, which depends on the parameter ρ, as in a linear model (ln (0.5)/ln(ρ)). This has the limitation that it does not consider the regime switching that takes place within and outside the band and provides misleading results. We compute the half-life taking into account the regime-switching nature of the SETAR model. This is important in the context of our model because the half-life takes different values depending on whether the SRER is within or outside the threshold band. The half-life is infinite with the threshold band and depend on ρ (more exactly, equal to ln(0.5)/ln(ρ)) outside the band. We compute the half-lives for a 10 percent, 20 percent, 30 percent, 40 percent and 50 percent shocks by stochastic simulation using the generalized impulse response functions procedure developed by Koop and others (1996).
Note that the three NAFTA countries studied here are all relatively large in terms of land area, so that for example the distance between two cities within a given country could well exceed the distance between two cities in different countries. This situation contrasts with the literature on price convergence within Europe.