Short run real exchange rate dynamics: a SUR approach

Abstract

This paper examines the convergence question by contrasting the half-lives of deviations across the producer price index (PPI) and consumer price index (CPI) in a bivariate error correction model. To improve efficiency, the models are estimated jointly using a seemingly unrelated regressions approach.

Acknowledgments

I thank Masao Ogaki, Donggyu Sul, and Mario J. Crucini for helpful comments and discussions. All remaining errors are the author's.

Notes

 See Wu (1996), Wei and Parsley (1996), and Canzoneri, Cumby and Diba (1996).

 In our empirical study, policy effects, transportation and other transaction costs, and other variables are considered stationary. See Mundlak and Larson (1992) for details.

 By setting l = 1 in Equation 2 and k = 1 in Equation 3 we avoid contemporaneous problems which would arise by including the respective current variables

and Δps _it . See Thompson et al. (2000) for details.

 Consider Equation 2 where the regressors differ over cross-sectional units (i = 1, … , 6). As we have higher cross-sectional correlation among ξ _{1, it} for i (i = 1, … , 6), a more efficient estimator of λ _0i can be obtained.

 It will be inefficient if all 12 equations are estimated by SUR for two reasons. First, the ECM system for i = 1, Equations 2 and 3, have exactly the same explanatory variables so that there is no efficiency gain over the two first equations. This argument can be applied to the ECM systems for i = 2, … , 6. Second, ξ _{1, it} may be correlated with ξ _2,jt where i ≠ j. However, if the correlation between ξ _1,it and ξ _2,jt is much lower than that between ξ _1,it and ξ _{1, jt} , or that between ξ _{2, it} and ξ _{2, jt} where i ≠ j, the inclusion of the second system into the first system provides less efficient estimators. See Thompson et al. (2000) for details.

 For EMU countries such as France, Italy, and Germany we use data from 1974:1 to 1998:2.

 Since many studies point out the problem of choosing the US dollar as the numeraire, other currencies are also considered as the numeraire currency. See Papell and Theodoridis (2001).

 The null hypothesis is H₀: λ ₀₁  = λ ₀₂  = ··· = λ ₀₆ and the test statistics has χ ² distribution with five degrees of freedom.

 The half-life is calculated as 0.25ln(0.5)/ln(1–

) because our data series are quarterly.

 See Murray and Papell (2003) for more recent work.