Efficient Estimation of the Seemingly Unrelated Regression Cointegration Model and Testing for Purchasing Power Parity

Abstract

This paper studies the efficient estimation of seemingly unrelated linear models with integrated regressors and stationary errors. We consider two cases. The first one has no common regressor among the equations. In this case, we show that by adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. In the second case we consider, there is a common regressor to all equations, and we discuss efficient minimum distance estimation in this context. Simulation results suggests that our new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of the proportionality and symmetry conditions implied by purchasing power parity (PPP) among the G-7 countries. The tests based on the efficient estimates easily reject the joint hypotheses of proportionality and symmetry for all countries with either the United States or Germany as numeraire. Based on individual tests, our results suggest that Canada and Germany are the most likely countries for which the proportionality condition holds, and that Italy and Japan for the symmetry condition relative to the United States.

Key Words:

• Seemingly unrelated regressions
• Efficient estimation
• Purchasing power parity
• Minimum distance

JEL Classification:

• C32
• F31

Acknowledgments

We thank Menzie Chinn, Elena Pesavento, Lynda Khalaf, and two anonymous referees for their valuable comments on an earlier version of the paper which was circulated under the title, The Seemingly Unrelated Dynamic Cointegration Regression Model and Testing for Purchasing Power Parity. We also thank participants at the 2001 Canadian Economic Association meeting in Montreal and the 2000 Meeting of the Société candienne de science économique (SCSE) for their comments. The financial assistance from the USC Faculty Development Fund is gratefully acknowledged, by the first author and the financial assistance from the Fonds FCAR and the Mathematics of Information Technology and Complex Systems (MITACS) network is gratefully acknowledged by the second author.