Testing the Granger Noncausality Hypothesis in Stationary Nonlinear Models of Unknown Functional Form

Abstract

In this article, we propose a general method for testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form. These tests are based on a Taylor expansion of the nonlinear model around a given point in the sample space. We study the performance of our tests by a Monte Carlo experiment and compare these to the most widely used linear test. Our tests appear to be well-sized and have reasonably good power properties.

Keywords:

• Granger causality
• Hypothesis testing
• Nonlinearity

Mathematics Subject Classification:

• C22
• C51

Acknowledgments

This research has been supported by Jan Wallander’s and Tom Hedelius’s Foundation, Grant No. J02-35, and the Danish National Research Foundation. A large part of the work for this article was done when the second and the third author were with the Department of Economic Statistics, Stockholm School of Economics. We wish to thank participants of the FPPE workshop (Helsinki, 2003) and seminar participants at the Econometric Institute, Erasmus University Rotterdam for discussion and comments. We also wish to thank Heather Anderson and an anonymous referee for useful comments but retain the responsibility for any errors and shortcomings in this work. The views expressed in this work are those of the authors’ and do not necessarily represent the official views of Bank of Estonia.

Notes

We are only going to consider the bivariate case. Extensions to higher-dimensional systems are straightforward.

We let the data-generating process run for a while to eliminate the possible initial effects, that is, we discard the first 500 observations and use only the following 150.

For a more comprehensive set of results and discussion, see Péguin-Feissolle et al. (2008).

Measured in worked hours in manufacturing and mining.

Industrial production divided by hours worked.