Permanent and transitory shocks in the presence of asymmetric error correction

Abstract

This article highlights the potential importance of asymmetries in the loading vector of a set of cointegrated variables for the construction, analysis and interpretation of permanent and transitory shocks using impulse response functions. We derive an asymmetric version of the Permanent–Transitory decomposition suggested by Gonzalo and Ng (2001) and illustrate the potential importance of such asymmetries using the ‘cay’ data of Lettau and Ludvigson (2004).

Keywords:

• impulse responses
• asymmetry
• cointegration
• permanent and transitory shocks

JEL Classification:

• C22
• C32
• C52

Acknowledgement

The authors would like to thank the editor and two anonymous referees for helpful comments.

Notes

¹ Proofs for Proposition 1 and Proposition 2 are in Appendix.

² The data spans from 1951:4 to 2003:1 and is available from Martin Lettau’s web page at http://faculty.haas.berkeley.edu/lettau/data_cay.html.

³ The cointegrating vector was (1,-0.2615,-0.6239) for (c,a,y).

⁴ Tests of zero restrictions on the elements of the loading vector are in footnotes below Table 1.

⁵ Because of the construction of the $G$ matrix the asymmetric negative case is essentially the same as the symmetric one and is therefore omitted for brevity.

⁶ The results differ slightly as we retained the cay ordering.

Additional information

Funding

The first author would like to acknowledge financial support from the Australian Research Council.