Improved Inference on Cointegrating Vectors in the Presence of a Near Unit Root Using Adjusted Quantiles

19 Pages Posted: 25 Apr 2017

See all articles by Massimo Franchi

Massimo Franchi

University of Copenhagen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Date Written: April 21, 2017

Abstract

It is well known that inference on the cointegrating relations in a vector autoregression (CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have rejection probabilities under the null, which vary from the nominal size to more than 90%. This paper formulates a CVAR model allowing for many near unit roots and analyses the asymptotic properties of the Gaussian maximum likelihood estimator. Then a critical value adjustment suggested by McCloskey for the test on the cointegrating relations is implemented, and it is found by simulation that it eliminates size distortions and has reasonable power for moderate values of the near unit root parameter. The findings are illustrated with an analysis of a number of different bivariate DGPs.

Keywords: Long-run inference, test on cointegrating relations, likelihood inference, vector autoregressive model, near unit roots, Bonferroni type adjusted quantiles

JEL Classification: C32

Suggested Citation

Franchi, Massimo and Johansen, Soren, Improved Inference on Cointegrating Vectors in the Presence of a Near Unit Root Using Adjusted Quantiles (April 21, 2017). Available at SSRN: https://ssrn.com/abstract=2958147 or http://dx.doi.org/10.2139/ssrn.2958147

Massimo Franchi

University of Copenhagen

Nørregade 10
Copenhagen, København DK-1165
Denmark

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

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