Econometrics 2017, 5(2), 25; https://doi.org/10.3390/econometrics5020025
Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles
Massimo Franchi 1 and Søren Johansen 2,3,*
1
Department of Statistical Sciences, Sapienza University of Rome, P.le A. Moro 5, 00198 Rome, Italy
2
Department of Economics, University of Copenhagen, Øster Farimagsgade 5 Building 26, 1353 Copenhagen K, Denmark
3
CREATES, Department of Economics and Business, Aarhus University, Building 1322, DK-8000 Aarhus C, Denmark
*
Author to whom correspondence should be addressed.
Academic Editor: Katarina Juselius
Received: 20 April 2017 / Revised: 25 May 2017 / Accepted: 7 June 2017 / Published: 14 June 2017
(This article belongs to the Special Issue Recent Developments in Cointegration)
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 multiple near unit roots and analyses the asymptotic properties of the Gaussian maximum likelihood estimator. Then two critical value adjustments suggested by McCloskey (2017) for the test on the cointegrating relations are implemented for the model with a single near unit root, and it is found by simulation that they eliminate the serious size distortions, with a 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. View Full-TextKeywords:
long-run inference; test on cointegrating relations; likelihood inference; vector autoregressive model; near unit roots; Bonferroni type adjusted quantiles
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Franchi, M.; Johansen, S. Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles. Econometrics 2017, 5, 25.
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