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

Massimo Franchi; Søren Johansen

doi:10.3390/econometrics5020025

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

Massimo Franchi, Søren Johansen

Department of Mathematical Sciences

1 Citation (Scopus)

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.

Original language	English
Journal	Econometrics
Volume	5
Issue number	2
Pages (from-to)	1-20
Number of pages	20
ISSN	2225-1146
DOIs	https://doi.org/10.3390/econometrics5020025
Publication status	Published - 14 Jun 2017

Keywords

Faculty of Social Sciences
long-run inference
test on cointegrating relations
likelihood inference
vector autoregressive model
near unit roots
Bonferroni type adjusted quantiles

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10.3390/econometrics5020025Licence: CC BY

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title = "Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles",

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.",

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T1 - Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles

AU - Franchi, Massimo

AU - Johansen, Søren

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N2 - 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.

AB - 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.

KW - Faculty of Social Sciences

KW - long-run inference

KW - test on cointegrating relations

KW - likelihood inference

KW - vector autoregressive model

KW - near unit roots

KW - Bonferroni type adjusted quantiles

U2 - 10.3390/econometrics5020025

DO - 10.3390/econometrics5020025

M3 - Journal article

SN - 2225-1146

VL - 5

SP - 1

EP - 20

JO - Econometrics

JF - Econometrics

IS - 2

ER -

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

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Keywords

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