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

*Massimo Franchi* () and
*Soren Johansen* ()

*Econometrics*, 2017, vol. 5, issue 2, 1-20

**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.

**Keywords:** long-run inference; test on cointegrating relations; likelihood inference; vector autoregressive model; near unit roots; Bonferroni type adjusted quantiles (search for similar items in EconPapers)

**JEL-codes:** B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)

**Date:** 2017

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**Related works:**

Working Paper: Improved inference on cointegrating vectors in the presence of a near unit root using adjusted quantiles (2017)

Working Paper: Improved inference on cointegrating vectors in the presence of a near unit root using adjusted quantiles (2017)

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**Persistent link:** https://EconPapers.repec.org/RePEc:gam:jecnmx:v:5:y:2017:i:2:p:25-:d:101429

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