Greetings. I have two I(1) variables. Johansen test, and bound test with ARDL showed non.cointegration. However Augmented Granger Causality showed one way causality. Can i use ARDL model to estimate the impact of that one way causality without the series been cointegrated?.
The Granger results showed causality of X to Y. so i'm estimating a model with 3 lags of each in one ARDL as it follows this:
Yt = B0 +B1X+ B2X_t-1 + B3X_t-2 + B4X_t-3 + B5Y_t+B6Y_t-1 + B7Y_t-2 + B8Y_t-3
Series X and Y are not co-integrated. so the B coefficient would anyway represent the associated change ? (Bound test also showed no cointegration)
Yes, in fact, often that is the correct thing to do since pretesting may not important here.
If your variables are I(1) and no cointegration, run OLS on the first difference of the variables and you can interprete the coefficients as the estimate of the relationship.
Given the fact that unit root tests are weak and unreliable to identify i(d) characteristics, a quick regression using only first differeneed variables would be misleading and unnecessarily unreliable.
Hi John,
Please follow the chart as given in Principle of Econometrics, 4th edition by R. Carter Hill, Willian E. Griffiths, Guay, C. lim. , page 494.
The authors write that for the variables with stochastic trend and no co-integration, simply estimate the ARDL in first difference.
In addition, I am curious whether you have used DF-GLS test to identify the order of integration or not.
For unit root, use "dfgls" code in stata and to run ARDL use "ardl" code in stata. If you use "ardl" code in stata, you need not worry about the number of lags, the software automatically provides for you.
Thank you!
Hi Rishi. So your knowledge of econometrics says DF-gels is an excellent measure. I hope you didn't mean that! My major point to John is that his question of cointegration is better represented within an ARDL (see my comment above) model. Right there, the reviewer sees the one period lagged ecm term and the first differences. The non significance ecm term would indicate no cointegration. He can sweeten the pie by showing bound tests.
Greetings Arize & Sigdel, I've tested the unitroots with ADF test and also with graphs with the series in levels and in first differences. The conclusion is that both series are integrated of first order I(1). Now Co-integration test failed, even with Johansen and even with Bound testing (from the ADRL). However i performed the Augmented Toda Yamamoto Approach of Granger Causality, which showed causality of one direction betwen X to Y.
So i want to know if the causality betwen X to Y is positive or negative. this causality considering that the Granger Approach took in account the variales in series (without differences). I don't want to loose the long-run information with the first differences. However i want to see if this causality is positive or negative. That's why i came up with the idea of using the ARDL model.
I did a model with ARDL with X and Y variables in series. The ARDL model shows stability, good especification, no serial correlation, absense of HT and residuals looks normally distribuited. also stationary residuals, and a good r^2.
Since toda & yamamoto approach confirmed the causality of one direction, and the tests of the ARDL regression, seems right to me (correct me if i'm wrong), would be worth to put in my paper, that effects of X over Y can be seen with the coefficients with the ARDL i made. In order to dig better about this one direction causality.
Yes, as I said earlier use ARDL. You can run 2 of the. First, make y your regressand
Then do another with X as the regressand. This allows you and reviewers to see everything. If both
ecm(-1) are nonsignificant. Then, you can make statements about Granger causality in the short-run mode. Which is what your TY test is telling you
Since both Johansen and bounds tests suggests evidence of no cointegration...You can simply proceed using ARDL but you end at the "short-run estimates", even the ecm term will indicate the absence of cointegration with it's t-stat been insignificant..or you can opt for a VAR model instead and proceed to innovation accounting, variance decomposition test and Granger causality
It is high time that econometric Methods and Packages should be developed as to accommodate both stationary and non-stationary data even without cointegration being present. One should be able to estimate simple ARDL model without ECM or cointegration being present. Of course one can estimate VAR or causality in differences but greatest demerit is that they would throw away lots of information by differnecing the non-stationary series.
People.who are econometricans know exactly what to do.it is unnecessary to not do an ARDL because unit tests lack power and a reviewer would like to see the lagged levels and insignificant coefficient before accommodating the first-difference model. Furthermore, economic s deals strictly with long run parameters
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