Dickey Fuller Test for Stationarity and Cointegration Test

[Lea Birm]

Hello,
I am currently working on a time series project analyzing the behavior between consumption and income.
I have quarterly data for the US for income and consumption.
Now I have used the Dickey Fuller Test to check whether those variables are stationary.

Therefore I have used the command:

[varsoc y //appropriate lag is 2
varsoc c //appropriate lag is 4

dfuller y, trend lags(2) regress
dfuller c, trend lags(4) regress

varsoc d.y
varsoc d.c

dfuller d.y, lags(1) regress

dfuller d.c, lags(4)regress


egranger d.c d.y, lags(4) reg
varsoc d.c d.y

//differenced version of c and y is cointegrated!

I included the trend in the dfuller test since income and consumption are obviously following a trend and come to the result, that the null of a unit root can not be rejected.
Then I used the difference of the variables and come to the result, that the null can be rejected, that the difference is stationary and so y and c are I(1). Am I right with this interpretation?
I used the varsoc command to check which lags I should include.
Moreover I tested whether the variables are cointegrated with the egragner command and came to the result that they are cointegrated.

I would really appreciate some feedback, since I want to start with my data analysis and do want it to have any mistakes.

Thank you very much in advance!

[Andrew Musau]

#1

Then I used the difference of the variables and come to the result, that the null can be rejected, that the difference is stationary and so y and c are I(1). Am I right with this interpretation?

Yes, if the variable in levels is nonstationary and stationary after first-differencing, then it is I(1) i.e., integrated of order 1. Most economic time-series are assumed to be I(1), so your finding is consistent with theory.

#2

You check whether the variables in levels are cointegrated, not their first differences. The rationale is that even though the individual variables might be nonstationary, if they are cointegrated (i.e., linear combinations of these nonstationary variables are stationary), then you can use the nonstationary variables in levels without concern that you will end up with spurious results. First-differencing throws away information, and this is not desirable if it can be avoided.

[Mazen Diwani]

Dear Andrew. suppose that I have a panel data (unbalanced) and I am using a fixed-effects model, I have one dependent variable and 7 regressors, 3 of these regressors are found to be Non-stationary at level but stationary at the first difference I(1), so my question is: do I have first to run a cointegration test (say by the stata command xtcointtest or xtdolshm) for these non-stationary variables? and if there is cointegration, how shall I proceed from there? shall I presume with my regression using the stationary variables I(1) (which is obtained by the first difference or by the use of log) along with the other I(0) variables in my regression? Or what exactly to do? I thank you sincerely for your patience and hope that my question is clear, because after the cointegration test, I am lost, I don't know how to proceed with my main analysis (the regression!!)

[Andrew Musau]

Mazen Diwani what are the dimensions of your panel? N and T?

[Mazen Diwani]

My N = 11 banks and my T=40 quarters (2009:Q1-2018:Q4)

[Andrew Musau]

so my question is: do I have first to run a cointegration test (say by the stata command xtcointtest or xtdolshm) for these non-stationary variables?

Yes, if you want to test for cointegration. These tests are designed for large N large T datasets, but I think you should still be OK.

and if there is cointegration, how shall I proceed from there?

There are a number of possibilities for estimation. In terms of static models, first differences in place of fixed effects may work as the variables will be stationary after differencing. Otherwise, look at the community contributed xtpmg command. The SJ paper is free to download.

https://journals.sagepub.com/doi/pdf...867X0700700204

[Mazen Diwani]

Dear Andrew, thank you so much for your response. Just to confirm whether I am on the right track with you, so if I have non-stationary variables, I will do a co-integration test (for their levels not their differences), and if I find that they are co-integrated, then I would use the non-stationary variables (not their differences) and proceed into my regression? OR I STILL HAVE TO USE THE DIFFERENCED VARIABLES? Many thanks in advance

[Andrew Musau]

Just to confirm whether I am on the right track with you, so if I have non-stationary variables, I will do a co-integration test (for their levels not their differences)

Yes, if using xtcointtest, you enter the variables in levels. See -help xtcointtest-.

and if I find that they are co-integrated, then I would use the non-stationary variables (not their differences) and proceed into my regression?

As stated in #2, the point of a cointegration test is to avoid differencing, which throws away information. So if the variables are cointegrated, you can estimate in levels.

[Mazen Diwani]

Thank you so much Dr. Andrew, I totally got the picture now. I really appreciate your help and support. My sincere regards to you.

[Sabrin Rahman]

Hi Dr. Andrew, I was just wondering if I have 2 nonstationary variables, and I have 9 variables in my regression model, when i use xtcointtest, I find my variables to be cointegrated. So can i use normal fixed effects estimation?

[Andrew Musau]

See https://www.statalist.org/forums/for...cts-estimation