Dumitrescu & Hurlin Test for Granger Causality

[Anass Wajib]

Hello,

I'm using a paneldataset (xtreg command 1985-2020 over 210 countries)

I did some research and found two threads (Dumitrescu & Hurlin (2012) Granger non-causality test - Statalist & xtgcause command: z bar or z bar tilde. What to use? - Statalist) here but none of the answers were clear-cut as to which p-value you'd have to go for to interpret your results.

xtgcause RND_L1 PT, lags(1)


Dumitrescu & Hurlin (2012) Granger non-causality test results:
--------------------------------------------------------------
Lag order: 1
W-bar =          8.0556
Z-bar =         11.1559   (p-value = 0.0000)
Z-bar tilde =    9.8458   (p-value = 0.0000)
--------------------------------------------------------------
H0: PT does not Granger-cause RND_L1.
H1: PT does Granger-cause RND_L1 for at least one panelvar (countryid).

. xtgcause RND_L1 PT, lags(2)


Dumitrescu & Hurlin (2012) Granger non-causality test results:
--------------------------------------------------------------
Lag order: 2
W-bar =          7.4954
Z-bar =          6.1441   (p-value = 0.0000)
Z-bar tilde =    5.1680   (p-value = 0.0000)
--------------------------------------------------------------
H0: PT does not Granger-cause RND_L1.
H1: PT does Granger-cause RND_L1 for at least one panelvar (countryid).

Since there's no difference in p-values here. Is it correct to say that we can reject the null hypotheses here, and as a result PT does Granger cause RND_L1?

Thank you

[George Ford]

According to the paper, Z-bar is valid only with large T, and over-rejects with small T. Z-bar-tilde is solid for any N and T and has higher power. The simulations suggest to me there's no reason not use Z-tilde.

https://shs.hal.science/file/index/docid/224434/filename/Causality_WP.pdf

[Anass Wajib]

George Ford Truly indebted to your detailed input. Thank you.

[Anass Wajib]

George Ford Sorry to bother you again. I just read that in order to perform this test, both variables have to be stationary. I've checked mine and found one has unit root as per null hypothesis.

I've read mixed views on this some people say stationarity isn't a requirement and others say it is. One comment has mentioned Toda yamamoto test to be indifferent in this regards but I couldn't find it as an option of test using xtunitroot command

Here are my results

xtunitroot llc PT, lags(1)

Levin–Lin–Chu unit-root test for PT
-----------------------------------
H0: Panels contain unit roots               Number of panels  =     13
Ha: Panels are stationary                   Number of periods =     36

AR parameter: Common                        Asymptotics: N/T -> 0
Panel means:  Included
Time trend:   Not included

ADF regressions: 1 lag
LR variance:     Bartlett kernel, 10.00 lags average (chosen by LLC)
------------------------------------------------------------------------------
                    Statistic      p-value
------------------------------------------------------------------------------
 Unadjusted t        -5.6055
 Adjusted t*         -1.9732        0.0242
------------------------------------------------------------------------------

. xtunitroot llc RND, lags(1)

Levin–Lin–Chu unit-root test for RND
------------------------------------
H0: Panels contain unit roots               Number of panels  =     13
Ha: Panels are stationary                   Number of periods =     36

AR parameter: Common                        Asymptotics: N/T -> 0
Panel means:  Included
Time trend:   Not included

ADF regressions: 1 lag
LR variance:     Bartlett kernel, 10.00 lags average (chosen by LLC)
------------------------------------------------------------------------------
                    Statistic      p-value
------------------------------------------------------------------------------
 Unadjusted t        -1.9379
 Adjusted t*          1.1992        0.8848
------------------------------------------------------------------------------

Edit:

On way to remedy against unit roots here is to compute the difference of the variable in question, here (RND)

xtunitroot llc dRND, lags(1)

Levin–Lin–Chu unit-root test for dRND
-------------------------------------
H0: Panels contain unit roots               Number of panels  =     13
Ha: Panels are stationary                   Number of periods =     35

AR parameter: Common                        Asymptotics: N/T -> 0
Panel means:  Included
Time trend:   Not included

ADF regressions: 1 lag
LR variance:     Bartlett kernel, 10.00 lags average (chosen by LLC)
------------------------------------------------------------------------------
                    Statistic      p-value
------------------------------------------------------------------------------
 Unadjusted t       -10.4871
 Adjusted t*         -3.7654        0.0001
------------------------------------------------------------------------------

Now I assume that in order to perform Granger causality test, we need to use d.RND (stationary variable) instead of RND (non-stationary). Otherwise, there's no point in generating this new variable. The issue here when I want to use d.RND as my new variable in Granger test, it says the variable has to be strongly balanced. Since d.RND is a difference the first obs. is missing compared to RND. I don't know how to proceed from here.