xtgcause command: z bar or z bar tilde. What to use?

[lakshya narula]

Hello.

I am using xtgcause command for granger causality analysis.

I have a dataset for gdp growth and housing prices that looks like this

* Example generated by -dataex-. To install: ssc install dataex
clear
input str3 code str7 time float(gdp_value hp_value)
"NLD" "2005-Q1"   .322858  120.8404
"NLD" "2005-Q2"    .70347 121.14498
"NLD" "2005-Q3"  1.342952 121.52393
"NLD" "2005-Q4"   .630551 122.07548
"NLD" "2006-Q1"   .623938 121.92136
"NLD" "2006-Q2"  1.497031 123.00626
"NLD" "2006-Q3"   .598153 123.21648
"NLD" "2006-Q4"     .8245 124.73105
"NLD" "2007-Q1"  1.145697 125.23947
"NLD" "2007-Q2"   .511647  125.9286
"NLD" "2007-Q3"  1.117502 127.33276
"NLD" "2007-Q4"  1.353024 127.85272
"NLD" "2008-Q1"   .327531   126.555
"NLD" "2008-Q2"   .492587  126.6092
"NLD" "2008-Q3"  -.122148 127.45116
"NLD" "2008-Q4"  -.659941   126.312
"NLD" "2009-Q1" -3.593641 125.50623
"NLD" "2009-Q2"   .002509 123.75813
"NLD" "2009-Q3"   .400708  121.3588
"NLD" "2009-Q4"   .602328 121.06926
"NLD" "2010-Q1"  -.181172 119.73282
"NLD" "2010-Q2"   .430196  119.9887
"NLD" "2010-Q3"   .429435 118.35582
"NLD" "2010-Q4"  1.130277 117.32396
"NLD" "2011-Q1"    .59237 116.83125
"NLD" "2011-Q2"  -.094369 115.03316
"NLD" "2011-Q3"  -.008004 113.31206
"NLD" "2011-Q4"  -.596028 111.14565
"NLD" "2012-Q1"  -.216573  108.9804
"NLD" "2012-Q2"   .064111 107.28593
"NLD" "2012-Q3"  -.426776 102.23032
"NLD" "2012-Q4"  -.708357 101.78844
"NLD" "2013-Q1"   .327541  98.08289
"NLD" "2013-Q2"  -.180949  96.39162
"NLD" "2013-Q3"   .605075  96.21662
"NLD" "2013-Q4"   .633838  96.30658
"NLD" "2014-Q1"  -.099695  95.78539
"NLD" "2014-Q2"   .585676  96.76814
"NLD" "2014-Q3"   .252766  96.58524
"NLD" "2014-Q4"   .900677   97.6215
"NLD" "2015-Q1"   .589031  99.25961
"NLD" "2015-Q2"   .316472  99.47125
"NLD" "2015-Q3"   .339938  100.1688
"NLD" "2015-Q4"   .016386 101.10033
"NLD" "2016-Q1"   .906044 102.56538
"NLD" "2016-Q2"   .220417  103.2975
"NLD" "2016-Q3"  1.145374 105.19594
"NLD" "2016-Q4"   .860028 106.61266
"NLD" "2017-Q1"   .490426 107.79723
"NLD" "2017-Q2"   .909608 109.81923
"NLD" "2017-Q3"   .690211 111.25238
"NLD" "2017-Q4"   .789482 114.22588
"NLD" "2018-Q1"   .575801 116.01057
"NLD" "2018-Q2"   .688609 117.69238
"NLD" "2018-Q3"   .265952 120.07318
"NLD" "2018-Q4"    .54636 121.69694
"NLD" "2019-Q1"   .484991 122.44673
"NLD" "2019-Q2"   .326844  124.3768
"NLD" "2019-Q3"   .418324  124.5507
"NLD" "2019-Q4"   .389318 126.31741
end

For each country, there are 60 observations, starting from 2005 q1 to 2019 q4.

The results look like this for Netherlands when I use 4 lags

. xtgcause gdp_value hp_value, lags(4)


Dumitrescu & Hurlin (2012) Granger non-causality test results:
--------------------------------------------------------------
Lag order: 4
W-bar =          3.9732
Z-bar =         -0.0095   (p-value = 0.9925)
Z-bar tilde =   -0.0649   (p-value = 0.9483)
--------------------------------------------------------------
H0: hp_value does not Granger-cause gdp_value.
H1: hp_value does Granger-cause gdp_value for at least one panelvar (country).

The results look like this when I use aic and big criteria. Here, the value of z bar is significant but not for z bar tilde.

. xtgcause gdp_value hp_value, lags(aic)


Dumitrescu & Hurlin (2012) Granger non-causality test results:
--------------------------------------------------------------
Optimal number of lags (AIC): 18 (lags tested: 1 to 18).
W-bar =         97.5175
Z-bar =         13.2529   (p-value = 0.0000)
Z-bar tilde =    1.4734   (p-value = 0.1407)
--------------------------------------------------------------
H0: hp_value does not Granger-cause gdp_value.
H1: hp_value does Granger-cause gdp_value for at least one panelvar (country).

. xtgcause gdp_value hp_value, lags(bic)


Dumitrescu & Hurlin (2012) Granger non-causality test results:
--------------------------------------------------------------
Optimal number of lags (BIC): 18 (lags tested: 1 to 18).
W-bar =         97.5175
Z-bar =         13.2529   (p-value = 0.0000)
Z-bar tilde =    1.4734   (p-value = 0.1407)
--------------------------------------------------------------
H0: hp_value does not Granger-cause gdp_value.
H1: hp_value does Granger-cause gdp_value for at least one panelvar (country).

Which one should I use for interpreting the causal relationship? Z bar or Z bar tilde?

Please help!

[Justin Niakamal]

I'm not really an expert on this subject, but FWIW here are some thoughts.

From the Stata Journal article on xtgcause, "Compared with their output, it turns out that the denomination “Zbar-Stat” used in EViews corresponds to the Z-bar tilde statistic (while the Z-bar statistic is not provided in EViews)."

While it's not a convincing argument, I would a priori trust the statistic that Eviews chose to report since it's more of a 'time-series' software. Or you could try using the bootstrap option if you have cross-sectional dependence.

"By default, 1,000 bootstrap replications are performed. We observe that the bootstrapped p-value for the Z-bar increases substantially compared with the asymptotic p-value obtained before (from 0.34 to 0.45), while that for the Z-bar tilde remains closer. This should be interpreted as a signal that the estimations suffer from small sample biases, so asymptotic p-values are underestimated." Given that you have 60 observations in a panel dataset, I would assume your p-values are underestimated (in other words, go with Z-bar tilde).

So examine the results of the following and go from there.

 xtgcause gdp_value hp_value, lags(bic) bootstrap
 xtgcause gdp_value hp_value, lags(aic) bootstrap

Hope this helps

Source:
Lopez, Luciano, and Sylvain Weber. "Testing for Granger causality in panel data." The Stata Journal 17, no. 4 (2017): 972-984.

[Devashish Singh]

heyy did you get the answer to your query? i too am facing a similar issue? would love to get any insights