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### Toda and Yamamoto causality test

Posted: **Mon Apr 21, 2014 3:17 am**

by **iboha**

Dear all,

I have two series, one is I(1) and another is I(0). I used Toda and Yamamoto way to test the causality between the two. However, the results of cointegration test and the granger causality test are contradictory. The cointegration test indicates 1 cointegration exists but the granger causality test indicate non-causality. For this kind of conflicting results, what would an experienced expert do please?

Thank you all very much in advance!!!

### Re: Toda and Yamamoto causality test

Posted: **Mon Apr 21, 2014 5:56 am**

by **trubador**

Normally, presence of cointegration implies causality, so one should reject Granger test in this case. However, you have one I(1) and one I(0) series. As the name Cointegration suggests, time series of interest must have the same order of integration. You may be misinterpreting the results (i.e. unit root, Johansen) or there is something more serious with the data.

### Re: Toda and Yamamoto causality test

Posted: **Mon Apr 21, 2014 6:54 am**

by **iboha**

Thank you so much dear Trubador.

As I understand from your reply,there may be something wrong with the unit root test results interpretation, I present herewith my unit root results in the attachment.

Since by visual check, there is clear trend shown by the data plot(please see the attachment), therefore at level, I choose to follow the second model(constant+trend) (correct me if I am wrong plz). That is why I conclude that lnec is I(0).

As you may notice that there is some conflicting results of the frist difference of lngpc, ADF and PP reject the null of unit root while KPSS also reject the null of stationarity. I let the democracy rule. However, do you think that this is the problem that cointegration test result and granger causality result conflict with each other?

Another thing Is that "is my Toda and Yamamoto test procedure correct plz?" I check the order of integration first to confirm the max order of integration. In my case, one is I(0) and another is I(1). Then regardless of the result I established a well specified VAR. Then I conduct cointegration test followed by granger causality test. The results of cointegration test and granger causality test should confirm each other. So if they conflict each other then there is something wrong with the unit root test. Is my understanding correct plz?

But what would the solution be plz?

### Re: Toda and Yamamoto causality test

Posted: **Mon Apr 21, 2014 12:03 pm**

by **trubador**

I am not familiar with Toda and Yamamoto causality test. But it looks like you have annual data between 1953 - 2010, which leaves only 58 data for testing. I do not know what your variables are but it may not be feasible to allow for too many lags from both theoretical and practical point of view. Other than that, I suspect the variable gpc is in nominal terms and therefore taking the logarithm does not help much. If that is the case, you may consider deflating this variable. Otherwise, it is evident that these series do not have same order of integration.

### Re: Toda and Yamamoto causality test

Posted: **Mon Apr 21, 2014 7:40 pm**

by **iboha**

Thank you very much Dear Trubardo again for your kind help.

The ec variable is energy consumption per capita and gpc is GDP per capita. They are both annual data. Actually I adjusted gpc to be in real term. But I am not sure whether the way I did is correct or not. Could you please comment on this? I got the data of GDP per capita at current price and the consumer price index(CPI) (base year 1978). I then obtained the real GDP per capita by the formula: real GDP per capita=GDP per capita at current price/CPI*100. For example, if GPC at current price for the year 1995 is 5046, CPI of 1978=100, CPI for 1995=396.9, then the real GDP of 1995 = 5046*396.9/100=20027.574.

And then I took the natural log for the real GDP per capita.

Is my approach correct or not please?

About the lags length issue, when I tried to establish VAR to determine the optimal lag length, other than the various criterion, we should also check for serial correlation,isn't it? If it is, then to what extent should we ensure that there is no serial correlation. What I mean is that if by checking LM test, should we stop until all the lags reject serial correlation or if most of them reject. For example, is following result sound to conclude rejection of serial correlation:

VAR Residual Serial Correlation LM Tests

Null Hypothesis: no serial correlation at lag order h

Date: 04/21/14 Time: 13:07

Sample: 1953 2010

Included observations: 56

Lags LM-Stat Prob

1 4.738838 0.0122

2 7.899848 0.0953

3 15.88944 0.0032

4 0.954501 0.9166

5 1.473743 0.8313

6 6.413722 0.1703

7 0.594069 0.9637

8 2.178056 0.7030

9 2.349100 0.6718

10 1.160943 0.8845

11 2.149208 0.7083

12 1.466070 0.8326

I read in some materials that if half of them reject the null then it should be safe to reject it. But no reference is provided so I doubt to take it.

What is your opinion please?

### Re: Toda and Yamamoto causality test

Posted: **Mon Apr 21, 2014 11:53 pm**

by **trubador**

Yes, you can deflate nominal GDP per capita with CPI. But you may also be able to find GDP figures at fixed prices.

Anyway, the serial correlation is mainly due to strong nonlinear trend in lngpc variable. Although a simple linear trend may be enough to capture the upward tendency in lnec, it seems that lngpc requires an additional term: trend^2. Instead, you may also consider to associate real economic or income growth with per capita energy consumption.

With these variables (and the annual frequency), considering higher lag orders really does not make much sense to me. Not to mention that your sample size is not enough.

### Re: Toda and Yamamoto causality test

Posted: **Sun Apr 27, 2014 10:05 am**

by **iboha**

Dear Trubador,

I am sorry that I could not follow up your reply in time because I could not access internet due to network maintainance for the past few days. I almost got mad without internet access. And finally the technician came and the internet connection is OK now.Thank God!

Anyway,thank you so much for your constructive analysis and suggestions. Now I understand much better about the problem. I tried to find the data at fixed prices however I failed. But I followed your suggestion to take time trend into account. And the problems are solved. Thank you so much!

However, I need one more guidance from you.

If I proceed with this modified VAR model, for example I proceed with T-Y causality test. I use the model to check block-exogeneity causality test. The coefficient of t will be not included in the wald test since it is inserted as exogenous variable. Is my understanding correct?What I mean is that the time trend added will not affect the causality test using the modified VAR. Is it correct?

Furthermore, when I use the same modified VAR to test the cointegration if both lnec and lngpc are I(1), the time trend will also not affect the cointegration test result, right? I am somehow confused about the time trend t I put to remove the serial correlation and the linear deterministic trend that we may choose to include in the cointegration test(please see the snapshot).

Are they the same thing?

Actually what I did is that after I included the time trend in the VAR model and then estimated the optimal lag, I use the lag selected to test for cointegration with the option 3 in the snapshhot(cointegration test specification). However, trace and max stats both indicate 2 cointegration relationship, which does not make sense of course. And if I select option 6, I got "near singular matrix" message. I just do not know which part went wrong. Is it because of the nature of the data? As you mentioned that they may not be integrated at the same level. Or is it due to any mistake I made in the testing procedure please?

Thank you very much in advance!

### Re: Toda and Yamamoto causality test

Posted: **Sun Apr 27, 2014 10:29 am**

by **iboha**

By the way, if KPSS cannot reject stationarity at 10% while ADF and PP both reject unit root at 10%,is it safe to conclude that the series is stationary please? I tend to use unit root test with structural breaks(e.g. ZA) to confirm the finding. However, if I am not mistaken, dear Trubardo, you reminded us before that tests such as ZA should be conducted only if the standard unit root tests fail to reject the null since they have low power towards the unit root.

But anyway, I ran the ZA test. Model A(constant) and C(both) fail to reject the null while model B(trend) reject the null at 5%. As far as I know, model C provide more reliable results(Sen,2003). So we should conclude that unit root does exist, which is contradictory with the previous testing results. Any thoughts on this problem please?

### Re: Toda and Yamamoto causality test

Posted: **Tue Apr 29, 2014 7:21 am**

by **samijo**

iboha wrote:I then obtained the real GDP per capita by the formula: real GDP per capita=GDP per capita at current price/CPI*100. For example, if GPC at current price for the year 1995 is 5046, CPI of 1978=100, CPI for 1995=396.9, then the real GDP of 1995 = 5046*396.9/100=20027.574

I hope that was a typo, otherwise u have just emphasized the trend. coz it should be the other way around. and the resulting series should be flatter (not steeper) than the original

### Re: Toda and Yamamoto causality test

Posted: **Wed Apr 30, 2014 1:33 pm**

by **trubador**

There are too many questions, some of which can simply be answered via searching the manual and others require a careful reading of the original study or a related textbook. However, once again, I would like emphasize my previous concerns:

1) Your sample size is not enough. When you allow for 9 lags, you estimate 38 coefficients in a VAR and 43 coefficients for a VEC even without the exogenous variables.

2) Regardless of what optimal lag length test says, such higher lag orders do not make much sense given the fact that you are using annual data. You should really have some apriori information or supporting evidence (other than the result of a statistical test) to take into account the impact from 9 years ago.

### Re: Toda and Yamamoto causality test

Posted: **Thu May 01, 2014 6:29 am**

by **iboha**

Dear samijo, thanks for the reply. Could you please explain more about how it should be done "the other way around"?

Dear Trubardo, thank you for your reply and truely sorry for many questions being asked. Thank you very much for your great patience.Well, I did refer to the manual, some books and papers. However, maybe because of my weak background in econometrics so that I could not comprehend enough or the inappropriate materials I am referring to, sometimes I could not get exactly what I want. My feeling is that some books or materials stop at explaining further on some practically important issues. So could you please suggest some materials for me to read? Currently, I am reading Enders' and Lütkepohl's books. Great materials. But maybe I am not able to absorb all the important information from these books. That's why I am still confused on some issues. So are there any other good materials please?

And about the sample size issue, I am going to dig more in order to get a larger sample size.Thank you for your suggestions.And I got your point on the lag issue. I am on the way to understand better.

### Re: Toda and Yamamoto causality test

Posted: **Thu May 08, 2014 11:15 am**

by **samijo**

Sorry for the late reply;

to correct your example which is

///if GPC at current price for the year 1995 is 5046, CPI of 1978=100, CPI for 1995=396.9, then the real GDP of 1995 = 5046*396.9/100=20027.574. ///

the correct thing to do is:

real GDP of 1995 = 5046*(100/396.9) = 1271.35

You see that most of the growth was in prices and not real

Secondly; you might take a look at the following link, I expect it to answer all your other questions:

http://davegiles.blogspot.com.es/2011/0 ... ality.htmlbest

### Re: Toda and Yamamoto causality test

Posted: **Wed Jul 19, 2017 6:59 pm**

by **Bouqui**

Hi,

Pls what version of Eview did you use and how did you use Toda Yamamoto in it?

Thanks

iboha wrote:Dear all,

I have two series, one is I(1) and another is I(0). I used Toda and Yamamoto way to test the causality between the two. However, the results of cointegration test and the granger causality test are contradictory. The cointegration test indicates 1 cointegration exists but the granger causality test indicate non-causality. For this kind of conflicting results, what would an experienced expert do please?

Thank you all very much in advance!!!

### Re: Toda and Yamamoto causality test

Posted: **Sun May 06, 2018 9:06 am**

by **elmst616**

sam SAM wrote:Good Morning, Hello,

Please, It's true this remark:

Toda-Yammamoto procedure requires that the maximum order of integration among the variables should not exceed the lags of the initial VAR?

Best wishes

There is a great blog post that explains the T-Y approach very clearly. Search Dave Giles professor emeritus who provides step by step instructions. Here is the link

http://davegiles.blogspot.com/2011/04/t ... ality.html

### Re: Toda and Yamamoto causality test

Posted: **Sun May 06, 2018 11:25 am**

by **startz**

The site, which is an excellent resource, was last updated a week ago.