I am currently conducting a multivariate time series analysis on Eviews. I am investigating the causal relation among various economic variables. I have estimated a VAR model using the Toda-Yamamoto Procedure, following the protocol described by Dr Giles in his blog, Econometrics Beat. I need help with some of the interpretation of my results. I know how to interpret the p-value results in terms of the null hypothesis. However, I wanted to know what is the direction of the causality (unidirectional or bidirectional). Or to get directional information of the relations among variables I have to look somewhere else other than he Granger Causality results? Here are the results: Granger Causality/Wald Test [![Granger/Wald Test][3]][3]

The variables are log transformed and they are:

  1. ln_gdp54: gross domestic product
  2. ln_gdfi54: gross domestic fixed investment
  3. ln_lf: labor force
  4. ln_mmtoe: energy consumption (million oil tons equivalent)
  5. ln_totco2: total CO2 emissions

Thank for the help!


1 Answer 1


I cannot guarantee whether the test has been carried out correctly, but here is what I can read in the table.

First block: the null hypothesis ln_totco2 $\not \xrightarrow{G}$ ln_mmtoe should not be rejected at the regular 5% level as the associated p-value is as high as 0.3301 (way above 0.05).

Second block: the null hypothesis ln_mmtoe $\not \xrightarrow{G}$ ln_totco2 should not be rejected at the regular 5% level as the associated p-value is as high as 0.1776 (way above 0.05).

x $\not \xrightarrow{G}$ y means "x does not Granger-cause y".

In sum, there is not enough evidence for causality either way. To answer the question directly, there is not enough evidence either for unidirectional or for bidirectional causality.

  • $\begingroup$ Thanks for taking the time to answer my question. I suppose that I have enough evidence to say that there is a neutral relation between energy consumption and CO2 emissions. $\endgroup$ Aug 11, 2015 at 20:32
  • $\begingroup$ Statisticians are often scrupulous about the statements they make, and yours does not exactly follow from Granger causality tests (although you seem to be going the right way). "Neutral" is not a statistical term. How do you define a "neutral relation"? In general, the relation between two variables in a VAR model is best revealed by impulse-response functions and forecast error variance decomposition. Check those, and it will be quite clear. $\endgroup$ Aug 12, 2015 at 6:20
  • $\begingroup$ Thanks for the advice! I am looking into the IRF results for my VAR model and the variance decomposition too. Thanks again! $\endgroup$ Aug 13, 2015 at 10:53

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