Granger Causality Test

Firstly, download the excel file called " US interest rates" from the "Sample Data" of Econ3600 homepage. In the data file, we will use three different types interest rate such as short-term rate: Federal Funds Rate (ffr) and Treasury Bill Rate (tbr); intermediate-term rate: Government Bond Yields 3 Years (mid), and long-term rate: Government Bond Yields 10 Years (long) to carry the Granger Causality Test. We want to test the causality among the three different types of interest rates.

First create a Workfile in EVIEWS and import the data from the excel. Specify the four variables as ffr, tbr, mid, and long as follow.

Example 1: If we want to know whether

  "ffr" causes "mid" or "mid" causes "ffr", or bilateral causes, 

"ffr" causes "long" or "long" causes "ffr", or bilateral causes,  

"mid" causes "long" or "long" causes "mid", or bilateral causes,   

Firstly, open the data of "ffr", "mid" and "long", then click the "view" and choose "Granger Causality" and set the "lags to include" is "2", 

 the result is 

The null hypotheses of the Granger-Causality test are:

H₀: X =/=> Y  (X does not granger-cause Y)

H₁: X ==> Y   (X does Granger-cause Y)

The F-test is :  F_{(r, n-m-k)} = [(ESS_r -ESS_u)/r]/[ESS_u/(n-m-k)] and ESS is the residual sum of squares.

As you can see, F-statistics are large and the probability values are all close to 0 except for Ho of  "MID does not Granger Cause LONG". It means that the variables are mutually Granger cause to each other except for the "MID does not Granger Cause LONG". 

When the lag length are changed from "lags: 2" to "lags: 6", the test results are different as:

The conclusion is basically the same. 

When the lags are changed to "lags: 12", the test results are changed as

The conclusion is still the same as the above except for the "LONG does not Granger Cause MID". 

Note: The Granger Causality Test for some variables are very sensitive to the selected number of lags in the analysis. Students should be careful to choose the reasonable lag lengths. For examples, for the monthly data, the reasonable lag terms can be range from 1 to 12 or 24, etc.; for the quarterly data, the reasonable lag terms can be range from 1 to 4, 8, 12, etc., and for the annual data, the reasonable lag terms should be less. And the reasonable lag-lengths should be determined by the significant change of the F-value.

Example 2: If we want to know whether 

"tbr" causes "mid" or "mid" causes "tbr", or bilateral causes,  

"tbr" causes "long" or "long" causes "tbr", or bilateral causes,  

"mid" causes "long" or "long" causes "mid", or bilateral causes,   

we can check them in similar way, the result are:

Since the "tbr" and the "ffr" are the similar indicators for measuring short term interest rate. Therefore, we get  similar causality conclusions as above.

The End