Bo Sjö
2013-12-16
Exercise 9
Test for Granger Non-Causality between
Kenya Exports and the Real Exchange Rate
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1. Introduction
This exercise deals with Granger non-causality tests, often referred to as Granger
causality tests. The basic idea is that if a variable can be found to predict another variable,
it might cause that variable (to change). On the other hand if a variable cannot predict
another variable it cannot cause it.1
The test concerns the lead and lag structure among a set of variables and tests specifically
if the lag structure of some variable predict another variable in a VAR model. For details
see Sjö (2013). Estimate a VAR, restrict the lags of the variable and test the significance.
If you cannot reject the null, all lags are zero, the variable cannot Granger cause the lefthand variable in the equation. If you reject the null, you can say that the variable is
Granger causing the other variable. (=it predicts the other variable).
2. The Problem
The export industry in Kenya is complaining to the Central Bank of Kenya that the
appreciation of the Kenyan shilling is making exports harder. They demand action
to curb the appreciation of the shilling. But, are they right? Is the shilling
appreciating too much and thereby reducing exports or is the other way around? Do
higher exports lead to an appreciation of the shilling? A GNC test of exports and the
real exchange rate might help to broaden/deepen the discussion.
The question is: “Is exports ‘causing’ appreciation, or is appreciation causing (a fall) in
exports?” To find out set up a VAR in log first differences, you might want to start with
12 lags (3 years). But, the choice is yours, where do you find the optimal lag structure
and white noise residuals?
2. Data
The data is in kenya_exports.xls. The data is quarterly.
Name
Exch
CPI
Exp
Imp
CPI_USA
Variable
Kenya shilling /USD FX rate
Consumer price index for Kenya
Kenya’s Export in domestic
currency (Nominal)
(imports for Kenya - not used)
U.S. Consumer price index
First, you need to construct the real exchange rate (qt) for Kenya according to
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Verbeck dicusses Grager causality on page 355 but is not very extensive on that subject.
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qt 
Pt , f  S t
Pd ,t
, and then take logs.
Second, you need to calculate the real export value, and take logs.
Third, form logs and first differences of the variables. Finally, look at the graphs of the
data you created.
3. Instructions
Here we are interested in first differences (changes) between the variables, under the
assumption that they are I(0), which should be tested of course.
Build a bivariate VAR model of the two data series (growth in exports and changes in the
real exchange rate) in logs. You might want to go around three year back (12 lags) to
account for all dynamics.
Check for outliers, remember to look at graphs.
Once a suitable VAR has been found, the GNC test is performed by restricting all the
lags of one variable in one equation to be zero.
This is usually done with a Chi-square or F-type of test. The null is that all parameters of
the restricted lag structure are zero, the alternative is that the lags are significantly
different from zero and predicts the equation-variable.
EViews: In EViews you get both Chi-square and F-test depending on where in the
program you do the causality testing. After estimation, under view find Lag structure, and
then Granger causality test. This gives you the chi-square distributed test. You can also
look under View for Lag exclusion test.
If you know the VAR and its lag order, you can go to Quick, Group Statistics and
Granger Causality Test. In the Window you name the series that makes up the VAR and
indicate the lag length. This leads to a GNC test using the F-distribution, which is the
better distribution. However, you do not get any output from the VAR itself, so you need
to estimate and test you VAR before coming here.
The null is that there is no Granger causality (all parameters associated with the lags of
the variable in that particular equation are set to zero), the rejection of the null is that
there is “Granger causality”.
PcGive:
Under the Test menu choose exclusion restrictions. The next window allows you to
restrict coefficients (lags) of you choice. Typically from the VAR, the exclusion test
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gives: variable1_lag_1@first equation; variable1_lag_2@first equation, etc. You can use
shift and arrow key to select more than one lag. The test has a chi-square distribution.
Final
What is your conclusion regarding exports and the real exchange rate?
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