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Granger Causality
K N Badhani
Correlation and Causality
? Correlation is not equivalent to causality.
? If two variables, x and y are correlated, it is
possible that:
– X is caused by y
– Y is caused by x
– Both x and y are caused by some other variable z.
? Causality can not be inferred from
contemporaneous correlations.
Granger Causality
? Granger Causality is based on the simple logic
that effect can not precede cause.
? If y(t) is correlated to x(t-i), y is caused by x.
? If x(t) is correlated to y(t-i), y is caused by x
Granger Causality
? We may have following situations:
– No causality between x and y.
– One way causality
– Two-way causality or feedback causality
Granger Causality
? “ Granger causes ” does not imply that y is
the effect or the result of x .
? Granger causality measures precedence and
information content but does not by itself
indicate causality in the more common use of
the term.
Traditional Granger Causality Test
t
l
j
j
t
j
i
t
l
i
i
t x
y
y ?
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? 1
1
Procedure of Traditional Granger
Causality Test
? Estimate the model without including lagged values of variable .
Suppose the R2 from this estimate is R2
1.
? Now estimate the model including lagged values of variable .
Suppose the R2 from this estimate is R2
2.
? F-ratio for improvement in the model is worked out as follows:
? ?
)
/(
)
1
(
/
2
2
*
1
2
2
2
k
n
R
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?

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Granger Causality.ppt for MBA and BBA Students

  • 2. Correlation and Causality ? Correlation is not equivalent to causality. ? If two variables, x and y are correlated, it is possible that: – X is caused by y – Y is caused by x – Both x and y are caused by some other variable z. ? Causality can not be inferred from contemporaneous correlations.
  • 3. Granger Causality ? Granger Causality is based on the simple logic that effect can not precede cause. ? If y(t) is correlated to x(t-i), y is caused by x. ? If x(t) is correlated to y(t-i), y is caused by x
  • 4. Granger Causality ? We may have following situations: – No causality between x and y. – One way causality – Two-way causality or feedback causality
  • 5. Granger Causality ? “ Granger causes ” does not imply that y is the effect or the result of x . ? Granger causality measures precedence and information content but does not by itself indicate causality in the more common use of the term.
  • 6. Traditional Granger Causality Test t l j j t j i t l i i t x y y ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 1 t j t l j j i t l i i t y x x ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 1
  • 7. Procedure of Traditional Granger Causality Test ? Estimate the model without including lagged values of variable . Suppose the R2 from this estimate is R2 1. ? Now estimate the model including lagged values of variable . Suppose the R2 from this estimate is R2 2. ? F-ratio for improvement in the model is worked out as follows: ? ? ) /( ) 1 ( / 2 2 * 1 2 2 2 k n R k R R F ? ? ? ?