I have 4 time series, $y, x_1, x_2$ and $x_3$, and I'm running the following reduced form VAR:

$ \Delta y_{t} = A_1 \,x_{1,\,t-1} + A_2 \,x_{2,\,t-1} + A_3 \,x_{3,\,t-1} + \varepsilon_t$

Is there any chance the regression estimates may suffer from reverse causality? My guess would be no, since it's unlikely that the future can affect the past, right?

  • 1
    $\begingroup$ Staying outside the realm of exotic physics, it's safe to assume that the future doesn't cause the past. But, common causes and spurious correlations are still possible, of course. So, non-zero coefficients wouldn't imply that $x_{t}$ causes $y_{t+1}$. $\endgroup$
    – user20160
    Commented Aug 31, 2018 at 21:15

1 Answer 1


If people have accurate expectations about the future, then that can certainly happen.

For example, if I know that I am going to go on vacation and eat out a lot at time $t$ (so $y_t$ is restaurant expenditure, so $(y_t - y_{t-1})>0$), my expenditures on wine, meat, and cheese at $t-1$ may reflect that ($x_{1,t-1},x_{2,t-1},x_{3,t-1}$ would be lower). That does not mean that lowered grocery expenditures cause the restaurant expenditure.

  • $\begingroup$ What if x_1, x_2 and x_3 are the volumes at time t-1 of a particular stock that is traded in three different exchanges, and y is the price of that stock in one of the three exchanges? Can the A coefficients be regarded as price impacts? Is this model any similar to the Kyle (1985) model? $\endgroup$
    – Mary
    Commented Sep 1, 2018 at 9:33
  • $\begingroup$ I am not a finance person, so I can't really say, and I have not even glanced at this paper. I expect all the coefficients to be one, so that would not be a a very interesting impact to interpret. $\endgroup$
    – dimitriy
    Commented Sep 1, 2018 at 16:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.