2
$\begingroup$

Let $Y_t$ be the amount of sales at time $t$ and $X_t$ be the amount of expenses in marketing activities. I want to estimate the effect of $X_t$ on $Y_t$.

However, we suppose that $X_t$ is determined by the sales in previous period, so $X_t$ depends on $Y_{t-1}$. Does this problem involve a case of simultaneity? Consider that $Y_t$ and $Y_{t-1}$ are independent. Can I use normal OLS or other methods are needed?

Specific references would be appreciated.

$\endgroup$
  • 1
    $\begingroup$ I am not an expert in this particular task, but I found this to be an interesting reading: statisticshowto.com/instrumental-variable As for me I suggest measuring the obsrved correlation between X t and Y t-1 to be sure the effect is significant to even consider it in the design. $\endgroup$ – Alexey Burnakov Oct 3 '17 at 10:53
  • 1
    $\begingroup$ It's hard to consider Y not autocorrelated. Sales data is very persistent and almost always autocorrelated. You may wont to look at differences both in Y and X, and lag dY on dX. Do you have marketing expense budget variable? You could look at the diff between expense and its budget as another predictor $\endgroup$ – Aksakal Oct 3 '17 at 11:37
  • $\begingroup$ Thank you both for your comments. @Aksakal, I know it seems unusual, but in my specific case Y is not autocorrelated (there would be a lot to write to justify this, but trust me). That's way I'm interested to know if in this specific case there is a simultaneity problem or not... $\endgroup$ – Andrea Oct 3 '17 at 12:32
  • $\begingroup$ Can you write down your equations? $\endgroup$ – Aksakal Oct 3 '17 at 12:35
  • $\begingroup$ $Sales_t$= $\alpha$ + $\beta_1$ $price_t$ + $\beta_2$ $mkt expenses_t$ + $\beta'$ $X'$ + $\epsilon_t$ where $X'$ is a vector of control variables don't change over time. On the other hand: $mkt expenses_t$=$\alpha$ + $Sales_{t-1}$ +$\beta'$ $Z'$ + $\epsilon_t$. I want to underline that this work is at a very preliminary stage..actually I'm only investigating what I can do with my dataset. $\endgroup$ – Andrea Oct 3 '17 at 12:58

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.