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I am currently trying to formulate an empirical design that works as follows. In a first step I regress a variable $y_t$ on another variable $x_{t-1}$ and controls $Z_t$: $$ y_t=\beta_1 x_{t-1}+Z_t\gamma+\varepsilon_t. $$ Then I test for Granger causality. I estimate these either in rolling window or with time-varying coefficients, so that for $t>T$ I get one coefficient per time period. I then create a vector $\xi_t$ of 1's and 0's, where a 1 means that there is Granger-causality at time $t$.

Then, in a second stage, I regress $\xi_t$ on a set of variables $W_t$: $$ \xi_t=W\delta+u_t. $$ The aim is to assess whether variation in $W_t$ can explain the Granger-causality patterns in $\xi_t$.

In addition, because I am working with firms, I can get a vector of Granger-causality dummies for each firm, $\xi_{i,t}$. Hence, I stack these vectors in a single vector and run the regression described above with time-fixed effects. The aim here is to see whether the variation in $W_t$ can explain cross-firm asymmetries in Granger-causalities.

Now, intuitively, this makes sense to me. However, I never saw this being done anywhere, which makes me suspicious about it. My questions:

  1. Does this sound plain wrong and why?
  2. Do you know of any similar methods?
Richard Hardy
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Daniel Pinto
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    Sounds fine to me. But it would be much clearer if you included equations to support your verbal description of what you are doing. I tried to do that for you. Feel free to undo or edit. – Richard Hardy Feb 04 '17 at 09:48
  • Thank you Richard. It fits perfectly. One problem I am facing in this specification is that $\xi$ is at weekly frequency whilst $W$ is at yearly frequency. One possibility would be to transform $\xi$ into yearly frequency if the number of weeks in a given year for which there is a 1 is above a certain threshold. Other approach is to just use weekly data and repeat the values of W every week in the same year. Both approaches sound sloppy. Does anyone have a suggestion here? – Daniel Pinto Feb 06 '17 at 11:38
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    Hmm, maybe use the proportion of weeks with Granger causality for a given year (e.g. 25/52 or 34/52 or the like) as the dependent variable and then all your variables are yearly. You might need to transform that proportion from $[0,1]$ to $\mathbb{R}$ to make a simple regression sensible. – Richard Hardy Feb 06 '17 at 12:17

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