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I understand the causality as used in microeconomics (in particular IV or regression discontinuity design) and also the Granger causality as used in time-series econometrics. How do I relate one with the another? For example, I have seen both approach being used for panel data (say $N=30$, $T=20$). Any reference to the papers in this regard would be appreciated.

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  • $\begingroup$ Specifically for panel data, there is an extension of the Granger (non-)causality test by Dumitrescu/Hurlin (2012): Testing for Granger Non-causality in Heterogeneous Panels, Economic Modelling, 2012, vol. 29, issue 4, 1450-1460 . $\endgroup$ – Helix123 May 10 at 15:14
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Say you have two vectors $$ \begin{align} F_{1,t} &= (y_t, y_{t-1}, y_{t-2},...) \newline F_{2,t} &= (y_t, z_t, y_{t-1}, z_{t-1},...) \end{align} $$ Then $z_t$ does not Granger cause $y_t$ if $E(y_t | F_{1,t-1}) = E(y_t | F_{2,t-1})$, i.e. $z_t$ cannot help to forecast $y_t$. So the term Granger "causality" is somewhat misleading because if a variable $A$ is useful in forecasting another variable $B$ this does not imply that $A$ actually causes $B$. See for instance the discussion in Hansen (2014) (p. 319).

As a stupid example, in the morning just before the sun rises the rooster will crow. If you run a Granger causality test on a series of rooster crows and sun rises, you will find that the rooster's crow causes the sun to rise. But then this can't really be truly a causal relationship. The reason I labeled this example as "stupid" is provided in the neat comment by Hao Ye. The example is useful to illustrate why an event may Granger cause another but not actually cause it in the sense that microeconometricians understand causation.

Causality in microeconometrics is mainly based on the potential outcomes framework by Donald Rubin (see Angrist, Imbens and Rubin (1996)). From the question it seems that you have read Mostly Harmless Econometrics, so I assume you are familiar with what kind of causal effects the different methods like IV, difference-in-differences, matching, or regression discontinuity designs estimate. Either way, there is no direct link between these microeconometric methods of estimating causal effects and Granger causality for the simple fact that Granger causality is not really causality.

In recent applications of difference-in-differences (DiD) the idea of Granger causality is used in assessing whether there are anticipatory or lagged effects of the treatment. For the usual DiD model that you can find in Mostly Harmless Econometrics (chapter 5, p. 237): $$Y_{ist} = \gamma_s + \lambda_t + \beta D_{s,t} + X'_{ist}\pi + \epsilon_{ist}$$ where in this example the indices $i$, $s$ and $t$ are for restaurants, states and time, whereas $D_{st}$ is a dummy equal to one for control group restaurants after the treatment. Given that $D_{st}$ changes at different times in different states, you can test whether past $D_{st}$ matter in predicting the outcome whilst future $D_{st}$ do not. The idea is that if there are anticipatory effects, the estimated treatment effect in the usual DiD setting will under-estimate the total effect. Likewise the fading out of a treatment effect over time might be interesting. You can assess this by including $K$ leads and $M$ lags which will capture anticipatory and lagged treatment effects, respectively, in the model: $$Y_{ist} = \gamma_s + \lambda_t + \sum^{M}_{m=0}\beta_{-m} D_{s,t-m} + \sum^{K}_{k=1}\beta_{+k} D_{s,t+k} + X'_{ist}\pi + \epsilon_{ist}$$ An application of this is provided in your textbook on the following pages using a study by Autor (2003) who assessed the anticipatory/lagged effects of increased employment protection on firms' use of temporary workers.

This idea picks up the argument made in coffeinjunky's answer. When we can already credibly make the point that there is a causal effect, we can use the idea of Granger causation to further explore the effect like Autor (2003) does. It cannot be used to prove it though.

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    $\begingroup$ I have to disagree with this interpretation of Granger Causality, as it seems to be narrow and not at all what Granger had in mind. In (Granger 1980), he notes that the hypothesized causal variable must have unique information about the dependent variable. In your example, sunrise can be predicted without the rooster data, and so the rooster has no unique information and is therefore not causal. Here, I see IV as a way to address how to isolate the unique information in the hypothesized causal variable. $\endgroup$ – Hao Ye Apr 25 '14 at 18:44
  • $\begingroup$ @Andy: Thank you for the excellent explanation (and excellent references). I will wait for other answers before marking your answer as accepted. $\endgroup$ – user227710 Apr 25 '14 at 19:56
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    $\begingroup$ @HaoYe thanks for your comment. Certainly there is some merit in Granger causality and the example was purposefully called "stupid" on my behalf. It is overly simplistic for the sake of making a point but I'm sure there are better examples for cases with Granger causality without a structural causal relation. @ user227710: I found one application of Granger causality in the treatment effects literature. I updated the answer accordingly. $\endgroup$ – Andy Apr 26 '14 at 11:30
  • $\begingroup$ Given T=20, I think there will be omitted variable bias because of ignoring long run information (error correction term) if the series are cointegrated. As in your example, if the treatment changes in different states and different times and if this treatment is cointegrated with the outcome, then obviously your dynamic model suffers from omitted variable bias. The question is whether the treatment, since it is a dummy variable, can be considered I(1). Alternatively,you consider treatment as an exogeneous variable in long-run and short-run eqns and obtain causal effect (long run and short-run) $\endgroup$ – Metrics Apr 26 '14 at 13:06
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    $\begingroup$ Okay, but that's like saying that OLS is suitable for causal inference if we have the right data, i.e. without endogeneity. With ideal data as you describe it, GNC works perfectly fine for this purpose. The problem is that we rarely have this kind of ideal data which is why those microeconometric methods for causal inference were developed in the first place. The definition of GNC here is the standard textbook definition and I'm talking about it as a method for causal inference with minimum assumptions on the data. $\endgroup$ – Andy Apr 29 '14 at 10:20
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I fully agree with Andy, and I was actually thinking of writing something similar, but then I started to wonder myself about this topic. I think we all agree that Granger causality itself really has not much to do with causality as understood in the potential outcomes framework, simply because Granger causality is more about time precedence than anything else. However, suppose there is a causal relationship between $X_t$ and $Y_t$ in the sense that the former causes the latter, and suppose that this happens along a temporal dimension with a lag of one period, say. That is, we can easily apply the potential outcomes framework to two time series and define causality in this way. The issue then becomes: while Granger causality has no "meaning" for causality as defined in the potential outcomes framework, does causality imply Granger causality in the time series context?

I have never seen a discussion on this, but I think if you or any researcher wants to make a case for this, you need to impose some additional structure. Clearly, the variables need to react sluggishly, i.e. the causal relationship here must not be simultaneous but defined with a lag. Then, I think, it might be reassuring to not reject Granger causality. While this is clearly no evidence in favour of a causal relationship, if you were to claim such, then I would take the GNC test as subjective evidence.

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