Causalité en microéconométrie versus causalité de Granger en économétrie temporelle

Disons que vous avez deux vecteurs Alorsne pas Granger causesi, c'est-à-dire

\begin{aligned} F_{1, t} & = (y_{t}, y_{t - 1}, y_{t - 2}, . . .) \\ F_{2, t} & = (y_{t}, z_{t}, y_{t - 1}, z_{t - 1}, . . .) \end{aligned}

$\begin{align} F_{1,t} &= (y_t, y_{t-1}, y_{t-2},...) \newline F_{2,t} &= (y_t, z_t, y_{t-1}, z_{t-1},...) \end{align}$

z_{t}

$z_t$

y_{t}

$y_t$

E (y_{t} | F_{1, t - 1}) = E (y_{t} | F_{2, t - 1})

$E(y_t | F_{1,t-1}) = E(y_t | F_{2,t-1})$

z_{t}

$z_t$ ne peut pas aider à prévoir

. Ainsi , le terme Granger « causalité » est quelque peu trompeur , car si une variable

est utile dans la prévision d'une autre variable

cela ne signifie pas que

cause réellement

. Voir par exemple la discussion dans Hansen (2014) (p. 319).

y_{t}

$y_t$

A

$A$

B

$B$

A

$A$

B

$B$

Par exemple, le matin juste avant le lever du soleil, le coq chantera. Si vous exécutez un test de causalité de Granger sur une série de corbeaux de coq et que le soleil se lève, vous constaterez que le corbeau du coq fait lever le soleil. Mais cela ne peut pas vraiment être vraiment une relation causale. La raison pour laquelle j'ai qualifié cet exemple de "stupide" est fournie dans le commentaire soigné de Hao Ye. L'exemple est utile pour illustrer pourquoi un événement peut que Granger en provoque un autre mais pas réellement le provoquer dans le sens où les microéconométriciens comprennent la causalité.

La causalité en microéconométrie est principalement basée sur le cadre de résultats potentiels de Donald Rubin (voir Angrist, Imbens et Rubin (1996) ). D'après la question, il semble que vous ayez lu Mostly Harmless Econometrics, donc je suppose que vous connaissez le type d'effets causals estimés par les différentes méthodes comme IV, différence dans les différences, appariement ou régression. Quoi qu'il en soit, il n'y a pas de lien direct entre ces méthodes microéconométriques d'estimation des effets causals et la causalité de Granger pour le simple fait que la causalité de Granger n'est pas vraiment une causalité.

Dans les applications récentes de la différence dans les différences (DiD), l'idée de causalité de Granger est utilisée pour évaluer s'il existe des effets anticipés ou décalés du traitement. Pour le modèle DiD habituel que vous pouvez trouver dans Mostly Harmless Econometrics (chapitre 5, p. 237): où dans cet exemple les indices , et sont pour les restaurants, les états et le temps, alors que

Y_{i s t} = γ_{s} + λ_{t} + β D_{s, t} + X_{i s t}^{'} π + ϵ_{i s t}

$Y_{ist} = \gamma_s + \lambda_t + \beta D_{s,t} + X'_{ist}\pi + \epsilon_{ist}$

i

$i$

s

$s$

t

$t$

D_{s t}

$D_{st}$

D_{s t}

$D_{st}$

D_{s t}

$D_{st}$

D_{s t}

$D_{st}$

K

$K$

M

$M$

Y_{i s t} = γ_{s} + λ_{t} + \sum_{m = 0}^{M} β_{- m} D_{s, t - m} + \sum_{k = 1}^{K} β_{+ k} D_{s, t + k} + X_{i s t}^{'} π + ϵ_{i s t}

$Y_{ist} = \gamma_s + \lambda_t + \sum^{M}_{m=0}\beta_{-m} D_{s,t-m} + \sum^{K}_{k=1}\beta_{+k} D_{s,t+k} + X'_{ist}\pi + \epsilon_{ist}$ 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.

Andy
la source

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.

Hao Ye

@Andy: Thank you for the excellent explanation (and excellent references). I will wait for other answers before marking your answer as accepted.

user227710

@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.

Andy

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)

Metrics

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.

Andy

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.

coffeinjunky
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Causalité en microéconométrie versus causalité de Granger en économétrie temporelle

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