A Rose
In Act II, Scene II of Shakespeare’s Romeo and Juliet, Juliet says,
Lu, X., L. Su, and H. White (2017), "Granger Causality and Structural Causality in Cross-Section andPanel Data," Econometric Theory, 33, 263-291
White, H. and X. Lu (2011), "Causal Diagrams for Treatment Effect Estimation with Application to Selection of Efficient Covariates," Review of Economics and Statistics, 93, 1453-1459
“What’s in a name? That which we call a rose by any other name would smell as sweet.”
I, however, am not Shakespeare. I am a bear of very little brain. I did awful in all my humanities classes.
So, I googled exactly what the heck Juliet was talking about. It says here
"The importance of a person or thing is the way it is; not because of what it is called. Simply, it means the names of things cannot affect what they actually are. This line is, in fact, very profound, suggesting that a name is just a label to distinguish one thing from another. It neither has any worth, nor gives true meaning."
I love this explanation! It offers a perfect segue to the topic of causality. Causality is the goal of much (most?) empirical work in economics, especially in microeconomics. Yes, there is definitively a role for non-causal empirical work and I am, increasingly, sensitive to this point. But, that's not the point here.
For purposes of this discussion, let's take it as a given that we are interested in performing econometric analysis to assess a causal relationship. Well, just as a rose isn't a rose just because it is called a rose, so too a relationship isn't causal just because it is called as such. The word causal ... neither has any worth, nor gives true meaning.
This leads us to a discussion of Granger-Sims (GS) causality ... attributable to Granger (1969) and Sims (1972), as well as Chamberlain (1982) who showed that the two were really talking about the same thing. As someone who is not a big fan of GS and someone who can be a bit cynical, I think that GS has and continues to be so popular simply because it has the word "causality" in the name. As such, it is a relatively "easy" way to perform "causal" analysis. But, as Juliet tells us, a name does not change the essence of a thing. In this case, calling something causal does not make it so.
For researchers trained in the tools of modern causal inference, your knowledge of and experience with GS causality may be limited, or perhaps even nonexistent. For many, the extent of your knowledge may be to have some sense that GS causality is really about prediction and, hence, irrelevant to your world.
To a large extent this is true. But, there is a paper that -- in my opinion -- should be read by all those interested in causal analysis. Lechner (2010).
Lechner has written and continues to write many wonderful papers, but this is my favorite. Judging by its Google Scholar citation count, it has probably been overlooked. Truth be told, it may not be anything you ever cite; but, it is something I think you should read.
Beyond the specific content, the paper is a truly great example of intellectual precision. Thus, all of us can learn from it; learn how to tackle a research question, whatever that question may be.
As someone well positioned in the microeconometric world of causal inference, Lechner could simply dismiss GS causality as not "real" causal analysis, tout the microeconometric framework based on potential outcomes, and call it a day.
Instead, as Lechner puts it, he "formally analyzes the relation between the two concepts, so that their differences are clearly explicable."
To accomplish this, Lechner begins by carefully explaining the history of GS; in particular, why causality was included in its name despite not assessing what we typically characterize as causality. He then moves on to formally define GS non-causality, as well as he calls Potential Outcome (PO) non-causality. This definition is based on the usual average treatment effect (ATE) that microeconomists are very familiar with. However, Lechner goes through a lot of trouble to recast the usual PO framework in notation consistent with that used to define GS non-causality. This is a lot of (mental) work for a short paper. By going through this work for us, he can then get to his main objective. Specifically, Lechner can then provide a single theorem stating under what assumptions GS non-causality implies PO non-causality and vice versa.
This final part is fantastic! By being painstakingly precise, Lechner is not dismissive of GS as have nothing to do with causality the way microeconometricians think about it. Instead, he lays out the conditions by which GS and PO definitions of causality coincide. As I said above, I think this is a wonderful example of science. He doesn't hand-wave or gloss over an important concept such as GS. Instead, he engages with the subject, he is precise in his notation, definitions, and assumptions, and then he can be precise in his conclusions. A valuable lesson to be learned for scientists at all levels of seniority.
The paper is not particularly long, so I am not going to rehash it in detail here. But, I will give the "Twitter thread" (twead?) version of the paper.
Lechner starts by describing GS as follows:
"Their basic idea is that (non) causality is very similar to, if not the same as, (non) predictability. Therefore, they consider one variable not to cause another variable if the current value of the causing variable does not help predict future values of that variable. This statement is conditional on the information set available at each point in time."
Formally, a variable, D, does not GS cause another variable, Y, if Y is independent of the history D conditional on the history of Y (and any other variables that be deemed by the researcher to part of the information set).
In contrast, he notes that the PO framework is
"... based on the idea that the relevant comparison is between different states of the world, each of which relates to a value of the causing variable."
Formally, Lechner says that a variable, D, does not PO cause another variable, Y, if the distribution of Y is the same across the states of the nature where D takes on different values.
With this setup, the first remark that Lechner makes is that the definition of GS is in terms entirely of observed variables. In contrast, the definition of PO involves counterfactual states that can never be observed. Thus, the "definition" and the "discovery" phases, as Lechner refers to them, are necessarily distinct in PO, because the PO concept cannot be taken to the data without further assumptions enabling one to identify the missing counterfactual. To put the definition of GS into practice, we only need data. See, time series is so easy!
To compare a test of GS non-causality with PO non-causality, we must first be able to identify PO non-causality. For this, Lechner considers the weakest assumption he can, referred to as the weak dynamic conditional independence assumption (W-DCIA). This assumption implies that, in a dynamic setting, this period's realization of D is independent of potential outcomes conditional on the history of D and Y. He also needs a common support assumption. Turns out, with these assumptions GS non-causality implies PO non-causality. In other words, under these assumptions, GS comes up smelling like roses!
Absent these assumptions, GS reverts back to its true essence as a prediction exercise. While prediction may be useful in some contexts, I fear it is not useful in many papers that set forth to assess GS. I fear it is used because it is called a rose despite not being one. I fear it is used because it is "easy" in the sense that it does not require researchers to overcome the problem of the missing counterfactual, yet still allows them to use the world "causality," not because it is actually the right tool for the job.
My cynicism aside, if you are interested in assessing GS causality, like most things in time series, it can be a bit difficult to actually figure out how to proceed. For that, I highly recommend David Giles' blog post on the subject. He always could cut through the weeds to make time series understandable to me.
If you are further interested in rigorous explorations of the relationship between GS and PO, see White & Lu (2011) and Lu et al. (2017).
UPDATE (7.11.20)
Hyperlinks for references now provided, per request of Marc Bellemare.
References
Chamberlain, G. (1982), "The General Equivalence of Granger and Sims Causality," Econometrica,
50, 569-581
Granger, C.W.J. (1969), "Investigating Causal Relations by Econometric Models and Cross-Spectral
Methods," Econometrica, 37, 424-438
Lechner, M. (2010), "The Relation of Different Concepts of Causality Used in Time Series and
Microeconometrics," Econometric Reviews, 30, 109-127
Sims, C.A. (1972), "Money, Income, and Causality," American Economic Review, 62, 540-552
