## PO vs. DAGs – Comments on Guido Imbens’ New Paper

Guido Imbens published a new working paper in which he develops a detailed comparison of the potential outcomes framework (PO) and directed acyclic graphs (DAG) for causal inference in econometrics. I really appreciate this paper, because it introduces a broader audience in economics to DAGs and highlights the complementarity of both approaches for applied econometric work. Continue reading PO vs. DAGs – Comments on Guido Imbens’ New Paper

## Why so much hate against propensity score matching?

I’ve seen several variants of this meme on Twitter recently.

This is just one example, so nothing against @HallaMartin. But his tweet got me thinking. Apparently, in the year 2019 it’s not possible anymore to convince people in an econ seminar with a propensity score matching (or any other matching on observables, for that matter). But why is that?

Here’s what I think. The typical matching setup looks somewhat like this:

You’re interested in estimating the causal effect of X on Y. But in order to do so, you will need to adjust for the confounders W, otherwise you’ll end up with biased results. If you’re able to measure W, this adjustment can be done in a propensity score matching, which is actually an efficient way of dealing with a large set of covariates.

The problem though is to be sure that you’ve adjusted for all possible confounding factors. How can you be certain that there are no unobserved variables left that affect both X and Y? Because if the picture looks like the one below (where the unobserved confounders are depicted by the dashed bidirected arc), matching will only give you biased estimates of the causal effect you’re after.

Presumably, the Twitter meme is alluding to exactly this problem. And I agree that it’s hard to make the claim that you’ve accounted for all confounding influence factors in a matching. But how’s that with economists’ most preferred alternative—the instrumental variable (IV) estimator? Here the setup looks like this:

Now, unobserved confounders between X and Y are allowed, as long as you’re able to find an instruments Z that affects X, but which doesn’t affect Y directly (other than through X). In that case, creates exogenous variation in X that can be leveraged to estimate X‘s causal effect. (Because of the exogonous variation in X induced by Z, we also call this IV setup a surrogate experiment, by the way.)

Great, so we have found a way forward if we’re not 100% sure that we’ve accounted for all unobserved confounders. Instead of a propensity score matching, we can simply resort to an IV estimator.

But if you think about this a bit more, you’ll realize that we face a very similar situation here. The whole IV strategy breaks down if there are unobserved confounders between Z and Y (see again the dashed arc below). How can we be sure to rule out all influence factors that jointly affect the instrument and the outcome? It’s the same problem all over again.

So in that sense, matching and IV are not very different. In both cases we need to carefully justify our identifying assumptions based on the domain knowledge we have. Whether ruling out $Z \dashleftarrow\dashrightarrow Y$ is more plausible than $X \dashleftarrow\dashrightarrow Y$ depends on the specific context under study. But on theoretical grounds, there’s no difference in strength or quality between the two assumptions. So I don’t really get why—as a rule—economists shouldn’t trust a propensity score matching, but an IV approach is fine.

Now you might say that this is just Twitter babble. But my impression is that most economists nowadays would be indeed very suspicious towards “selection on observables”-types of identification strategies.* Even though there’s nothing inherently implausible about them.

In my view, the opaqueness of the potential outcome (PO) framework is partly to blame for this. Let me explain. In PO you’re starting point is to assume uncofoundedness of the treatment variable

$(Y^1, Y^0) \perp X | W$.

This assumption requires that the treatment X needs to be independent of the potential outcomes of Y, when controlling for a vector of covariates W (as in the first picture above). But what is this magic vector W that can make all your causal effect estimation dreams come true? Nobody will tell you.

And if the context you’re studying is a bit more complicated than in the graphs I’ve showed you—with several causally conected variables in a model—it’ becomes very complex to even properly think this through. So in the end, deciding whether unconfoundedness holds becomes more of guessing game.

My hunch is that after having seen too many failed attempts of dealing with this sort of complexity, people have developed a general mistrust against unconfoundedness and strong exogeneity type assumptions. But we still don’t want to give up on causal inference altogether. So we move over to the next best thing: IV, RDD, Diff-in-Diff, you name it.

It’s not that these methods have weaker requirements. They all rely on untestable assumptions about unobservables. But maybe they seem more credible because you’ve jumped through more hoops with them?

I don’t know. And I don’t want to get too much into kitchen sink psychology here. I just know that the PO framework makes it incredibly hard to justify crucial identification assumptions, because it’s so much of a black box. And I think there are better alternatives out there, based on the causal graphs I used in this post (see also here). Who knows, maybe by adopting them we might one day be able to appreciate a well carried out propensity score matching again.

* Interestingly though, this only seems to be the case for reduced-form analyses. Structural folks mostly get away with controlling for observables; presumably because structural models make causal assumptions much more explicit than the potential outcome framework.

## Sample Selection Vs. Selection Into Treatment

This is an issue that bothered me for quite some time. So I finally decided to settle it with a blog post. I see people constantly confusing the two most common threats to causal inference—sample selection and endogeneity. This happens, for example, quite often in management research, where it is common to recommend a sample selection model in order to deal with endogenous treatments. But the two concepts are far from being equivalent. Have a look at the following graph, which describes a typical case of endogeneity. Continue reading Sample Selection Vs. Selection Into Treatment

## Why you shouldn’t control for post-treatment variables in your regression

This is a slight variation of a theme, I was already blogging about some time ago. But I recently had a discussion with a colleague and thought it would be worthwhile to share my notes here. So what might go wrong if you control for post-treatment variables in your statistical model? Continue reading Why you shouldn’t control for post-treatment variables in your regression

## Econometrics and the “not invented here” syndrome: suggestive evidence from the causal graph literature

[This post requires some knowledge of directed acyclic graphs (DAG) and causal inference. Providing an introduction to the topic goes beyond the scope of this blog though. But you can have a look at a recent paper of mine in which I describe this method in more detail.]

Graphical models of causation, most notably associated with the name of computer scientist Judea Pearl, received a lot of pushback from the grandees of econometrics. Heckman had his famous debate with Pearl, arguing that economics looks back on its own tradition of causal inference, going back to Haavelmo, and that we don’t need DAGs. Continue reading Econometrics and the “not invented here” syndrome: suggestive evidence from the causal graph literature

## Why Tobit models are overused

In my field of research we’re often running regressions with innovation expenditures or sales with new products aon the left-hand side. Usually we observe many zeros for these variables because firms do not invest at all in R&D and therefore also do not come up with new products. Many researchers then feel inclined to use Tobit models. But frankly, I never understood why. Continue reading Why Tobit models are overused

## Follow-up on “IV regressions without instruments” (technical)

Some time ago I wrote about a paper by Arthur Lewbel in the Journal of Business & Economic Statistics in which he develops a method to do two-stage least squares regressions without actually having an exclusion restrictions in the model. The approach relies on higher moment restrictions in the error matrix and works well for linear or partly linear models. Back then, I expressed concerns that the estimator does not seem to work when an endogenous regressor is binary though; at least not in the simulations I have carried out.

After a bit of email back-and-forth we were able to settle the debate now. Continue reading Follow-up on “IV regressions without instruments” (technical)

## IV regressions without instruments (technical)

Arthur Lewbel published a very interesting paper back in 2012 in the Journal of Business & Economic Statistics (ungated version here). The paper attracted quite some attention because it lays out a method to do two-stage least squares regressions (in order to identify causal effects) without the need for an outisde instrumental variable. Continue reading IV regressions without instruments (technical)

## Econometrics: When Everybody is Different

Nowadays everybody is talking about heterogeneous treatment effects. That is, response to an economic stimulus that varies across individuals in a population. However, so far the discussion was concentrated on the instrumental variable setting where a randomized (natural or administered) experiment affects the treatment status of a so-called complier population. An average of the individual treatment effects can only be estimated for this group of compliers. Instead, for the always and never-takers we cannot say anything. But if individual treatment responses are different for everybody in the population, how can we be sure that what we’re estimating for the compliers is representative for the whole population? Continue reading Econometrics: When Everybody is Different

## Successfully Mastering Econometrics

Because I’m currently sitting in the same lecture room in Strasbourg as Steve Pischke and yet another paper on labor markets is presented, I feel inspired to comment on the newest Angrist and Pischke piece on econometrics education. Furthermore, my own graduation doesn’t lie too much in the past, so I might still be part of the target group for an improved coursework in quantitative methods. Continue reading Successfully Mastering Econometrics