Let’s take the con out of randomization10 October, 2012 at 12:47 | Posted in Statistics & Econometrics, Theory of Science & Methodology | 1 Comment
Evidence-based theories and policies are highly valued nowadays. Randomization is supposed to best control for bias from unknown confounders. The received opinion is that evidence based on randomized experiments therefore is the best.
More and more economists have also lately come to advocate randomization as the principal method for ensuring being able to make valid causal inferences.
Renowned econometrician Ed Leamer has responded to these allegations, maintaning that randomization is not sufficient, and that the hopes of a better empirical and quantitative macroeconomics are to a large extent illusory. Randomization – just as econometrics – promises more than it can deliver, basically because it requires assumptions that in practice are not possible to maintain:
We economists trudge relentlessly toward Asymptopia, where data are unlimited and estimates are consistent, where the laws of large numbers apply perfectly andwhere the full intricacies of the economy are completely revealed. But it’s a frustrating journey, since, no matter how far we travel, Asymptopia remains infinitely far away. Worst of all, when we feel pumped up with our progress, a tectonic shift can occur, like the Panic of 2008, making it seem as though our long journey has left us disappointingly close to the State of Complete Ignorance whence we began.
The pointlessness of much of our daily activity makes us receptive when the Priests of our tribe ring the bells and announce a shortened path to Asymptopia … We may listen, but we don’t hear, when the Priests warn that the new direction is only for those with Faith, those with complete belief in the Assumptions of the Path. It often takes years down the Path, but sooner or later, someone articulates the concerns that gnaw away in each of us and asks if the Assumptions are valid … Small seeds of doubt in each of us inevitably turn to despair and we abandon that direction and seek another …
Ignorance is a formidable foe, and to have hope of even modest victories, we economists need to use every resource and every weapon we can muster, including thought experiments (theory), and the analysis of data from nonexperiments, accidental experiments, and designed experiments. We should be celebrating the small genuine victories of the economists who use their tools most effectively, and we should dial back our adoration of those who can carry the biggest and brightest and least-understood weapons. We would benefit from some serious humility, and from burning our “Mission Accomplished” banners. It’s never gonna happen.
Part of the problem is that we data analysts want it all automated. We want an answer at the push of a button on a keyboard … Faced with the choice between thinking long and hard verus pushing the button, the single button is winning by a very large margin.
Let’s not add a “randomization” button to our intellectual keyboards, to be pushed without hard reflection and thought.
Especially when it comes to questions of causality, randomization is nowadays considered some kind of “gold standard”. Everything has to be evidence-based, and the evidence has to come from randomized experiments.
But just as econometrics, randomization is basically a deductive method. Given the assumptions (such as manipulability, transitivity, Reichenbach probability principles, separability, additivity, linearity etc) these methods deliver deductive inferences. The problem, of course, is that we will never completely know when the assumptions are right. [And although randomization may contribute to controlling for confounding, it does not guarantee it, since genuine ramdomness presupposes infinite experimentation and we know all real experimentation is finite. And even if randomization may help to establish average causal effects, it says nothing of individual effects unless homogeneity is added to the list of assumptions.] Real target systems are seldom epistemically isomorphic to our axiomatic-deductive models/systems, and even if they were, we still have to argue for the external validity of the conclusions reached from within these epistemically convenient models/systems. Causal evidence generated by randomization procedures may be valid in “closed” models, but what we usually are interested in, is causal evidence in the real target system we happen to live in.
When does a conclusion established in population X hold for target population Y? Only under very restrictive conditions!
Science philosopher Nancy Cartwright has succinctly summarized the value of randomization. In The Lancet 23/4 2011 she states:
But recall the logic of randomized control trials … They are ideal for supporting ‘it-works-somewhere’ claims. But they are in no way ideal for other purposes; in particular they provide no better bases for extrapolating or generalising than knowledge that the treatmet caused the outcome in any other individuals in any other circumstances … And where no capacity claims obtain, there is seldom warrant for assuming that a treatment that works somewhere will work anywhere else. (The exception is where there is warrant to believe that the study population is a representative sample of the target population – and cases like this are hard to come by.)
And in BioSocieties 2/2007:
We experiment on a population of individuals each of whom we take to be described (or ‘governed’) by the same fixed causal structure (albeit unknown) and fixed probability measure (albeit unknown). Our deductive conclusions depend on that cvery causal structure and probability. How do we know what individuals beyond those in our experiment this applies to? … The [randomized experiment], with its vaunted rigor, takes us only a very small part of the way we need to go for practical knowledge. This is what disposes me to warn about the vanity of rigor in [randomized experiments].
Ideally controlled experiments (still the benchmark even for natural and quasi experiments) tell us with certainty what causes what effects – but only given the right “closures”. Making appropriate extrapolations from (ideal, accidental, natural or quasi) experiments to different settings, populations or target systems, is not easy. “It works there” is no evidence for “it will work here”. Causes deduced in an experimental setting still have to show that they come with an export-warrant to the target population/system. The causal background assumptions made have to be justified, and without licenses to export, the value of “rigorous” and “precise” methods is despairingly small.
Here I think Leamer’s “button” metaphor is appropriate. Many advocates of randomization want to have deductively automated answers to fundamental causal questions. But to apply “thin” methods we have to have “thick” background knowledge of what’s going on in the real world, and not in (ideally controlled) experiments. Conclusions can only be as certain as their premises -and that also goes for methods based on randomization.