LARS P. SYLL

The dangers of randomization idolatry

How, then, can social scientists best make inferences about causal effects? One option is true experimentation … Random assignment ensures that any differences in outcomes between the groups are due either to chance error or to the causal effect … If the experiment were to be repeated over and over, the groups would not differ, on average, in the values of potential confounders. Thus, the average of the average difference of group outcomes, across these many experiments, would equal the true difference in outcomes … The key point is that randomization is powerful because it obviates confounding …

Thad Dunning’s book Natural Experiments in the Social Sciences (CUP 2012) is a very useful guide for economists interested in research methodology in general and natural experiments in specific. Dunning argues that since random or as-if random assignment in natural experiments obviates the need for controlling potential confounders, this kind of “simple and transparent” design-based research method is preferable to more traditional multivariate regression analysis where the controlling only comes in ex-post via statistical modelling.

The point of making a randomized experiment is often said to be that it ‘ensures’ that any correlation between a supposed cause and effect indicates a causal relation. This is believed to hold since randomization (allegedly) ensures that a supposed causal variable does not correlate with other variables that may influence the effect.

The problem with that simplistic view of randomization is that the claims made are exaggerated and sometimes even false:

• Even if you manage to do the assignment to treatment and control groups ideally random, the sample selection certainly is — except in extremely rare cases — not random. Even if we make a proper randomized assignment, if we apply the results to a biased sample, there is always the risk that the experimental findings will not apply. What works ‘there,’ does not work ‘here.’ Randomization hence does not ‘guarantee ‘ or ‘ensure’ making the right causal claim. Although randomization may help us rule out certain possible causal claims, randomization per se does not guarantee anything!

• Even if both sampling and assignment are made in an ideal random way, performing standard randomized experiments only gives you averages. The problem here is that although we may get an estimate of the ‘true’ average causal effect, this may ‘mask’ important heterogeneous effects of a causal nature. Although we get the right answer of the average causal effect being 0, those who are ‘treated’  may have causal effects equal to -100 and those ‘not treated’ may have causal effects equal to 100. Contemplating being treated or not, most people would probably be interested in knowing about this underlying heterogeneity and would not consider the average effect particularly enlightening.

• There is almost always a trade-off between bias and precision. In real-world settings, a little bias often does not overtrump greater precision. And — most importantly — in case we have a population with sizeable heterogeneity, the average treatment effect of the sample may differ substantially from the average treatment effect in the population. If so, the value of any extrapolating inferences made from trial samples to other populations is highly questionable.

• Since most real-world experiments and trials build on performing single randomization, what would happen if you kept on randomizing forever, does not help you to ‘ensure’ or ‘guarantee’ that you do not make false causal conclusions in the one particular randomized experiment you actually do perform. It is indeed difficult to see why thinking about what you know you will never do, would make you happy about what you actually do.

• And then there is also the problem that ‘Nature’ may not always supply us with the random experiments we are most interested in. If we are interested in X, why should we study Y only because design dictates that? Method should never be prioritized over substance!

Nowadays many mainstream economists maintain that ‘imaginative empirical methods’ — especially ‘as-if-random’ natural experiments and RCTs — can help us to answer questions concerning the external validity of economic models. In their view, they are, more or less, tests of ‘an underlying economic model’ and enable economists to make the right selection from the ever-expanding ‘collection of potentially applicable models.’

It is widely believed among mainstream economists that the scientific value of randomization — contrary to other methods — is more or less uncontroversial and that randomized experiments are free from bias. When looked at carefully, however, there are in fact few real reasons to share this optimism on the alleged ’experimental turn’ in economics. Strictly seen, randomization does not guarantee anything.

‘Ideally’ controlled 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. Causes deduced in an experimental setting still have to show that they come with an export warrant to the target population. The causal background assumptions made have to be justified, and without licenses to export, the value of ‘rigorous’ and ‘precise’ methods — and ‘on-average-knowledge’ — is despairingly small.

The almost religious belief with which its propagators — including ‘Nobel prize’ winners like Duflo, Banerjee and Kremer  — portray it, cannot hide the fact that RCTs cannot be taken for granted to give generalizable results. That something works somewhere is no warranty for us to believe it to work for us here or that it works generally.

Leaning on an interventionist approach often means that instead of posing interesting questions on a social level, the focus is on individuals. Instead of asking about structural socio-economic factors behind, e.g., gender or racial discrimination, the focus is on the choices individuals make.  Esther Duflo is a typical example of the dangers of this limiting approach. Duflo et consortes want to give up on ‘big ideas’ like political economy and institutional reform and instead go for solving more manageable problems ‘the way plumbers do.’ Yours truly is far from sure that is the right way to move economics forward and make it a relevant and realist science. A plumber can fix minor leaks in your system, but if the whole system is rotten, something more than good old fashion plumbing is needed. The big social and economic problems we face today are not going to be solved by plumbers performing interventions or manipulations in the form of RCTs.

The present RCT idolatry is dangerous. Believing randomization is the only way to achieve scientific validity blinds people to searching for and using other methods that in many contexts are better. Insisting on using only one tool often means using the wrong tool.

Randomization is not a panacea. It is not the best method for all questions and circumstances. Proponents of randomization make claims about its ability to deliver causal knowledge that is simply wrong. There are good reasons to be sceptical of the now popular — and ill-informed — view that randomization is the only valid and the best method on the market. It is not.

Statistical significance and effect size (student stuff)

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The shocking truth about econometric ‘precision’ and ‘rigour’

Leverage is a measure of the degree to which a single observation on the right-hand-side variable takes on extreme values and is influential in estimating the slope of the regression line. A concentration of leverage in even a few observations can make coefficients and standard errors extremely volatile and even bias robust standard errors towards zero, leading to higher rejection rates.

To illustrate this problem, Young (2019) went through a simple exercise. He collected over fifty experimental (lab and field) articles from the American Economic Association’s flagship journals: American Economic Review, American Economic Journal: Applied, and American Economic Journal: Economic Policy. He then reanalyzed these papers, using the authors’ models, by dropping one observation or cluster and reestimating the entire model, repeatedly. What he found was shocking:

“With the removal of just one observation, 35% of 0.01-significant reported results in the average paper can be rendered insignificant at that level. Conversely, 16% of 0.01-insignificant reported results can be found to be significant at that level. “

Propensity scores — bias-reduction gone awry

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Bayesian absurdities

In other words, if a decision-maker thinks something cannot be true and interprets this to mean it has zero probability, he will never be influenced by any data, which is surely absurd.

So leave a little probability for the moon being made of green cheese; it can be as small as 1 in a million, but have it there since otherwise an army of astronauts returning with samples of the said cheese will leave you unmoved.

To get the Bayesian probability calculus going you sometimes have to assume strange things — so strange that you should perhaps start wondering if maybe there is something wrong with your theory …

Added: For those interested in these questions concerning the reach and application of statistical theories, do read Sander Greenland’s insightful comment:

My take is that the quoted passage is a poster child for what’s wrong with statistical foundations for applications. Mathematics only provides contextually void templates for what might be theories if some sensible mapping can be found between the math and the application context. Just as with frequentist and all other statistical “theories”, Bayesian mathematical theory (template) works fine as a tool when the problem can be defined in a very small world of an application in which the axioms make contextual sense under the mapping and the background information is not questioned. There is no need for leaving any probability on “green cheese” if you aren’t using Bayes as a philosophy, for if green cheese is really found, the entire contextual knowledge base is undermined and all well-informed statistical analyses sink with it.

The problems often pointed out for econometrics are general ones of statistical theories, which can quickly degenerate into math gaming and are usually misrepresented as scientific theories about the world. Of course, with a professional sales job to do, statistics has encouraged such reification through use of deceptive labels like “significance”, “confidence”, “power”, “severity” etc. for what are only properties of objects in mathematical spaces (much like identifying social group dynamics with algebraic group theory or crop fields with vector field theory). Those stat-theory objects require extraordinary physical control of unit selection and experimental conditions to even begin to connect to the real-world meaning of those conventional labels. Such tight controls are often possible with inanimate materials (although even then they can cost billions of dollars to achieve, as with large particle colliders). But they are infrequently possible with humans, and I’ve never seen them approached when whole societies are the real-world target, as in macroeconomics, sociology, and social medicine. In those settings, at best our analyses only provide educated guesses about what will happen as a consequence of our decisions.