Tag Archives: Statistics & Econometrics

David Freedman — uncovering where the statistical skeletons are buried Invariance assumptions need to be made in order to draw causal conclusions from non-experimental data: parameters are invariant to interventions, and so are errors or their distributions. Exogeneity is another concern. In a real example, as opposed to a hypothetical, real questions would have to be asked about these assumptions. Why are the equations “structural,” in the sense that the...

When I present this argument … one or more scholars say, “But shouldn’t I control for everything I can in my regressions? If not, aren’t my coefficients biased due to excluded variables?” This argument is not as persuasive as it may seem initially. First of all, if what you are doing is misspecified already, then adding or excluding other variables has no tendency to make things consistently better or worse … The excluded variable argument only works if you are sure your...

RCTs in the Garden of Eden Suppose researchers come to a town and do an RCT on the town population to check whether the injection of a green chemical improves memory and has adverse side effects. Suppose it is found that it has no side effects and improves memory greatly in 95% of cases. If the study is properly done and the random draw is truly random, it is likely to be treated as an important finding and will, in all likelihood, be published in a major...

Machine learning and causal inference  [embedded content]

Econometric causality and Simpson’s paradox Which causal relationships we see depend on which model we use and its conceptual/causal articulation; which model is bestdepends on our purposes and pragmatic interests. Take the case of Simpson’s paradox, which can be described as the situation in which conditional probabilities (often related to causal relations) are opposite for subpopulations than for the whole population. Let academic salaries be higher for...

Individuals, households and firms behave so irrationally and their behaviour in groups is so little understood that it is hard to think of an economic law with any claim to universality. This is a strong statement. If the statement is true, this is unfortunate, not only for its own sake, but also because of its consequences. Let me briefly discuss one consequence of a universal law. The example is a very famous one taken from physics, a discipline where everything is easier...

How not to be wrong What is 0.999 …, really? It appears to refer to a kind of sum: .9 + + 0.09 + 0.009 + 0.0009 + … But what does that mean? That pesky ellipsis is the real problem. There can be no controversy about what it means to add up two, or three, or a hundred numbers. But infinitely many? That’s a different story. In the real world, you can never have infinitely many heaps. What’s the numerical value of an infinite sum? It doesn’t have one — until...

Keynes on the ‘devastating inconsistencies’ of econometrics In practice Prof. Tinbergen seems to be entirely indifferent whether or not his basic factors are independent of one another … But my mind goes back to the days when Mr. Yule sprang a mine under the contraptions of optimistic statisticians by his discovery of spurious correlation. In plain terms, it is evident that if what is really the same factor is appearing in several places under various...

Reading an applied econometrics paper could leave you with the impression that the economist (or any social science researcher) first formulated a theory, then built an empirical test based on the theory, then tested the theory. But in my experience what generally happens is more like the opposite: with some loose ideas in mind, the econometrician runs a lot of different regressions until they get something that looks plausible, then tries to fit it into a theory (existing or...

The results reported here suggest that an exam school education produces only scattered gains for applicants, even among students with baseline scores close to or above the mean in the target school. Because the exam school experience is associated with sharp increases in peer achievement, these results weigh against the importance of peer effects in the education production function … Of course, test scores and peer effects are only part of the exam school story. It may be...