Tag Archives: Statistics & Econometrics

Keynes’ critique of econometrics — the nodal point In my judgment, the practical usefulness of those modes of inference, here termed Universal and Statistical Induction, on the validity of which the boasted knowledge of modern science depends, can only exist—and I do not now pause to inquire again whether such an argument must be circular—if the universe of phenomena does in fact present those peculiar characteristics of atomism and limited variety which...

What inferential leverage do statistical models provide? Experimental (and non-experimental) data are often analyzed using a regression model of the form Yi =a+bZi +Wiβ+εi, where Wi is a vector of control variables for subject i, while a, b, and β are parameters (if Wi is 1×p, then β is p×1). The effect of treatment is measured by b. The disturbances εi would be assumed independent across subjects, with expectation 0 and constant variance. The Zi and Wi...

The trouble with econometrics In the process of translating a theory into implications about data, so many auxiliary assumptions are made that all contact with reality is lost. Any conflict can be resolved by adjusting the auxiliary assumptions. For example, suppose we want to learn if a production process satisfy diminishing, constant, or increasing returns to scale. The issue is of substantial significance from the point of view of theory. In carrying out...

How to save us from inferential mistakes when doing econometrics This is where statistical analysis enters. Validation comes in many different forms, of course, and much good theory testing is qualitative in character. Yet when applicable, statistical theory is our most powerful inductive tool, and in the end, successful theories have to survive quantitative evaluation if they are to be taken seriously. Moreover, statistical analysis is not confined to...

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...