Home > Uncategorized > Simpson’s paradox, Trump voters and the limits of econometrics

Simpson’s paradox, Trump voters and the limits of econometrics

from Lars Syll


From a more theoretical perspective, Simpson’s paradox importantly shows that causality can never be reduced to a question of statistics or probabilities, unless you are — miraculously — able to keep constant all other factors that influence the probability of the outcome studied.

To understand causality we always have to relate it to a specific causal structure. Statistical correlations are never enough. No structure, no causality.  

Simpson’s paradox is an interesting paradox in itself, but it can also highlight a deficiency in the traditional econometric approach towards causality. Say you have 1000 observations on men and an equal amount of  observations on women applying for admission to university studies, and that 70% of men are admitted, but only 30% of women. Running a logistic regression to find out the odds ratios (and probabilities) for men and women on admission, females seem to be in a less favourable position (‘discriminated’ against) compared to males (male odds are 2.33, female odds are 0.43, giving an odds ratio of 5.44). But once we find out that males and females apply to different departments we may well get a Simpson’s paradox result where males turn out to be ‘discriminated’ against (say 800 male apply for economics studies (680 admitted) and 200 for physics studies (20 admitted), and 100 female apply for economics studies (90 admitted) and 900 for physics studies (210 admitted) — giving odds ratios of 0.62 and 0.37).

Econometric patterns should never be seen as anything else than possible clues to follow. From a critical realist perspective it is obvious that behind observable data there are real structures and mechanisms operating, things that are  — if we really want to understand, explain and (possibly) predict things in the real world — more important to get hold of than to simply correlate and regress observable variables.

Math cannot establish the truth value of a fact. Never has. Never will.

Paul Romer

  1. February 28, 2017 at 1:15 pm

    There are so many concepts like simpson’s paradox —some called paradoxes (conjunction paradox or fallacy) ,illusions (of randomness) , fallacies (ecological fallacy—looks similar to the one above.). Many are named for people (Allais, Linda, etc.) which makes them hard to remember (like equations.named for people). I think this may be why they persist. You can’t see the forest for the trees, or the logic hidden in words.

    Regarding causality and discrimination, one could also look to find clues about what may cause causes males and females to apply to different positions. Neither math, words or arguments and reasons can establish the truth, value, or truth value of a fact, theorem, data, etc. If you look in a pool of rain or mirror you may not know what you are seeing or how to interpret it. It may be just a random collection of photons (‘black body radiation’).

    when i was taking math and physics, it was almost all white, straight males; that is changing. I read alot of econ papers, but the demographic was mostly the same (elinor ostrom i think got the first ‘econ noble’ given to a women. .
    I later learned there were quite alot of non-white, straight people in academic fields, but they were a small proportion so you might not see any from undergrad to grad and postdoc levels. .

  2. March 1, 2017 at 11:40 am

    A large part of my consulting work involves just such things as “Simpson’s Paradox.” Although I will never use that name or any other such statistical anomalies’ names with clients. For example, I work with companies to help them improve their planning and resource management. Companies focus a great deal on planning and resource planning reports. These reports are full of graphs and statistical tables. I tell the companies they can include in reports only those tables and graphs for which they have a story. Most find this requirement difficult to meet. Two things are in play here. The report writers are schooled (both in colleges and as part of their on-the-job sector training) that the graphs and tables, the numbers are firm, absolute, and present the world and events as the really are. How can they tell the story of the obviously real? It’s just reality. Second, most of these planners are mathematicians, engineers, and economists. Numbers are their job. Not stories. Then, I ask them what alternative stories they could present in their graphs and tables? This is even more difficult for them. They often resist telling “unreal” stories.

    Stories are never part of their jobs in the company. The CEO might tell stories. But he’s a politician, not really a planner. It’s my background in mathematics combined with history and anthropology that allows me to help them overcome these limitations. Limitations that are unfortunately built into the current educational and business/commerce arrangements.

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