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We have really everything in common with machine learning nowadays, except, of course, language. “A much bigger problem is the tension between the difficulty of statistics and the demand for it to be simple and readily available.” After my talks at the University of North Carolina, Cindy Pang asked me a question regarding causal inference and spatial statistics: both topics are important in statistics but you don’t often see them together.

I brought up the classical example of agricultural studies, for example in which different levels of fertilizer are applied to different plots, the plots have a spatial structure (for example, laid out in rows and columns), and the fertilizers can spread through the soil to affect neighboring plots. This is known in causal inference as the spillover problem, and the way I’d recommend attacking it is to set up a parametric model for the spillover as a function of distance, which affects the level of fertilizer going to each plot, so that you could directly fit a model of the effect of the fertilizer on the outcome.

The discussion got me thinking about the way in which we use the term “causal inference” in statistics.

Consider some familiar applications of “causal inference”: – Clinical trials of drugs – Observational studies of policies – Survey experiments in psychology.

And consider some examples of problems that are not traditionally labeled as “causal” but do actually involve the estimation of effects, in the sense of predicting outcomes under different initial conditions that can be set by the experimenter: – Dosing in pharmacology – Reconstructing climate from tree rings – Item response and ideal-point models in psychometrics.

So here’s my thought: statisticians use the term “causal inference” when we’re not trying to model the process. Causal inference is for black boxes. Once we have a mechanistic model, it just feels like “modeling,” not like “causal inference.” Issues of causal identification still matter, and selection bias can still kill you, but typically once we have the model for the diffusion of fertilizer or whatever, we just fit the model, and it doesn’t seem like a causal inference problem, it’s just an inference problem. To put it another way, causal inference is all about the aggregation of individual effects into average effects, and if you have a direct model for individual effects, then you just fit it directly.

This post should have no effect in how we do any particular statistical analysis; it’s just a way to help us structure our thinking on these problems.

P.S. Just to clarify: In my view, all the examples above are causal inference problems. The point of this post is that only the first set of examples are typically labeled as “causal.” For example, I consider dosing models in pharmacology to be causal, but I don’t think this sort of problem is typically included in the “causal inference” category in the statistics or econometrics literature.