Nelson Goodman’s concept of “cotenability” is a somewhat convoluted way of saying, among other things, that A cannot be a valid counterfactual for B if B’s treatment somehow affects A. Nonetheless, much of historical economics rests on the unrealistic assumption that treatment effects can be contained.
The stable unit treatment value assumption (SUTVA) is a symptom of this problem. As formalized by Donald B. Rubin, one of its conditions is that the treated and control groups must not interfere with each other. Scott Cunningham explains in his book Causal Inference: The Mixtape (2021):
Rubin argues that there are a bundle of assumptions behind this kind of calculation, and he calls these assumptions the stable unit treatment value assumption, or SUTVA for short. That’s a mouthful, but here’s what it means: our potential outcomes framework places limits on us for calculating treatment effects. When those limits do not credibly hold in the data, we have to come up with a new solution. And those limitations are that each unit receives the same sized dose, no spillovers (“externalities”) to other units’ potential outcomes when a unit is exposed to some treatment, and no general equilibrium effects.
First, this implies that the treatment is received in homogeneous doses to all units. It’s easy to imagine violations of this, though—for instance, if some doctors are better surgeons than others. In which case, we just need to be careful what we are and are not defining as the treatment.
Second, this implies that there are no externalities, because by definition, an externality spills over to other untreated units. In other words, if unit 1 receives the treatment, and there is some externality, then unit 2 will have a different Y⁰ value than if unit 1 had not received the treatment. We are assuming away this kind of spillover. When there are such spillovers, though, such as when we are working with social network data, we will need to use models that can explicitly account for such SUTVA violations… (pp. 140–141)
For any historian who is skeptical of historical economics, the externalities point is catnip, given that interconnectedness has been one of the discipline’s basic working principles for some time now. And for all the discipline’s other faults, this principle is sound. Nonetheless, economists have to assume that these connections are irrelevant for their regressions to be valid.
It then gets worse when Cunningham returns to a discussion of SUTVA later in the book. “Probably no other identifying assumption is given shorter shrift than SUTVA,” Cunningham notes. “Rarely is it mentioned in applied studies, let alone taken seriously” (p. 348n13).
Two prominent articles that I have previously discussed on this blog – Acemoglu, Johnson, and Robinson’s famous study “The Colonial Origins of Comparative Development” and Nunn’s analysis “The Long-Term Effects of Africa’s Slave Trades” – give some indication of why SUTVA’s long shadow may have been ignored. I believe the cotenability problem may invalidate both research designs.
