The envelope math everyone remembers · ↗ voxdev.org

Economist Benjamin Moll and Oliver Hanney have an interesting post on VoxDev about a methodological issue in economics they dub the “missing intercept” problem.

Let’s say you have a study comparing places that were more or less affected by some economic shock or policy, like increased trade exposure or government spending, on some outcome. You try very hard to set up your study design and statistical analysis to isolate the causal effect of the exposure. This is the microeconomic part of the analysis.

Then you take that carefully estimated coefficient, multiply it by the national change in exposure, and report how much of some economy-wide change the shock caused. This is an attempt at translating the microeconomic analysis to a macroeconomic estimate.

The problem, the piece explains, is that the first part of the analysis identifies differences between places; it doesn’t necessarily tell you what happens when the whole country is exposed at once. This is because the economy-wide effects are absorbed into the intercept in the first analysis: they are constant across places in the cross-sectional comparison.

They cite as a prominent example the claim from a 2013 paper that “import competition explains one-quarter of the contemporaneous aggregate decline in US manufacturing employment.” The authors estimated the regional effect of increased Chinese import competition, then multiplied that coefficient by the national increase in Chinese import penetration.

So while the causal estimate gets an elaborate identification strategy, the nationwide number gets back-of-the-envelope math.

And it’s the envelope math that everyone remembers.