Three Strikes and You.re Out: Reply to Cooper and Willis



5 Final Remarks

The first paragraph in the conclusion of CW illustrates the flawed logic of their approach. It
concludes that “despite the overwhelming evidence that plant-level adjustment is nonlinear, the
question of whether this matters for aggregate employment dynamics remains an open issue.”
But if the goal is to show whether
clearly established microeconomic lumpiness matters at the
aggregate level, then the natural approach is to start from a model with microeconomic lumpiness
and determine whether aggregation removes all traces of micro nonlinearities, which is precisely
what our methodology is designed to do. Instead, Cooper and Willis start with simulated data that
does not resemble actual microeconomic data at all, and test whether a procedure designed to test
competing hypotheses that satisfy the microeconomic lumpiness condition provides false positives
when applied to their counterfactual data. This is twisted logic at best.

In our reply, however, we have made an effort to take their claims seriously. But there is very
little than can be rescued from the sequel of CW’s attempts. The results they claim to find are
either wrong, or irrelevant, or driven by an extraneous ingredient. Let us recap what they did and
the conclusions they should have drawn:

1. CW relax both of our maintained assumptions — that microeconomic adjustments are lumpy
and that driving forces follow a random walk — in an extreme fashion. The evidence on
lumpy microeconomic adjustment is overwhelming, even Cooper and Willis acknowledge
it at times, and our assumption of a random walk is definitely closer to reality than their
assumption of an annual first order correlation as low as 0.28.

2. Correctly interpreted, their main result implies the exact opposite of their Claim 1. When the
microeconomic gaps are observed, our methodology does not detect significant nonlinear-
ities when applied to data generated even with the major departures from our assumptions
considered by CW.

3. When the microeconomic gaps are not observed but need to be estimated from microeco-
nomic data, one should not use our identification strategy (which relies on microeconomic
lumpiness) with their data, where adjustment is know to be smooth. In any event, the pa-
rameter estimates they find with their counterfactual data are not statistically significant, in
sharp contrast with those we found with actual data.

4. Finally, when only aggregate data are available and the path of the cross-sectional distri-
bution needs to be simulated, the assumptions about the serial correlation of the driving
processes become more important. This is not new. The surprising feature of CW’s results



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