In section IV we show that Claim 3 has nothing to do with lumpy vs. non-lumpy microeoco-
nomic adjustment. Their finding comes from relaxing to an extreme the maintained assumption of
our analysis that the driving forces are random walks.4 This result is neither new nor quantitatively
comparable to what we found with actual data.
Somewhat paradoxically, the work of CW can be used to show that our approach is robust
to departures from the random walk assumption. In fact, nothing can be found with the serial
correlation of 0.81 used in CW (2002), and (almost) nothing with the low serial correlation of 0.47
assumed in CW (2001). CW (2003) dropped it further to 0.28, and even then the gain in R2 from
adding higher moments is substantially less than half of what we found. Section V concludes.
2 Their main critique
In the main part of their critique, CW compute from their artificial data the cross-sectional moments
of static gaps and estimate an equation analogous to (1):
∆EtCW = λMt(1),CW + γMt(3),CW, (2)
where ∆ECW and M(i),CW stand for the rate of growth of aggregate employment and the ith moment
of the cross section distribution of static gaps respectively, when the underlying data are generated
with CW’s quadratic adjustment cost model.
Their main finding is that they estimate a positive and statistically significant γ, not very differ-
ent from the one we find using actual data. Cooper and Willis then argue that this is evidence that a
researcher testing for aggregate nonlinearities on their data would conclude, erroneously, that these
are important for aggregate dynamics. It follows, they argue, that our methodology is flawed and
our results may well be due to misspecification error.
However, finding similar values of γ does not mean that a researcher will conclude that the
nonlinear term is equally important for aggregate dynamics in the two cases. For this, one needs
to also look at whether the regressor that is multiplied by γ has similar variability in the two
cases. It turns out that it does not: The variability of M(3) in CW’s quadratic adjustment model is
much smaller than that of the corresponding moment when micro-adjustments are lumpy. Thus,
4In our derivations, and as is standard in much of the (S, s)-literature, we assumed that the driving forces follow a
random walk, an assumption that cannot be easily rejected in the data. In this case, one can show that the static gap (the
difference between current employment and the optimal level of employment if there are no adjustment costs) is equal
to the frictionless gap (the difference between current employment and the optimal level of employment if adjustment
costs are removed only today) plus a constant that depends on the drift. This is a very useful result since the static gap
is straightforward to calculate while its frictionless counterpart involves more complex dynamic calculations.