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



for aggregate dynamics.3 This case can be obtained from a scenario where microeconomic adjust-
ment is lumpy and the probability of such adjustment is increasing in the gap (the increasing hazard
model of CE). There is ample microeconomic evidence for this behavior, the question is whether
it matters for aggregate adjustment. We find that it does, since our aggregate regressions show a
very significant
γ > 0 and a large contribution of γMt(3) to aggregate employment fluctuations.

CW’s critique has changed over time, but as of today, it can be split into three claims, all of them
based on applying our procedures to data generated with a model with smooth microeconomic
adjustment:

Claim 1: When our measure of microeconomic gaps are computed from their artificial data,
there exist parameter configurations for which estimates of
γ are similar to ours, even though
there is no microeconomic lumpiness or nonlinearities. This has been their main claim, and
the common denominator in CW (2001, 2002, 2003).

Claim 2: When the microeconomic gaps are not directly observed but can be estimated with
microeconomic data, the procedures used in CEH give nonsensical results when applied to
their data.

Claim 3: When only aggregate data are used, coupled with the Kolmogorov equations re-
quired to keep track of the simulated cross section distribution of gaps, as in CE, our esti-
mates can be found even when their (linear) data are used.

Not only are these claims incorrect, as we will argue below, but they also reflect a fundamental
misunderstanding of the point of our papers. We developed a methodology to study whether lumpy
microeconomic adjustment has aggregate implications, not to infer from aggregate data whether
the underlying microeconomic adjustments are lumpy.

In section II we show that due to a basic interpretation error of their own results, Claim 1 is
incorrect. In section III we argue that since the identification strategy we adopt for estimating
gaps with microeconomic data is built on the
observation that microeconomic data are lumpy, it
should not be used if microeconomic data are not lumpy. Therefore Claim 2 is not surprising.
Furthermore, the fact that CW find nonsensical results while we find meaningful and statistically
significant results, indicates that our findings do not arise when microeconomic adjustments are
smooth.

3The higher moment that matters in specification (1) is the third moment. We focus on this specification because
it is simple and shows up often both in our work and in CW’s critique. Yet there are other specifications in their and
our work that involve higher moments different from the third moment, which explains why we generically refer to
‘higher moments’.



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