3 Estimating unobserved gaps with microeconomic data
The second and third points of CW’s critique stem from the fact that in practice the gaps are not
observed and hence neither are the cross-sectional distributions of these gaps. They argue that
our procedures to estimate these gaps and moments introduce new errors which can lead to false
positives and nonsensical results. Again, Cooper and Willis are mistaken.
To explain why, we begin by making a distinction between the procedure in Caballero, Engel
and Haltiwanger (1997) (in this section) and that in Caballero and Engel (1993) (in the next sec-
tion), since Cooper and Willis’ specific critique differs between these cases (corresponding to their
claims 2 and 3, respectively).
In CEH we observe the microeconomic data but have no direct observation of the gaps. In
order to construct the microeconomic gaps, we use information on hours. The idea being that
when hours exceed certain normal level, there is a shortage of labor while the opposite is true
when hours are below normal. Still, one needs to estimate the mapping from the hours-gap to
the employment-gap, and the equation that does this suffers from classic simultaneity problems.
Our way out relies heavily on our observation that microeconomic adjustment is lumpy. In this
context, the relationship between hours and employment gaps can be estimated if one only uses
observations where large adjustments took place; the basic logic behind this procedure being that
during these episodes the variability of the regressor swamps the variability of the error term in that
regression. Yet if one knows that microeconomic data are not lumpy, as is the case with Cooper
and Willis’ data, no sensible researcher would use our procedure. Cooper and Willis make the
mistake of not understanding that the microeconomic estimation procedure in CEH is conditional
on the observation that microeconomic behavior is lumpy. Fortunately for us, the latter holds in
reality, a fact explicitly acknowledged by CW.9
4 Estimating unobserved gaps using only aggregate data
In Caballero and Engel (1993) we do not observe microeconomic data and hence generate the
cross-sectional moments from an internally consistent model. This model starts from the well es-
tablished fact that microeconomic adjustment is lumpy, and uses this information to construct the
Kolmogorov/Markov functional equation for the evolution of the cross-section distribution corre-
sponding to a given set of parameters. Cooper and Willis apply our procedure to data generated by
9“[There is] overwhelming evidence that plant level adjustment is nonlinear”, CW (2003), first paragraph in the
Conclusion.