their quadratic adjustment cost model, and find evidence that γ in equation (2) is positive when it
should be zero.
Here CW fail to identify the real reason behind their finding, which is the very low serial
correlation assumed in their driving processes.
In our derivations we assumed that the driving forces follow a random walk. As mentioned in
the Introduction, in this case the static gap is equal to the frictionless gap plus a constant. It is well
known within the (S, s) literature that if the random walk assumption is relaxed, the static gap no
longer is a sufficient statistic for the probability of adjustment, so that the difference between static
and frictionless gap now depends on the state. The first step in CW is to rediscover this result.10
They then drop the serial correlation of the driving forces from one to around 0.28 (we report
all serial correlation coefficients at annualized rates) and go on to generate microeconomic data
with a quadratic adjustment cost model. It is only then that they find, under some circumstances,
results qualitatively similar to ours. But this is neither new (we already knew that for very large
departures from the random walk assumption static and frictionless gaps could not be exchanged)
nor quantitatively comparable to our findings.
Paradoxically, the findings in CW are encouraging for the gap approach, since it is only when
the serial correlation is dropped to very low levels that things start breaking down. In fact, for
the values of serial correlation used in CW (2001), which are already low,11 there would be no
significant false positive finding.
Table 2 reports the gains in R2 that we found in CE from adding a hazard term increasing in
the (absolute) gap, versus those that would be obtained from doing the CW exercise with different
degrees of serial correlation in the driving processes.12 Clearly, there is no risk of false positives
(i.e., of finding an increasing hazard when there is none) if serial correlation is not too far from the
assumed random walk. CW had to stretch things a lot to find parameters similar to ours, and even
then the gain in fit was less than half of the gain we found.
10Although they fail to highlight the connection between their sharp departure from the random walk assumption and
the difference between both gap measures. Also, beginning in their abstract, they mislead their readers by repeatedly
claiming that our approach assumes that the optimal policy depends on the gap. In the final sentence of Section II (in
CW, 2003) they finally acknowledge that the “gap approach” can be derived from optimizing behavior when shocks
follow a random walk, yet credit a previous version of their comment for this well known result (see, for example,
Nickell, 1985).
11The annualized serial correlation they use in CW (2001) is close to 0.50. The serial correlation in the actual
driving force we used in Caballero and Engel (1993) is above 0.80. Also note that the standard value used to calibrate
RBC models (see, e.g., Cooley and Prescott, 1995) is 0.81.
12We replicate CW’s procedure and use 1000 observations as they did. We also add i.i.d. normal noise to the
aggregate shock in order to calibrate the R2 of the constant-hazard / quadratic adjustment cost model to match the R2
in CE for this model (0.75).