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**Unformatted text preview: **tion of
the Cross-Sectional
Distribution of
the Firm-Speciﬁc
Parameters
0.2300
0.2934 ˆ
Larcker [1987]. We report the results in table 3. The mean β 1 obtained from
ˆ
these regressions is 0.7156 (aggregate z -statistic = 139.82) and the mean β 2 is
−0.2403 (aggregate z -statistic = −14.48), supporting the sticky costs hypothesis. The z -statistics require the assumption of cross-sectional independence
¯
(i.e., r = 0). To check the validity of the cross-sectional independence assumption, we randomly selected 100 ﬁrms with complete time series of data
from our sample ﬁrms and estimated the pairwise correlation between the
regression residuals. The mean correlation is only 0.0289, indicating that
cross-sectional dependence is not a serious concern in our data.
When there is cross-sectional variation in the coefﬁcients, an alternative
and more direct approach (to aggregation of individual time-series regressions) is to estimate a single random coefﬁcients model (Green [1997,
p. 669]). We estimated a random coefﬁcients model under the assumption that the coefﬁcients β1 and β2 are normally distributed across ﬁrms. We
report the results of estimating this model for the 1,817 ﬁrms in table 3, as
ˆ
well. The mean β 1 obtained from these estimations is 0.6717 (t -statistic =
ˆ
76.36) and the mean β 2 is −0.1405 (t -statistic = −9.46), supporting the
sticky costs hypothesis. 58 3.5 M. C. ANDERSON, R . D. BANKER , AND S. N. JANAKIRAMAN OTHER ROBUSTNESS TESTS To provide assurance that the results were not systematically affected
by inﬂation, we converted all SG&A and revenue amounts to equivalent
1984 dollars and reestimated model (I) for the pooled sample with the
ˆ
inﬂation-adjusted amounts. The results, β 1 = 0.5466 (t -statistic = 160.92)
ˆ2 = −0.1721 (t -statistic = −24.18), are similar to those reported for
and β
model (I). One of the components of SG&A expense is foreign currency
translation adjustments (annual Compustat #150). Because these adjustments introduce noise into the measure of SG&A, we removed them from
the SG&A data and estimated model (I) again. Results of this estimation,
ˆ
ˆ
β 1 = 0.5983 (t -statistic = 85.81) and β 2 = −0.2077 (t -statistic = −13.84), are
also similar to those reported for the initial estimation.
It may be argued that there are two-way relations between SG&A costs
and sales revenue. Expenditures on SG&A costs, such as marketing costs,
affect sales volume whereas sales volume affects SG&A costs. To address
this potential simultaneity, we estimated a simultaneous equations model
that included changes in SG&A expenditures and sales revenue as endogenous variables. In the ﬁrst equation of this model, the change in SG&A
costs is expressed as a function of the change in sales revenue. In the second equation, the change in sales revenue is expressed as a function of the
change in SG&A costs. Lagged variables are included in both...

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