*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **minishes
with the length of the aggregation period, consistent with hypothesis 2b.
We also estimated model (I) on a year-by-year basis for the 20 years of data
and found that the estimated coefﬁcients are robust over time. For the yearˆ
by-year estimations, the mean value of β 1 is 0.5261 (standard deviation =
ˆ
0.1015) and the mean value of β 2 is −0.1591 (standard deviation = 0.1589).
ˆ
The ﬁrst and third quartiles are 0.4947 and 0.5748 for β1 and −0.2727 and
ˆ
ˆ
−0.0264 for β 2 . The aggregated z -statistics of 112.07 for β 1 and −15.41 for
ˆ
β 2 support the sticky costs hypothesis. 3.4 TIME-SERIES MODELS The sticky costs hypothesis may be interpreted as a time-series hypothesis for individual ﬁrms. To test the hypothesis on a ﬁrm-by-ﬁrm basis, we
estimated individual time-series models for 2,081 ﬁrms that had at least 10
valid observations and three or more reductions in sales revenue during the
ˆ
sample period. Because the sticky costs hypothesis is conditional on β 1 > 0,
ˆ
we excluded 214 ﬁrms with negative values of β 1 . We also trimmed 50 ﬁrms
with extreme values of the coefﬁcients in their time-series regressions, leaving 1,817 ﬁrms. We aggregated the t -statistics from the ﬁrm-speciﬁc timeseries regressions, as in Dechow, Huson, and Sloan [1994] and Lambert and STICKY COSTS 57 TABLE 3
Results of Estimating Time-Series Regressions of Annual Changes in SG&A on Annual Changes in
Sales Revenue for Individual Firms from 1979 to 1998
log SG&At
SG&At −1 = β0 + β1 log Revenue t
Revenue t
+ β2 ∗ Decrease Dummyt ∗ log
+ εt
Revenue t −1
Revenue t −1 Decrease Dummyt takes the value of 1 when revenue in period t is less than revenue in t − 1,
0 otherwise. Firms are included in the analysis if they have at least 10 valid observations during
the sample period and at least 3 of those with reductions in the activity level (as measured by
sales revenue) in the current year compared with the previous year. Of the total number of
ﬁrms, 2,081 satisﬁed this criterion; 214 ﬁrms were excluded because the estimated value of
β1 from a ﬁrm-speciﬁc OLS regression was negative and 50 ﬁrms were excluded because they
had extreme values of estimated coefﬁcients (top and bottom 0.5% of the distribution of the
estimated values) in ﬁrm-speciﬁc OLS regressions. The ﬁnal sample consisted of 1,817 ﬁrms.
¯
˜
¯
˜˜
˜
In the random coefﬁcients model, β1i = β 1 + β 1ε ; β2i = β 2 + β 2ε ; β 1ε and β 2ε are distributed
bivariate normally with mean 0.
Coefﬁcient Estimates
Firm-by-Firm Estimation
Mean of the
Estimated
Firm-Speciﬁc
Parameters
(aggregated
z -statistic)
ˆ
β1
ˆ
β2 0.7156
(139.82)
−0.2403
(−14.48) Random Coefﬁcients Estimation
Standard Deviation of
the Cross-Sectional
Distribution of
the Firm-Speciﬁc
Parameters
0.3756
0.8615 Mean of the
Estimated
Firm-Speciﬁc
Parameters
(t -statistic)
0.6717
(76.36)
−0.1405
(−9.46) Standard Devia...

View
Full
Document