**Unformatted text preview: **εi ,t
Revenue i ,t −2
Revenue i ,t −2 Decrease Dummyi ,t takes a value of 1 when revenue of ﬁrm i for period t is less than that in the
preceding period.
Coefﬁcient Estimates
(t -statistics)
Model (I)
One-Year
Periods ˆ
β1
ˆ
β2
ˆ
β3 Model (I)
Two-Year
Periods Model (I)
Three-Year
Periods Model (I)
Four-Year
Periods 0.0481
(39.88)
0.5459
(164.11)
−0.1914
(−26.14) ˆ
β0 Model (II)
One-Year
Periods
0.0333
(25.90)
0.5328
(130.43)
−0.1876
(−23.47)
0.1038
(29.79)
0.1042
(13.23)
0.3893
56,420 0.0574
(25.12)
0.6816
(141.91)
−0.1569
(−13.40) 0.0603
(16.31)
0.7148
(104.71)
−0.0919
(−5.56) 0.0783
(16.67)
0.7427
(97.00)
−0.0343
(−1.76) 0.5349
26,052 0.5933
12,398 0.6513
8,565 ˆ
β4
Adjusted R2
Number of
observations 0.3663
63,958 without the interaction variable for revenue decreasing periods. The coefﬁˆ
cient β 1 estimated for this limited model is 0.4909, representing the variation
of SG&A costs with revenue changes that would be measured if no allowance
were made for asymmetry in the change in costs with revenue increases and
revenue decreases. 3.3 LAGGED EFFECTS AND AGGREGATION OF PERIODS To test hypothesis 2a—that stickiness is reversed in subsequent periods—
we extended model (I) by including terms for one-period lagged changes
to sales revenue. M. C. ANDERSON, R. D. BANKER, AND S. N. JANAKIRAMAN 56 Model (II):
log SG&Ai,t
SG&Ai,t −1 = β0 + β1 log
∗ log Revenue i,t
+ β2 Decrease D ummy i,t
Revenue i,t −1 Revenue i,t
Revenue i,t −1
+ β3 log
Revenue i,t −1
Revenue i,t −2 + β4 Decrease D ummy i,t −1 ∗ log Revenue i,t −1
+ εi,t .
Revenue i,t −2 Results of estimating this empirical speciﬁcation are presented alongside the
ˆ
results for model (I) in table 2. The signiﬁcant and positive coefﬁcient β 1 of
0.5328 (t -statistic = 130.43) is similar to its counterpart in the model (I)
ˆ
estimation (table 2), as is the signiﬁcant and negative coefﬁcient β 2 of
−0.1876 (t -statistic = −23.47), supporting contemporaneous stickiness. The
ˆ
signiﬁcant and positive coefﬁcient β 3 of 0.1038 (t -statistic = 29.79) indicates
a lagged adjustment to SG&A for changes in sales revenue. The estimated
ˆ
coefﬁcient β 4 of 0.1042 is also signiﬁcant and positive (t -statistic = 13.23),
indicating a partial reversal of stickiness in the period after a revenue deˆ
ˆ
cline (β 4 < |β 2 |, t -statistic = 9.09). These results support the hypothesis that
managers delay decisions to make reductions to committed resources.
The remaining columns in table 2 present the results of estimating
model (I) for two-, three-, and four-year aggregation periods (changes in
SG&A costs and sales revenue are deﬁned for adjacent two-, three-, and
ˆ
four-year periods). These results show that β 2 decreases as the aggregation
ˆ2 for each pair of aggregation periods
period increases (test of equality of β
is rejected at the 5% signiﬁcance level), indicating that stickiness di...

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