Period coefcient estimates t statistics model i one

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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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