Years of data and found that the estimated coefcients

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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...
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This document was uploaded on 09/24/2013.

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