Access the full text.
Sign up today, get DeepDyve free for 14 days.
(1992)
Patterns of inventory management and policy: a study of four industries
H. Grünwald, L. Fortuin (1992)
Many steps towards zero inventoryEuropean Journal of Operational Research, 59
R. Obermaier, Andreas Donhauser (2009)
Disaggregate and aggregate inventory to sales ratios over time: the case of German corporations 1993–2005Logistics Research, 1
S. Rajagopalan, A. Malhotra (2000)
Have U.S. Manufacturing Inventories Really Decreased? An Empirical StudyManuf. Serv. Oper. Manag., 3
RGD Allen (1975)
Index numbers in theory and practice
A. Chikán, E. Kovacs, Zsolt Matyusz (2011)
Inventory investment and sectoral characteristics in some OECD countriesInternational Journal of Production Economics, 133
(2006)
Ohio T a b le 6 co n ti n u ed
Rachna Shah, Hojung Shin (2007)
Relationships among information technology, inventory, and profitability: An investigation of level invariance using sector level dataJournal of Operations Management, 25
WH Greene (2008)
Econometric analysis
J. Wooldridge (1999)
Introductory Econometrics: A Modern Approach
J. Durbin, G. Watson (1950)
Testing for serial correlation in least squares regression. II.Biometrika, 38 1-2
J. Durbin, G. Watson (1950)
Testing for serial correlation in least squares regression. I.Biometrika, 37 3-4
V. Gaur, M. Fisher, A. Raman (2005)
An Econometric Analysis of Inventory Turnover Performance in Retail ServicesManag. Sci., 51
J. Haan, Masaru Yamamoto (1999)
Zero inventory management: facts or fiction? Lessons from JapanInternational Journal of Production Economics, 59
Hong Chen, Murray Frank, Owen Wu (2007)
U.S. Retail and Wholesale Inventory Performance from 1981 to 2004Manuf. Serv. Oper. Manag., 9
F. Irvine (2003)
Long term trends in US inventory to sales ratiosInternational Journal of Production Economics, 81
(2008)
Econometric analysis, 6th edn. Pearson
Hong Chen, Murray Frank, Owen Wu (2005)
What Actually Happened to the Inventories of American Companies Between 1981 and 2000?Manag. Sci., 51
(1983)
Management specs for stockless production
(1954)
Trend estimation and serial correlation, cowles commission discussion paper statistics
F. Irvine (2003)
Problems with using traditional aggregate inventory to sales ratiosInternational Journal of Production Economics, 81
A. Blinder, Louis Maccini (1991)
Taking Stock: A Critical Assessment of Recent Research on InventoriesJournal of Economic Perspectives, 5
Logist. Res. (2012) 4:3–18 DOI 10.1007/s12159-012-0068-y OR IGINAL PAPER Variable versus fixed weighted aggregate inventory to sales ratios: the effect on long-term trends for Germany Robert Obermaier Andreas Donhauser Received: 5 April 2011 / Accepted: 12 January 2012 / Published online: 25 January 2012 Springer-Verlag 2012 Abstract This study is aimed at analyzing the difference ‘‘just-in-time’’ (JIT) or ‘‘zero inventory’’ arguing that of using fixed weight aggregate inventory to sales ratios inventory reflects waste and should be eliminated causing rather than ‘‘traditional’’, that is, variable weighted, productivity to rise [6, 11, 15]. From the managerial aggregated inventory to sales ratios. It shows that inter- viewpoint, it is therefore necessary to measure and control pretations of these ratios may be problematic because dif- inventory holdings both at the level of specific processes ferent aggregation methods are signaling different time and on firm level. From the viewpoint of empirical trends under certain circumstances. Analyzing the inven- research, inventory performance over time could be studied tory performance of German corporations between 1993 either on firm or on industry level. In the majority of cases, and 2005, we find that the total inventory to sales ratio firm-level data are publicly available for stock-listed cor- decreased in a statistically significant extent in the majority porations, which could be aggregated to industry level. of industry sectors during the period investigated. Con- Aggregated industry level data are also available from sidering the effects of using fixed aggregation weights on several official institutions conducting their own firm-level our results, some changes concerning significance of databases aggregating them on industry level. results occur. The additional use of fixed aggregation There are only few empirical studies analyzing inven- weights is helpful because it isolates any trends observed in tory performance over time. With respect to national the aggregated inventory to sales ratio series to fluctuations economies, there is only one country in which inventories in the underlying (sub) sectors’ inventory to sales ratio, not are sufficiently studied: the United States (US). Blinder and shifts in the composition of the aggregate. Maccini [2] state that the inventory to sales ratio of US companies’ inventories shows no decreasing trend between Keywords Inventory Inventory to sales ratios 1959 and 1986, a result ‘‘which casts serious doubt on Measurement Trends Time series analysis buffer stock theories of inventory behavior since comput- erization should have reduced the need for inventories as buffers’’ [[2], p. 79]). The result of Blinder and Maccini 1 Empirical inventory research and data aggregation [2], based on aggregate data, served as point of departure problems for a series of other studies mainly concerned with inven- tory levels, mainly in the US. Loar [14], for example, Inventory reduction is a prevalent topic in business studied a sample of 72 firms between 1970 and 1987 research and practice. Many articles and case studies have aggregating them into four manufacturing sectors (chemi- been written about firms’ needs and efforts to reduce cal, food, electronics, and pharmaceutical), where he finds inventories. Many of them refer to concepts such as significant reductions in the levels of inventory to sales ratios. Rajagopalan and Malhotra [18], using aggregate industry data published by the US Department of Com- R. Obermaier (&) A. Donhauser merce Bureau of Economic Analysis, observe in a majority Faculty of Business Administration and Economics, of the 20 manufacturing sectors analyzed decreasing raw University of Passau, Passau, Germany material and work-in-process inventories during the period e-mail: robert.obermaier@uni-passau.de 123 4 Logist. Res. (2012) 4:3–18 between 1961 and 1994. Irvine [12], also analyzing On the one hand, this study is interested on how aggregate inventory to sales ratios, published by the US inventory data could be aggregated from firm to industry Department of Commerce Bureau of Economic Analysis, level. This study is analyzing the difference in using fixed finds sharp downtrends in US manufacturing inventory to weight aggregate inventory to sales ratios rather than sales ratios since the early 1980s, which have occurred ‘‘traditional’’, that is, variable weighted, aggregated mainly in manufacturing sectors carrying durable goods on inventory to sales ratios. Difficulties arise because different all three inventory stages (raw materials, work-in-process, aggregation methods are signaling different time trends and finished goods), while nondurable goods manufacturers under certain circumstances. Hence our main research remained at nearly the same inventory level on average. question is ‘‘Which problems arise in analyzing time trends Since the mid-1980s merchant wholesalers and since 1990 of inventory to sales ratios when data are aggregated using retailers carrying durable goods have significantly reduced ‘traditional’, that is, variable weighted, aggregated inven- their inventory to sales ratios. Nondurable goods manu- tory to sales ratios compared to the use fixed weight facturers, wholesalers, and retailers show upward inventory aggregate inventory to sales ratios?’’ We will discuss the trends. After investigating the inventories of 7.433 US implications of these methods and illustrate them not only manufacturing firms, Chen et al. [3] report that while ‘‘the by artificial examples but also by applying them on real-life medians of raw materials, finished goods, and total data of inventory to sales ratios of German firms. Among inventory days drop, the means actually rise between 1981 total inventories, inventories are analyzed on each stage of and 2000’’ (p. 1021). Focusing on medians as means may the production process individually, that is, raw materials, be influenced by outliers they find a significantly decreas- work-in-process, and finished goods. ing time trend for total inventories, raw materials, and The article is organized as follows: In the following work-in-process. While work-in-process inventories section, we will present alternative methods of aggregating declined most significantly, finished goods inventories inventory ratios, for example, from firm to industry level, show nearly no trend. Chen et al. [4] continued their study and illustrate them by example. In the subsequent section, design for 1662 US wholesale and retails firms between we apply these methods on actual inventory data of a 1981 and 2004. While wholesalers increased their inven- sample of German stock-listed companies and discuss their tory turnover by about 3% per year over the period, implications in the analysis of time trends. We conclude retailers kept their inventory turns fairly constant until with recommendations, limitations, and further research 1995. After 1995, retail firms also started to improve the opportunities. inventory turnover. Analyzing panel data from quarterly financial reports of 311 US retailers, Gaur et al. [9] find downward sloping inventory turnover ratios during 2 Different aggregation methods and problem 1987–2000. This result is surprising in so far as capital illustration intensity has increased as well and is positively correlated with inventory turnover. Based on aggregate US industry Studying inventory performance on firm level, a widely level data, Shah and Shin [19] find that inventory levels used ratio is inventory to sales (IS). Let I and S denote it it trended downwards in the manufacturing sector, which the inventory and the sales, respectively, of firm i in year t, occurred rapidly during the 1990s. However, their analysis the inventory to sales ratio is: indicates that the average inventory levels have trended it upwards for both the retail and wholesale sectors. Outside IS ¼ : ð1Þ it it the US empirical inventory research is largely unexplored [5]. This is the more surprising as there is much capital tied Studying inventory performance on industry level, firm- up in inventories, costing firms (not only in recession level data have to be aggregated. The ‘‘traditional’’ times) a lot of money. For example, at the end of 2005, approach is to simply divide the sum of inventories across German businesses held more than 400 billion EUR worth firms by the sum of sales across firms. We apostrophize this of inventory. Obermaier and Donhauser [16] analyze approach as ‘‘traditional’’ as it is the common approach in inventory performance of 100 German stock-listed corpo- inventory research using aggregate data. rations. On firm level, they find that half of the firms with a In order to calculate such ‘‘traditional’’ aggregate, IS significant decrease in total inventories are based in ratios in period t for a certain industry j, inventory held in industry sectors that are especially known for their use of the industry’s firms i = 1, 2, …, n, are summed up and JIT techniques. Aggregating these firm-level data, their then divided by the sum of sales across the n firms: findings indicate that total inventory to sales ratio it vaw i¼1 decreased in a statistically significant extent in four out of IS ¼ : ð2Þ jt n it i¼1 six industry sectors during the time frame investigated. 123 Logist. Res. (2012) 4:3–18 5 This can be reformulated as: them via a numerical example (Table 1) that extends a problem description proposed by Irvine [13]. S I S I S I 1t 1t 2t 2t nt nt vaw IS ¼ P þ P þ þ P : n n n We observe four firms over four periods in our hypo- jt S S S S S S it 1t it 2t it nt i¼1 i¼1 i¼1 thetical sample. In period 1, they all achieve 100 EUR sales ð3Þ but differ in inventories ranging from 500 to 100 EUR, which implies IS ratios ranging from 5 to 1. The ‘‘tradi- By Eq. 3, it is obvious that the aggregation weight tional’’ aggregate IS ratio using variable aggregation S S of a particular firm’s IS ratio is its proportion it it i¼1 weights (vaw) can be calculated by dividing the sum of of aggregate sales in this industry. Fluctuations in these inventories by the sum of sales; hence, the aggregated IS time-variable aggregation weights may cause shifts in the ratio is 3. In period 2, we observe firm 1 doubling sales and aggregate IS ratio that are unrelated to shifts in the inventory. Hence, its IS ratio remains stable at 5. But the underlying IS ratios from year to year, which can be mis- aggregated IS ratio increases to 3.4. In period 3, we find leading in the case when changes in the variable aggrega- firm 4 doubling sales and inventories, while firm 1 falls tion weights dominate the shifts in the individual IS ratios, back to its original values. Again, the individual IS ratios which are similar to a current weighted Paasche index. do not change compared to period 1. But the aggregated IS Although Paasche index numbers have the advantage of ratio now decreases to 2.6. Although we detect no change reflecting the actual and current situation in a certain period in the underlying IS ratios on firm level in periods 2 and 3, of time, there are serious difficulties in interpreting runs of the aggregated IS ratio may fluctuates in two different Paasche index numbers because of these varying weights directions. In period 4, finally, we can see an actual over time (e.g. [1]). increasing IS ratio of firm 4. But while the other firm’s IS These interpretation problems can be resolved using a ratios remain constant; we would expect an aggregated IS Laspeyres index with fixed aggregation weights (faw) S S with respect to a certain base year s instead of is is i¼1 variable weights in Eq. 3. This aggregation calculus also Table 1 Numerical example holds for aggregating from sectors instead of firms. Hence, Firm Inventory Sales IS ratio we obtain: vaw faw faw S I S I S I fawðsÞ 1s 1t 2s 2t ns nt P P P IS ¼ þ þ þ : (period 1) (period 4) n n n jt S S S S S S is 1t is 2t is nt i¼1 i¼1 i¼1 Period 1 ð4Þ 1 500 € 100 € 55 5 Generally speaking, using fixed aggregation weights 2 400 € 100 € 44 4 assures that any trend observed in the time series of the 3 200 € 100 € 22 2 aggregated IS ratios is caused by variations in the under- 4 100 € 100 € 11 1 lying firms’ IS ratios. Hence, it is argued that runs of Total 1.200 € 400 € 3 3 2.6 Laspeyres index numbers can be better compared and Period 2 interpreted. Nevertheless, the disadvantage of this index 1 1.000 € 200 € 55 5 number is that the actual and current situation is only 2 400 € 100 € 44 4 represented for the base year period. Furthermore, the 3 200 € 100 € 22 2 researcher has to choose which base year s to use. Three 4 100 € 100 € 11 1 alternative years are regularly used in ex-post analyses: the Total 1.700 € 500 € 3.4 3 2.6 first, the middle (if the length of the period is odd-num- Period 3 bered), and the last (e.g. current) year of the time frame 1 500 € 100 € 55 5 investigated. While a time series of aggregated IS ratios 2 400 € 100 € 44 4 using the last (first) year as base year measures up to the 3 200 € 100 € 22 2 variable aggregated time series exactly in the last (first) 4 200 € 200 € 11 1 year, using the mid-year has an analogous effect and may Total 1.300 € 500 € 2.6 3 2.6 be reasonable when studying a particular historical period. Period 4 In order to better understand the use and interpretation 1 500 € 100 € 55 5 of these different aggregation methods, we will illustrate 2 400 € 100 € 44 4 3 200 € 100 € 22 2 4 300 € 200 € 1.5 1.5 1.5 Hence we add the superscript for variable aggregation weights Total 1.400 € 500 € 2.8 3.125 2.8 (vaw) to the IS ratio symbol in Eqs. 2 and 3. 123 6 Logist. Res. (2012) 4:3–18 ratio being higher compared to period 1. Nevertheless, we disaggregated data on firm level using the sample of find it decreasing to 2.8. Obermaier and Donhauser [16]. With respect to the Obviously, our example clearly illustrates that shifting research question stated above, this study is aimed at IS ratios on firm level do not necessarily lead to according analyzing the difference of using fixed weight aggregate IS shifts on an aggregate level. This would only be true if the ratios rather than ‘‘traditional’’, that is, variable weighted, mixture of sales remained stable over time. Irvine [13] aggregated IS ratios that are commonly used. Among total concludes: ‘‘Hence with the composition of sales remain- inventories, inventories are analyzed on each stage of the ing the same, movements in the aggregate IS ratio accu- production process individually, that is, raw materials, rately reflect changes in the underlying […] IS ratios. This, work-in-process, and finished goods. however, is not the case when the composition of sales The sample chosen spans the time frame from 1993 to shifts […].’’ Instead, the example given illustrates that 2005 and covers 100 firms listed at the German stock shifts in sales mixture may actually countervail shifts in IS market. The firms in the sample are assigned to the ratios on firm level leading to shifts in aggregate IS ratios Standard Industrial Classification (SIC) manufacturing in the contrarian direction. division, which includes firms engaged in the mechanical Referring to Eq. 3, we can see that a firm’s aggregation or chemical transformation of materials or substances into new products. This division is split into two groups. The weight S S increases if its sales grow at a higher it it i¼1 first group covers firms 20 B SIC B 29, which are mainly rate compared to total sales. But the effect this has on the in the food products (SIC 20), textiles (SIC 22) and aggregate IS ratio depends further on the level of a single wearing apparel (SIC 23), and chemical (SIC 28) indus- firm’s IS ratio: is it higher (lower) than average than an tries. The second group covers firms 30 B SIC B 39, increasing aggregation weight will lead an increasing including manufacturing firms mainly in industries such as (decreasing) aggregate IS ratio. This is the case in our rubber and plastics (SIC 30), stones, clay, and glass (SIC example comparing period 1 with period 2 and period 3, 32), primary metal (SIC 33), fabricated metal products respectively. In period 4, we see increasing aggregation (SIC 34), machinery (SIC 35), electronics and electrical weights and IS ratios as well for firm 4. But as the IS ratio equipment (SIC 36), transportation equipment (SIC 37), of firm 4 remains below average, the effect is more than measuring instruments (SIC 38), and miscellaneous man- absorbed. Hence, the aggregated IS ratio decreases to 2.8. ufacturing (SIC 39) industries. Accordingly, firm-level data Using fixed aggregation weights S S with is is i¼1 were aggregated on industry level according to these SIC respect to a certain base s year instead of these traditional codes on a two-digit basis. For the case that some two-digit variable weights can assure that any trend observed in the SIC code sectors in our sample contained a too small time series of the aggregated IS ratios is caused by shifts in number of firms to calculate meaningful aggregate IS the underlying firms’ IS ratios but not by shifts in aggre- ratios, we used the firms secondary industry sector gation weights. Referring back to our example, we will assignments. Thus, we could achieve that all SIC code consider two cases: the first with period 1 as base year and sectors are comprised of at least ten firms. With only a set the second with period 4 as base year. Hence, the fixed of six firms, SIC 30 is the sole exception, because it was aggregation weights are equally a quarter for each firm in impossible, to reassign the companies in a sensible way. the first case. Accordingly, we find constant aggregated IS We have furthermore merged the SIC codes 22 and 23 due ratios for the first three periods because the individual IS to their similarity. The result of our aggregation spans eight ratios are also constant. Only in period 4, where the IS ratio industry sector classes. of firm increases, this shift upwards is correctly reflected In order to better understand the degree of improvement using fixed aggregation weights. These observations also at each of the different inventory stages as well as potential hold for the second case with period 4 as base year. shifts between them, IS ratios can be analyzed separately for total inventories as well as its constituents: raw material (RM), work-in-process (WP), and finished goods (FG). 3 Discussion of the problem using German aggregate Total inventory is defined as the sum of these three inventory to sales ratios components. After illustrating the problems that might occur when See Appendix. As an indicator for relative size, each firm’s proportion of the corresponding SIC industry class sales on average is interpreting time series of aggregate IS ratios based on also reported. variable aggregation weights, we go further by applying the For example: SIC 33: 1 firm, SIC 34: 3 firms, SIC 38: 2 firms, SIC different aggregation methods on data of IS ratios of 39: 1 firm. For rearranging the Thomson Financial’s Worldscope German firms in order to analyze their implications in Global Database offers up to eight different SIC codes per firm, inventory performance over time. The study is based on whereas the ranking depends on the extent of a firm’s activities. 123 Logist. Res. (2012) 4:3–18 7 A linear regression model with time (i.e., year) as decreased (increased) significantly in five (two) industries. independent variable is applied in order to investigate the Finished goods IS ratios decreased (increased) significantly rate of change in inventory ratios over time. To assess the in four (one) sector(s). corresponding overall trend coefficients for our sample Using fixed aggregation weights with the first year as over time, a simple linear regression model for total base year (faw1993), total IS ratios decreased (increased) inventory levels as well as for each of the three inventory significantly in three (one) sector(s). Raw material IS ratios types is applied: decreased (increased) significantly in one (two) industry sector(s). Work-in-process IS ratios decreased (increased) IS ¼ a þ b t þ e ; ð5Þ it i i i significantly in five (two) industries. Finished goods IS In Eq. 5, t represents the time period (year), a the inter- ratios decreased (increased) significantly in three (one) sector(s). cept, and b the slope, that is, the trend coefficient, of firm i. In order to check for first-order autocorrelation of the Using fixed aggregation weights with the mid-year as residuals e , we are conducting the Durbin-Watson test base year (faw 1999), total IS ratios decreased (increased) statistic [7, 8]. Applying the Durbin-Watson test, we found significantly in four (one) sector(s). Raw material IS ratios first-order autocorrelation in nearly all of the time series in decreased (increased) significantly in one (one) industry the sample. As main consequence, OLS test statistics are sector. Work-in-process IS ratios decreased (increased) no longer valid because standard errors are biased and, significantly in four (two) industries. Finished goods IS therefore, causing serious misleading signals [10, 20]. In ratios decreased significantly in four sectors. No significant order to take autocorrelation into account, iterated Prais- increase was found. Further, on applying fixed aggregation weights with the Winsten estimation is employed [17]. For a brief overview of the industries analyzed, their final year as base year (faw 2005), total IS ratios SIC classifications, the means, medians, and variation decreased (increased) significantly in four (one) sector(s). coefficients of the different IS ratios are given in Table 2. Raw material IS ratios show no significant shift at all. The variation coefficients indicate the relative degree of Work-in-process IS ratios decreased (increased) signifi- movements inside a sector’s inventory ratios. cantly in four (two) industries. Finished goods IS ratios On an aggregated level (SIC classes), the results of our decreased significantly in four sectors. Again no signifi- time series regression analysis are provided in Table 3.In cant increase was found. All these findings are summa- order to save space, the intercept parameter estimates rized in Table 4. obtained are not reported. Only the trend coefficients On a further aggregated level, the regression results for (slope), together with t-statistics (p-value) and coefficients our sample in total are provided in Table 5, whereas of determination (R ), are reported. aggregation was executed from firms as well as from the Using variable aggregation weights (vaw), total IS ratios SIC code classes (sectors). It is remarkable that no decreasing IS ratios are found (with one exception) on that decreased (increased) significantly in four (two) sectors. Raw material IS ratios decreased (increased) significantly level of aggregation. These results will be discussed in the in two (three) industry sector(s). Work-in-process IS ratios following. Table 2 Descriptive measures 1993–2005 (SIC code classes) SIC TI RM WP FG Proportion of total sales (%) Mean Median Varc Mean Median Varc Mean Median Varc Mean Median Varc (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 20 11.87 7.50 96.83 3.69 2.55 76.47 3.02 0.89 221.42 5.16 2.74 115.56 2.39 22/23 19.11 18.04 34.67 4.25 4.32 64.83 2.72 2.50 98.68 12.15 12.04 47.51 2.35 28 17.93 15.49 50.27 4.51 4.02 59.37 4.13 1.38 170.43 9.29 7.95 37.76 25.62 30 13.58 14.48 33.78 4.72 4.52 26.90 2.74 1.54 101.89 6.12 5.75 73.76 2.52 32 15.51 12.68 50.72 3.83 3.46 62.97 3.03 1.29 135.38 8.65 6.78 64.69 3.01 35 21.60 20.47 45.25 5.19 4.91 53.14 9.79 6.91 91.76 6.61 4.73 81.43 8.47 36 18.22 17.17 28.49 6.02 5.69 43.20 5.65 4.16 78.76 6.55 5.45 70.25 18.20 37 17.62 14.37 51.60 4.25 3.73 66.43 5.64 3.69 97.07 7.73 7.35 57.54 37.43 Total 17.57 16.15 51.72 4.56 4.18 59.80 5.07 2.87 131.46 7.94 6.87 70.16 100.00 123 8 Logist. Res. (2012) 4:3–18 Table 3 Overall trend coefficients for SIC classes 1993–2005 SIC TI RM WP FG 2 2 2 2 b p-value R b p-value R b p-value R b p-value R vaw 20 0.6058*** 0.0010 0.6793 0.0441*** 0.0063 0.5417 0.3008*** 0.0011 0.6705 0.2618*** 0.0042 0.5755 22/23 -0.4390*** 0.0062 0.5442 -0.1936*** 0.0000 0.8852 -0.0671** 0.0108 0.4937 -0.1695 0.3131 0.1014 28 -0.2716*** 0.0000 0.9037 0.0246 0.3988 0.0721 -0.0547*** 0.0068 0.5354 -0.2532*** 0.0000 0.8401 30 -0.5093*** 0.0000 0.8391 -0.0228 0.3279 0.0957 -0.0861*** 0.0000 0.8356 -0.4004*** 0.0000 0.8765 32 -0.0928** 0.0105 0.4966 0.0885** 0.0178 0.4450 -0.0268 0.1062 0.2397 -0.1443*** 0.0000 0.8869 35 -0.1862 0.1552 0.1912 0.1108*** 0.0051 0.5606 -0.3004** 0.0204 0.4308 0.0084 0.6831 0.0174 36 0.4372** 0.0485 0.3353 -0.0124 0.6280 0.0244 0.6445*** 0.0048 0.5648 -0.2012*** 0.0000 0.9414 37 -0.0255 0.8150 0.0057 -0.0226* 0.0977 0.2503 -0.1727*** 0.0000 0.8491 0.1497 0.2014 0.1575 faw (1993) 20 0.2792 0.1450 0.1999 0.0433*** 0.0016 0.6485 0.1835** 0.0227 0.4199 0.0448 0.6881 0.0168 22/23 -0.1664 0.1291 0.2148 -0.0737*** 0.0002 0.7542 -0.0530** 0.0142 0.4673 -0.0459 0.5823 0.0313 28 -0.1898*** 0.0000 0.8219 0.0360 0.2493 0.1302 -0.0729*** 0.0001 0.8152 -0.1641*** 0.0003 0.7475 30 -0.4869*** 0.0000 0.8548 0.0090 0.6892 0.0167 -0.0677*** 0.0002 0.7634 -0.4281*** 0.0000 0.8993 32 -0.0011 0.9778 0.0001 0.0321 0.3961 0.0729 0.0149 0.3505 0.0875 -0.0406 0.1665 0.1821 35 -0.2472** 0.0183 0.4422 0.0837* 0.0908 0.2594 -0.3127*** 0.0009 0.6812 -0.0407 0.1787 0.1730 36 0.4394** 0.0499 0.3321 -0.0153 0.5653 0.0342 0.6472*** 0.0050 0.5627 -0.1980*** 0.0000 0.9424 37 0.1289 0.1410 0.2036 -0.0146 0.2095 0.1524 -0.1352*** 0.0032 0.5982 0.2327* 0.0631 0.3040 faw (1999) 20 0.2839 0.2658 0.1220 0.0258* 0.0759 0.2816 0.1988* 0.0783 0.2778 0.0468 0.7563 0.0101 22/23 -0.4743*** 0.0041 0.5778 -0.0266*** 0.0099 0.5021 -0.0146 0.3940 0.0735 -0.4346*** 0.0058 0.5502 28 -0.2427*** 0.0000 0.8975 0.0194 0.4448 0.0595 -0.0872*** 0.0000 0.8440 -0.1825*** 0.0002 0.7720 30 -0.5357*** 0.0000 0.8558 -0.0069 0.7711 0.0089 -0.0656*** 0.0000 0.8240 -0.4636*** 0.0000 0.9011 32 0.0288 0.2548 0.1274 0.0554 0.1821 0.1706 -0.0006 0.9590 0.0003 -0.0263 0.5583 0.0354 35 -0.4539*** 0.0001 0.8058 0.0500 0.1945 0.1621 -0.5063*** 0.0000 0.9278 -0.0087 0.7659 0.0093 36 0.4394** 0.0469 0.3393 -0.0145 0.5670 0.0339 0.6504*** 0.0045 0.5698 -0.2025*** 0.0000 0.9428 37 0.1033 0.2841 0.1136 -0.0128 0.2821 0.1145 -0.1041*** 0.0038 0.5844 0.1897 0.1213 0.2228 faw (2005) 20 0.2727 0.2809 0.1150 0.0243 0.1039 0.2425 0.1963* 0.0880 0.2634 0.0416 0.7812 0.0081 22/23 -0.3925** 0.0155 0.4588 -0.0181 0.1028 0.2438 0.0411 0.2918 0.1102 -0.4294*** 0.0056 0.5524 28 -0.2721*** 0.0000 0.8880 0.0240 0.3957 0.0730 -0.0983*** 0.0000 0.8366 -0.2044*** 0.0002 0.7770 30 -0.5464*** 0.0000 0.8560 -0.0080 0.7320 0.0123 -0.0665*** 0.0001 0.8105 -0.4722*** 0.0000 0.8994 32 0.0287 0.2823 0.1144 0.0557 0.2069 0.1541 -0.0104 0.3965 0.0728 -0.0154 0.7216 0.0133 35 -0.4482*** 0.0000 0.8833 0.0522 0.1194 0.2248 -0.4812*** 0.0000 0.9698 -0.0265 0.1676 0.1813 36 0.4333** 0.0471 0.3387 -0.0140 0.5823 0.0313 0.6456*** 0.0044 0.5719 -0.2041*** 0.0000 0.9422 37 0.0969 0.3160 0.1002 -0.0119 0.3191 0.0990 -0.0922*** 0.0043 0.5738 0.1778 0.1328 0.2112 t-statistic (* p \ 0.1, ** p \ 0.05, *** p \ 0.01) Regarding our results on an aggregated level based on industry can be traced back to the fact of decreasing raw variable weights, we find remarkably decreasing total IS materials and work-in-process inventories over the whole ratios in the rubber and plastics, textile and wearing time frame investigated, whereas in the second half we find apparel, and chemical industry. A slight but nevertheless efforts in reducing finished goods inventories. The chemi- significant increase can be found in the stones, clay, and cal industry owes its inventory reduction mainly in glass industry. The achievements in the rubber industry are decreased finished goods and work-in-process inventories. due to decreasing finished goods inventories over the whole The food sector shows significantly increasing total IS time frame. The inventory performance in the textile ratios, which is mainly due to increasing work-in-process 123 Logist. Res. (2012) 4:3–18 9 Table 4 Number of significant vaw faw (1993) faw (1999) faw (2005) de-/increasing SIC classes 1993–2005 (-)(?)(-)(?)(-)(?)(-)(?) TI 4 2 314 14 1 RM 2 3 121 10 0 WP 5 2 524 24 2 (±) denotes significant de-/ FG 4 1 314 04 0 increasing SIC classes Table 5 Overall trend coefficients for total sample 1993–2005 SIC TI RM WP FG 2 2 2 2 bp-value R bp-value R bp-value R bp-value R vaw Total (firms) -0.0401 0.5228 0.0420 -0.0082 0.3599 0.0843 -0.0017 0.9524 0.0004 -0.0324 0.3868 0.0757 Total (sectors) -0.0401 0.5228 0.0420 -0.0082 0.3599 0.0843 -0.0017 0.9524 0.0004 -0.0324 0.3868 0.0757 faw (1993) Total (firms) 0.0241 0.6905 0.0165 0.0172 0.1116 0.2335 0.0217 0.4882 0.0492 -0.0143 0.6720 0.0187 Total (sectors) -0.0213 0.6938 0.0162 0.0129 0.1943 0.1622 0.0160 0.5541 0.0361 -0.0535* 0.0930 0.2564 faw (1999) Total (firms) 0.0087 0.8990 0.0017 0.0044 0.5807 0.0316 0.0238 0.4838 0.0502 -0.0233 0.5588 0.0353 Total (sectors) -0.0136 0.8324 0.0047 0.0042 0.6108 0.0269 0.0210 0.5198 0.0426 -0.0420 0.2525 0.1285 faw (2005) Total (firms) -0.0049 0.9419 0.0006 0.0053 0.5416 0.0384 0.0134 0.6550 0.0208 -0.0308 0.4813 0.0508 Total (sectors) -0.0290 0.6457 0.0220 0.0022 0.7977 0.0069 0.0030 0.9189 0.0011 -0.0383 0.3342 0.0933 t-statistic (* p \ 0.1, ** p \ 0.05, *** p \ 0.01) IS ratios. The electronics and electrical equipment sector, frame. In the first half, we find a decrease when using which is in our sample dominated by the Siemens AG, fixed aggregation weights, in contrast to a constant trend shows a significant increase in total inventories, which can using variable weights (see Fig. 1). Obviously, the be explained by strongly increasing work-in-process decrease in IS ratios in the years until 1999 is covered by inventories in the second half of our time frame investi- a shift in sales. gated. Nevertheless, we also find a significant reduction in Analyzing the textiles and wearing apparel industry finished goods inventories in this sector. next, we have divergent results only when using Considering the effects of using fixed aggregation 1993-based fixed weights. This has a lot to do with strong weights on our results (with 1993 as base period), some efforts in reducing finished goods inventories in the second changes concerning significance of results occur, while the half of the time frame (see Fig. 2), which is clearly results remain stable for rubber and plastics, chemicals, and underestimated when using 1993 as base period (see electronics. The major changes are that the increasing Fig. 3). (decreasing) effect in the food (textiles and wearing The chemical sector (see Fig. 4) as well as rubber apparel) industry becomes nonsignificant. Furthermore, the and plastics (Fig. 5) shows clear and consistent results so far nonsignificant decrease in total inventories in the independent from which aggregated IS ratios are machinery industry becomes significant. These changes calculated. also hold for other base periods (1999 and 2005), with the The sector stones, clay, and glass show a slight textiles and wearing apparel as an exception remaining decreasing trend when using variable weights. This does significant. not hold for any fixed aggregation weight (see Fig. 6). Analyzing the food industry first, we see consistently The reason can be found in finished goods inventories increasing total IS ratio in the second half of the time showing a decreasing trend when using variable weights, 123 10 Logist. Res. (2012) 4:3–18 25,08% 19,27% 20_TI_1993 20_TI_1999 23,08% 20_TI_2005 18,27% 20_TI_vaw 21,08% 17,27% 19,08% 16,27% 28_TI_1993 17,08% 15,27% 28_TI_1999 28_TI_2005 15,08% 14,27% 28_TI_vaw 13,08% 13,27% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 1 Food—total inventory to sales ratio 1993–2005 Fig. 4 Chemicals—total inventory to sales ratio 1993–2005 22,96% 17,55% 21,96% 16,55% 20,96% 15,55% 19,96% 14,55% 18,96% 13,55% 12,55% 17,96% 22/23_TI_1993 30_TI_1993 11,55% 22/23_TI_1999 16,96% 30_TI_1999 22/23_TI_2005 30_TI_2005 10,55% 15,96% 22/23_TI_vaw 30_TI_vaw 9,55% 14,96% 8,55% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 2 Textiles and wearing apparel—total inventory to sales ratio Fig. 5 Rubber and plastics—total inventory to sales ratio 1993–2005 1993–2005 19,84% 16,18% 18,84% 15,68% 15,18% 17,84% 14,68% 16,84% 14,18% 15,84% 13,68% 13,18% 14,84% 32_TI_1993 12,68% 22/23_FG_1993 13,84% 32_TI_1999 22/23_FG_1999 12,18% 32_TI_2005 12,84% 22/23_FG_2005 11,68% 32_TI_vaw 22/23_FG_vaw 11,18% 11,84% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 6 Stones, clay, and glass—total inventory to sales ratio Fig. 3 Textiles and wearing apparel—finished goods inventory to 1993–2005 sales ratio 1993–2005 The decrease in total IS ratio in the machinery industry which is obviously caused by a sales shift as fixed becomes significant when using fixed aggregation weights. weighted finished goods, IS ratios discover a constant Using variable weights, we see significant trends in raw trend (see. Fig. 7). 123 Logist. Res. (2012) 4:3–18 11 8,54% 5,50% 8,04% 5,00% 7,54% 4,50% 7,04% 4,00% 6,54% 3,50% 6,04% 3,00% 5,54% 37_WP_1993 32_FG_1993 2,50% 37_WP_1999 5,04% 32_FG_1999 37_WP_2005 32_FG_2005 4,54% 2,00% 37_WP_vaw 32_FG_vaw 4,04% 1,50% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 7 Stones, clay, and glass—finished goods inventory to sales Fig. 8 Transportation equipment—work-in-process inventory to ratio 1993–2005 sales ratio 1993–2005 materials and work-in-process IS ratios but in the opposite direction. This observation changes when using fixed 11,11% 37_FG_1993 weights as the work-in-process decreasing trend remains as 37_FG_1999 10,11% a dominant component. 37_FG_2005 37_FG_vaw The transportation equipment industry shows no sig- 9,11% nificant results concerning total IS ratios. Digging a bit deeper, we find two interesting effects: (a) significantly 8,11% decreasing work-in-process IS ratios (see Fig. 8) and 7,11% (b) sharply increasing finished goods IS ratios in the second half of our time frame investigated (see Fig. 9). These 6,11% findings hold independent from using fixed or variable weights. In sum, we find a trend break in total IS ratios in 5,11% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 the middle of our time frame (see Fig. 10). Finally, we have to discuss our results for our sample in Fig. 9 Transportation equipment—finished goods inventory to sales total where no significant results (with one exception) were ratio 1993–2005 found. The reason is easy to explain: there is a trend break in the data (see Fig. 11). In the first (second) half of our time frame, we find decreasing (increasing) finished goods (see Fig. 12) and work-in-process (see Fig. 13) IS ratios. 16,63% 37_TI_1993 This also holds independent if aggregation was executed 37_TI_1999 from firms or from SIC code classes (sectors), whereas 15,63% 37_TI_2005 finished goods IS ratios show a constant trend in the second 37_TI_vaw 14,63% half of the time frame when aggregated from sectors (instead of a slightly increasing trend in the other case) and 13,63% therefore causing this exception in the data we already mentioned. 12,63% 11,63% Nevertheless, it has to be pointed out that within the time frame analyzed, several firms changed from national (according to German 10,63% Commercial Code, HGB) to International Financial Reporting 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Standards (IFRS); most of them during the last year investigated. Fig. 10 Transportation equipment—total inventory to sales ratio We scrutinized for possible conversion effects, resulting in structural 1993–2005 interruptions in the data. As a cause in the majority of cases we identified the accounting of long term construction contracts, which are no longer reported as inventories but accounts receivable. In the remaining of this section, we will discuss some Accordingly, we found evidence for such conversion effects mainly implications and limitations linked with the use of fixed in decreasing work-in-process inventories in the machinery industry. aggregated weights for trend analysis. Certain effects that Therefore, this sectors’ work-in-process inventory to sales perfor- are due to the specific size of our sample as well as its mance has to be interpreted carefully. 123 12 Logist. Res. (2012) 4:3–18 composition will be our point of departure, as these effects congruent with the curve shape of the biggest company hold for any other sample with similar characteristics. (in terms of sales). In both cases, the biggest company In two sector classes (SIC 30 and SIC 36), we find the contributes by far the lion’s share to the sector’s total curve shape of the aggregated IS ratio over time almost sales volume (Continental AG accounts for 93.43% in SIC 30 and Siemens AG for 95.84% in SIC 36; see also Fig. 14). Besides this fact, another characteristic typically for 16,44% sectors with some extraordinary big companies can be 15,94% identified. From Eq. 4, it can be easily concluded that IS ratios with fixed aggregated weights, no matter what 15,44% specific year selected, do not remarkably differ from the 14,94% IS ratio with variable aggregated weights. The closer the value of the fixed term of Eq. 4 for the big company, 14,44% S S , is to 1, the more the impact of the fixed is is i¼1 13,94% TO_TI_1993_F aggregate weight is extinguished. As a result of this TO_TI_1999_F concentration effect, the curve shapes based on fixed 13,44% TO_TI_2005_F aggregation weights are almost congruent to the curve TO_TI_vaw_F 12,94% shape of the variable aggregation weights. Because the 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 firm level is almost equal to the industry level, there is Fig. 11 Total sample (aggregated from firms)—total inventory to not much to be aggregated. For the aggregated total, IS sales ratio 1993–2005 ratio in the electronics and electric equipment industry, for instance, a year’s maximal difference between the 9,29% variable ratio and one of the three fixed weights, amounts to a negligibly small value of 0.11%. In order to isolate this concentration effect, we tentatively 8,79% removed the top 10% companies per sector in terms of sales from our sample. We will now exemplarily dem- 8,29% onstrate this for SIC class 36. If Siemens AG were excluded from the electronics sector, the development of 7,79% TO_FG_1993_F the total IS ratio over time shows especially in the TO_FG_1999_F second half of the time frame an overall decreasing 7,29% TO_FG_2005_F trend, instead of an altogether increasing trend (Figs. 14, TO_FG_vaw_F 15). As expected, Fig. 15 also presents different curve 6,79% shapes for each of the fixed aggregation weights 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 selected. Fig. 12 Total sample (aggregated from firms)—finished goods inventory to sales ratio 1993–2005 4,97% 20.88% 36_TI_1993 19.88% 4,47% 36_TI_1999 18.88% 36_TI_2005 36_TI_vaw 3,97% 17.88% 16.88% 3,47% 15.88% TO_WP_1993_F 14.88% 2,97% TO_WP_1999_F 13.88% TO_WP_2005_F 12.88% 2,47% TO_WP_vaw_F 11.88% 1,97% 10.88% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 14 Electronic and other electric equipment—total inventory to Fig. 13 Total sample (aggregated from firms)—work-in-process sales ratio 1993–2005 inventory to sales ratio 1993–2005 123 Logist. Res. (2012) 4:3–18 13 24.66% merger and acquisition activities. The plots of the curve with the time frame’s midpoint as base year may give a 23.66% clue for the shift (see e.g. Fig. 10). The fact, that the fixed 22.66% aggregated IS ratio curve with base year 1999 runs in 21.66% between the curves with base year 1993 and 2005, may 20.66% indicate a slight but continuous adjustment. This effect is 19.66% exemplarily demonstrated for the aggregated total IS ratio 18.66% 36_TI_1993 of SIC 35. In the base year 1993, Gea Group AG (average 36_TI_1999 17.66% total sales to inventory ratio: 10.62%) accounts for 44.66% 36_TI_2005 16.66% of the industry’s total sales volume, while Rheinmetall AG 36_TI_ohne (average total sales to inventory ratio: 20.28%) and Salz- 15.66% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 gitter AG (average total sales to inventory ratio: 16.82%) account only for 5.37 and 10.07%, respectively. Fig. 15 Electronic and other electric equipment (without Siemens For the base year 2005, a completely different picture AG)—total inventory to sales ratio 1993–2005 emerges. Gea Group AG only contributes 13.74% to the industry’s total sales volume, while Rheinmetall AG and Salzgitter AG have a share of 10.55 and 21.84% of total Obviously, the insights deducible from the use of fixed industry’s sales, respectively. Based on these companies’ aggregate weights depend to a significant extent on the shift in the percentage shares of the industry’s sales volume sales proportion of the biggest firm (subsector) in a specific as well as their different total IS ratio levels, it can be industry; that is, on the amount of concentration in the concluded that the total IS ratio curve for the base year sample. 2005 runs on a higher level than the IS ratio curve for the Another interesting aspect is the choice of a specific base year 1993 (see also Fig. 16). base year for calculating IS ratios with fixed aggregation Taking a closer look at the b-values in Tables 4, 5 one weights. If we compare the plots of the IS ratio time series finds that the slopes of the IS ratio curves with fixed with a fixed weight from the end of the sample (base year aggregated weights are often just a fraction of its coun- 2005) with the ones with a fixed weight from the beginning terparts with variable aggregated weights (e.g. TI, WP and of the sample (base year 1993), it is quite obvious that in FG of SIC 20 or RM of SIC 22/23). The answer to this most cases from our sample the two curves run quasi effect goes along with the above-mentioned spread of the parallel to each other with a distinct spread (see for quasi parallel curves for the fixed IS ratios with different example Figs. 1, 4, 6–11, and 13 as well as the b-values in base years. The variable aggregated weight curve Tables 4, 5). For our data sample, the maximum spread bridges—metaphorically speaking—the spread between reaches an average value of 3.54% (total IS ratios in SIC the two base year curves over the time frame investigated 20). The reason is that particular firms (subsectors) in our (as revealed by the plots in Fig. 1), as the fixed IS ratio for sample exhibit a massive shift in percentage shares of the a certain base year must correspond with the base years’ subsector’s (sector’s) total sales between the time frame’s variable IS ratio (see Eq. 4). This explains the stronger beginning and the end year. As a consequence, firms (subsectors) with an above subsector (sector) average IS ratio, whose proportion of the aggregated weight increases 23.83% over the time frame investigated, gain a much stronger impact on the end of sample fixed aggregated weight in 21.83% comparison with the beginning of sample fixed aggregated weight. Altogether, the result is a higher level of the 19.83% aggregated IS curve. Firms (subsectors) with a below average IS ratio, on the other hand, cause the aggregated IS 17.83% curve to run on a lower level. The opposite effect holds for 15.83% 35_TI_1993 firms (subsectors), whose proportion of the aggregated 35_TI_1999 sales share decreases between the samples’ beginning and 13.83% 35_TI_2005 the end year. The reason for the shift in sales share can be 35_TI_vaw found either in a slight but continuous adjustment over the 11.83% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 complete time period investigated, for example, some industries are hit harder than others by economic down- Fig. 16 Industrial machinery and equipment—total inventory to sales ratio 1993–2005 turns, or in a one time shift, for example, associated with 123 14 Logist. Res. (2012) 4:3–18 decrease or increase compared to its corresponding fixed IS the sample’s first year as base year for the fixed aggregated ratio curves. As a second result, we find that the varying weights. To a certain extent, this selection may also help to levels of the fixed aggregated IS ratio curves for the dif- absorb the impact of emerging trends during the time frame ferent base years are caused by noticeable shifts in sales that could intermingle with the effects actually accounted shares of certain firms (subsectors) within a specific sub- for. sector (sector) leading to shifts in the composition of the aggregated weight. Comparing the b-values underlines the effect resulting 4 Conclusion from the use of variable aggregated weights and simulta- neously raises the question of the adequate base year for This study is aimed at analyzing the difference in using the fixed weights. This question is a tough one and seems to fixed weight aggregate IS ratios rather than ‘‘traditional’’, allow for no general answer. To a certain extent, we do that is, variable weighted, aggregated IS ratios. After agree with Irvine’s [13] findings, as the shifts in the com- illustrating the implications of these methods, we applied position of several aggregated weights in our sample them on empirical data of IS ratios of German firms. We clearly demonstrate that fixed weights tend to be overstated show that difficulties arise because different aggregation in periods before the base year and understated in periods methods are signaling different time trends under certain after the base year. We do also share Irvine’s [13] rec- circumstances. Analyzing the inventory performance of ommendation to use end of sample fixed weights if a 100 German corporations between 1993 and 2005, our specific observed trend in the aggregate IS ratio, relevant to findings indicate that the total IS ratio decreased in a sta- the current composition of firms (subsectors) making up the tistically significant extent in the majority of industry aggregate, should be assured (e.g. forecasting purposes). sectors during the time frame investigated. Regarding our But choosing the midpoint of a sample as base year, as results on an aggregated level based on variable weights, Irvine [[13], p. 49, fn. 5] proposes for a particular historical we find remarkably decreasing total IS ratios in different period, for example, from 1993 to 2005, reveals a some- sectors. The results for our sample in total show a trend what mixed picture and may be a much too global break in the data. In the first (second) half of our time approach, as can be demonstrated by means of our sample frame, we find decreasing (increasing) IS ratios. Consid- data. In some cases, the curve with base year 1999 is ering the effects of using fixed aggregation weights on our plotted right in between the beginning and the end base results, some changes concerning significance of results year curves. This may indicate a slightly but continuous occur. The use of fixed aggregation weights in addition to shift from the aggregated IS ratio curve running on a higher variable aggregation weights is helpful because it isolates any trends observed in the aggregated IS ratio series to (lower) level to the aggregated IS ratio curve running on a lower (higher) level during the time frame observed (e.g. fluctuations in the underlying (sub) sectors’ IS ratios, not RM IS ratio for SIC 22/23 or FG IS ratio for SIC 28). In shifts in the composition of the aggregate. Nevertheless, we this case, the period’s midpoint may be a good selection for also discussed some implications and limitations that are the base year. But in the majority of cases, the fixed linked with fixed aggregation weights, whereas the ques- aggregated IS ratio curve for the midterm base year has an tion for an adequate base year offers an interesting starting almost identical shape and level like one of the other base point for further research. year’s curves, which questions the selection of the time frame’s midpoint as an appropriate base year. For us, it seems that if the effect researchers are focused on is Appendix believed to show a stronger manifestation in the beginning of the time frame, it may be a reasonable approach to use See Table 6. 123 Logist. Res. (2012) 4:3–18 15 Table 6 Sample formation and descriptive measures Nr. SIC Firm TI RM WP FG Proportion of total sector Mean Median Varc Mean Median Varc Mean Median Varc Mean Median Varc sales (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 1 20 A. Moksel AG 3.79 3.69 16.07 0.42 0.31 41.89 0.02 0.00 165.61 3.35 3.33 14.41 20.83 2 20 Actris AG 5.06 5.12 17.24 2.11 2.08 27.12 0.83 0.89 22.65 2.13 2.23 16.84 2.25 3 20 ADM Hamburg AG 11.15 11.37 19.64 8.94 9.45 19.95 0.25 0.28 18.74 1.96 2.03 30.49 12.95 4 20 Berentzen-Gruppe AG 12.00 11.46 16.76 2.84 2.75 25.75 3.21 3.21 41.25 5.95 5.36 28.33 2.41 5 20 Dom Brauerei AG 5.13 4.88 22.54 2.02 1.90 21.71 1.48 1.06 60.80 1.63 1.50 32.52 0.28 6 20 Frosta AG 15.64 15.91 9.20 6.42 6.23 26.34 2.54 2.71 37.10 6.68 6.57 9.62 3.08 7 20 Kulmbacher Brauerei AG 6.01 5.90 8.63 2.63 2.44 26.52 1.10 1.07 21.11 2.28 2.33 22.91 1.94 8 20 Mineralbrunnen AG 4.20 4.22 22.37 2.54 2.31 19.38 0.00 0.00 n. def. 1.66 1.47 31.44 1.86 11 20 Sektkellerei Schloss 35.80 26.18 46.67 5.91 4.59 47.92 21.11 14.32 56.17 8.77 8.00 46.17 45.99 Wachenheim AG 9 20 Staatl. Mineralbrunnen AG 3.28 3.09 20.98 1.23 1.21 26.01 0.00 0.00 n. def. 2.05 2.02 26.60 2.03 10 20 Su ¨ dzucker AG 30.61 29.10 15.54 2.31 2.11 20.30 5.48 4.53 43.00 22.82 22.98 10.51 0.13 12 20 VK Muehlen AG 9.83 10.02 17.74 6.91 7.12 20.07 0.23 0.29 59.78 2.68 2.58 23.20 6.24 13 22 Bremer Woll-Ka ¨mmerei AG 23.96 26.17 29.60 9.62 9.96 31.53 0.19 0.19 34.52 14.14 12.78 35.02 3.10 14 22 Gruschwitz Textilwerke AG 22.41 21.45 10.21 6.41 6.30 48.78 8.58 5.91 42.38 7.42 7.50 17.05 0.10 15 22 Kunert AG 34.39 35.34 6.04 5.18 4.93 10.06 5.55 5.78 21.99 23.67 24.05 10.54 2.11 16 22 Textilgruppe Hof AG 20.31 19.57 18.24 4.71 4.86 16.48 3.94 3.27 44.82 11.67 10.77 36.31 3.17 17 22 Vereinigte Filzfabriken AG 14.02 13.02 17.70 4.90 4.87 9.75 2.93 2.99 19.51 6.20 5.36 26.63 0.19 18 23 adidas AG 19.18 20.86 22.09 0.64 0.64 47.47 0.15 0.13 38.57 18.39 20.46 24.10 52.33 19 23 Ahlers AG 20.30 20.67 15.37 7.09 7.10 17.48 0.67 0.69 36.17 12.54 12.75 15.77 3.47 20 23 Escada AG 18.89 19.61 17.57 3.08 3.11 18.92 2.16 1.84 27.76 13.66 15.22 27.24 7.93 21 23 Etienne Aigner AG 14.07 16.81 29.06 1.38 1.23 35.30 0.00 0.00 n. def. 12.69 14.78 30.15 0.47 22 23 Gerry Weber International AG 12.56 11.83 23.25 1.88 1.97 27.33 3.96 3.97 39.08 6.72 7.45 26.55 3.32 23 23 Hirsch AG 15.55 16.10 20.93 4.63 4.50 19.94 3.18 3.06 12.02 7.74 8.27 32.08 0.46 24 23 Hucke AG 10.60 10.91 13.84 5.33 5.61 16.53 1.08 1.44 92.92 4.18 4.05 17.32 3.54 25 23 Hugo Boss AG 17.32 16.31 13.29 4.49 4.46 13.88 0.84 0.86 14.27 11.99 11.27 20.15 9.33 26 23 Puma AG 18.61 18.80 18.81 0.24 0.13 86.88 3.59 4.28 70.96 14.77 15.14 12.00 7.51 27 23 Triumph International AG 24.46 24.21 6.11 4.10 4.12 12.30 3.97 3.99 13.38 16.40 16.82 8.08 2.96 28 28 Altana AG 12.73 12.72 8.76 4.14 4.09 9.36 1.93 1.93 13.40 6.66 6.64 12.70 2.06 29 28 BASF AG 14.12 14.46 7.78 2.20 2.73 51.22 0.22 0.22 41.17 11.69 11.50 15.28 31.88 30 28 Bayer Aktiengesellschaft 20.34 20.53 3.38 3.67 3.51 10.62 0.00 0.00 n. def. 16.68 16.85 3.33 28.15 31 28 Beiersdorf AG 13.44 14.02 8.36 3.43 3.35 19.38 1.02 0.98 17.26 8.99 8.45 12.44 3.94 32 28 Biotest AG 44.01 45.60 17.28 11.47 10.79 33.48 23.88 23.11 32.46 8.66 8.50 9.02 0.21 16 Logist. Res. (2012) 4:3–18 Table 6 continued Nr. SIC Firm TI RM WP FG Proportion of total sector Mean Median Varc Mean Median Varc Mean Median Varc Mean Median Varc sales (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 33 28 Fresenius SE 11.75 9.56 32.35 2.77 2.03 44.64 1.67 1.39 41.34 7.31 6.16 26.31 4.98 34 28 Fuchs Petrolub AG 12.97 12.60 6.05 5.38 5.37 6.18 0.62 0.59 11.56 6.97 6.85 8.22 0.92 35 28 Henkel KGaA 12.00 12.91 12.75 3.81 4.01 18.09 1.11 1.32 45.64 7.08 7.24 8.76 10.58 36 28 Linde AG 17.55 19.03 31.70 2.88 3.01 22.26 8.02 9.38 55.61 6.65 6.54 11.15 7.10 37 28 Merck KGaG 19.69 19.44 11.87 4.22 4.30 20.57 0.00 0.00 n. def. 15.48 15.14 10.43 5.38 39 28 Schering AG 19.56 19.25 11.67 4.08 3.96 12.29 8.00 7.86 13.77 7.48 7.29 12.38 0.74 38 28 Su ¨ d Chemie AG 17.03 16.88 6.88 6.10 6.00 9.53 3.11 3.01 17.37 7.82 7.98 9.19 4.05 40 30 Continental AG 12.32 11.86 18.79 3.21 3.26 9.36 1.53 1.51 19.18 7.58 7.13 25.65 93.43 41 30 Ehlebracht AG 11.88 12.94 28.36 4.64 4.29 25.85 2.13 2.41 45.14 5.12 5.56 37.78 1.06 42 30 Innotec TSS AG 14.39 14.66 13.96 6.04 6.21 18.62 6.12 5.87 37.72 2.23 2.32 36.60 1.40 43 30 New York-Hamburger 17.72 17.97 9.52 4.01 3.91 15.76 6.30 6.21 17.25 7.41 7.56 20.50 0.31 Gummi-Waaren Compagnie AG 44 30 Simona AG 18.71 18.79 8.14 4.88 5.12 14.22 0.00 0.00 n. def. 13.82 13.81 8.67 1.78 45 30 WERU AG 6.44 6.38 13.29 5.53 5.43 16.07 0.35 0.33 27.25 0.56 0.54 21.82 2.01 46 32 BHS tabletop AG 16.75 16.53 23.75 2.94 2.56 33.80 1.53 1.66 48.55 12.28 12.01 21.86 1.16 47 32 Didier-Werke AG 16.87 17.32 19.59 5.24 5.44 23.77 3.52 3.23 34.60 8.11 6.96 29.88 5.28 48 32 Dyckerhoff AG 9.93 10.01 9.66 4.34 3.99 13.77 1.56 1.41 27.13 4.03 4.10 24.46 14.33 49 32 Erlus AG 9.19 10.01 41.32 1.52 1.65 30.41 0.30 0.31 16.92 7.36 7.85 45.61 0.83 50 32 Heidelbergcement AG 10.27 10.25 5.79 5.26 5.28 9.45 1.32 1.27 20.92 3.69 3.53 12.78 45.94 51 32 Keramag AG 10.07 10.19 8.82 0.72 0.61 34.31 0.54 0.38 51.87 8.82 8.86 8.52 1.28 52 32 Pilkington Deutschland AG 7.48 7.86 22.68 1.86 1.68 31.13 0.39 0.21 90.13 5.24 5.33 22.67 4.92 53 32 Rosenthal AG 29.22 27.77 16.24 2.62 2.66 16.31 6.08 5.20 70.23 20.52 21.03 16.43 1.62 54 32 Saint Gobain Oberland AG 13.76 13.17 21.84 3.59 3.08 52.32 0.38 0.22 97.38 9.79 9.64 11.60 3.26 55 32 SGL Carbon AG 27.57 26.78 9.32 7.22 7.10 12.37 14.66 14.46 9.05 5.68 5.64 13.66 8.87 56 32 Sto AG 7.76 7.79 6.50 2.00 1.95 8.57 0.18 0.16 32.00 5.59 5.58 7.81 4.38 57 32 Teutonia Zementwerk AG 16.49 15.59 17.60 8.73 8.48 19.37 4.87 4.26 34.37 2.89 2.51 35.47 0.37 58 32 Villeroy & Boch AG 26.19 25.95 7.20 3.75 3.75 6.50 4.02 3.56 16.85 18.42 18.20 9.61 7.76 59 35 Alexanderwerk AG 37.82 37.18 30.69 3.78 4.01 31.50 25.52 23.72 47.27 8.52 6.57 65.12 0.08 60 35 Bertold Hermle AG 18.32 17.15 25.43 3.27 3.29 67.97 8.80 5.56 56.15 6.25 6.60 31.04 0.32 61 35 Deutz AG 32.44 26.71 44.24 11.13 11.35 13.62 15.69 10.05 84.28 5.62 5.40 21.55 4.49 62 35 Du ¨ rkopp Adler AG 28.70 28.51 8.89 7.22 7.01 25.82 9.09 9.14 13.28 12.39 12.36 18.99 0.53 63 35 Du ¨ rr AG 15.25 15.03 72.70 2.23 2.16 16.37 12.86 12.03 89.27 0.16 0.05 90.25 4.47 Logist. Res. (2012) 4:3–18 17 Table 6 continued Nr. SIC Firm TI RM WP FG Proportion of total sector Mean Median Varc Mean Median Varc Mean Median Varc Mean Median Varc sales (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 64 35 GEA Group AG 10.62 10.32 18.17 2.13 2.46 29.64 4.74 4.51 30.34 3.75 3.93 16.13 26.90 65 35 Gildemeister AG 29.52 26.16 33.74 10.10 8.80 34.76 11.69 8.31 66.41 7.72 7.84 25.38 2.24 66 35 Jagenberg AG 19.34 21.00 25.92 4.48 4.02 20.86 12.18 13.50 26.93 2.68 2.77 57.44 1.19 67 35 Johann F. Behrens AG 26.47 26.29 6.97 6.54 5.91 26.18 1.90 2.21 75.73 18.03 18.12 8.33 0.28 68 35 Jungheinrich AG 11.36 10.19 20.50 5.41 4.69 24.30 1.79 1.91 52.49 4.15 4.18 13.63 4.25 69 35 Kloeckner-Werke AG 18.10 15.57 37.52 6.33 5.53 31.06 9.58 7.74 54.91 2.19 2.01 28.94 5.83 70 35 Koenig & Bauer AG 34.08 36.71 16.60 6.37 6.23 32.46 27.48 28.33 15.19 0.23 0.14 93.12 3.26 71 35 Krones AG 12.74 11.92 27.93 3.44 3.12 37.08 5.70 5.62 20.58 3.60 3.37 40.63 3.44 72 35 KSB AG 19.60 20.36 13.41 6.07 5.92 8.21 8.38 8.67 27.00 5.16 5.26 12.14 3.63 73 35 KUKA AG 26.87 27.20 22.05 5.75 5.87 10.69 18.73 19.19 28.53 2.40 2.24 17.79 5.45 74 35 Norddeutsche Affinerie AG 15.89 16.20 14.41 5.82 5.80 13.61 6.31 6.03 21.50 3.76 3.77 32.01 5.21 75 35 Rheinmetall AG 20.28 20.29 18.76 5.40 4.83 21.80 10.94 11.53 32.57 3.94 3.41 23.80 10.75 76 35 Salzgitter AG 16.82 16.25 9.81 4.43 4.22 25.44 3.47 3.77 22.89 8.92 9.04 7.13 13.18 77 35 Sartorius AG 18.29 18.39 15.19 3.83 3.83 14.02 5.47 5.75 15.72 8.99 8.70 22.80 1.05 78 35 Triumph Adler AG 15.97 15.82 28.00 1.71 1.90 61.98 2.55 1.64 103.03 11.70 12.52 35.11 1.74 79 35 WMF AG 25.06 25.00 8.31 3.58 3.61 11.06 2.82 2.80 8.79 18.66 18.79 9.61 1.72 80 36 Brilliant AG 22.83 23.02 10.35 6.44 7.38 57.35 1.89 1.87 64.04 14.51 13.43 23.68 0.11 81 36 Ceag AG 20.28 21.02 19.51 6.60 6.72 17.96 3.70 3.45 59.15 9.98 10.13 27.54 0.31 82 36 Draegerwerk AG 21.91 23.28 17.76 5.30 5.68 19.86 6.70 7.22 32.15 9.92 10.36 16.77 1.61 83 36 Leifheit AG 15.60 15.20 13.21 4.02 3.66 28.17 1.85 1.65 37.33 9.73 8.95 23.49 0.41 84 36 M tech AG 20.15 18.58 28.14 5.17 5.02 18.02 14.52 12.20 35.28 0.46 0.00 115.87 0.11 85 36 Schweizer Electronic Ag 11.26 11.40 8.38 4.68 4.42 16.01 3.61 3.61 15.13 2.97 2.96 36.56 0.12 86 36 Sedlbauer AG 15.98 14.59 21.55 8.61 7.40 30.69 4.60 4.35 18.01 2.77 2.51 27.25 0.04 87 36 Siemens AG 15.01 14.07 17.82 2.98 2.96 9.86 7.27 5.23 44.05 4.76 4.67 16.21 95.84 88 36 Vogt Electronic AG 17.82 17.18 22.43 8.77 8.76 19.55 4.39 3.62 38.74 4.66 3.62 50.76 0.46 89 36 Vossloh AG 21.40 18.16 28.43 7.64 7.89 29.76 8.00 6.96 54.91 5.76 6.64 49.07 0.97 90 37 Audi AG 6.31 5.94 16.88 1.36 1.38 19.64 1.42 1.45 16.87 3.54 3.44 32.96 11.76 91 37 BBS Fahrzeugtechnik AG 22.10 21.96 14.04 5.22 4.91 22.16 5.76 5.54 20.05 11.12 11.53 21.18 0.10 92 37 BMW AG 12.06 12.07 12.49 1.36 1.37 10.43 1.75 1.77 16.01 8.95 9.09 14.33 24.12 93 37 Hymer AG 21.75 20.35 15.26 8.94 8.99 19.74 1.75 1.76 15.52 11.06 10.05 18.73 0.29 94 37 MAN AG 37.18 36.60 13.46 3.76 3.71 7.89 18.76 18.39 18.85 14.66 16.34 39.41 9.35 95 37 Porsche AG 11.01 10.86 16.57 1.46 1.21 50.90 3.41 3.39 43.21 6.15 6.65 23.74 2.46 96 37 Progress-Werke Oberkirch AG 14.44 14.15 16.88 5.20 4.78 27.74 6.29 6.14 31.43 2.95 3.06 15.41 0.10 18 Logist. Res. (2012) 4:3–18 References 1. Allen RGD (1975) Index numbers in theory and practice. Mac- Millan, London 2. Blinder AS, Maccini LJ (1991) Taking stock: a critical assess- ment of recent research on inventories. J Econ Perspect 5(1991):73–96 3. Chen H, Frank MZ, Wu OQ (2005) What actually happened to the inventories of American companies between 1981 and 2000? Manage Sci 51(2005):1015–1031 4. Chen H, Frank MZ, Wu OQ (2007) US retail and wholesale inventory performance from 1981 to 2004. Manuf Ser Oper Manage 9:430–456 ´ ´ 5. Chikan A, Kovacs E, Matyusz Z (2011) Inventory investment and sectoral characteristics in some OECD countries. Int J Prod Econ 133(2011):2–11 6. De Haan J, Yamamoto M (1999) Zero inventory management: facts or fiction? Lessons from Japan. Int J Prod Econ 59(1999): 65–75 7. Durbin J, Watson GS (1950) Testing for serial correlation in least squares regression. I. Biometrika 37(1950):409–428 8. Durbin J, Watson GS (1951) Testing for serial correlation in least squares regression. II. Biometrika 38(1951):159–178 9. Gaur V, Fisher ML, Raman A (2005) An econometric analysis of inventory turnover performance in retails services. Manage Sci 51(2005):181–194 10. Greene WH (2008) Econometric analysis, 6th edn. Pearson, Prentice Hall, Upper Saddle River, NJ 11. Gru ¨ nwald HJ, Fortuin L (1992) Many steps towards zero inven- tory. Eur J Oper Res 59(1992):359–369 12. Irvine FO (2003) Long term trends in US inventory to sales ratios. Int J Prod Econ 81–82(2003):27–39 13. Irvine FO (2003) Problems with using traditional aggregate inventory to sales ratios. Int J Prod Econ 81–82(2003):41–50 14. Loar T (1992) Patterns of inventory management and policy: a study of four industries. J Bus Logist 13(1992):69–96 15. Nakane J, Hall RW (1983) Management specs for stockless production. Harv Bus Rev 61(1983):84–91 16. Obermaier R, Donhauser A (2009) Disaggregate and aggregate inventory to sales ratios over time: the case of German corpo- rations 1993–2005. Logist Res 1(2009):95–111 17. Prais SJ, Winsten CB (1954) Trend estimation and serial corre- lation, cowles commission discussion paper statistics, no. 383 18. Rajagopalan S, Malhotra A (2001) Have U.S. manufacturing inventories really decreased? An empirical study. Manuf Ser Oper Manage 3(2001):14–24 19. Shah R, Shin H (2007) Relationships among information tech- nology, inventory, and profitability: An investigation of level invariance using sector level data. J Oper Manage 25(2007): 768–784 20. Wooldridge JM (2006) Introductory econometrics—a modern approach, 3rd edn. Thomson, South-Western, Mason, Ohio Table 6 continued Nr. SIC Firm TI RM WP FG Proportion of total sector Mean Median Varc Mean Median Varc Mean Median Varc Mean Median Varc sales (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) (%) 97 37 Schaltbau Holding AG 25.10 25.89 20.00 9.00 8.45 14.93 12.08 11.30 31.65 4.01 3.74 28.18 0.21 98 37 Veritas AG 9.84 9.48 16.48 3.57 3.30 25.12 2.64 2.45 46.89 3.63 3.56 21.25 0.14 99 37 Volkswagen AG 11.37 10.83 13.21 2.24 2.22 7.01 1.67 1.45 19.14 7.47 7.33 20.52 51.24 100 37 Wanderer-Werke AG 22.62 23.79 12.48 4.61 3.85 29.63 6.53 6.58 13.79 11.48 11.96 19.45 0.24 Source:[16] with own calculations
Logistics Research – Springer Journals
Published: Jan 25, 2012
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.