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An Econometric Analysis of Inventory TurnoverPerformance in Retail ServicesVishal Gaur, Marshall L. Fisher, Ananth Raman,
To cite this article:Vishal Gaur, Marshall L. Fisher, Ananth Raman, (2005) An Econometric Analysis of Inventory Turnover Performance in RetailServices. Management Science 51(2):181-194. http://dx.doi.org/10.1287/mnsc.1040.0298
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Ananth RamanHarvard Business School, Morgan Hall, Soldiers Field, Boston, Massachusetts 02163, [email protected]
Inventory turnover varies widely across retailers and over time. This variation undermines the usefulness ofinventory turnover in performance analysis, benchmarking, and working capital management. We develop
an empirical model using financial data for 311 publicly listed retail firms for the years 1987–2000 to investigatethe correlation of inventory turnover with gross margin, capital intensity, and sales surprise (the ratio of actualsales to expected sales for the year). The model explains 66.7% of the within-firm variation and 97.2% of thetotal variation (across and within firms) in inventory turnover. It yields an alternative metric of inventoryproductivity, adjusted inventory turnover, which empirically adjusts inventory turnover for changes in grossmargin, capital intensity, and sales surprise, and can be applied in performance analysis and managerial decisionmaking. We also compute time trends in inventory turnover and adjusted inventory turnover, and find thatboth have declined in retailing during the 1987–2000 period.
Key words : benchmarking; inventory turnover; retail operations; performance measuresHistory : Accepted by Wallace J. Hopp, design and operations management; received November 21, 2003. This
paper was with the authors 4 months for 3 revisions.
1. IntroductionThe total inventory investment of all U.S. retailersaveraged $449 billion during the year 2003.1 On aver-age, inventory represents 36% of total assets and 53%of current assets for retailers.2 Because such a signif-icant fraction of the retailers’ assets are invested ininventory, retailers and stock market analysts focus-ing on retailers pay close attention to inventoryproductivity. Retailers continuously seek to improvetheir inventory management processes and systems toreduce inventory levels. Stock market analysts tracksuch practices and reward retailers on gains in theirinventory productivity; see, for example, Standard &Poor’s surveys on the retailing industry (Sack 2000).
1 According to the 2003 Monthly Retail Trade Surveys of the U.S.Census Bureau.2 These values are computed from our data set, which containsquarterly values of inventory, total assets, current assets, and othervariables for all public retailers across 10 product-market segmentsfor the period 1985–2000. The data set includes 311 firms. It isconstructed using Standard and Poor’s Compustat database and issummarized in §2.
Inventory turnover, the ratio of a firm’s cost ofgoods sold to its average inventory level, is com-monly used to measure performance of inventorymanagers, compare inventory productivity acrossretailers, and assess performance improvements overtime. However, we find that the annual inventoryturnover of U.S. retailers varies widely—not onlyacross firms, but also within firms from one year toanother. For example, during the 1987–2000 period,the annual inventory turnover at Best Buy Stores,Inc. (Best Buy), a consumer electronics retailer, rangedfrom 2.85 to 8.53. The annual inventory turnoverat three peer retailers of Best Buy during the sameperiod shows similar variation: at Circuit City Stores,Inc. from 3.97 to 5.60, at Radio Shack Corporationfrom 1.45 to 3.05, and at CompUSA, Inc. from 6.20to 8.65. The factors influencing these variations havenot been studied systematically to our knowledge.Thus, the extent to which they indicate better orworse performance in inventory productivity is notknown.
In addition, inventory turnover can be correlatedwith other performance measures in a firm. Figure 1
Figure 1 Plot of Annual Inventory Turns vs. Annual Gross Marginfor Four Consumer Electronics Retailers for the Years1987–2000
0
1
2
3
4
5
6
7
8
9
10
0 0.1 0.2 0.3 0.4 0.5 0.6Gross Margin
Inve
nto
ry T
urn
s
Best Buy Co. Inc. Circuit City Stores CompUSA Radio Shack
plots the annual inventory turnover of the above fourconsumer electronics retailers against their gross mar-gins (the ratio of gross profit net of markdowns tonet sales) for the period 1987–2000. The figure showsa strong correlation between inventory turnover andgross margin. Such correlation could possibly becaused by many factors studied in the operations liter-ature, such as differences in variety and price. It raisesthe question of whether inventory turnover should beused, per se, in performance analysis.
This paper uses public financial data to conduct adescriptive investigation of inventory turnover per-formance in retail services. We identify the follow-ing variables that should be correlated with inventoryturnover and can be measured from public financialdata: gross margin, capital intensity (the ratio of aver-age fixed assets to average total assets), and sales sur-prise (the ratio of actual sales to expected sales forthe year). Using results from the existing literature,we formulate hypotheses to relate these variables toinventory turnover. We then propose an empiricalmodel to represent these relationships and apply it toa panel of retailing data.
Our paper reports three main findings. First, wefind that the explanatory variables explain a signif-icant 66.7% of the within-firm variation and 97.2%of the total variation (i.e., within and across firms)in inventory turnover. Annual inventory turnover isfound to be negatively correlated with gross marginand positively correlated with capital intensity andsales surprise.
Second, we estimate time trends in inventoryturnover in retailing, both with and without taking
account of the correlations with the explanatory vari-ables. We find that, on average, inventory turnoverin retailing has declined during the 1987–2000 period,even though it is positively correlated with capitalintensity, and capital intensity has increased dur-ing this period. However, there are marked differ-ences in the time trends in inventory turnover acrossfirms: 43% of the firms have increased their inventoryturnover with time, and, on average, firms that haveinvested more in capital assets have achieved higherinventory turnover.
Third, using the estimates from our model, we con-struct an alternative metric of inventory productivity,adjusted inventory turns, which empirically modelsthe trade-off between inventory turnover and theexplanatory variables. This metric can be applied inperformance analysis, benchmarking, and manage-rial decision making because it enables comparisonof inventory productivity across firms and years. Weillustrate its interpretation with examples.
There is considerable interest in the operationsmanagement community in evaluating time trends ininventory turnover and assessing the impact of opera-tional improvements on operational and financial per-formance. However, there are few empirical studieson these topics. Balakrishnan et al. (1996) comparethe performance of a sample of 46 firms that adoptedjust-in-time processes (JIT) during 1985–1989 with amatched sample of 46 control firms, and find that JITfirms achieved larger improvements in their inven-tory turns. Billesbach and Hayen (1994), Chang andLee (1995), and Huson and Nanda (1995) also studythe impact of JIT on inventory turns for different sam-ples of firms. Hopp and Spearman (1996, Chapter 5)summarize the findings of several survey-based stud-ies on whether U.S. manufacturing firms that imple-mented MRP systems achieved better inventory turnsas a result. Hendricks and Singhal (1997, 2001) exam-ine the impact of implementation of total qualitymanagement programs on the operating incomes andshareholder values of firms.
In contrast to the above research, Rajagopalan andMalhotra (2001) use aggregate industry-level datafrom the U.S. Census Bureau for 20 industrial sec-tors for the period 1961–1994 to determine whetherthe inventory turns for U.S. manufacturers havedecreased with time for each of raw material inven-tory, work-in-process inventory, and finished-goodsinventory. They find that six sectors show increasingtrends in inventory turns for finished goods, and foursectors show larger trends in the years 1980–1994,when JIT became popular compared to the previousperiod (1961–1979). The results for raw material andwork-in-process inventories are marginally better.
This paper contributes to the operations literatureas it studies inventory productivity in retail services,
and utilizes firm-level panel data for all publiclylisted firms in this sector. Panel data are advanta-geous because they enable us to control for the effectsof unobserved firm-specific or time-specific factorsin measuring the trade-offs between the variables ofinterest. We exploit the flexibility of panel data tocompare alternative model specifications and assesstheir suitability for modeling inventory turnoverempirically. We also introduce the variable sales sur-prise to control for the effect of unexpectedly highsales on inventory turnover. Our model can be usedby managers to assess inventory turnover perfor-mance, benchmark it against competing firms, andmanage working capital requirements. The model canalso be applied in future research to assess the impactof improvements in operations on the inventory pro-ductivity of firms.
The rest of this paper is organized as follows. Sec-tion 2 summarizes the data and defines the perfor-mance variables used. Section 3 develops hypothesesto relate inventory turnover with gross margin, cap-ital intensity, and sales surprise using results fromthe existing literature. In §4, we discuss the empiri-cal model used in estimation. We present our empiri-cal results in §5, discuss their managerial implicationsin §6, and conclude in §7 with a discussion of the limi-tations of our study and directions for future research.
2. Data Description and Definition ofVariables
We use financial data for all publicly listed U.S. retail-ers for the 16-year period 1985–2000, drawn fromtheir annual income statements and quarterly andannual balance sheets. These data are obtained fromStandard & Poor’s Compustat database using theWharton Research Data Services (WRDS).
The selection of firms is based on a four-digitStandard Industry Classification (SIC) code assignedto each firm by the U.S. Department of Commerceaccording to its primary industry segment. Our dataset includes 10 segments in the retailing industry.Table 1 lists the segments, the corresponding SICcodes, and examples of firms in each segment. All
Table 1 Classification of Data Using SIC Codes into Retailing Segments
Retail industry segment SIC codes Examples of firms
Apparel and accessory stores 5600–5699 Ann Taylor, Filenes Basement, Gap, LimitedCatalog, mail-order houses 5961 Amazon.com, Lands End, QVC, SpiegelDepartment stores 5311 Dillard’s, Federated, J. C. Penney, Macy’s, SearsDrug and proprietary stores 5912 CVS, Eckerd, Rite Aid, WalgreenFood stores 5400, 5411 Albertsons, Hannaford Brothers, Kroger, SafewayHobby, toy, and game shops 5945 Toys R UsHome furniture and equip. stores 5700 Bed Bath & Beyond, Linens N’ ThingsJewelry stores 5944 Tiffany, ZaleRadio, TV, consumer electronics stores 5731 Best Buy, Circuit City, Radio Shack, CompUSAVariety stores 5331 K-Mart, Target, Wal-Mart, Warehouse Club
segments except apparel and accessories and foodstores correspond to unique four-digit SIC codes. Inapparel and accessories, we group together all firmsthat have SIC codes between 5600 and 5699 becausethere is substantial overlap among their products.This grouping enables us to increase the number ofdegrees of freedom by estimating one set of coeffi-cients for all apparel firms instead of estimating sep-arate coefficients for each SIC code. Likewise, in foodstores, we group together supermarket chains (SICcode 5400) and convenience stores (SIC code 5411)because of the overlap among their products.
Let Ssit denote the sales, net of markdowns, of firm iin segment s in year t, and CGSsit denote the cor-responding cost of goods sold. Both sales and costof goods sold are obtained from the annual incomestatements of the firms. Let GFAsitq denote the grossfixed assets, comprised of land, property, and equip-ment, of firm i in segment s at the end of quarter qin year t; NFAsitq denote the net fixed assets, com-prised of gross fixed assets less accumulated depreci-ation; Invsitq denote the inventory, valued at cost; andTAsitq denote the total assets. These four data items areobtained from the quarterly closing balance sheets ofthe firms. From these data, we compute the followingperformance variables for our study:
inventory turnover (also called inventory turns):
ITsit =CGSsit
14
∑4q=1 Invsitq
�
gross margin:
GMsit =Ssit −CGSsit
Ssit�
capital intensity:
CIsit =∑4
q=1 GFAsitq∑4q=1 Invsitq +
∑4q=1 GFAsitq
� and
sales surprise:
SSsit =Ssit
sales forecastsit�
Here, average inventory and average gross fixedassets are computed using quarterly closing values to
control for systematic seasonal changes in these vari-ables during the year. The method for obtaining thesales forecast will be described in §3.3.
We also note that there are alternative measuresof capital intensity that could be considered insteadof that defined above. In particular, NFAsitq could beused in place of GFAsitq to measure capital invest-ment, or TAsit could be used in the denominator asthe scaling variable instead of the sum of the aver-age inventory and the average gross fixed assets. Wetested our hypotheses with these alternative mea-sures and found that the results are consistent withthose reported in this paper. The reader is referred toStickney and Weil (1999) for detailed descriptions ofthe income statement and balance-sheet variables.
Our original data set contains 5,088 observationsacross 576 firms. After computing all the variables,the first two years of data for each firm are omitted.They could not be used in the analysis because thecomputation of sales forecast required two years ofsales data at the beginning of each time series. Wealso omit from our data set those firms that have lessthan five consecutive years of data available for anysubperiod during 1985–2000; there are too few obser-vations for these firms to conduct time-series analysis.These missing data are caused by new firms enter-ing the industry during the period of the data set,and by existing firms getting delisted due to merg-ers, acquisitions, liquidations, etc. Further, we omit
Table 2 Summary Statistics of the Variables for Each Retail Segment: 1985–2000
Average MedianNumber of annual Average Average Average annual Median Median Median
Number annual sales inventory gross capital sales inventory gross capitalRetail industry segment of firms observations ($ million) turnover margin intensity ($ million) turnover margin intensity
Note. The values for each variable are its mean and standard deviation across all observations in the respective segments.
firms that had missing data or accounting changesother than at the beginning or the end of the mea-surement period. These missing data are caused bybankruptcy filings and subsequent emergence frombankruptcy, leading to fresh-start accounting. Therewere also accounting changes related to the inven-tory valuation method. Out of 10 inventory valuationmethods identified by the Compustat database, fourare commonly used by retailers: FIFO (first in firstout), LIFO (last in first out), average cost method,and retail method (see the Compustat data manualfor the definitions of these methods). Most retailersin our data set use a combination of these methods.After removing the firms with missing observations,there were only three firms that switched betweenexclusively FIFO and exclusively LIFO inventory val-uations during the subject time period.
Our final data set contains 3,407 observations across311 firms, an average of 10.95 years of data perfirm. Table 2 presents summary statistics by retailingsegment for the performance variables used in ourstudy. It lists the mean and standard deviation foreach variable within each segment. For example, themean of inventory turnover for apparel and accessorystores is 4.57 and the standard deviation is 2.13. Thecoefficient of variation of inventory turnover rangesfrom 0.36 for hobby, toy, and game shops to 1.92 forhome furniture and equipment stores. Thus, the vari-ability of inventory turnover is not limited to a few
firms, but is widely prevalent. Hereafter, we use IT,GM, CI, and SS without the subscripts s, i, and t asabbreviations for the respective variable names. Wecollectively call GM, CI, and SS “explanatory vari-ables;” and IT, GM, CI, and SS “performance vari-ables” or “firm-level performance variables.”
3. Hypothesis DevelopmentIn this section, we set up the hypotheses to relateinventory turnover to gross margin, capital intensity,and sales surprise. An important aspect of our modelis that we focus attention on year-to-year variationswithin a firm, rather than differences across firms.This is done because differences in IT across firmsmay be associated not only with their GM, CI, andSS, but also with factors such as accounting policies,location strategy, management, etc. These factors areexogenous to our data set. Focusing on variationswithin a firm enables us to limit their influence. In theempirical analysis in subsequent sections, we controlfor variation across firms by using firm-specific fixedeffects.
We also note that firm-level aggregated variableshave several shortcomings that limit their usefulness.We identify these shortcomings at appropriate pointsin the analysis.
3.1. Gross MarginWe test the following hypothesis:
Hypothesis 1. Inventory turnover is negatively corre-lated with gross margin.
We motivate this hypothesis in two ways: by obser-vations of managerial practice, and based on resultsin the academic literature. In surveys of retailingfirms conducted by us, we find that managers tradeoff inventory turns and gross margin in their deci-sion making. They set their business targets partlyin terms of the product of gross margin and inven-tory turnover (this measure is called gross marginreturn on inventory, abbreviated as GMROI). Itemswith higher margins are given lower turns targetsthan items with lower margins. This trade-off is com-monly referred to by retailing managers as the “earnsversus turns” trade-off. It is consistent with the DuPont model in accounting, and is prescribed in retail-ing textbooks; see, for example, the strategic profitmodel in Levy and Weitz (2001, Chapter 7). However,no theoretical or empirical justification for this trade-off is provided in retailing textbooks. Thus, it is notclear whether the practice of trading off earns versusturns is based on observed trade-offs between inven-tory turns and gross margin, or whether it is simplya heuristic to allocate a targeted return on investmentto different items.
We explain below that the existing literature, eventhough it is largely based on item-level models,supports a negative correlation between inventoryturnover and gross margin, and more importantly,identifies several factors that could explain this cor-relation. In particular, gross margin can be relatedto inventory turnover directly because it determinesthe optimal service level. Further, gross margin canbe related to inventory turnover indirectly throughprice, product variety, and length of product lifecycle because they affect both inventory turnover andgross margin. The following discussion explains theserelationships.
Service Level. According to the classical newsboymodel, an increase in gross margin implies an increasein the average inventory level. It can further be shownthat in the newsboy model, an increase in inven-tory level implies a decrease in expected inventoryturnover regardless of the form of the demand distri-bution. Therefore, an increase in gross margin impliesa decrease in expected inventory turnover.
Price. For a given set of items with given costs,an increase in price increases the gross margin of thefirm. Further, because demand is negatively corre-lated with price, an increase in price decreases thedemand for the item and increases the coefficientof variation of demand, thus decreasing inventoryturnover.
Product Variety. Multiple papers in marketing andeconomics consider the effect of product variety onprice. According to Lancaster (1990), Chamberlin(1950), and Dixit and Stiglitz (1977), higher varietyleads to an increase in the consumers’ utility, either byreducing the distances of consumers from their per-ceived “ideal product” profiles (the Lancaster demandmodel), or because consumers have a built-in prefer-ence for variety (the Chamberlin demand model). Fur-ther, from consumer utility theory, higher consumerutility implies higher prices for a given cost (Kotler1986, Nagle 1987). According to Lazear’s model ofretail pricing and clearance sales (Lazear 1986), highervariety increases the retailer’s uncertainty about price,which further increases the average price.
In empirical research, Pashigian (1988) shows thatprice is positively correlated with variety in a study oftime-series price and sales data for department stores,and Kekre and Srinivasan (1990) show that firms withhigher variety have higher relative prices in a cross-sectional study of over 1,400 business units. Thus,according to the above papers, price increases withvariety for given cost. Therefore, variety has a pos-itive effect on gross margin through price. We notethat these papers do not address the cost of variety.
Numerous papers and case studies using risk pool-ing as the basis of their argument have examined
the impact of product variety on inventory turnover.Lower variety through delayed differentiation is usedto increase inventory turnover in the Benetton casestudy (Heskett and Signorelli 1989), at Hewlett-Packard (Feitzinger and Lee 1997), and in researcharticles that explore these relationships (Lee and Tang1997, Swaminathan and Tayur 1998). Zipkin (2000,Chapter 5) constructs an index of product variety, andobserves from experience with a large firm that anincrease in variety is associated with a decrease ininventory turnover. Van Ryzin and Mahajan (1999)also analyze the effects of variety on price and inven-tory using a model of assortment choice. While theydo not explicitly consider inventory turnover, theyshow that total inventory increases with variety, andthat variety under market equilibrium is increasing inprice given fixed procurement costs.
Length of the Product Life Cycle. The length ofproduct life cycle has a similar effect on gross marginand inventory turnover as product variety. A shorterproduct life cycle implies rapid changes to productsto better match consumer requirements, and thus,increased consumer utility (Pashigian 1988). As dis-cussed above, higher consumer utility implies higherprices and higher gross margin. A shorter productlife cycle also implies less availability of historicaldata for forecasting. Because the accuracy of demandforecasts increases with the availability of historicaldata, products with longer life cycle and greater avail-ability of historical data should have lower demanduncertainty, less safety stock requirement, and higherinventory turnover than products with shorter prod-uct life cycle and less availability of historical data.
Because service level, price, variety, and life-cyclelength are not measured in our model, separate testsof the linkages of these factors with inventory turnsand gross margin are beyond the scope of our study.Instead, Hypothesis 1 is limited to estimating the cor-relation of inventory turnover with gross margin.
3.2. Capital IntensityInvestments in warehouses, information technology,and inventory and logistics management systemsinvolve capital investment by a firm, which isaccounted as fixed assets, and is therefore measuredby an increase in CI. Thus, we formulate the follow-ing hypothesis:
Hypothesis 2. Higher capital intensity increases in-ventory turnover.
We expect that the addition of a new warehouseshould result in a decrease in total inventory at theretailer, and thus an increase in its inventory turnoverfor two reasons. First, the warehouse enables the
retailer to reduce safety stock over the supplier leadtime by postponing the decision to allocate inventoryacross stores (“the joint ordering effect;” see Eppenand Schrage 1981). Second, the warehouse enablesthe retailer to centralize safety stock and rebalancestore inventories between shipments from the sup-plier (“the depot effect;” see Jackson 1988).
We also expect inventory turns to increase withinvestment in information technology. According toCachon and Fisher (2000), the benefits of imple-menting information systems for the management ofinventory include better allocation of the inventory tothe stores, shorter ordering lead times, smaller batchsizes, and a lower cost of processing orders. Clarkand Hammond (1997), in a cross-sectional study, showthat food retailers who adopt a continuous replen-ishment process (CRP) enabled by the adoption ofelectronic data interchange (EDI) achieve 50%–100%higher inventory turns than traditional ordering pro-cesses. For further documentation of the benefitsof information technology, see Kurt Salmon Asso-ciates (1993), Campbell Soup Company (Cachon andFisher 1997), Barilla SpA (Hammond 1994), H. E. ButtGrocery Co. (McFarlan 1997), and Wal-Mart Stores,Inc. (Bradley et al. 1996).
Because capital intensity is measured from grossfixed assets, it does not isolate the effects of differ-ent kinds of capital investments made by a firm. Fur-ther, it includes other capital investments of a retaileras well—for example, investments in stores. Thesecould dilute the effect of capital intensity on inventoryturnover.
3.3. Sales SurpriseInventory turnover can be affected by unexpectedlyhigh sales. If the sales realized by a retailer in a givenperiod are higher than its forecast, then the aver-age inventory level for the period will be lower thanexpected, and realized inventory turnover, which is aratio of realized unit sales to the average inventoryfor the period, will be higher than expected. The out-come will be reversed if realized sales are lower thanexpected sales.
Therefore, we use sales surprise as defined in §2 tomeasure unexpectedly high sales, and formulate thefollowing hypothesis.
Hypothesis 3. Inventory turnover is positively corre-lated with sales surprise.
Sales surprise should, ideally, be measured withrespect to the management’s forecast of sales becauseinventory decisions taken by the management arebased on these forecasts. Because managements’ salesforecasts are not publicly reported, we estimate salesforecasts from historical data using Holt’s linear
exponential smoothing method.3 The sales forecast forperiod t is
sales forecastsit = Lsi� t−1 + Tsi� t−1�
where Lsi� t−1 and Tsi� t−1 are smoothed series defined as
Lsit = Ssit + �1−��Lsi� t−1 + Tsi� t−1��
Tsit = �Lsit −Lsi� t−1�+ �1− �Tsi� t−1�
and �0 < < 1� and �0 < < 1� are weight-ing constants. We compared the forecast errors forseveral values of and . The best forecasts wereobtained for = = 0�75. Thus, these values areused to compute all the results reported in this paper.We also computed sales forecasts using simple expo-nential smoothing and double exponential smooth-ing. These forecasts had higher forecast errors andwere biased compared to Holt’s linear exponentialsmoothing.
4. Model Specification and AnalysisWe propose the following log-linear model to test thehypotheses:
log ITsit = Fi + ct + b1s logGMsit + b2
s logCIsit
+ b3s log SSsit + �sit� (1)
Here, Fi is the time-invariant firm-specific fixed effectfor firm i; ct is the year-specific fixed effect for year t;b1s , b
2s , and b3
s are the coefficients of logGMsit, logCIsit,and log SSsit, respectively, for segment s; and �sitdenotes the error term for the observation for year tfor firm i in segment s. Hypotheses 1, 2, and 3 implythat, for each segment s, b1
s must be less than zero,and b2
s and b3s must be greater than zero.
We use a log-linear specification for three rea-sons: (1) A log-linear relationship between the vari-ables is suggested by plotting IT against GM, CI,and SS. (2) Retail industry reports (see, for exam-ple, Sack 2000) and surveys of retailers that we haveconducted show that multiplicative measures suchas GMROI and return on assets are widely used tomeasure and reward the performance of inventoryplanners and merchants. (3) We simulated a periodic-review inventory model with stationary demand fordifferent values of gross margin, lead time and vari-ance of demand, and collected data on the variables ofinterest to compare log-linear and linear model spec-ifications. We found that the log-linear specificationhad significantly lower prediction errors than the lin-ear specification.
3 Alternatively, one could use the I/B/E/S data set to obtain salesforecasts. This data set provides analysts’ forecasts of sales for asubset of the publicly listed firms for the period 1997 onwards.For the time period used in this paper, I/B/E/S provides forecastsonly for a few firms, giving a total of less than 300 observations.However, this data set could be useful in future research.
The following aspects of the model need elabora-tion:
Firm-Specific Fixed Effects, Fi. Inventory turnovercan be correlated with factors that are omitted inour data set, such as managerial efficiency, marketing,location strategy, accounting policy, etc. These factorscan result in biased and inconsistent estimates of theparameters (see Hausman and Taylor 1981). There-fore, we minimize their effect by using firm-specificcontrol variables, Fi. These control variables can bemodeled either as fixed effects or as random effects.We model them as fixed effects because they can beused to compare average inventory turnover perfor-mance across firms over the period of analysis.
Omitted variables also imply that cross-sectionaldata for a single year or longitudinal data for a singlefirm are unsuitable for estimating the model becausethey cannot distinguish the effects of the explanatoryvariables from differences in Fi (see Hoch 1962).
Time-Specific Fixed Effects, ct . These variablescontrol for changes in secular characteristics overtime, such as in economic conditions, in the inter-est rates, in price level, etc., and thus enable us tocompare inventory turnover across years. They alsoenable us to measure trends in average inventoryturnover in the retailing industry over time aftercontrolling for the effects of the other explanatoryvariables.
Segment-Specific Coefficient Estimates, b1s , b
2s , b
3s .
The coefficients of the explanatory variables mightdiffer across retailing segments. Thus, we estimatesegment-specific coefficients to test for heterogeneityacross segments.
It is useful to estimate other model specificationswith different combinations of the control variablesto ascertain the correctness of the model and drawfurther insights. First, to test whether the coefficientsof the explanatory variables differ across segments,we compare (1) with the following specification (withpooled coefficients of explanatory variables instead ofsegmentwise coefficients):
log ITsit = Fi + ct + b1 logGMsit + b2 logCIsit
+ b3 log SSsit + �sit� (2)
Second, to test whether the firmwise fixed effects Fiare statistically significant, we compare (1) withthe following specification (with segmentwise fixedeffects instead of firmwise fixed effects):
log ITsit = Fs + ct + b1s logGMsit + b2
s logCIsit
+ b3s log SSsit + �sit� (3)
Here, Fs is the segmentwise fixed effect, and the otherterms have their usual meaning. Both (2) and (3)
are useful because they have fewer parameters, andhence can allow more precise estimation. However,(3) should not be used if firmwise fixed effects arestatistically significant.
Third, because IT and GM are both functions of costof goods sold, it is possible that we observe a nega-tive correlation between IT and GM even if inventorylevels are independent of the gross margin realizedby a firm. A similar argument could be applied toIT and CI because they are both functions of aver-age annual inventory. To test for this problem, weestimate an alternative model using average annualinventory level, Invsit �= 1
4
∑q Invsitq�, as the depen-
dent variable instead of ITsit. We add CGSsit to the listof explanatory variables in this model to control forscale:
log Invsit = Fs + ct + b1s logGMsit + b2
s logCIsit
+ b3s log SSsit + b4 logCGSsit + �sit� (4)
For this model, we measure capital intensity as theratio of GFA to TA, rather than as defined in §2, toavoid having a term in the explanatory variables thatis a function of Invsit. Further, we also test for thisproblem using Models (1) and (2). We estimate thesemodels with values of gross margin and capital inten-sity lagged by one year, logGMsi� t−1 and logCIsi� t−1,as the explanatory variables instead of logGMsit andlogCIsit.
Other model specifications can be constructed totest if b1
s , b2s , and b3
s change with time or if the time-specific fixed effect ct differs across segments. Wecompare the results of different specifications in §5.The main results of the paper are based on (1) and (2).We estimate all models assuming that the error term,�sit, has first-order autocorrelation, and is segment-wise heteroscedastic; i.e., the variance of �sit varies bysegment. The estimation process and statistical testsof assumptions are presented in the appendix. Thereader is referred to Greene (1997, Chapter 14), Hsiao(1986), and Judge et al. (1985, Chapter 13) for furtherdiscussion of the specification and estimation of paneldata models such as ours.
5. Results5.1. Basic ResultsTable 3 shows the fit statistics for Models (1) and (2),estimated using MLE. The overall fit of Model (1) isstatistically significant �p < 0�0001�. The coefficientsof all the explanatory variables, logGMsit, logCIsit,and log SSsit, are also significantly different from zero�p < 0�0001�. Comparing the results for Models (1)and (2), we find that the likelihood ratio test thatModel (1) is preferred to Model (2) is statistically sig-nificant �p < 0�0001�. Separate F -tests to determine
Table 3 Fit Statistics for the Maximum Likelihood Estimates ofModels (1) and (2)
Tests of significance of variables (F -tests)Firm 12�24 20�13Year 6�09 4�18log GM 119�28 290�99log CI 129�14 139�05log SS 448�12 403�16
Differences in coefficient estimates across segments (F -tests)log GM 4�19log CI 30�26log SS 12�20
Note. All the statistics are significant with p < 0�0001.
whether each coefficient differs across segments arealso significant (p < 0�0001 for each of logGMsit,logCIsit, and log SSsit�. Therefore, the coefficients’ esti-mates differ significantly across segments.
We determine the fraction of variation in log ITsitexplained by each model by computing the over-all prediction accuracy and the within-firm predic-tion accuracy of each model using the usual formulafor R2:
overall prediction accuracy
= 1−∑
s� i� t�log ITsit − l̃og ITsit�2
∑s� i� t�log ITsit − log IT�2
�
within-firm prediction accuracy
= 1−∑
s� i� t�log ITsit − l̃og ITsit�2
∑s� i� t�log ITsit − log ITsi�
2�
where l̃og ITsit is the predicted value of log ITsitobtained from (1) or (2), log IT is the overall meanof log ITsit, and log ITsi is the within-firm meanof log ITsit.4 The overall prediction accuracy forModel (1) is 97.16% and for Model (2) is 96.83%.The within-firm prediction accuracy for Model (1) is66.7% and for Model (2) is 62.8%. The within-firmaccuracy is remarkable because it shows that year-to-year changes in the IT of a firm are highly correlatedwith simultaneous changes in GM, CI, and SS. Theoverall prediction accuracy is higher than the within-firm accuracy because the between-firm variation in
4 There are several measures of R-square for the generalized regres-sion model. One alternative would be to apply the formula forR-square to the transformed model obtained in FGLS estimation.Because the R-square thus determined need not lie between 0and 1, we do not use this procedure. See Kmenta (1996, Chapter 12)for details.
Pooled coefficients from Model (2) −0�285a 0.017 0�252a 0.021 0�143a 0.007
Note. Pooled coefficients are for Model (2) and segmentwise coefficients are for Model (1).a�bStatistically significant at p < 0�001 and p < 0�02, respectively, for two-tailed tests.
inventory turnover is larger than the within-firmvariation, and is fully explained by the firm-specificfixed effects.
Table 4 shows the coefficients’ estimates for Mod-els (1) and (2). The pooled coefficient for logGMsit is−0�285 �p < 0�0001�, and strongly supports Hypoth-esis 1. The segmentwise coefficients also supportHypothesis 1 for nine of the ten segments. Thus,inventory turns are negatively correlated with grossmargin. Because we have a log-linear model, thecoefficient of logGMsit gives the elasticity of inven-tory turns with respect to gross margin. Thus, a1% increase in gross margin (for example, from 0.5to 0.505) is associated with an estimated −0�285%change in inventory turns.
Across segments, the coefficient estimate forlogGMsit varies from −0�153 for apparel and acces-sories retailers to −0�571 for hobby, toy, and gameshops. From the discussion in §3, there can be sev-eral reasons for this variation. For example, for thesame value of GM, product variety, life-cycle lengthand demand uncertainty may vary across segments,resulting in different coefficients. Because price, vari-ety, and life-cycle length are not included in our dataset, we cannot ascertain the causes of the differencesin coefficients’ estimates across segments. These couldbe investigated in a further study.
The pooled coefficient for logCIsit is 0.252 �p <0�0001�, and strongly supports Hypothesis 2. Seg-mentwise estimates of the coefficient of logCIsit alsostrongly support Hypothesis 2 for seven of the ten seg-ments. The value of the coefficient ranges from 0.106to 1.085 across segments where it is statistically signif-icant �p < 0�02�. Thus, investment in capital assets ispositively correlated with inventory turnover.
The pooled and segmentwise estimates of the coef-ficient of log SSsit are all positive and statisticallysignificant at p < 0�001. They strongly support
Hypothesis 3. The value of the pooled coefficient is0.143, and the segmentwise coefficients range between0.053 and 0.279. These estimates are useful becausethey enable us to control for the effect of surprisinglyhigh sales on inventory turnover.
5.2. Time Trends in Inventory ProductivityThe year-specific fixed effects, ct , in our model canbe used to estimate the time trend in inventory pro-ductivity after adjusting for the correlation with grossmargin, capital intensity, and sales surprise. Table 5shows the estimates of ct obtained from Models (1)and (2), and Figure 2 shows a time-series plot of ctfor Model (2). Note that these estimates are decreas-ing with time. Taking the standard errors of theestimates into account, we find that the estimatesof ct for the initial years, t = 1987� � � � �1993, are
Table 5 Estimates of Time-Specific Fixed Effects ct for Models (1)and (2)
Figure 2 Plot of Time-Specific Fixed Effects ct for Model (2)
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1986 1988 1990 1992 1994
1996 1998
2000
Time (in years)
c(t
)
Note. The error bars show intervals of 2× standard error.
significantly larger than the estimates of ct for thelatter years, t = 1996� � � � �2000 �p < 0�01�. This showsthat controlling for sales surprise and changes in cap-ital intensity and gross margin, inventory turns havedecreased with time during 1987–2000.
The trend in ct can be compared with the “unad-justed” time trend in inventory turns (i.e., ignoringthe correlation with GM, CI, and SS) by fitting thefollowing model:
ysit = gi +ht+nsit� (5)
Here, ysit equals ITsit to estimate a linear time trendand log ITsit to estimate an exponential time trend,gi is the intercept for firm i, and h is the commonslope with respect to time across all firms. We alsoapply this model to CIsit, GMsit, logCIsit, and logGMsitto estimate the trends in their values. Table 6 givesthe results obtained. We find that inventory turnshave decreased significantly with time �p < 0�0001�,capital intensity has increased significantly with time�p < 0�0001�, and gross margin has no significant timetrend.
Now consider the trends in inventory turns forindividual firms. These trends can be estimated withthe following models, after slight changes to (1)and (5):
ysit = gi +hit+nsit� (6)
log ITsit = Fi +h′it+ b1
s logGMsit + b2s logCIsit
+ b3s log SSsit + �sit� (7)
Here, (6) measures the “unadjusted” time trend, hi, inthe inventory turns for each firm i; and (7) measuresthe “adjusted” time-trend, h′
i, after controlling forthe correlation with the explanatory variables. Wefind that the estimate of hi is negative for 176 firms(of these, 76 are statistically significant �p < 0�05�),and positive for 135 firms (59 statistically significant
Table 6 Time Trends in IT, CI, and GM Estimated Using Equation (5)
In summary, the overall trend in inventory turnsin the retailing industry is downward sloping dur-ing 1987–2000. This result is consistent with the resultobtained by Rajagopalan and Malhotra (2001) forseveral sectors in the manufacturing industry. How-ever, we additionally find that capital intensity hasincreased significantly during this period, and is pos-itively correlated with inventory turnover. Thus, eventhough the overall trend in inventory turns is neg-ative, firms with a greater increase in capital inten-sity have shown a larger increase in inventory turnsover time compared to their peers. Further, as shownusing (6) and (7), we also find that the trend ininventory turns varies across firms. During the sub-ject period, 43% of the firms have shown an increasein inventory turns, and 38% of the firms have shownan increase in inventory turns controlling for thechanges in capital intensity, gross margin, and salessurprise.
Rajagopalan and Malhotra offer several conjecturesto explain the observed downward trends in inven-tory turns; for example, product variety may haveincreased with time, product life cycles may havebecome shorter with time due to faster introduc-tion of new products, average lead times may haveincreased due to greater global sourcing. While theseconjectures apply to retailing as well, like Rajagopalanand Malhotra, we currently cannot offer conclusiveevidence.
5.3. Econometric IssuesWe find that Models (1) and (2) are more suitablefor our analysis than Model (3) because the firmwisefixed effects Fi are statistically significant, as shown inTable 3. We also find that the estimates from Model (4)and from Models (1) and (2) with lagged explana-tory variables, logGMsi� t−1 and logCIsi� t−1, supportHypotheses 1, 2, and 3 at p < 0�0001. Therefore, theestimated correlations between inventory turns andgross margin, and between inventory turns and capi-tal intensity, are not artifacts of the way the variablesare defined.
Please see the appendix for the results regardingheteroscedasticity and autocorrelation in the data set.
6. Managerial ImplicationsOur results show that inventory turnover should notbe used per se in performance analysis. For example,if a firm realizes an increase in inventory turnoverwith a concurrent decrease in gross margin, it doesnot necessarily indicate an improvement in its capa-bility to manage inventory. Likewise, if two firmshave similar inventory turnover and gross marginvalues, but different capital intensities, then the firmwith the lower capital intensity could possibly have abetter capability to manage inventory than the otherfirm. Finally, if a firm realizes an increase in inventoryturnover with an unexpected increase in sales, thenthe increased inventory turnover may not indicatean improved capability to manage inventory. Thus,changes in gross margin, capital intensity, and salessurprise should be incorporated in the evaluation ofinventory productivity of a firm.
Our results give a trade-off curve that computesthe expected inventory turnover of a firm for givenvalues of sales surprise, gross margin, and capitalintensity. We term the distance of the firm from itstrade-off curve as its adjusted inventory turnover (AIT).The value of AIT for firm i in segment s in year t iscomputed as
logAITsit = log ITsit − b1 logGMsit
− b2 logCIsit − b3 log SSsit�
or, equivalently, as
AITsit = ITsit�GMsit�−b1
�CIsit�−b2
�SSsit�−b3
� (8)
AIT is an empirical measure to compare inventoryproductivity across firms and across years by control-ling for differences in gross margin, capital intensity,and sales surprise.
According to our results, managers of firms withlow AIT should investigate whether their firms areless efficient than their peers, and identify steps theymight take to improve their inventory productivity.Firms with higher inventory turnover may differ sys-tematically from firms with lower inventory turnover.On the one hand, such differences may be attributedto differences in accounting policies and may not haveoperational implications. On the other hand, they mayindicate differences in efficiency that cannot be recti-fied simply by increased spending. This possibility issupported in our discussions with managers. Fisheret al. (2000) discuss differences between retailers andidentify best practices in retail operations through on-site interviews, surveys, and workshops in a four-yearstudy of 32 retailers.
We present two examples to illustrate the interpre-tation of adjusted inventory turns. The first example
shows that inventory turns may overstate differencesin inventory productivity across firms. The secondexample shows that time trends in inventory turnscan be misleading.Example 1. Consider again the example of four
consumer electronics retailers in Figure 1. Weapply (8) to find the AIT for these firms. For exam-ple, in year 1996, the inventory turns of these firmsare 5.9 (Best Buy), 4.1 (Circuit City), 8.2 (CompUSA),and 3.0 (Radio Shack). The corresponding values ofgross margin are 0.15, 0.26, 0.14, and 0.32, respectively,and the corresponding values of capital intensity are31%, 47%, 33%, and 42%, respectively. After apply-ing these values and sales surprise, we find that theadjusted inventory turns of the four firms are 3.1,2.6, 4.1, and 2.2, respectively. Thus, we observe thatthe differences between the adjusted inventory turnsturns of Best Buy, Circuit City, CompUSA, and RadioShack are smaller than the differences between theirinventory turns because the differences in inventoryturns are partly compensated for by the differencesin gross margin. For example, the inventory turns ofCompUSA are 2.8 times those of Radio Shack, but theadjusted inventory turns of CompUSA are 1.9 timesthose of Radio Shack.
The gross margins of these firms might differ dueto any one or more of the factors listed in §3. Indeed,the annual reports to shareholders of these firmsshow that their product mixes differ from each other.CompUSA has a higher proportion of personal com-puters in its sales (high turns, low margins), Best Buyand Circuit City have higher proportions of homeelectronics and appliances (midrange turns and mar-gins), and Radio Shack has a higher proportion ofspare parts and accessories in its sales (low turns,high margins). Because the adjusted inventory turnsof these firms are less disparate than their inven-tory turns, it suggests that the differences in inven-tory turns between these firms may not indicate betteror worse inventory productivity. Figure 3 shows thetrade-off between inventory turns and gross marginfor the four firms obtained using (8) (assuming con-stant capital intensity and no sales surprise to avoidyear-to-year variations in these variables).Example 2. Ruddick Corporation is a holding com-
pany that owns Harris Teeter, a regional supermar-ket chain in the southeastern United States with137 stores and sales of $2.7 billion in the year 2000.Figure 4 shows time-series plots and linear trends ofIT and AIT for Harris Teeter for the years 1987–2000.The inventory turns of Harris Teeter do not show anysignificant time trend. During the same period, thegross margin of Harris Teeter has increased steadilyfrom 23.4% to 30.9%, and its capital intensity hasincreased marginally. After applying (8), we find thatthe adjusted inventory turns of Harris Teeter have
Figure 3 Trade-off Curves Between Inventory Turnover and GrossMargin Estimated for the Four Consumer ElectronicsRetailers in Figure 1 for the Years 1987–2000
0
2
4
6
8
10
12
14
0 0.1 0.2 0.3 0.4 0.5 0.6
Gross Margin
Invento
ryT
urn
s
Best Buy Co. Inc.
Circuit City Stores
CompUSA
Radio Shack
Note. These curves are computed using (8). CI is set to its average value foreach firm and SS is set to 1 to avoid year-to-year variations in these variables.
increased significantly at an average rate of 0.055per year. Thus, the adjusted inventory turns showthat the lack of time trend in inventory turnovermay not imply that the inventory productivity of thefirm has not improved with time. Indeed, we dis-covered from retailing managers that Harris Teeterswitched to private-label brands during this period.Because private-label brands have higher gross mar-gins, Harris Teeter increased the service level forprivate-label merchandise in its stores, affecting itsinventory turns.
Figure 4 Plot of Inventory Turnover and Adjusted Inventory Turnoverfor Ruddick Corp.
y = -0.0194x + 8.3937
R2
= 0.0592
y = 0.0548x + 5.5045
R2
= 0.52035
5.5
6
6.5
7
7.5
8
8.5
9
9.5
1987 1989 1991 1993 1995 1997 1999
Inve
nto
ryT
urn
ove
r
Inventory Turnover Adjusted Inventory Turnover
Linear (Inventory Turnover) Linear (Adjusted Inventory Turnover)
7. Limitations and Directions forFuture Research
We have shown that inventory turns in retail ser-vices have a high correlation with gross margin, cap-ital intensity, and sales surprise. Therefore, inventoryturns should not be used, per se, in performanceanalysis. Instead, we have proposed an empiricalmetric derived from our model, adjusted inventoryturns, which controls for the correlation betweenthese variables and enables comparison of inventoryproductivity across firms and across years. We havealso computed time trends in inventory turns in theretailing industry for the period 1987–2000. We findthat inventory turns in the industry, on average, havedeclined during this period even though they are pos-itively correlated with capital intensity, and capitalintensity has increased during this period. Further,there are marked differences between the time trendsin inventory turnover across firms. Inventory turns of43% of the firms in our data set have improved withtime, while the rest have declined.
Because our paper is based on aggregate financialdata, it has many limitations that can be addressed infuture research using more detailed data sets. The firstis the issue of omitted variables. Operational charac-teristics such as product variety, length of product lifecycle, and price are omitted in our model. Thus, ourresults are limited to estimating the structural rela-tionship between inventory turns and gross margin;they do not explain the causes of this relationship.Our model can be enriched by including the omit-ted variables and directly measuring their effects oninventory turns and gross margin.
A second limitation of our study is that the vari-ables are measured at an aggregate level. The variablefor capital intensity does not distinguish between therelative merits of different kinds of investments, suchas in information technology, warehouses, logisticsmanagement systems, etc. Disaggregated data couldbe used to extend our analysis and test for the effec-tiveness of different kinds of investments made by afirm. Further, some firms have more than one retailchain under one corporate ownership (for example,Gap, Inc.), or own stores in many countries. Data atthe level of retail chain and country of location forsuch firms would be useful to analyze the trade-offsbetween the performance variables more accurately.
A third limitation of our study is related to the mea-surement of accounting data. We have sought to min-imize the effects of accounting policies by focusingonly on intrafirm variation in inventory turns. Fur-ther, we have controlled for firms that report changesin accounting policies, mergers, acquisitions, and fil-ing of bankruptcy during the period of the study.However, the constitution of the variables measured
in our study may change even when accounting poli-cies remain unchanged. Therefore, our results need tobe interpreted with caution.
Our paper identifies opportunities for futureresearch on inventory productivity. One valuable areaof research is to investigate why some firms realizehigher inventory productivity than others even aftercontrolling for differences in capital investment, grossmargin, and sales surprise. This question could beof relevance to both the operations and the businessstrategy literature. In the latter, it would contributeto research on the role of industry-level, corporate-level, and firm-level strategy on the operating per-formance of firms (see, for example, Beard and Dess1981, McGahan and Porter 1997, Rumelt 1991, andSchmalensee 1985). A related research question is tounderstand why the elasticities of inventory turnswith respect to the explanatory variables differ acrosssegments. We have hypothesized some plausible rea-sons for these differences that could be tested infuture research. Finally, we have tested our modelfor many alternative specifications, data sets, andtime periods. We have found the estimates to bevery robust with respect to these variations. Thismodel could be applied to control for correlationsbetween performance variables in future research asto how operational improvements affect operatingperformance and financial performance of firms.
AcknowledgmentsThe authors thank the referees and the editors for their valu-able feedback on the previous versions of this work.
Appendix
Estimation and Econometric IssuesBecause our data contain observations across firms andyears, it is likely that the variance of �sit varies acrossfirms, and that �sit is correlated across years. Further, wefind that the standard deviations of all the variables dif-fer substantially across segments. For example, as shownin Table 2, the standard deviation of inventory turnoverranges from a low of 0.58 for jewelry stores to a high of10.42 for home furniture and equipment stores. Likewise,the standard deviation of gross margin ranges from a lowof 0.12 for food stores to a high of 1.02 for catalog and mail-order houses. Therefore, we consider a flexible structureof the variance-covariance matrix of �sit with segmentwiseheteroscedasticity and first-order autocorrelation. Segmen-twise heteroscedasticity implies that the variance of �sit isidentical across firms within a retailing segment, but differsacross segments. Autocorrelation is also a common charac-teristic of financial time-series data. Because our data areannual time series, we use a first-order autoregressive pro-cess; higher-order autoregressive processes would be suit-able for monthly or quarterly data.
For this variance structure, ordinary least squares (OLS)estimators are not efficient and the tests of significanceperformed on OLS estimators are not valid. Therefore, we
use maximum likelihood estimation (MLE) to estimate theparameters of our model.5 See Greene (1997, Chapter 13)for a description of the estimation methodology, and Judgeet al. (1985) for a survey of the research on the asymptoticproperties of various estimation methods.
We obtain the following results regarding the spec-ification of the error term. We find that segmentwiseheteroscedasticity and first-order autocorrelation are alsostatistically significant in our data set.6 The standard errorranges from 0.011 for department stores to 0.145 for homefurnishings and equipment stores. The autocorrelation coef-ficient ranges from 0.29 for hobby toys and games stores to0.92 for home furnishings and equipment stores. Thus, theuse of MLE with segmentwise heteroscedastic and AR(1)autocorrelated errors is suitable for our analysis.
Further, we find that the coefficients’ estimates for theexplanatory variables are robust with respect to changesin model specification if the assumptions of heteroscedas-tic and AR(1) autocorrelated errors are applied. For exam-ple, even though firmwise fixed effects Fi are statisticallysignificant, Model 3 with segmentwise fixed effects givessimilar coefficients’ estimates as Models (1) and (2). (Theautocorrelation coefficient becomes very large and capturessome of the differences across firms.) However, Model 3does not give the same results when errors are assumedto be homoscedastic and independent. We think that thisindicates the presence of a correlation between the firm-wise fixed effects and the explanatory variables as discussedin §4. Other changes, such as segment-specific year effectsor linear time trends also do not have any significant effecton the coefficients of the explanatory variables.
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