Do Inventory Holding Costs and Stockout Costs Explain Inventory Investment
Behavior of U.S. Public Retailers During Economic Shocks?
Saravanan Kesavan†
Tarun Kushwaha‡
October 2011
Abstract
In this paper we analyze how the inventory investment behavior during economic shocks varies across
retailers. We investigate if inventory holding costs and stockout costs can explain the differences in observed
behavior. We use data on macro-economic indicators and quarterly filings of US public retailers from 1985 to
2009 to estimate dynamic model of short and long term impact of macroeconomic shocks on inventory turns.
Our results show that inventory turns move counter-cyclically with macro-economic shocks and are
asymmetric in magnitude. Retailers increase their inventory investments significantly more during expansions
than curtailing them during contractions. During expansion shocks, retailers with low inventory holding costs
increase their inventory investment significantly more than those with high inventory holding costs. On the
contrary, retailers with low stockout costs curtail their inventory investments significantly more than those
with high stockout costs during contraction shocks.
Keywords: Inventory Turns, Macro-Economic Shocks, Expansion, Contraction, Inventory Holding Cost, Stockout Cost
Assistant Professor of Operations, Technology and Information Management (saravanan_kesavan@unc.edu)
Assistant Professor of Marketing (tarun_kushwaha@unc.edu)
Both are at the Kenan-Flagler Business School. We thank Barry Bayus, Vishal Gaur, Girish Mallapragada, Andrew
Petersen, Federico Rossi, Brad Staats, Seminar participants at Harvard Business School and University of North Carolina
for providing useful feedback on earlier versions of this manuscript.
0
†
‡
1. Introduction
The state of the economy has a great impact on the retailing industry. In the U.S., the correlation
between GDP1 and retail sales during the period from 1979 to 2009 is .98. This high correlation is driven by
the increasing contribution of personal consumption expenditure to the overall GDP, which rose from 62.5%
in the 1970s to 70% in 2009. Thus, changes in the overall U.S economy are largely driven by changes in
consumer spending, which directly affects retail demand. In fact, recent research in operations management
has shown that it is possible to improve sales forecast accuracy of retailers by incorporating macroeconomic
signals (Gaur et al. 2011).
It is therefore not surprising that retailers become concerned about their inventory investment when
there are economic shocks, or unanticipated fluctuations to the overall economy, as they increase uncertainty
about future demand. Inventory is the largest asset in the majority of retailers’ balance sheets (Gaur and
Kesavan 2007) and managing this critical asset is important for retailers’ future financial performance
(Kesavan and Mani 2011). Inventory control becomes especially important during economic shocks when
there may be sudden surge or decline in demand for retailers resulting in large out-of-stocks or excess
inventory. Out-of-stocks could cause customers to switch to competitors (Gaur and Park 2007) and excess
inventory could result in lower profitability due to higher inventory holding costs, larger discounts to get rid
of this inventory or inventory write-offs (Hendricks and Singhal 2009; Larson et al. 2011).
In this paper, we examine how the inventory investment behavior during economic shocks varies
across retailers. Empirical evidence on how firms change their inventory investment during economic cycles
is provided by macroeconomics literature. This literature has shown that firms increase their inventory
investments during expansion periods and decrease them during contraction periods resulting in their
inventory turns moving counter-cyclically with economic cycles. Because this literature is concerned with
aggregate industry-wide and economy-wide changes in inventory investment, it largely ignores the firm
characteristics that moderate inventory investments in the face of economic shocks2. Thus, it is unclear
whether factors such as inventory holding costs and stockout costs that are critical in determining stocking
quantity at the SKU-level, help explain differences in inventory investment behavior observed at the firmlevel during economic shocks.
Empirical examination of how retailers change their inventory investment in response to economic
shocks is important for several reasons. First, suppliers to retailers are impacted by not only changes in endconsumer demand due to economic shocks but also by changes in retailers’ inventory levels. For example,
GDP, retail sales, and personal consumption expenditure data obtained from Bureau of Economic Analysis and
COMPUSTAT.
1
2
We discuss the exceptions in §2.
1
when Procter & Gamble’s sales declined in fiscal year 2009, it blamed the decline in consumer demand as well
as inventory reductions at retailers as contributing to its financial downturn34. Therefore, knowledge of how
retailers change their inventory levels during economic shocks would help their suppliers to plan inventory
efficiently. Second, interest in studying factors that drive firm-level inventories in the operations management
literature has increased (Gaur et al. 2007, Gaur and Kesavan 2009, Rumyantsev and Netessine 2007,
Rajagopalan 2009), making benchmarking inventory performance of firms easier. Understanding the impact
of economic shocks on inventory turns would help in determining how to benchmark inventory performance
during economically turbulent periods.
We examine the differences in inventory investment behavior across retailers during economic
shocks by categorizing economic shocks as expansion and contraction shocks and classifying retailers based
on their inventory holding costs and stockout costs. We use inventory turns as our primary dependent
variable to examine how retailers change their inventory investment in the face of economic shocks. We do
so for the following reasons. First, economic shocks could affect both inventory investment as well as sales of
retailers. The inventory turns metric helps us capture how inventory investment changes relative to sales.5
Second, inventory turns metric remains the most popular measure of inventory performance in industry so
understanding the impact of economic shocks on inventory turns would be of managerial interest. Third, we
are able to build on the operations management literature that has used inventory turns, or its reciprocal daysinventory, as the dependent variable (Gaur et al. 2005, Gaur and Kesavan 2007, Rumyantsev and Netessine
2007; Rajagopalan 2010). All of our analysis is conducted at the firm-level using quarterly data from 1985 to
2009.
We have the following results. First, we quantify the impact of economic shocks on inventory levels
in the overall sample. We find that 1% unexpected increase in GDP (expansion shock) in a quarter leads to a
1.32% decrease in inventory turns by the end of subsequent quarter, and 1% unexpected decrease in GDP
(contraction shock) leads to a .41% increase in inventory turns by the end of subsequent quarter in the overall
sample. We call this the short-term impact. The long term impact, or the total impact, of expansion and contraction
shocks on inventory turns are 3.49% decrease and 1.10% increase, respectively. While the direction of our
results support the counter-cyclical movement of inventory turns documented in the macroeconomics
literature, the magnitude of the short-term and long-term impacts of expansion and contraction shocks show
3
http://www.pginvestor.com/phoenix.zhtml?c=104574&p=irol-newsArticle&ID=1316941
4 Our conversations with P&G business intelligence group confirmed that the question of how retailers change their
inventory investment during recessions is of direct relevance to them. 5
One disadvantage of the inventory turns metric is that it is difficult to make out if a change to this metric is the result
of a change in sales or inventory or both. We tried alternate model specifications and determined that both sales and
inventory change during economic shocks and inventory turns is therefore a good metric to capture the relative change. 2
the strong asymmetry in the inventory investment behavior of retailers. Based on the short-term and longterm impacts of inventory turns, we determine that 76% of the change in inventory turns during expansion
and contraction shocks dissipates in 4 quarters. Thus, the impact of economic shocks on inventory levels can
last a long time and should be of significant managerial interest.
Second, we examine the retailer characteristics that explain the heterogeneity in inventory investment
behavior across retailers. We find that retailers with low inventory holding costs react more aggressively to
expansion shocks by increasing inventory investment compared to retailers with high inventory holding costs.
On the other hand, we find that retailers with low stockout costs tend to react more aggressively to
contraction shocks by reducing inventory levels compared to those with high stockout costs. Our results are
consistent with the newsvendor logic that postulates stocking more with lower overage costs and higher
underage costs. Thus, both inventory holding-costs and stockout costs that are vital factors in determining
stocking quantities at the SKU-level also explain differences in inventory investment behavior observed at the
firm-level.
Our paper makes the following contributions to the operations management literature. First, the
firm-level inventory literature in operations management that has examined factors that explain variations in
inventory levels has typically used time dummies to capture macroeconomic conditions (example, Gaur et al.
2005). Our paper uses methodologies from marketing to quantify expansion and contraction shocks and
shows that both types of shocks contain significant explanatory power over changes in inventory turns of
retailers. Second, our paper shows that both inventory holding costs and stockout costs that play a critical
role in driving stocking quantities at the SKU-level also help explaining firm-level investment behavior. By
demonstrating that the insights from SKU-level models hold at the firm-level, we show that even high-level
managers who deal with firm-level inventory will benefit from understanding classical inventory models
(Rumyantsev and Netessine 2007). Finally, our paper makes methodological contributions to the firm-level
inventory literature. Our paper is the first to use a dynamic model specification to study firm-level inventory.
Such dynamic models have been extensively used in marketing, economics, and other fields where it was
important to consider the lagged effects of their explanatory variables. Using a dynamic model specification,
we are able to capture the short-term and long-term impacts of economic shocks and show that a
considerable portion of the impact of economic shocks on retailers’ inventory levels is lagged.
Economic shocks are exogenous and unpredictable by definition, thereby limiting the managerial
implications of our study results to retailers. However, suppliers to retailers may benefit from knowing how
retailers reacted to past shocks since it may help them to predict orders from retailers, which are likely to be
placed after the economic shock with a lag. In fact, our results show that the impact on retailers’ inventory
peaks one quarter after the incidence of shock suggesting that there may be a significant lag between the
incidence of a shock and when the retailers react by placing change orders. Our study provides the following
3
forecasting guidelines for such suppliers. Since retailers with different inventory holding costs and stockout
costs react differently to economic shocks, it is important for their suppliers to adopt different forecasting
policies based on the type of retailer they serve. Further, the asymmetric inventory investment behavior
during expansion and contraction shocks suggests that the probabilistic structure of the inventory time-series
may be different during expansion and contraction periods. Therefore, suppliers may need to develop
forecasts by accounting for the change in stochastic behavior along with the conditional means during these
shocks. This may involve developing non-linear models for forecasting as linear forecasts will not be optimal
under these conditions.
2.
Literature Review, Conceptual Model, and Hypotheses
2.1
Literature Review
In this section, we review operations management literature that identifies factors that explain
changes in firm-level inventory in the retail sector. We also briefly discuss the literature in macroeconomics
that studies aggregate inventory in the context of business cycles.
First, we consider the operations management literature that deals with the retail sector. Gaur et al.
(2005) is one of the first papers to systematically study this sector, using publicly available financial data to
examine the correlations between firm-level factors and inventory turns. Using a panel dataset of a large
number of retailers from 1987 to 2000, its authors show that changes in gross margin, capital intensity, and
sales surprise are correlated with changes in annual inventory turns for retailers. They also propose adjusted
inventory turns as a new metric to benchmark inventory performance for public retailers. Subsequently, Gaur
and Kesavan (2007) retest the hypotheses from Gaur et al. (2005) and enhance their model by additionally
considering, the effect of scale and replacement of sales surprise by sales growth to separately account for
growth effects.
Rumyantsev and Netessine (2007) are motivated to examine whether findings from the classical
inventory model hold at the firm-level. This was the first study in Operations Management that used highfrequency quarterly data to explain changes in inventory turns at the quarterly-level. They use data from retail,
manufacturers, and distributors to test hypotheses driven from the theoretical inventory management
literature. They find significant correlations between lead time, demand uncertainty, gross margin, and size
but obtain mixed results on the correlation between inventory holding costs, measured using the T-bill rate,
and inventory. They conclude that the classical inventory models explain the behavior of firm-level inventory
as well. Again, this paper largely considers only firm-level factors in explaining changes in inventory turns and
finds that the one economic factor, T-bill rate, produces mixed results.
Rajagopalan (2009), like our paper, studies inventory turns of retailers. This paper augments
secondary data from Compustat database with primary data on product variety for its analysis. It finds that
4
gross margin, product variety, economies of scale, and seasonality impact inventory turns of retailers. Like
Rumyantsev and Netessine (2007), this paper also does not find support for inventory holding costs
impacting inventory turns of retailers. We use the common set of variables that were found to be significant
across the above studies as control variables in ours. Our paper differs from the previous literature in that it is
the first to explicitly consider the impact of economic shocks on inventory turns.
Several papers in macroeconomics deal with the business cycles and aggregate inventory. Motivating
many of these studies is the observation that inventory disinvestment can account for most of the decline in
GDP changes during recessions. For example, Blinder and Maccini (1991) state that decreases in inventory
investment account for 87% of the decline in GNP during recessions in post-war United States. Blinder
(1981) concludes that “indeed to a great extent, business cycles are inventory fluctuations” (p. 500). Kahn (1987, 1992)
and Bils and Kahn (2000) report similarly high correlations. This observation of the pro-cyclical behavior of
inventory investment with business cycles has fueled research into building theoretical models, so an
understanding of inventory investment may shed light on changes in the overall economy. This research has
led to examination of several models, such as the production smoothing model, stock adjustment model, and
(S,s) model, to explain the observed behavior of inventory. However, most of these papers conduct analysis
using industry-level data (Maccini and Rossana 1981; Blinder 1981).
Our paper differs from the above macroeconomics papers in the research objective and
methodology employed. The main difference between our paper and the macroeconomic literature is that,
while, the papers in macroeconomics were primarily motivated in examining how the average inventory turns
of an industry change with economic cycles, we are interested in examining whether inventory holding costs
and stockout costs faced by retailers explain the differential reaction of retailers to economic shocks. Even
papers that examined firm-level inventory behavior (Carpenter et al. (1994) and McCarthy and Zakrajsek
(2000)) do not consider inventory holding costs and stockout costs as explanatory variables. Also, our paper
differs from the macroeconomics paper in the methodology employed. While most of the authors were
primarily interested in examining the co-movements of inventory turns and business cycle time-series, we are
interested in quantifying the short-term impact, long-term impact, and duration of the impact of economic
shocks on inventory turns.
2.2
Theory and Hypotheses Development
In this section, we formalize our definition of economic shocks, state our assumptions about
retailers’ behavior, and develop our hypotheses.
We define economic shocks as unexpected changes in macroeconomic conditions. Macroeconomics
literature shows that economic shocks could be triggered by changes in oil prices, monetary policy,
government purchases, taxes, technology, and international factors (Cochrane 1994). This literature also
5
posits difficulties in pinpointing exactly the cause of an economic shock, let alone quantifying how those
changes might impact the overall economy. For example, Cochrane (1994, p. 295), who studied different
types of shocks, concludes “we will forever remain ignorant of the fundamental causes of economic fluctuations.” In our
study, we are agnostic about the exact cause of the shock and the propagation mechanism by which that
shock impacts consumers’ demand of a retailer. Finally, we assume that retailers are rational decision makers
and can change their inventory investments to maximize their profits.
The economics literature has offered strong empirical support for the pro-cyclical behavior of
inventory investment and counter-cyclical movement of inventory turns during economic cycles. While there
is a lack of consensus on the theoretical model that might explain the observed behavior, two arguments
dominate this literature (Blinder 1981). The first argument is based on cost shocks that might occur during
economic cycles. Economic cycles could be trigged by change in oil prices or taxes or shifts in technology
that could also change the cost structure for firms. Thus, expansion periods could be accompanied by decline
in costs while contraction periods by increase in costs. Since the marginal cost of production is typically
assumed to be convex in many models including the production smoothing model, profit maximizing firms
may take advantage of low costs to build/purchase inventory ahead and cut inventories when the costs are
high resulting in a pro-cyclical behavior in inventory investment. The second argument is based on demand
shocks induced during economic cycles. Economic shocks could affect affect customer sentiment resulting in
a demand shock. Since demand tends to be auto-correlated, the proponents of this theory argue that firms
change their inventory investment in anticipation of future demand. Therefore, firms invest more during
expansion shocks in anticipation of higher demand while they reduce their inventory investment during
contraction shocks in anticipation of lower demand.
Next consider the predictions for inventory investment during economic shocks based on the
operations management literature. While empirical studies on how inventory investment changes during
economic shocks are absent in the operations management literature, this literature provides a vast array of
normative policies for ordering inventory under different distributions of demand. Some of the papers have
even explicitly incorporated economic condition by modeling demand rate as being dependent on an
underlying state-of-the-world variable and derive optimal policies for stocking inventory (see Song and Zipkin
1993; Sethi and Cheng 1997). We use the commonly used newsvendor model to generate our predictions for
inventory investment when there are economic shocks.
As shown in the macroeconomics literature, expansion (contraction) shocks may be accompanied by
decrease (increase) in costs and/or increase (decrease) in mean demand. Because the standard deviation of
demand typically increases with mean demand (Silver et al. 1998), this implies that economic shocks would
impact inventory investment through changes to costs, mean demand, and demand uncertainty. Based on the
newsvendor logic, we would expect firms to increase their cycle stock in response to increase in mean
6
demand and their safety stock in response to decline in costs and increase in uncertainty. Thus, we expect
increase in inventory investment during expansion periods. Similarly, we expect inventory investments to
decrease during contraction periods as both cycle stock and safety stock are expected to decrease due to
decrease in mean demand and uncertainty and increase in costs.
We also present an alternative argument to the above. For a given level of inventory, the EOQ
model suggests that an increase (decrease) in demand would result in an increase (decrease) in inventory
turnover. Therefore, one may expect inventory turns to move pro-cyclically with economic shocks. However,
to observe the pro-cyclical movement it is important to precisely measure the timing of the shock when it
affects the retailer’s demand and then observe inventory levels right after the shock. This would require highly
disaggregate temporal data with knowledge of precise ordering times and lead time of each retailer. Because
we use aggregate quarterly data, it is not possible to observe the precise time when an economic shock affects
a retailer’s demand or to observe retailers’ inventory positions right after that moment. Therefore, our
observations are more likely to be made after retailers responded to economic shocks by changing their
inventory levels than before they had a chance to respond.
Our first hypothesis re-tests the countercyclical movement of inventory turns observed at the
industry-level in the macroeconomics literature.
H1a: Inventory turns of retailers decrease during expansion shocks.
H1b: Inventory turns of retailers increase during contraction shocks.
While the above hypotheses examine the change in inventory turns for the average retailer in our
sample, we next argue that there is significant heterogeneity in the changes to inventory turns across retailers
driven by the differences in stockout costs across retailers. From the newsvendor logic, we know that the
safety stock held by retailers would vary based on the underage and overage costs. So, we expect retailers with
higher stockout costs to invest more compared to retailers with lower stockout costs for a given demand
distribution. Therefore the inventory turns of retailers with higher stockout costs are expected to decrease
more during expansion shock compared to those with lower stockout costs if the expansion shock is
associated with an increase in demand. For similar reasons, we expect retailers with higher stockout costs to
reduce inventory investment by less than those with lower stockout costs when contraction shocks are
associated with lower demand. This should result in inventory turns of retailers with lower stockout costs to
increase more than that of retailers with higher stockout costs during contraction shocks.
If the economic shocks are associated with a change in cost structure but not a change in the
demand, then we do not expect differences in stockout costs across retailers to cause a difference in their
inventory investment behavior. As noted earlier, it is not possible to identify whether a particular economic
shock causes a change in costs or demand or both. Hence, we state the unconditional hypotheses as follows:
7
H2a: Inventory turns of retailers with high stockout costs decrease more than those of retailers with low
stockout costs during expansion shocks.
H2b: Inventory turns of retailers with low stockout costs increase more than those of retailers with high
stockout costs during contraction shocks.
Next we argue that the extent to which inventory turns of retailers change during expansion and
contraction shocks depends upon their inventory holding costs. Similar to the previous hypothesis, our
argument presupposes that both expansion and contraction shocks affect the demand faced by the retailer.
Since retailers with higher inventory holding costs are expected to have a higher overage costs, the
newsvendor model postulates that the amount of inventory investment would decrease with inventory
holding costs for a given demand distribution. Thus, we expect retailers with higher inventory holding costs
to invest lesser during expansion periods and reduce investments more during contraction periods compared
to retailers with lower inventory holding costs.
This leads to the following hypotheses:
H3a: Inventory turns of retailers with low inventory holding costs decrease more than those of retailers with
high inventory holding costs during expansion shocks.
H3b: Inventory turns of retailers with high inventory holding costs increase more than those of retailers with
low inventory holding costs during contraction shocks.
3.
Research Methodology
We test our hypotheses in two stages. First, we discuss the methodology that we employ to measure
economic shocks. This methodology is adopted from Lamey et al. (2007; 2011). Second, we explain the
autoregressive distributed lag model (ARDL) that permits the dynamic specification required to quantify the
short-term and long-term impacts of economic shocks on inventory turns.
3.1.
Measuring Economic Shocks
Economic shocks are generated from GDP time series using a two step process from Lamey et al.
(2007; 2011). In the first step, we use a standard Hodrick-Prescott (HP) filter to extract the cyclical
component of GDP. Next, we generate measures of macro-economic shocks from the extracted cyclical
component.
The observed GDP series is composed of two components: a linear trend and cyclical variation
around the trend as follows
GDPt  GDPt l  GDPt c
(1)
where, GDPt and GDPt are trend and cyclical components of observed GDP at time t. The HP filter
l
c
(Hodrick and Prescott 1997) is used to decompose the GDP series into its two components. The HP filter
extract cyclical component from the observed GDP series by solving the following minimization problem:
8
T

minl  GDPt  GDPt
GDPt
t 1
2
l

T 1

 
   GDP  GDPt  GDPt  GDP
t 2
l
t 1
l
l
l
t 1

2
(2)
where,  is the smoothing parameter. The objective is to minimize the first term in the above equation,
subject to the second term in the equation. As 0, the long-term trend approximates the series, and
as, all variation in the observed GDP series is attributed to cyclicality. The smoothing parameter is not
estimable from data, but rather provided by the researcher. Extensive work in the macroeconomic literature
suggests that =1600 for quarterly data is most appropriate (see Hodrick and Prescott 1997; Ravn and Uhlig
2002). Since the evolution in a GDP series can be attributed to change in inflation, consisted with literature
we use constant dollars by chaining our GDP series to 1983 dollars and using natural log of the series before
applying the filter.
The positive cyclical component represents the expansion in the economy while the negative values
are indicative of contraction in the economy. Consistent with prior literature, we measure magnitude of
shocks in following way (see Lamey et al. 2007):
SHOCK tExp  GDPt c  GDPPrc iorTrough
(3a)
SHOCK tCont  GDPPrc iorPeak  GDPt c
(3b)
where, SHOCKtExp and SHOCKtCont are the expansion and contraction shocks. GDPPrc iorTrough and GDPPrc iorPeak
are the values of GDPc on prior trough and prior peak, respectively. Thus, with this operationalization
SHOCKtCont and SHOCK tExp take a positive value.6
By distinguishing between expansion and contraction
shocks, we are able to examine retailers’ response to these two types of shocks and determine whether they
are symmetric or not.
3.2.
Impact of Macro-Economic Shocks on Inventory Turns
We now explain the model used to study the impact of economic shocks on inventory turns. We
consider two options when deriving the model. First, we consider appending economic shocks to previous
retailer-level models used in the literature. However, the models in the literature such as Gaur et al. (2005),
Gaur and Kesavan (2007), and Rumyantsev and Netessine (2007) primarily deal with the contemporaneous
effects of retailer-level factors on inventory turns. For our study, we need a dynamic specification since
economic shocks could impact inventory investment with a lag. Further, it is ex ante unclear which lag of the
expansion and contraction shock might impact inventory investments. Hence we use the model from prior
literature as a robustness check and develop a new dynamic model that is flexible enough to let us consider
different lag lengths for shocks and use it to generate our main results.
6
The absolute value for contraction shock makes it easy to interpret the coefficients.
9
We chose the autoregressive distributed lag model to estimate the impact of economic shocks on
retailer-level inventory for the following reasons: (1) is theoretically well motivated because it is derived from
adaptive expectations model of manager’s response to changes; (2) permits us to calculate the short- and
long-term impact of macroeconomic shocks on changes in inventory turns; and (3) is flexible enough to
permit different lag lengths and permit us to test asymmetry in responses of expansion and contraction
shocks. The ARDL model was first proposed by Nerlove (1958) and has been used extensively since, in
studying short- and long-run impacts of sales promotion (Mela et al. 1997), real interest rates (Edison and
Pauls 1993), leading output indicators (Clements and Galvao 2009), and many other variables of interest. The
details of model derivation appear in Appendix A1.
3.2.1
Autoregressive Distributed Lag Formulation
Retail industries exhibit strong seasonal trends; therefore, a quarterly analysis of inventory turns
should take into consideration seasonality that can explain significant variation in inventory turns across
quarters. To account for this we use change in inventory turns between quarter t and t-4 (ΔITit) as our
dependent variable. We use the symbol Δ to indicate fourth difference. In addition to accounting for
quarterly seasonality, fourth differencing also has the following advantages. It enables us to get rid of the
retailer-fixed effect that would be typically included in the retailer-level inventory turns model (Gaur et al.
2007; Gaur and Kesavan 2007; and Rumyantsev and Netessine 2007) and the fourth-differenced variables
have a nice interpretation. They may be interpreted as the year-on-year change in the respective quarterly
variable.
We use a general ARDL(p,q) model to test our hypotheses. Here p is number of lags of the
dependent variable and q is number of lags of the independent variable. We model changes in inventory turns
(ΔITit) as a function lagged change(s) in inventory turns (ΔITit-p), changes in several contemporaneous control
Cont
variables (ΔXit), and contemporaneous and lagged effect(s) of shocks ( SHOCK tExp
,
). Finally, we
 q SHOCKt  q
use fixed effects for industries at two-digit SIC (INDij) to capture industry segment specific unobserved
heterogeneity and quarters (QTRt) to be conservative and account for any residual seasonality effects that may
not be captured by the fourth differencing. Our proposed model specification is:
P
5
9
Q
p 1
k 3
l 6
q 0
ITit   0   1p ITit  p   2 X it   k QTRt   l INDij   1q SHOCKtExp
q
(4)
Q
   2q SHOCK tCont
 q   it
q 0
where,i, j, and t are notations for retailers, industry, and quarter respectively. The above autoregressive
formulation permits the impact of macroeconomic shocks on inventory turns to peak immediately or in up to
qth subsequent quarter and thereafter decline geometrically. The delay in impact of shock on inventory turns
10
could be an artifact of lead time in supply chains. As no theory underlies when the shocks should peak, we
test for multiple values of p and q to allow our data to determine the best values. While doing so, we also keep
in mind that higher order value of q can be problematic, as it leads to greater multicolinearity. We test for lag
length using Schwarz Bayesian Criterion (SBC) = -2*LL + [Log(N)]*K, where LL is log likelihood, N is
sample size, and K is number of estimated parameters. Please note that in the above equation, inventory turn
and other explanatory variables (X) are fourth differenced while the shock variables are differenced with
respect to their previous peak or trough.7
3.2.2
Short and Long-Term Effects
This dynamic model specification permits us to capture the short as well as long term impact of
shocks on inventory turns. An illustration of our econometric model specification is shown in Figure 1. For
illustration purposes we use ARDL(1,1) specification. The inventory turn of retailer i at time t is impacted by
shock at time t and that from time t-1. These impacts are measured by coefficients 10 and  11 respectively. The
sum of these two coefficients (  10   11 ) is the short term effect (STE) of shocks. The shock from t-2 impacts
inventory turn at time t-1 which in turn impacts inventory turn at time t through the coefficient 1. Similarly,
the shock from t-3 impacts inventory turn at time t-2 through the coefficient 1 and so on and so forth. Thus
the coefficient of autoregressive term (also called as decay parameter) captures the impact all shocks preceding t1. This impact is called as carryover impact of shocks. The sum total of short term effect and carryover effect
is called as long term effect (LTE) given by (  10   11 ) /( 1   1 ) . The larger the value of 1 the more persistent
are the the effects of macroeconomic shocks on change in inventory turns (i.e. impact of shocks on inventory
turns decays slowly).
For the general ARDL(p,q) formulation we calculate the STE and LTE of macroeconomic shocks on
change in inventory turns using the parameters 1q and 2q , and the decay parameter 1.
Expansion
Contraction
 Q q
 Q q
  1 
  2 




 q 0 
 q 0 
 Q q
 Q q
  2 
  1 




LTE
 q 0 
 q 0 
(11 )
(11 )
To test the statistical significance of the STE and LTE and test for asymmetry across expansion and
STE
We use this definition of shock to be consistent with prior literature (Lamey et al. 2007). The conceptual reasoning
underlying this definition is that in a manager’s or consumer’s mind the current state of economy is always compared
with the previous best or previous worst of the recent times. Additionally, this measurement permits us to decompose a
shock into expansion and contraction components. However, in our robustness analyses we report results in which we
measure shock as fourth differencing of cyclical component of GDP.
7
11
contraction effects we calculate the variance associated with them using Cramer’s Theorem. The detailed
expression for variance of these terms appears in the Appendix A2.8
3.2.3
Controls
Consistent with our theorization and extant literature, we control for demand and supply side factors
that may impact inventory turns. The two demand side factors that influence inventory turns are sales growth
(ΔSGit) and gross margin (ΔMRGNit). On the supply side the lead time of a retailer determines the rate at
which the purchases made by a retailer shows up in the books of a retailer hence impacting the observed
inventory turns. Consistent with Rumyantsev and Netessine (2007), we proxy for lead time using days payable
(DPit). Additionally, we control for impact of new store opening or existing store closing on change in
inventory turns by including lagged change in assets held by retailer (ΔASTit-2). These control variables
replace the ΔX in Eq (4):
P
ITit   0    1p ITit  p   2 SGit   3 MRGNit   4 DPit   5 ASTit 2
p 1
8
12
Q
Q
k 6
l 9
q 0
q 0
(5)
q
Cont
   k QTR t    l INDij    1q SHOCK tExp
 q    2 SHOCK t  q   it
3.2.4
Estimation, Moderation Impact, and Disentangling Endogeneity
There are five issues related to estimating Eq (5). First, to test the impact of inventory holding cost
and stock out cost on the relationship between macro-economic shocks and change in inventory turns, we
test Eq 5 separately on subsample of retailers high and low on inventory holding cost and stockout cost.9
Second, the contemporaneous shock terms ( SHOCK tExp , SHOCK tCont ) simultaneously impact the
dependent variable (ΔITit) as well as the contemporaneous terms (ΔSGit and ΔMRGNit), thereby biasing the
estimates of θ. The economic shocks could impact sales growth by influencing the primary demand or impact
gross margins by influencing the composition of product basket bought by consumers. We handle this
simultaneity using lagged values of change in sales growth ( SGit  q 1 , SGit  q  2 , SGit  q 3 ) and lagged values
of change in margin ( MRGN it  q 1 , MRGN it  q  2 , MRGN it  q  3 ) as our instruments. Our instruments
predate the last included economic shocks by at least one quarter.
Please note that in general in sequential estimation, a variable ‘estimated’ in first stage is subsequently used in second
stage. Under such conditions one needs to account for variance associated with estimated coefficient from first stage by
conducting bootstrap replication in the second stage. However, in our sequential estimator, cyclical component is
extracted from a time series rather than estimated. Since the ‘Shock’ components are deterministic rather than stochastic
the bootstrap replications are not necessary for second stage in our case.
8
9 We discuss the measurement of these variables and classification of firms in high and low group in next section. The
subsample analysis is more conservative approach to testing moderating impact as it reduces multicollinearity and sample
size.
12
Third, the lagged dependent variable (ΔITit-p) can be influenced by lagged value of economic shocks (
Cont
) thereby biasing the estimates of θ. In other words lagged dependent variable (ΔITitSHOCK tExp
 q , SHOCK t  q
p)
incorporates the impact of lagged shocks which are also hypothesized to impact the dependent variable
(ΔITit). We instrument it using lagged value of dependent variable predating the last shock included in the
model by at least one quarter (ΔITit-q-1, ΔITit-q-2, ΔITit-q-3).
Fourth, use of lagged dependent variable on the right-hand side typically results in dynamic panel
data bias. We argue that such a bias is not an issue in our case, as fourth differencing should remove any
correlation between ΔITit-1 and  it . This is because  it   it   it 4 and error in ITit 1 is
 it 1   it 1   it 5 have no common error terms, and we find that the errors are not autocorrelated.
Additionally, please note that ΔITit-1 is instrumented using previous lagged values thus further reducing any
residual autocorrelation. We perform the Arrellano-Bond estimation as a robustness test.
Fifth, we wish to test for asymmetry in impact of shocks (i.e. expansion and contraction have
different impacts) in short and long term. We estimate Eq(5) separately for expansion and contraction shock
periods. This is required for two reasons: (a) since the shock values are exclusive (i.e. only one type of shock
exists at a give point of time), including both shocks in same equation would render estimation impossible;
(b) the differential long term impact of expansion and contraction shocks can be ascertained only if the decay
parameter, 1, has differential values for expansion and contraction shock components.
4. Data
The data for our empirical testing is primarily is obtained from COMPUTSTAT which maintains
database of quarterly SEC filings of publicly traded retailers. The quarterly data for retailer level variables is
obtained from COMPUSTAT. We extract 25 years of quarterly data (1985-2009) for all publicly traded
retailers in two-digit SIC 52 to 59, corresponding to retail sector. These SIC codes cover the following
segments within retail: construction and home improvement (SIC = 52), department store (SIC = 53),
groceries and produce (SIC = 54), automobile dealers (SIC = 55), clothing and accessories (SIC = 56),
furniture and white goods (SIC = 57), restaurants and eating outlets (SIC = 58), and others (drug stores,
direct retailers, bookstores, stationery, florist, optical stores, news vendors, etc.) (SIC = 59). We obtain data
on Consumer Price Index (CPI), used for adjusting variables in our analyses to constant dollars from Bureau
of Economic Analysis. We use the 2005 value of the CPI as base to adjust the variables. Thus values of
variables prior to 2005 are inflated while those observed after 2005 are deflated. Similarly, we obtain the
quarterly GDP series of US from 1947 to 2009 from BEA.
4.1
Data Merging and Cleanup
First we apply the HP filter on the transformed (CPI adjusted and logged) quarterly GDP series
13
(from 1947-2009) to detrend the series and extract the cyclical component. Second, we generate
macroeconomic shocks from the cyclical component of GDP for merging with the remainder of the retailerlevel data. Since the quarterly GDP reports follow calendar time (Q1 = Jan-Mar, Q2=Apr-Jun, Q3=Jul – Sep,
and Q4=Oct-Dec), we retain retailers which have financial year ending in either December or January.10
Additionally, consistent with Kesavan et al. (2010), we drop SIC 58 (restaurants and eating outlets) and 55
(automobile dealers) from our analyses because retailers in these industries have a significant service
component, and consequently, inventory management behavior is only partly related to economic shocks.
Additionally, we drop SIC 54 (groceries and produce) from our analysis as this industry is acyclical to macroeconomic shocks.11 In addition to Wal-Mart, we also, drop the 12 retailers that changed their financial year
end during our observation period. We compare the market shares, calculated as retailer’s revenue for the
quarter divided by total revenue of the industry in that quarter, of the dropped retailers (Mean=2.04%,
SD=4.89%) with those that we retain in our sample (Mean =2.16%, SD=5.91%). Though the small
difference is statistically significant at a very large sample size, the effect size is particularly small, thereby
enhancing our confidence that the dropped retailers are not systematically much different from those retained
in our sample.
4.2
Measuring Inventory Turns
The details of variables, their measures and data source are summarized in Table 1. The dependent
variable, inventory turns is measured as ITit = Log[COGSit/((INVTit + INVTit-1)/2)]. The changes in these
variables are generated by fourth differencing them. We trim the top 1% and bottom 1% of observations
based on Inventory Turns (ITt). This approach ensures that our analyses are not unduly influenced by
extreme outliers. Our final sample thus consists of over 350 retailers and about 10,000 retailer quarter
observations. We generate the following independent variables for our analyses: Sales Growth (SGit), Gross
Margin (MRGNit), Days Payable (DPit), and Asset (ASTit).
4.3
Measuring Inventory Holding Costs and Stockout Costs
We follow Irvine (1981), Raman and Kim (2002), and Rumyantsev and Netessine (2007) and use
weighted average cost of capital (WACC) as our measure of inventory carrying cost. WACC is measured as
weighted average of cost of debt incurred and cost of equity earned by a retailer. The weights are the relative
proportion of debt and equity. The debt cost is measured as interest paid on outstanding short and long term
10 We found that January was the second most popular month (after December) to have the fiscal year end in the retail
industry. About 38% of the firms had their fiscal year end in January. To avoid discarding such a large amount of data,
we decided to include the retailers having January fiscal year ends along with those having December fiscal year ends.
We align the economic shock from January-March with the first quarter data for retailers with fiscal year ends in January.
11 In an acyclical industry, the industry sales do not significantly co-vary with the unexpected changes in GDP. Past
research has shown that consumers switch to private label brands and mass merchandise retail formats during
recessionary times; however the overall sales in the industry do not change significantly. We test sensitivity of our results
to inclusion of SIC54. The results are reported in robustness analyses section.
14
debt. The equity cost is measured as quarterly return generated on the outstanding market value of the
retailer. We obtain this data from COMPUSTAT. Next, we classify a retailer in high or low group if they are
in the top 66.67th and bottom 33.34th percentile of WACC within their industry for at least three of the four
quarters predating the last economic shock included in the model.
The stockout cost, or the opportunity cost of lost sales, at the firm-level is unobservable to an
econometrician. We use gross margin as a proxy for stockout cost as it captures the markup that retailers
obtain on the merchandise they sell. Therefore, larger the gross margin, higher the opportunity cost of lost
sales. We classify a firm in high or low group if they are in the top 66.67th and bottom 33.34th percentile of
gross margin within their industry for at least three of the four quarters predating the last economic shock
included in the model.
5.
Results
We first examine the raw data to look for evidence of whether inventory turns of retailers change
with economic shocks. Figure 2 plots the average change in inventory turns of retailers in each quarter against
economic shocks in that quarter. Next we discuss our statistical results in four steps. First, we explain our
model selection results by comparing the results of models with different lag length specification. Second, we
discuss our results of testing Hypotheses 1a and 1b. Third, we discuss the moderating impact of inventory
holding cost and stock out cost and discuss results for Hypotheses 2a through 3b. Lastly, we discuss several
robustness checks.
5.1.
Model Selection
In Table 2 we report the model fit statistics of different model specifications. We start with the
simplest model with no autoregressive term and no distributed lags of the macroeconomic shocks, ADL(0,0).
We subsequently add lags and autoregressive terms in the model. We report fit statistics separately for
expansion and contraction period. The comparative model fit statistics suggest that the Schwarz Bayesian
Criterion is lowest for ARDL(1,1) specification both during expansion and contraction shocks. Thus we use
ARDL (1,1) specification for testing our hypotheses. This one lag of macroeconomic shock variable suggests
that the impact of these shocks on change in inventory turns can peak one quarter after the shock hits the
retailer. We discuss the robustness of our results to alternate model specification in §5.4.
5.2.
Inventory Turn Hypotheses
Consider the results of testing Hypotheses 1a and 1b using the ARDL(1,1) model as shown in Table
3. As the independent and dependent variables in the model are logged the coefficients can be interpreted as
elasticities. We find that a 1% increase in expansion (contraction) shock is associated with a decrease
(increase) in inventory turns by 1.320%, p<.01 (.409%, p<.01) in short term. This 1% increase in expansion
15
(contraction) shock corresponds to a 1% increase (decrease) in the GDP compared to previous trough (peak)
(Lamey et al. 2007). Similarly, we find that a 1% increase in expansion (contraction) shock leads to a total of
3.486%, p<.01 (1.099%, p<.01) decrease (increase) in inventory turn. We find that 38% of total impact is
realized in first two quarters. The impact peaks in the quarter after the shock hits and thereafter declines at a
geometric rate. Since the decay parameter for both expansion and contraction shocks are similar (.621 and
.628) we find that 90% of both types of shocks are dissipated within four and five quarters. Thus in support
of H1a and H1b we find that inventory turns move counter-cyclically to macro-economic shocks.
The impact of expansion and contraction shocks are not only asymmetric in direction, but in
magnitude as well. The impact of expansion shocks is more severe than that of contraction shocks on
changes in inventory turns (Absolute Difference=2.387, t=3.630, p<.01). This asymmetric magnitude of
impact suggests that on average retailers make significantly more inventory investments during expansions
than inventory disinvestments they make during contractions. Consistent with prior literature, we find that
sales growth in positively related to inventory turns, while gross margin and lead time are negatively related to
inventory turns.
5.3.
Inventory Holding Cost and Stockout Cost Hypotheses
In our theorization and conceptual development, we hypothesized that inventory holding cost and
stockout cost of retailers will drive inventory investment decisions during economic shocks. We estimate our
proposed model specification on different subsamples of high and low inventory holding and stockout costs
retailers. The estimation results are presented in Tables 4 and 5. We find that retailers with high stockout
costs and those with low stockout costs increase their inventory investment during expansion shocks causing
their inventory turns to decline significantly (p<0.05). However, the difference between inventory turns of
retailers with high and low stockout costs is not significant. Thus, H2a is not supported. During contraction
shocks, we find that retailers with low stockout costs (1.802, p<.01) increase their inventory turns more than
those with high stockout costs (.099, p>.10). The difference between the two is statistically significant
(Difference=1.703, t=2.961, p<.01), supporting H2b. Our results suggest that stockout costs faced by retailers
explain the differences in inventory investment behavior among retailers during contraction shocks but not
during expansion shocks.
We find that inventory turns of retailers with low inventory holding costs (-3.553, p<.01) decrease
during expansions but that of retailers with higher inventory holding costs do not (p>.10). The difference
between the two is statistically significant (Difference=4.556, t=3.635, p<.01), supporting H3a. This is
consistent with our theorization that retailers with low inventory holding costs have relatively lower inventory
financing cost, hence they capitalize on expansion shocks by increasing their inventory investments. We
hypothesized that during contraction shock, retailers with high inventory holding costs will decrease their
16
inventory investments significantly more than those with low inventory holding costs. Ceteris paribus, the
inventory turns of retailers with high inventory holding cost should increase more than inventory turns of
those with low inventory holding cost. We do not find a statistically significant difference between the change
in inventory turns of retailers with high inventory carrying costs (1.086, p<.10) and those of retailers with low
inventory carrying costs (1.022, p>.10). Thus, H3b is not supported. Therefore our results suggest that
inventory holding costs explain differences in inventory investment behavior across retailers during expansion
shocks but not contraction shocks.
In summary, the above results suggest that during periods of expansion, retailers with low inventory
holding cost react more aggressively by increasing their inventory investment significantly more than that of
retailers with high inventory holding costs, while those with low stockout cost react more aggressively to
contraction shocks by reducing their inventory investment significantly more than that of retailers with high
stockout cost. The observed differences in behavior between the two types of retailers appear rational based
on the profit maximizing motive of the newsvendor model. Future research may examine the implications of
the difference in actions during economic shocks on the financial performance of these retailers.
5.4.
Robustness Checks
We perform several robustness checks to enhance confidence in our empirical analyses. In general
we find that macro-economic shocks are exogenous to the system and our findings are robust to alternate
model specification, alternate measures of shock, several other macro-economic time series, inclusion of one
acyclical industry, and an alternate estimation technique.
First, we perform Durbin-Wu-Hausman augmented regression to test for exogenity of macroeconomic shocks. First, we regress macro-economic shocks (expansion and contraction separately) on their
lags from t-2 through t-5. These are appropriate instruments because they predate the included shocks by at
least one quarter and they do not meet the temporal ordering condition for the decisions made by retailer at
time t. Second, we include the residuals from the first stage (current and one lag) in our Eq 5. If the
coefficients for residuals are statistically significant one cannot rule out edogeneity of the shock terms. The
detailed results for second step regression are reported in Table 6. The coefficients for residual current and lag
term of expansion shock are -1.099 (p=.25) and 1.625 (p=.08) respectively. The calculated total short term effect
is .526 (p=.53). The coefficients for residual current and lag term for contraction shock are .007 (p=.99) and .321
(p=.26) respectively. The calculated total short term effect is .329 (p=.58). The results suggest that both types
of macro-economic shocks are exogenous to the system. Most importantly, at an aggregate level the inventory
investment across all industries can drive business cycle fluctuations; it is very unlikely that inventory
investment decision made by one retailer has potential to impact the cyclicality in the economy. In other
words, for a retail manager making inventory management decisions, the state of the economy is exogenously
17
determined. No one retailer’s inventory investment decision can bring about expansion and contractions in
large capitalistic economy as the U.S.12
Second, we test sensitivity of our results to several alternate model specifications. The results of these
robustness analyses are reported in Table 7. Recall that we developed a general ARDL model and chose the
ARDL(1,1) specification based on model fit. We estimate a simple model with no autoregressive term and no
distributed lag term (ARDL(0,0)). This model specification would be consistent with previous research in
empirical operations management literature (see Gaur et al. 2005; Gaur and Kesavan 2007; and Rumyantsev
and Netessine 2007). The results suggest that directionality and significance of coefficients of shock terms as
well as control variables are consistent with the results reported in Table 3. We subsequently add one
distributed lag term making it a ARDL(0,1) specification. This is closest to our proposed specification, except
for lack of autoregressive term. Again the significance and directionality of coefficients of shock terms
suggest that adding autoregressive term to the model does not influence our substantive conclusions.13 In our
results we find that 90% of impact of shocks is dissipated between four and five quarters, we report results of
model with no autoregressive term but four distributed lag terms. Again the total effect of expansion and
contraction shocks is similar in directionality and significance.14 The results pertaining to impact of inventory
holding cost and stockout cost are also consistent with those reported in Table 4 and 5.15
Third, since we fourth difference our dependent and independent variables, to be consistent with this
operationalization we measure macro-economic shock as fourth difference of cyclical component of GDP (
SHOCKt  GDPt c  GDPt c4 ).
With this operationalization positive (negative) values of shock indicate
unexpected increase (decrease) in GDP. The results of this analysis are reported in Table 8. The results
suggest that for a 1% unexpected increase (decrease) in GDP the inventory turns decrease (increase) in short
and long term by .572% and 1.547%. These findings are consistent with those reported on Table 3. Thus our
results are not sensitive to operationalization of shocks. The results pertaining to impact of inventory holding
We exclude Wal-Mart from our empirical analyses for this very reason. Wal-Mart, the largest retailer in the US
constitutes about 0.3% of US GDP.
12
13 In absence of autoregressive term, the impact of contraction shocks and gross margins are significantly exaggerated
while those expansion shocks are significantly marginalized. While the substantive findings remain unchanged, the
difference in size of coefficients indicates the bias that would be introduced if we do not include the autoregressive term.
This result echoes similar findings in economics and marketing that have shown that ignoring state dependence in
aggregate firm-level variables can lead to significant bias in evaluating the impact of exogenous variables (for e.g. see
Jacobson 1990). Additionally, as discussed in §5.1, we find that specifications with no autoregressive terms have
relatively poor model fit. Thus in interest of maximizing variance explained by maintaining parsimony, we retain the
specification with autoregressive term.
We choose to retain our proposed ARDL(1,1) specification because including multiple distributed lag terms can
introduce severe multicolinearity thereby inflating the standard errors and hence leading to incorrect interpretation of the
coefficients.
14
15
To conserve space we do not report these results in the manuscript. They are available from authors upon request.
18
cost and stockout cost are also consistent with those reported in Table 4 and 5.16
Fourth, we use quarterly GDP per capita series instead of GDP to measure macroeconomic shocks.
We find that cyclical components of both series have a correlation of .99. In addition, the substantive results
from our analyses are consistent.
Fifth, we use the quarterly Personal Consumption Expenditure (PCE) series instead of GDP to
measure macroeconomic shocks. We find that PCE accounted for 62.5% of the GDP in 1970 and this
percentage increased to 70% by 2009. We obtain similar results when we also measure economic shocks with
the PCE series. This result provides additional support to our finding that macroeconomic shocks impact
consumer spending and thus retailer’s demand forecast and inventory management decisions.
Sixth, every month the U.S. Bureau of Economic Analysis releases updates on the state of the
economy, including the seasonally adjusted GDP expectations for the current quarter and the current fiscal
year. These releases are widely followed by managers and investors alike and are used as signals of current and
future economic conditions. Additionally, the correlation between the forecasted GDP and actual GDP
numbers are fairly high. However, it can be argued that the numbers used in our GDP series are not released
until a few days after the end of the quarter therefore the GDP series used by us may not be forward looking.
Thus we need to test the robustness of our findings to alternate measure of macro-economic series which
captures the forward looking behavior of consumers. We use Consumer Confidence Index (CCI) reported by
Conference Board as an alternate measure of the state of the economy. CCI is measured through extensive
survey of consumer perceptions about the current state of the economy and their anticipated consumption
behavior in the near future. While GDP has a clear linear trend and a high frequency cyclical component
around it, the CCI series essentially is cyclical in nature.17 Thus changes in CCI are akin to unexpected
changes in cyclical component of GDP (see above analysis). We operationalize macro-economic shock as
fourth difference change in CCI (SHOCKt = CCIt – CCIt-4). With this operationalization positive (negative)
values of shock indicate increase (decrease) in consumer confidence. The results of this analysis are reported
in Table 9. The results suggest that for a 1% increase (decrease) in consumer confidence the inventory turns
decrease (increase) in short and long term by .020% and .056%. These findings are consistent with those
reported on Table 3. This suggests that the quarterly GDP series maps consistently well with forward looking
measure of consumer confidence. The results pertaining to impact of inventory holding cost and stockout
cost are also consistent with those reported in Table 4 and 5.18
Seventh, we test the sensitivity of results to inclusion of retailers in SIC 54 (Groceries and Produce).
16
To conserve space we do not report these results in the manuscript. They are available from authors upon request.
17
Therefore we do not need to decompose the CCI series into linear trend and a cyclical component around it.
18
To conserve space we do not report these results in the manuscript. They are available from authors upon request.
19
The results of this analysis are reported in Table 10. The results are consistent in magnitude, directionality,
and significance to those reported in Table 3. The results pertaining to impact of inventory holding cost and
stockout cost are also consistent with those reported in Table 4 and 5.19
Lastly, we use Arrellano-Bond estimation and find the directionality and significance of results similar
to those reported here. This confirms that dynamic panel data bias is not a problem in our analyses because
we use fourth differencing of all variables on a quarterly data.
6.
Conclusions
The main conclusion of our paper is that inventory holding costs and stockout costs faced by
retailers have a significant explanatory power over the aggregate inventory investment behavior of retailers
during economically turbulent periods as well. Prior literature in macroeconomics has either tended to focus
on industry-level inventory investment behavior or ignore these two fundamental factors when studying firmlevel inventory investment behavior. Our paper shows that these two costs that are critical in determining the
optimal inventory level at the SKU-level also explain why different retailers react differently to different types
of shocks. Our results are summarized in Figure 3.
Our paper also quantifies the impacts of economic shocks on inventory turns of retailers. We find
that the magnitude of impact of an expansion shock on inventory turns is larger than that of the impact of a
contraction shock. In other words, retailers appear to be investing more in inventory in response to an
expansion shock compared to reducing their inventory investment in reaction to a contraction shock. This
mirrors the findings from economics literature that have shown that variables such employment rate (Neftci
1984), wages (Bils 1985), and prices (Ball and Mankiw 1994) increase and decrease at different rates during
expansion and contraction periods.
Our paper suggests following venues for future research. Prior empirical work on examining the bull
whip effect tended to aggregate across firms and also time periods and have largely failed to find evidence for
this effect. For example, Cachon et al. (2007) who studied this phenomenon using industry-level data could
not find any evidence of bull whip effect in the retail industry. Aggregation of observations across firms
without consideration to their inventory holding costs and stockout costs would attenuate the bull whip effect
at the industry-level. Similarly, aggregating across periods of expansion and contraction shocks would lead to
an attenuation bias that may make it difficult to detect the bullwhip effect at the industry-level. Future
research may examine the bull whip effect separately for different types of retailers and for different types of
shocks identified in this paper. Our result also suggests that the impact of economic shocks on suppliers may
depend on the portfolio of retailers they serve. For example, a supplier who delivers to only retailers with low
19
To conserve space we do not report these results in the manuscript. They are available from authors upon request.
20
inventory holding cost (high stockout costs) may face pronounced bullwhip effect during expansion
(contraction) periods. Future research may examine if the choice of retailers to serve is a viable supply chain
strategy to manage economic risk. Finally, future research may also examine the impact of lead time in supply
chains and contracting choice with suppliers on the inventory investment behavior of retailers.
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22
Variable
Table 1
VARIABLES AND DATA SOURCES
Measure
Data Source
CPI
Consumer price index as measure of inflation
Gross Domestic Product (GDPt)
Log(CPI adjusted GDP)
Bureau of Economic
Analysis (BEA)
BEA
INVT
CPI adjusted inventory (INVTQ)
COMPUSTAT
COGS
CPI adjusted cost of goods sold (COGSQ)
COMPUSTAT
REVT
CPI adjusted revenues (REVTQ)
COMPUSTAT
AP
CPI adjusted accounts payable (APQ)
COMPUSTAT
ACT
CPI adjusted current assets (ACTQ)
COMPUSTAT
LCT
CPI adjusted current liabilities (LCTQ)
COMPUSTAT
AT
CPI adjusted total assets (ATQ)
COMPUSTAT
INT
CPI adjusted interest paid (XINTQ)
COMPUSTAT
LTD
CPI adjusted long term debt (DLTTQ)
COMPUSTAT
SHO
Number of shares outstanding (CHSOQ)
COMPUSTAT
SHPRC
Closing share price at end of quarter (PRCCQ)
COMPUSTAT
NI
Net income in quarter (NIQ)
COMPUSTAT
Inventory Turns (ITit)
Log[COGSit/((INVTit + INVTit-1)/2)]
Change in Inventory Turns (ΔITit)
ITit - ITit-4
Sales Growth (SGit)
Log(COGSit) - Log(COGSit-4)
Change in Sales Growth (ΔSGit)
SGit - SGit-4
Gross Margin (MRGNit)
Log[(REVTit - COGSit)/REVTit)]
Change in Gross Margin (ΔMRGNit)
MRGNit - MRGNit-4
Lead Time - Days Payable (DPit)
Log[(365/(4*COGSit /APit))]
Change in Lead Time (ΔDPit)
DPit - DPit-4
Change in Asset Position (ΔASTit)
Log(ASTit) – Log(ASTit-4)
Debt Cost (DCit)
INTit/(LCTit + LTDit)
Equity Cost (ECit)
NIit /(SHOit * SHPRCit)
Weighted Average Cost of Capital (WCCit)
Weighted average of (DCit + ECit)
Inventory Holding Cost (HICit, LICit) a
HICit = 1 if WCCit-q-1 >66.67th percentile, else HICit = 0
LICit = 1 if WCCit-q-1<33.34th percentile, else LICit = 0
Stock Out Cost (HSCit, LSCit) a
HSCit = 1 if MRGNit-q-t’>66.67th percentile, else HSCit = 0
LSCit = 1 if MRGNit-q-t’<33.34th percentile, else LSCit = 0
Note: a We classify a firm in high or low group if they are in the top 66.67th and bottom 33.34th percentile in their
industry in at least three of the four quarters predating the last economic shock included in the model.
23
Table 2
RESULTS: MODEL COMPARISON
Schwartz’s Bayesian Criterion
Expansion
Contraction
ARDL (0,0)
-4288.62
-5649.83
ARDL (0,1)
-4292.00
-5653.23
ARDL (0,2)
-4289.54
-5667.48
ARDL (1,0)
-5064.45
-6367.89
ARDL (1,1)
-5066.89*
-6376.34*
ARDL (1,2)
-5066.70
-6370.01
ARDL (2,0)
-5048.92
-6353.85
ARDL (2,1)
-5055.71
-6354.08
ARDL (2,2)
-5049.02
-6346.72
Note:
ARDL (p,q) where, p is number of lags of dependent variable and q is number of lags of economic shocks.
* Selected model specification with lowest SBC.
Table 3
RESULTS: IMPACT OF MACRO-ECONOMIC SHOCKS ON INVENTORY TURNS
Expansion
Contraction
Dependent
Variable - ΔITit
Coeff.
S.E.
Coeff.
S.E.
ΔITit-1 a
.621
.016
.628 .015
ΔSGit a
.116
.014
.107 .013
ΔMRGNit a
-.175
.045
-.049 .033
ΔASTit-2
.028
.010
.026 .009
ΔDPit
-.097
.006
-.093 .004
SHOCKtExp
-.548
.580
SHOCKtExp
-.772
.564
1
Cont
SHOCKt
-.256 .373
Cont
SHOCKt 1
.666 .445
Intercept
.027
.010
.010 .006
Quarter Fixed Effects
Three Significant
None Significant
Industry Fixed Effects
None Significant
One Significant
Short Term Effects
-1.320
.290
.409 .152
Long Term Effects
H1a: -3.486
.876 H1b: 1.099 .312
Sample Size N
4,326
5,533
No. of Retailers
359
364
Note:
All italicized coefficients have p<.05.
a These variables are instrumented using their respective lags from t-2 through t-4.
24
Dependent
Variable - ΔITit
ΔITit-1 a
ΔSGit a
ΔMRGNit
ΔASTit-2
ΔDPit
a
SHOCKtExp
SHOCKtExp
1
SHOCKtCont
SHOCKtCont
1
Intercept
Quarter Fixed Effects
Industry Fixed Effects
Short Term Effects
Long Term Effects
Table 4
RESULTS: STOCK OUT COST
High (HSCit = 1)
Low (LSCit = 1)
Expansion
Contraction
Expansion
Contraction
Coeff.
S.E.
Coeff.
S.E. Coeff.
S.E.
Coeff.
S.E.
.653
.033
.650
.028
.619
.027
.603
.028
.106
.028
.053
.024
.162
.029
.125
.026
-.189
.091
-.141
.067
-.148
.107
-.054
.065
-.005
.020
-.019
.017
.032
.019
.050
.018
-.077
.010
-.080
.008
-.109
.014
-.096
.008
-1.344
1.131
-.613
1.181
.474
1.090
-.823
1.143
.019
.727
-1.240
.781
.016
.875
1.954
.924
.043
.020
.006
.013
.005
.017
.015
.015
None Significant None Significant None Significant
Two Significant
None Significant None Significant None Significant
None Significant
-.870
.571
.035
.307 -1.436
.592
.715
.314
-2.504
1.281
.099
.584 -3.774
1.336
1.802
.566
H2a
Short Term Effects (High – Low)
Long Term Effects (High – Low)
Note:
Expansion
Diff
S.E.
.566 .582
1.270 1.309
H2b
Contraction
Diff
S.E.
-.680
.311
-1.703
.575
All italicized coefficients have p<.05
a These variables are instrumented using their respective lags from t-2 through t-4.
25
Dependent
Variable - ΔITit
ΔITit-1 a
ΔSGit a
ΔMRGNit
ΔASTit-2
ΔDPit
a
SHOCKtExp
SHOCKtExp
1
SHOCKtCont
SHOCKtCont
1
Intercept
Quarter Fixed Effects
Industry Fixed Effects
Short Term Effects
Long Term Effects
Table 5
RESULTS: INVENTORY HOLDING COST
High (HICit = 1)
Low (LICit = 1)
Expansion
Contraction
Expansion
Contraction
Coeff.
S.E.
Coeff.
S.E. Coeff.
S.E.
Coeff.
S.E.
.735
.050
.570
.042
.413
.043
.596
.042
.045
.033
.125
.031
.034
.046
.034
.038
-.208
.064
-.134
.048
-.518
.147
-.159
.125
-.007
.027
.044
.028
-.033
.026
.035
.025
-.083
.014
-.068
.012
-.086
.016
-.085
.013
-1.102
1.942
-.722
1.626
1.367
1.888
-1.363
1.574
-.867
1.193
-.820
1.016
1.334
1.436
1.168
1.204
.015
.020
.014
.016
.041
.024
.007
.023
One Significant
One Significant None Significant None Significant
None Significant
None Significant None Significant None Significant
.266
.889
.468
.481 -2.085
.773
.348
.433
1.003
1.448
1.086
.648 -3.553
1.022
.861
.945
H3a
Short Term Effects (High – Low)
Long Term Effects (High – Low)
Expansion
Diff
S.E.
2.351
.833
4.556
1.253
H3b
Contraction
Diff
S.E.
.120
.458
.225
.810
Note: All italicized coefficients have p<.05
a These variables are instrumented using their respective lags from t-2 through t-4.
26
Table 6
ROBUSTNESS TEST: DURBIN-WU-HAUSMAN AUGMENTED REGRESSION TEST
Expansion
Contraction
Dependent Variable ΔITit
Coeff.
S.E.
Coeff. S.E.
a
ΔITit-1
.611
.016
.592 .021
ΔSGit a
.124
.015
.087 .016
ΔMRGNit a
-.163
.043
-.148 .056
ΔASTit-2
.025
.010
.005 .012
ΔDPit
-.096
.006
-.088 .005
SHOCKtExp
.518 1.075
Exp
SHOCKt 1
-2.281
.983
Cont
SHOCKt
.416 .557
Cont
SHOCKt 1
.227 .477
Exp Residualt
-1.099
.950
Exp Residualt-1
1.625
.909
Cont Residualt
.007 .455
Cont Residualt-1
.321 .287
Intercept
.029
.009
.002 .006
Quarter Fixed Effects
Two Significant None Significant
Industry Fixed Effects
None Significant
Two Significant
Short Term Effects
-1.763
.704
.643
.329
Residualt + Residualt-1
.526
.831
.329
.569
Note:
All italicized coefficients have p<.05.
a These variables are instrumented using their respective lags from t-2 through t-4.
27
Table 7
ROBUSTNESS TESTS: ALTERNATE MODEL SPECIFICATIONS WITHOUT AUTOREGRESSIVE TERM
Expansion
Contraction
Dependent
Variable - ΔITit
ARDL(0,0)
ARDL(0,1)
ARDL(0,4)
ARDL(0,0)
ARDL(0,1)
ARDL(0,4)
Coeff.
S.E. Coeff.
S.E.
Coeff.
S.E.
Coeff.
S.E.
Coeff.
S.E. Coeff.
S.E.
ΔSGit a
.091
.019
.078
.020
.077
.020
.114
.017
.101
.017
.102
.017
ΔMRGNit a
-.423
.052
-.439
.059
-.437
.059
-.296
.041
-.349
.043
-.350
.042
ΔASTit-2
-.068
.013
-.067
.013
-.065
.013
-.068
.012
-.071
.011
-.071
.012
ΔDPit
-.111
.008
-.101
.008
-.101
.008
-.103
.006
-.098
.005
-.095
.005
Exp
SHOCKt
-1.105
.382 -1.353
.764
-1.409
.781
Exp
SHOCKt 1
.340
.743
.845
.810
Exp
SHOCKt  2
.139
.621
Exp
SHOCKt 3
-1.004
.758
Exp
SHOCKt 4
-.551
.522
Cont
SHOCKt
-.165
.163
-.502
.223
-.292
.319
Cont
SHOCKt 1
1.413
.245
1.275
.335
Cont
SHOCKt  2
.898
.503
Cont
SHOCKt 3
-1.373
.620
Cont
SHOCKt 4
.761
.293
Intercept
.054
.015
.057
.014
.059
.014
.034
.011
.038
.011
.032
.011
Quarter Fixed Effects Three Significant Three Significant
Three Significant
None Significant None Significant
None Significant
Industry Fixed Effects None Significant None Significant
None Significant
Three Significant
Four Significant
Three Significant
Total Effect
-1.105
.382 -1.013
.383
-1.980
.545
-.165
.163
.911
.221
1.268
.313
Note: All italicized coefficients have p<.05
a These variables are instrumented using their respective lags from t-2 through t-4.
28
Table 8
ROBUSTNESS TEST: SHOCK MEASURED AS 4TH DIFFERENCE OF CYCLICAL COMPONENT
Expansion
Dependent Variable - ΔITit
Coeff.
S.E.
a
ΔITit-1
.630
.010
ΔSGit a
.106
.010
ΔMRGNit a
-.094
.026
ΔASTit-2
.024
.006
ΔDPit
-.095
.003
SHOCKt ( GDPt c  GDPt c4 )
.114
.170
SHOCKt-1( GDPt c1  GDPt c5 )
-.686
.169
Intercept
Quarter Fixed Effects
Industry Fixed Effects
Short Term Effects
Long Term Effects
Note:
.009
.004
None Significant
None Significant
-.572
.105
-1.547
.285
All italicized coefficients have p<.05.
a These variables are instrumented using their respective lags from t-2 through t-4.
Table 9
ROBUSTNESS TEST: CONSUMER CONFIDENCE INDEX a
Expansion
Dependent Variable - ΔITit
Coeff.
S.E.
ΔITit-1 b
.634
.010
b
ΔSGit
.103
.010
ΔMRGNit b
-.096
.026
ΔASTit-2
.023
.006
ΔDPit
-.095
.003
SHOCKt (CCIt – CCIt-4)
.035
.007
SHOCKt-1 (CCIt-1 – CCIt-5)
-.055
.007
Intercept
.009
.004
Quarter Fixed Effects
None Significant
Industry Fixed Effects
None Significant
Short Term Effects
-.020
.006
Long Term Effects
-.056
.015
Note:
All italicized coefficients have p<.05.
a CCI data is available to us upto Q4 2007 only.
b These variables are instrumented using their respective lags from t-2 through t-4.
29
Table 10
ROBUSTNESS TEST: INCLUSION OF SIC 54 (GROCERIES AND PRODUCE)
Expansion
Contraction
Dependent Variable
- ΔITit
Coeff.
S.E.
Coeff.
S.E.
a
ΔITit-1
.616
.014
.645 .014
ΔSGit a
-.186
.044
-.038 .033
ΔMRGNit a
.120
.013
.105 .012
ΔASTit-2
.034
.009
.038 .008
ΔDPit
-.098
.006
-.097 .004
SHOCKtExp
Exp
t 1
SHOCK
-1.039
-.126
.544
.528
SHOCKtCont
SHOCKtCont
1
Intercept
Quarter Fixed Effects
Industry Fixed Effects
Short Term Effects
Long Term Effects
Sample Size N
No. of Retailers
Note:
.025
.009
Three Significant
None Significant
-1.165
.266
-3.035
.634
4,964
402
-.833 .446
1.729 .533
.006 .007
None Significant
Two Significant
.895 .198
2.523 .533
5,796
404
All italicized coefficients have p<.05.
a These variables are instrumented using their respective lags from t-2 through t-4.
30
Figure 1
ILLUSTRATION OF PROPOSED ECONOMETRIC MODEL SPECIFICATION
ΔXit-T
ΔXit-2
ΔITit-T
ΔITit-2
 10 Shockt-T
t-T
 11
 10 Shockt-2
t-2
ΔXit
ΔXit-1
1
 11
ΔITit-1
 10 Shockt-1
t-1
1
 11 ΔITit
 110 Shockt
t
t+T’
Controlled Effects, Endogenous Variables Instrumented Out
Hypothesized Short Term Effects
Note: For illustration purposes expansion shock coefficients and ARDL (1,1) specification are exemplified.
31
Figure 2
CHANGES IN INVENTORY TURNS AND MACROECONOMIC SHOCKS
0.1
0.08
Change in Inventory Turns/ Economic Shock
Shock
Del IT
0.06
0.04
0.02
0
‐0.02
‐0.04
2009Q1
2008Q1
2007Q1
2006Q1
2005Q1
2004Q1
2003Q1
2002Q1
2001Q1
2000Q1
1999Q1
1998Q1
1996Q1
1995Q1
1994Q1
1993Q1
1992Q1
1991Q1
1990Q1
1989Q1
1988Q1
1987Q1
1986Q1
1985Q1
1997Q1
Year Quarter
‐0.06
Note: For graphical asymmetry the expansion shocks are shows to be positive and contraction shocks are shown to be
negative. DELIT is change in inventory turns and Shock is magnitude of expansion or contraction shock.
Figure 3
IMPACT OF SHOCKS, INVENTORY HOLDING AND STOCKOUT COSTS ON INVENTORY
TURNS
2.00
1.50
Retailers with Low Stockout
Costs during Contractions
Change in Inventory Turns
1.00
Overall Contraction
.50
.00
-.50
Overall Contraction
Retailers with Low Inventory Holding
Costs during Expansions
-1.00
-1.50
t
t+1
t+2
t+3
t+4
t+5
Quarters
t+6
t+7
t+8
t+9
t+10
Note: The graph illustrates the dynamic impact of shock on inventory turns using coefficient estimates shown in Tables
3, 4, and 5. The above graph summarizes impact of shock that hits a retailer in quarter t on changes in its inventory turns
in 10 subsequent quarters. The sum of these effects across all quarters is the Long Term Effect (or Total Effect).
32
Online Appendix A1
Adaptive Expectations Model
To begin, we start with a simple manager’s adaptive expectations model and subsequently add several relevant
variables. We hypothesize that a forward-looking manager determines levels of current inventory based on his
or her expectations of several explanatory variables in the upcoming future. Thus, the level of a retailer i’s
inventory turn in a given time period t is a linear function of that retailer’s expectation of explanatory
variables for the upcoming time period t+1 given by:
ITit   0   1 X it* 1   it
(A1)
where, ITit is inventory turn of retailer i and X it* 1 are expectations of retailer specific factors. As X it* 1 is
unobservable, a retail managers make adaptive expectations based on the deviation between actual observed
value of these variables at time t (Xit) and their expectation that she had of the same ( X it* ):
X it* 1  X it*   ( X it  X it* )
(A2)
where, 0<<1 is the proportion of discrepancy. Rearranging
X it* 1  X it  ( 1   ) X it*
(A3)
Thus, as 0, there is no adaptation, and if 1, the faster the expectations change in response to actual
observed values of X’s. Substituting back equation (A3) in (A1) yields
ITit   0  (  1 ) X it   1 (1   ) X it*   it
(A4)
Taking a lag of equation (A3) yields
X it*  X it 1  ( 1   ) X it* 1
(A5)
Substituting back equation (A5) in (A4) yields
ITit   0   1X it   1 (1   ) X it 1   1 (1   ) 2 X it* 1   it
(A6)
Thus inventory turns at time period t is a function of observed value of X’s at time period t and t-1 and
expectations of X at time period t-1. We can keep recursively plugging back the value of X it* 1 with the
observed value and expected value from the previous time period. If there at T time periods, after lagging the
expectations process and substituting it back in the above equation T times yields
ITit   0   1X it   1 (1   ) X it 1   1 (1   ) 2 X it  2  ....   1 (1   ) T 1 X it T 1
 1( 1   ) X
T
*
it T 1
(A7)
  it
In the above recursive terms can be substituted by lagged value of ITt-1 as
ITit   0   1X it  ( 1   )ITit 1   it
(A8)
We can reparameterize above as
ITit   0   1 ITit 1   2 X it   it
(A9)
As discussed in the text we use fourth differencing (presented by Δ) of dependent and independent variables
to account for seasonality. We include industry and quarter dummies to control for unobserved heterogeneity.
Thus the adaptive expectations model from Eq A9 transforms to:
i
5
9
k 3
l 6
ITit   0   1 ITit 1   2 X it    k QTRt    l INDij   it
(A10)
where, QTRt and INDj are three and four dummies for quarter and industry specific fixed effects, and X are
control variables. The error component in the above model subsumes two different effects as follows:
 it   t   it
(A11)
where, Δψt is a temporal effect on change in inventory turns because of unexpected changes in exogenous
macro economic conditions and Δξit ~ N(0,σit) is the normally distributed random error. We capture ψt
through macroeconomic shocks as measured in the previous section.
5
9
k 3
l 6
ITit   0   1 ITit 1   2 X it    k QTRt    l INDij   1 SHOCK tExp
(A12)
  2 SHOCK tCont   it
The above autoregressive formulation assumes that the impact of explanatory variables and macroeconomic
shocks on inventory turn peaks immediately and that this effect declines subsequently with a geometric decay
rate of 1-1. We relax this assumption by introducing distributed lags of the economic shocks. We use the
more general ARDL(p,q) formulation where, p is number of lags of the dependent variable and q is number of
lags of the independent variable. The updated ARDL(p,q) changes in inventory turn model is given by
P
5
9
Q
p 1
j 3
j 6
q 0
ITit   0   1p ITit  p   2 X it   j QTR jt   j INDijt   1q SHOCKtExp
q
(A13)
Q
   2q SHOCK tCont
 q   it
q 0
The above equation appears as Eq (4) in main text.
ii
Appendix A2
Variance of STE and LTE
The variance of STE and LTE for expansion effects in ARDL (1,1) is given by
Var( STE )  Var(  11 )  Var(  12 )  2Cov(  11 , 12 )
Var( LTE ) 
(A14)
(  11   12 )2
1
Var(  1 ) 
[ Var(  11 )  Var( 12 )  2Cov(  11 , 12 )]
exp 4
( 1  1 )
( 1   1exp )2
(A15)

2(    )
[ Cov(  1exp , 11 )  Cov(  1exp , 12 )]
( 1   1exp )3
1
1
2
1
The variance of STE and LTE for contraction effects in ARDL (1,1) is given by
Var( STE )  Var(  21 )  Var(  22 )  2Cov(  21 , 22 )
Var( LTE ) 
(A16)
(  21   22 )2
1
Var(  1 ) 
[ Var(  21 )  Var(  22 )  2Cov(  21 , 22 )]
( 1   1cont )4
( 1   1cont )2
(A17)
2(  21   22 )
[ Cov(  1cont , 21 )  Cov(  1cont , 22 )]

( 1   1cont )3
iii