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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.

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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 firm-

level 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 end-

consumer demand due to economic shocks but also by changes in retailers’ inventory levels. For example,

                                                            1 GDP, retail sales, and personal consumption expenditure data obtained from Bureau of Economic Analysis and COMPUSTAT.

2 We discuss the exceptions in §2.

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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 days-

inventory, 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. 

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the strong asymmetry in the inventory investment behavior of retailers. Based on the short-term and long-

term 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

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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 high-

frequency 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

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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

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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

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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:

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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

ct

ltt GDPGDPGDP (1)

where, ltGDP and c

tGDP are trend and cyclical components of observed GDP at time t. The HP filter

(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:

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21T

2t

l1t

lt

lt

l1t

2T

1t

ltt

GDPGDPGDPGDPGDPGDPGDPmin

lt

(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):

ciorTroughPr

ct

Expt GDPGDPSHOCK (3a)

ct

ciorPeakPr

Contt GDPGDPSHOCK (3b)

where, ExptSHOCK and Cont

tSHOCK are the expansion and contraction shocks. ciorTroughPrGDP and c

iorPeakPrGDP

are the values of cGDP on prior trough and prior peak, respectively. Thus, with this operationalization

ConttSHOCK and Exp

tSHOCK 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.

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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

variables (ΔXit), and contemporaneous and lagged effect(s) of shocks ( ExpqtSHOCK , Cont

qtSHOCK ). Finally, we

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:

Q

0q

Expqt

q1

9

6lijl

5

3ktkit2

P

1ppit

p10it SHOCKINDQTRXITIT

(4)

it

Q

0q

Contqt

q2 SHOCK

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

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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 01 and 1

1 respectively. The

sum of these two coefficients ( 11

01 ) 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 t-

1. 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 )1/()( 111

01 . 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 q1 and q

2 , and the decay parameter 1.

Expansion Contraction

STE

Q

0q

q1

Q

0q

q2

LTE

)1( 1

Q

0q

q1

)1( 1

Q

0q

q2

To test the statistical significance of the STE and LTE and test for asymmetry across expansion and

                                                            7 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.

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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):

2it5it4it3it2

P

1ppit

p10it ASTDPMRGNSGITIT

(5)

it

Q

0q

Contqt

q2

Q

0q

Expqt

q1

12

9lijl

8

6ktk SHOCKSHOCKINDQTR

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 Expt

ConttSHOCK ) 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 ( 3qit2qit1qit SG,SG,SG ) and lagged values

of change in margin ( 3qit2qit1qit MRGN,MRGN,MRGN ) as our instruments. Our instruments

predate the last included economic shocks by at least one quarter.

                                                            8 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.

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.

13  

Third, the lagged dependent variable (ΔITit-p) can be influenced by lagged value of economic shocks (

Contqt

Expqt SHOCK,SHOCK ) thereby biasing the estimates of θ. In other words lagged dependent variable (ΔITit-

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 4ititit and error in 1itIT is

5it1it1it 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

14  

(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 retailer-

level 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 macro-

economic 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.

15  

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

16  

(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

17  

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 macro-

economic 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

18  

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 (

c4t

ctt GDPGDPSHOCK ). 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

                                                            12 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.

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.

14 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.

15 To conserve space we do not report these results in the manuscript. They are available from authors upon request.

19  

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.

20  

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 firm-

level 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.

21  

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.

References

Ball, L., N.G. Mankiw. 1994. Asymmetric price adjustment and economic fluctuations. NBER Working Paper No. 4089.

Beaudry, P., G. Koop. 1993. Do recessions permanently change output? J. Monetary Economics 31(2) 149-163.

Bils, M. 1985. Real wages over business cycles: Evidence from panel data. J. of Political Econ. 93(4) 666-689.

Bils, M., J.A. Kahn. 2000. What inventory behavior tells us about business cycles. American Econ. Rev. 90(3) 458-481.

Blinder, A.S. 1981. Retail inventory behavior and business fluctuations. Brooking Papers on Economic Activity 2 443-520.

Blinder, A.S., L.J. Maccini. 1991. The resurgence of inventory research: What have we learned? J. Econ. Surveys 5(4) 291-328.

Cachon, G.P., T. Randall, G.M. Schmidt. 2007. In search of the bullwhip effect. Manufacturing and Service Oper. Management 9(4) 457-479.

Callioni G., X. de Montgros., R. Slagmulder, L. N. Van Wassenhove., L. Wright. 2005. Inventory-driven costs. Harvard Business Review March 2005.

Carpenter, R.E., S.M. Fazzari, B.C. Petersen. 1998. Financing constraints and inventory investment: A comparative study with high-frequency panel data. The Review of Economics and Statistics 80(4) 513-519.

Chen, X., M. Sim, D. Simchi-Levi, P. Sun. 2007. Risk aversion in inventory management. Oper. Res. 55(5) 828-42.

Clements, M.P., A.B. Galvao. 2009. Forecasting U.S. output growth using leading indicators: an appraisal using MIDAS models. J. of Applied Econometrics. 24(7) 1187-1206.

Cochrane, J.H. 1994. Shocks. Carnegie-Rochester Conference Series on Public Policy 41 295-364.

Larson, C.R., D. Turcic., F. Zhang. 2011. Inventory Write-downs, Sales Growth, and Ordering Policy: An Empirical Investigation. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1762892

Gaur, V. and Y. Park. 2007. Asymmetric Consumer Learning and Inventory Competition. Management Science. 53 (2) 227-240.

Gaur, V., S. Kesavan. 2007. The Effects of Retailer Size and Sales Growth Rate on Inventory Turnover Performance in U.S. Retail Services. Retail Supply Chain Management, edited by N. Agrawal and S. Smith, Kluwer Publishers. 25-52.

Gaur, V., S. Kesavan, A. Raman, M. Fisher. 2007. Estimating demand uncertainty using judgmental forecasts. Manufacturing and Service Oper. Management. 9(4) 480-491.

Gaur, V., N. Osadchiy., S. Sheshadri. 2011. Sales forecasting with financial indicators and experts’ input. Working paper, Johnson School Research Paper Series No. #06-09.

Hendricks, K.B., V.R. Singhal. 2009. Demand – Supply Mismatches and Stock Market Reaction: Evidence from Excess Inventory Announcement. Manufacturing & Service Operations Management. 11 (3) 509 - 524.

Hodrick, R.J., E.C. Prescott. 1997. Postwar U.S. business cycles: An empirical investigation. J. of Money, Credit and Banking. 29 1-16.

22  

Irvine, F. O., Jr. 1981. Retail inventory investment and the cost of capital. Amer. Econom. Rev. 71 633–668.Jacobson, R.D. 1990. Unobservable effects and business performance. Marketing Sci. 9 (1), 74-85.

Kahn, J.A. 1987. Inventories and the volatility of production. American Econ. Rev. 77 667-669.

Kahn, J.A. 1992. Why is production more volatile than sales? Theory and evidence on the stockout-avoidance motive for inventory-holding. Quart. J. Econom. 107 481-510.

Kesavan, S., V. Gaur, A. Raman. 2010. Do inventory and gross margin data improve sales forecasts for U.S. public retailers? Management Sci. 56(9) 1519-1533.

Kesavan, S., V. Mani. 2010. The predictive power of abnormal inventory growth: Application to earnings forecasting for retailers. Working Paper.

Lamey, L., B. Deersnyder, M.G. Dekimpe, J.B.E.M. Steenkamp. 2007. How business cycles contribute to private-label success: Evidence from the U.S. and Europe. J. Marketing 71 1-15.

Lamey, L., B. Deersnyder, J.B.E.M. Steenkamp, M.G. Dekimpe. 2011. The effect of business cycle fluctuations on private-label share: what has marketing conduct got to do with it?. J. Marketing. forthcoming.

Maccini, L., R.J. Rossana. 1981. Investment in finished goods inventories: An analysis of adjustment speeds. American Econ. Rev. 71(2) 17-22.

Makridakis, S., S. Wheelwright, R.J. Hyndman. 1998. Forecasting: methods and applications. John Wiley and Sons, New York.

McCarthy, J., E. Zakrajsek. 2000. Microeconomic inventory adjustment: Evidence from firm level data. Working paper, Finance and Economics Discussion Series 2000-24, Board of Governors of the Federal Reserve System.

Mela, C.F., S. Gupta, D.R. Lehmann. 1997. The long-term impact of promotion and advertising on consumer brand choice. J. Marketing Res. 34(2) 248-261.

Neftci, Salih. 1984. Are economic time series asymmetric over the business cycle?. J of Pol Econ. 92 (2) 307-328.

Nerlove, M. 1958. The dynamics of supply: Estimation of farm supply responses to price. John Hopkins University Press, Baltimore.

Rajagopalan, S. 2009. Factors driving inventory levels at US retailers. Working paper. University of Southern California.

Raman, A., B. Kim. 2002. Quantifying the impact of inventory holding cost and reactive capacity on an apparel manufacturer’s profitability. Production and Operations Management 11(3) 358–373.

Ravn, M.O., H. Uhlig. 2002. On adjusting the Hodrick-Prescott Filter for the frequency of observations. The Review of Economics and Statistics 84(2) 371-375.

Rumyantsev, S., S. Netessine. 2007. What can be learned from classical inventory models? A cross-industry exploratory investigation. Manufacturing and Service Oper. Management. 9(4) 409-429.

Sethi, S., F. Cheng. 1997. Optimality of (s, S) policies in inventory models with markovian demand. Oper. Res. 45(6) 931-939.

Song, J.S., P. Zipkin. 1993. Inventory control in a fluctuating demand environment. Oper. Res. 41(2) 351-370.

Terwiesch, C., Z. J. Ren., T.H. Ho., M. A. Cohen. An Empirical Analysis of Forecast Sharing in the Semiconductor Equipment Supply Chain. Management Sci.51(2) 208-220.

23  

Table 1 VARIABLES AND DATA SOURCES

Variable Measure Data Source

CPI Consumer price index as measure of inflation Bureau of Economic Analysis (BEA)

Gross Domestic Product (GDPt) Log(CPI adjusted GDP) 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.

24  

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

Dependent Variable - ΔITit

Expansion Contraction 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

ExptSHOCK -.548 .580 Exp

1tSHOCK -.772 .564 ConttSHOCK -.256 .373 Cont

1tSHOCK .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.

25  

Table 4 RESULTS: STOCK OUT COST

Dependent Variable - ΔITit

High (HSCit = 1) Low (LSCit = 1) Expansion Contraction Expansion Contraction

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E.ΔITit-1 a .653 .033 .650 .028 .619 .027 .603 .028ΔSGit a .106 .028 .053 .024 .162 .029 .125 .026ΔMRGNit a -.189 .091 -.141 .067 -.148 .107 -.054 .065ΔASTit-2 -.005 .020 -.019 .017 .032 .019 .050 .018ΔDPit -.077 .010 -.080 .008 -.109 .014 -.096 .008

ExptSHOCK -1.344 1.131 -.613 1.181 Exp

1tSHOCK .474 1.090 -.823 1.143 ConttSHOCK .019 .727 -1.240 .781Cont

1tSHOCK .016 .875 1.954 .924Intercept .043 .020 .006 .013 .005 .017 .015 .015Quarter Fixed Effects Two Significant None Significant None Significant None SignificantIndustry Fixed Effects None Significant None Significant None Significant None SignificantShort Term Effects -.870 .571 .035 .307 -1.436 .592 .715 .314Long Term Effects -2.504 1.281 .099 .584 -3.774 1.336 1.802 .566

H2a

Expansion H2b

Contraction Diff S.E. Diff S.E.

Short Term Effects (High – Low) .566 .582 -.680 .311 Long Term Effects (High – Low) 1.270 1.309 -1.703 .575

Note: All italicized coefficients have p<.05 a These variables are instrumented using their respective lags from t-2 through t-4.

26  

Table 5 RESULTS: INVENTORY HOLDING COST

Dependent Variable - ΔITit

High (HICit = 1) Low (LICit = 1) Expansion Contraction Expansion Contraction

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E.ΔITit-1 a .735 .050 .570 .042 .413 .043 .596 .042ΔSGit a .045 .033 .125 .031 .034 .046 .034 .038ΔMRGNit a -.208 .064 -.134 .048 -.518 .147 -.159 .125ΔASTit-2 -.007 .027 .044 .028 -.033 .026 .035 .025ΔDPit -.083 .014 -.068 .012 -.086 .016 -.085 .013

ExptSHOCK -1.102 1.942 -.722 1.626 Exp

1tSHOCK 1.367 1.888 -1.363 1.574 ConttSHOCK -.867 1.193 -.820 1.016Cont

1tSHOCK 1.334 1.436 1.168 1.204Intercept .015 .020 .014 .016 .041 .024 .007 .023Quarter Fixed Effects One Significant One Significant None Significant None SignificantIndustry Fixed Effects None Significant None Significant None Significant None SignificantShort Term Effects .266 .889 .468 .481 -2.085 .773 .348 .433Long Term Effects 1.003 1.448 1.086 .648 -3.553 1.022 .861 .945

H3a

Expansion H3b

Contraction Diff S.E. Diff S.E.

Short Term Effects (High – Low) 2.351 .833 .120 .458 Long Term Effects (High – Low) 4.556 1.253 .225 .810

Note: All italicized coefficients have p<.05 a These variables are instrumented using their respective lags from t-2 through t-4.

27  

Table 6 ROBUSTNESS TEST: DURBIN-WU-HAUSMAN AUGMENTED REGRESSION TEST

Dependent Variable - ΔITit

Expansion Contraction Coeff. S.E. Coeff. S.E.

ΔITit-1 a .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

ExptSHOCK .518 1.075 Exp

1tSHOCK -2.281 .983 ConttSHOCK .416 .557 Cont

1tSHOCK .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.

28  

Table 7 ROBUSTNESS TESTS: ALTERNATE MODEL SPECIFICATIONS WITHOUT AUTOREGRESSIVE TERM

Dependent Variable - ΔITit

Expansion Contraction 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 .017ΔMRGNit a -.423 .052 -.439 .059 -.437 .059 -.296 .041 -.349 .043 -.350 .042ΔASTit-2 -.068 .013 -.067 .013 -.065 .013 -.068 .012 -.071 .011 -.071 .012ΔDPit -.111 .008 -.101 .008 -.101 .008 -.103 .006 -.098 .005 -.095 .005

ExptSHOCK -1.105 .382 -1.353 .764 -1.409 .781 Exp

1tSHOCK .340 .743 .845 .810 Exp

2tSHOCK .139 .621 Exp

3tSHOCK -1.004 .758 Exp

4tSHOCK -.551 .522 ConttSHOCK -.165 .163 -.502 .223 -.292 .319Cont

1tSHOCK 1.413 .245 1.275 .335Cont

2tSHOCK .898 .503Cont

3tSHOCK -1.373 .620Cont

4tSHOCK .761 .293Intercept .054 .015 .057 .014 .059 .014 .034 .011 .038 .011 .032 .011Quarter Fixed Effects Three Significant Three Significant Three Significant None Significant None Significant None SignificantIndustry Fixed Effects None Significant None Significant None Significant Three Significant Four Significant Three SignificantTotal 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.

29  

Table 8 ROBUSTNESS TEST: SHOCK MEASURED AS 4TH DIFFERENCE OF CYCLICAL COMPONENT

Note: 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

Dependent Variable - ΔITit Expansion

Coeff. S.E. ΔITit-1 b .634 .010ΔSGit b .103 .010ΔMRGNit b -.096 .026ΔASTit-2 .023 .006ΔDPit -.095 .003SHOCKt (CCIt – CCIt-4) .035 .007SHOCKt-1 (CCIt-1 – CCIt-5) -.055 .007Intercept .009 .004Quarter Fixed Effects None SignificantIndustry Fixed Effects None SignificantShort Term Effects -.020 .006Long 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.

Dependent Variable - ΔITit Expansion

Coeff. S.E. ΔITit-1 a .630 .010ΔSGit a .106 .010ΔMRGNit a -.094 .026ΔASTit-2 .024 .006ΔDPit -.095 .003SHOCKt ( c

4tc

t GDPGDP ) .114 .170SHOCKt-1( c

5tc

1t GDPGDP ) -.686 .169Intercept .009 .004Quarter Fixed Effects None SignificantIndustry Fixed Effects None SignificantShort Term Effects -.572 .105Long Term Effects -1.547 .285

30  

Table 10 ROBUSTNESS TEST: INCLUSION OF SIC 54 (GROCERIES AND PRODUCE)

Dependent Variable - ΔITit

Expansion ContractionCoeff. S.E. Coeff. S.E.

ΔITit-1 a .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

ExptSHOCK -1.039 .544 Exp

1tSHOCK -.126 .528 ConttSHOCK -.833 .446 Cont

1tSHOCK 1.729 .533 Intercept .025 .009 .006 .007 Quarter Fixed Effects Three Significant None Significant Industry Fixed Effects None Significant Two Significant Short Term Effects -1.165 .266 .895 .198 Long Term Effects -3.035 .634 2.523 .533 Sample Size N 4,964 5,796 No. of Retailers 402 404

Note: All italicized coefficients have p<.05. a These variables are instrumented using their respective lags from t-2 through t-4.

31  

Figure 1 ILLUSTRATION OF PROPOSED ECONOMETRIC MODEL SPECIFICATION

t-2 t-1 tt-T t+T’

Shockt-2 Shockt-1 Shockt

ΔXit-1

ΔITit-1

ΔXit-2

ΔITit-2

Controlled Effects, Endogenous Variables Instrumented Out Hypothesized Short Term Effects

ΔXit

ΔITit

11  

11

Note: For illustration purposes expansion shock coefficients and ARDL (1,1) specification are exemplified.

01  

11  0

1  11

Shockt-T

ΔXit-T

ΔITit-T

11

01  0

1  

32  

Figure 2 CHANGES IN INVENTORY TURNS AND MACROECONOMIC SHOCKS

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

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).

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2.00

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10

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Overall Contraction

Retailers with Low Stockout Costs during Contractions

Retailers with Low Inventory Holding Costs during Expansions

Overall Contraction

i  

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:

ititit XIT *

110 (A1)

where, ITit is inventory turn of retailer i and *1itX are expectations of retailer specific factors. As *

1itX 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 ( *

itX ):

)XX(XX *itit

*it

*1it (A2)

where, 0<<1 is the proportion of discrepancy. Rearranging

*itit

*1it X)1(XX (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

itititit XXIT *110 )1()( (A4)

Taking a lag of equation (A3) yields

*1it1it

*it X)1(XX (A5)

Substituting back equation (A5) in (A4) yields

ititititit XXXIT *

12

11110 )1()1( (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 *

1itX 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

11

122

11110 )1(....)1()1(

TitT

itititit XXXXIT (A7)

it*

1TitT

1 X)1(

In the above recursive terms can be substituted by lagged value of ITt-1 as

it1itit10it IT)1(XIT (A8)

We can reparameterize above as

itit21it10it XITIT (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:

ii  

it

9

6lijl

5

3ktkit21it10it INDQTRXITIT

(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:

ittit (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.

Expt1

9

6lijl

5

3ktkit21it10it SHOCKINDQTRXITIT

(A12)

itContt2 SHOCK

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

Q

0q

Expqt

q1

9

6jijtj

5

3jjtjit2

P

1ppit

p10it SHOCKINDQTRXITIT (A13)

it

Q

0q

Contqt

q2 SHOCK

The above equation appears as Eq (4) in main text.

iii  

Appendix A2

Variance of STE and LTE The variance of STE and LTE for expansion effects in ARDL (1,1) is given by

),(Cov2)(Var)(Var)STE(Var 21

11

21

11 (A14)

)],(Cov2)(Var)(Var[)1(

1)(Var

)1(

)()LTE(Var 2

111

21

112exp

114exp

1

221

11

(A15)

)],(Cov),(Cov[)1(

)(2 21

exp1

11

exp13exp

1

21

11

The variance of STE and LTE for contraction effects in ARDL (1,1) is given by

),(Cov2)(Var)(Var)STE(Var 22

12

22

12 (A16)

)],(Cov2)(Var)(Var[)1(

1)(Var

)1(

)()LTE(Var 2

212

22

122cont

114cont

1

222

12

(A17)

)],(Cov),(Cov[)1(

)(2 22

cont1

12

cont13cont

1

22

12