The effect of information precision and information reliability on manufacturer-retailer...

I. INTRODUCTION

This paper examines how both the extent to which a retail firm is willing to share internal accounting information with a manufacturer and the reliability of the information transmission from the retailer to the manufacturer affect the total supply-chain profits resulting

from two alternative inventory management systems: a traditional system and a Vendor Managed Inventory (VMI) system. In a traditional system, manufacturers and retailers forecast demand independently; the retailer determines an order quantity and the manufacturer selects a production quantity. In contrast, a retailer using a VMI system delegates her inventory decisions to the manufacturer; the manufacturer determines both the order and the production quantities.

To investigate the relation between internal accounting information, the way firms share this information, and the relative profitability of traditional vis-a-vis VMI systems, I develop a model that incorporates (1) the different sales and inventory (i.e., demand) information that the manufacturer and the retailer hold, (2) the extent to which the retailer shares information with the manufacturer, (3) the manufacturer's transmission and receipt of the shared information, and (4) the contract between the two parties about inventory decision rights. Based on the model analysis, I generate conditions under which VMI systems lead to higher supply-chain profits than do traditional systems.

Traditionally, manufacturers and retailers operate independently. Each uses its forecast of demand to determine the quantity to produce (manufacturers) or to buy (retailers) (Cooke 1992, 57). By contrast, in VMI systems, the retailer relinquishes inventory decision rights to the manufacturer and communicates inventory and/or sales information to the manufacturer. The manufacturer views the retailer's accounting information as a proxy for consumer demand and uses this information to plan production and delivery. The parties expect that through coordination and information sharing, VMI will increase supply-chain profits and efficiency.

The supply-chain-profit benefits the retailer and manufacturer derive from VMI depend on the information the retailer transmits to the manufacturer. The level of detail of the information varies. For example, some retailers share regional warehouse inventory information, while others share store-level sales and inventory information; the latter more finely captures underlying consumer demand. The detail with which the retailer chooses to disclose internal accounting information to the manufacturer (I label this information precision) affects the ultimate success of the VMI system. Additionally, the manufacturer must correctly capture the retailer's internal accounting information (I label this information reliability). The information has no value if the manufacturer cannot incorporate it into his decision making. Thus, the properties of the information shared between parties influences the success of--and consequently the use of--VMI systems.

The study analytically models both a traditional and a VMI system, compares the expected profits derived under each system, and details the effect of the precision and reliability of the retailer's internal accounting information on the resulting profits. I formulate a double newsboy model in which both parties make quantity decisions and the wholesale price is endogenously determined. In the model, the retailer holds information about consumer demand. This information varies in its precision, representing the extent to which the retailer shares internal accounting information with the manufacturer. The retailer communicates the information to the manufacturer; however, the information transfer may be imperfect. Thus, the consumer demand information received by the manufacturer may be less reliable than the retailer's information. I use the model to compare the traditional and VMI systems in order to generate specific hypotheses about the conditions under which firms will choose to use VMI.

In selecting a system, the manufacturer compares the profit earned from a traditional system with that earned from a VMI system. In the traditional system, the retailer uses a more precise demand signal to make order-quantity decisions, but does not consider total supply-chain costs. In the VMI system, the manufacturer determines the production and order quantity based on total supply-chain costs and less precise and/or less reliable demand information. The model suggests that VMI systems do not necessarily lead to higher expected profits than traditional systems. Rather, the success of VMI depends on the choices both parties make about the information properties. If the manufacturer receives information from a relatively imprecise or unreliable system, then the traditional relationship results in higher expected profits.

I use survey data on 53 manufacturer divisions to test these predictions. The empirical tests support the hypothesis that manufacturers' use of VMI increases with the detail of information transmitted from the retailer and with the manufacturers' ability to capture this information.

The study's findings are relevant to management accountants and supply-chain management executives. The information shared between supply-chain partners influences the type of relationship formed (VMI or traditional) and the success of that relationship. The implication that VMI does not necessarily improve supply-chain performance may surprise management accountants and supply-chain management executives considering implementing VMI. To maximize the supply-chain-profit benefits of VMI, the retailer and the manufacturer should ensure that the internal sales and inventory information the retailer offers is as precise as possible and that the manufacturer is able to receive and use this information accurately.

The paper is organized as follows: Section II describes the related literature. Section III presents the theoretical model and related analyses. Section IV details the hypotheses derived from the models. Section V describes the field-based investigation and empirical tests, and Section VI presents the empirical results. Section VII summarizes the findings and concludes the study.

II. LITERATURE REVIEW

This research relates to four distinct streams of prior work: (1) practitioner and case research, (2) accounting research, (3) operations management research, and (4) transfer-pricing research.

Prior practitioner and case evidence highlights the relation between VMI and supply-chain profitability. Vergin and Barr (1999) find that 80 percent of manufacturers polled increased sales due to VMI (which the authors term "continuous replenishment program"). However, only two out of ten improved the production process, and only one lowered inventory. The authors suggest that these companies may not have adequately integrated the VMI process into their corporate cultures. McKenney (1994, 1995) and Hammond (1995) document that supply-chain management initiatives at Procter & Gamble, Campbell Soup Company, and Barilla SpA are associated with increased profits, lower costs, and more efficient operations, respectively. My research questions whether VMI unambiguously leads to improved supply-chain performance. I specifically examine the conditions under which VMI systems might lead to higher profitability and focus on the effect of properties of the internal accounting information on VMI's success.

The accounting literature contains limited theoretical development on how internal accounting information affects the success of supply-chain management initiatives. (1) Xu (1996) focuses on the relative bargaining power of supply-chain partners and the effect this power has on the resulting contract. Narayanan and Raman (1998) model the use of supply-chain contracts, such as VMI, to mitigate the misalignment of retailers' and manufacturers' incentives regarding stockouts. My study extends this analytical work to show how the properties of the internal accounting information can influence the profitability of VMI systems.

The operations management literature analyzes various supply-chain management contracts, both analytically and, to a lesser extent, empirically. Tsay et al. (1999) provide a detailed review of this research. I extend the newsboy model from operations research to formulate models of both the VMI and the traditional systems. Additionally, I ensure that the model is consistent with Lee et al.'s (1997) finding that consumer demand variability is amplified up the supply-chain. In one of the few studies empirically investigating VMI and the related benefits, Clark and Hammond (1997) find that VMI and electronic data interchange (EDI) are associated with better supply-chain performance, and that large-scale VMI is associated with greater benefits. Cachon and Fisher (1997) find that VMI benefits stem partially from sharing demand information. Both studies concentrate on one manufacturer's extensive use of VMI.

My study adds to the existing literature on supply-chain management by modeling the interaction among the properties of the information that the retailer shares, the manufacturer's use of this information, and the resulting inventory management contract. I then test the analytical predictions using a sample of 53 manufacturer divisions (rather than one company's adoption).

Finally, the transfer-pricing literature studies decentralized decision making and information sharing within a firm. One may view VMI as an extreme form of decentralization. However, Lambert (2001) points out that inter- and intrafirm relationships differ significantly. Within a firm, no real money transfer occurs; the transfer price acts as an incentive mechanism. By contrast, the wholesale price exchanged between firms results in a money transfer that directly affects both firms' profits. Thus, it is important to study how interfirm initiatives affect profits. Harris et al. (1982) and Melumad et al. (1992) investigate the tradeoff between delegating decisions to informed managers and these managers' potential to make myopic decisions. Similarly, this paper examines the allocation of decision rights and the potential for myopic decision making. In the current study, the retailer holds both the decision rights and the information; the manufacturer must set the wholesale price to induce the retailer to transfer both to the manufacturer. (2)

III. THEORETICAL MODEL

Basic Model

Consider a manufacturer-retailer relationship in which both parties are risk-neutral and inventory-related costs are common knowledge. The manufacturer is the principal and the retailer is the agent. (3) I compare two asymmetric information models of the manufacturer-retailer relationship. (4) In the first, the manufacturer selects the production quantity and the retailer determines the order quantity, without either party's sharing information (traditional system). In the second, the manufacturer selects both the production and the (retailer's) order quantities, after the retailer provides demand information (VMI system). In selecting a system, the manufacturer must trade off the retailer selecting a myopic, but informed, order quantity (traditional system) against the manufacturer making an "optimal," but less informed, quantity decision (VMI system).

The retailer purchases a finished product from the manufacturer and resells it at an exogenously determined price, p, to the end consumer; the manufacturer produces each unit at a cost, c. The parties contract on wholesale price, w. The manufacturer sets the wholesale price to maximize his expected profit while offering the retailer at least a reservation amount of profit, [U.sub.r], in expectation. I assume, without loss of generality, that [U.sub.r] is zero. (5)

I use a double newsboy model, in which the contracting parties select both the production quantity, [Q.sub.m], and the order quantity, [q.sub.i], to analyze the quantity and wholesale price choices under the traditional and VMI systems. The subscript, i, refers to the party making the related decision; i = r if the retailer makes the decision and i = m if the manufacturer makes the related decision. The theoretical results generalize to models that include return policies, stockout penalties, and additional layers of stockout and holding costs (Cohen 2000). Figure 1 presents the timeline of both the traditional and the VMI systems. The systems differ in the manner in which the retailer communicates information to the manufacturer. In the traditional system, the retailer does not reveal the demand signal directly to the manufacturer. The retailer orders [q.sub.r](j) based on the actual signal received (j [member of] {1,2,...,J}) and the manufacturer produces [Q.sub.m]() according to his priors (i.e., the manufacturer does not receive a signal from the retailer prior to production).

[FIGURE 1 OMITTED]

The VMI system incorporates communication. The retailer communicates the demand signal directly to the manufacturer, who produces [Q.sub.m](j) and delivers [q.sub.m](j) based on the transmitted signal. I assume that the retailer reports the information truthfully. The contract ensures that using a VMI system will not harm the retailer. Distorting the information would cause the manufacturer to determine the order quantity based on inaccurate information; a suboptimal order quantity and higher inventory costs would result. Thus, it is in the retailer's best interest to communicate the signal truthfully.

The retailer truthfully communicates the information; however, the transmission and/ or receipt of the information still may be unreliable (i.e., information may be lost during or omitted from the transmission). I operationalize the reliability of the manufacturer's information through [alpha], the probability that the signal is correctly communicated to and received by the manufacturer (i.e., the level of signal reliability). That is, [alpha] represents the amount of information not lost. Due to lost information, the signal is unreliable with probability 1 - [alpha]. (6)

In both systems, the parties have the same initial priors about consumer demand, D (i.e., D ~ U[[mu] - [[sigma]/2], [mu] + [[sigma]/2]]). The length of the distribution, [sigma], represents consumer demand variability and [mu] represents expected demand. (7) As [sigma] increases, the variance of consumer demand also increases. After signing the contract but before placing an order, the retailer receives refined consumer demand information and updates her priors. The retailer's private internal accounting information about sales and inventory proxies for consumer demand. The retailer's information indicates which of J equal-sized partitions of the demand distribution will occur. Consumer demand is distributed uniformly on this partition. For example, signal j indicates that D ~ U[[mu] + ([sigma](2j - J - 2))/2J, [mu] + ([sigma](2j - J))/2J]. The variable J represents information precision. As J increases, the distribution is segmented into finer divisions. Small J may be associated with the transmission of warehouse information, whereas large J may be associated with more precise point-of-sales (POS) data. Therefore, a large J enables the retailer to predict consumer demand more accurately.

After the manufacturer transfers the goods at the wholesale price, demand is realized. The retailer incurs stockout costs, s, if demand exceeds available product, and holding/ disposal costs, h, if demand falls short of available product. (8) Consistent with the operations management literature, I assume that a manufacturer that does not have enough inventory on hand must produce or obtain the shortfall and deliver the units to the retailer prior to consumer demand realization.

Based on the above description, the manufacturer's profit, [PI], given inventory decisionmaker i, signal j, and inventory management system k can be expressed as (variable definitions are summarized in Table 1):

(1) [[PI].sup.k.sub.m] ([q.sub.i](j),[Q.sub.m](j),w) = w[q.sub.i](j) - c[Q.sub.m](j)

k [member of] {Trad,VMI}, i [member of] {r,m}, j [member of] {1,2,...,J}.

The manufacturer sells the quantity ordered, [q.sub.i](j), to the retailer at a price of w per unit and incurs a unit production cost of c on the amount produced, [Q.sub.m](j). The party responsible for determining the order (i.e., i) differs between the two systems; the retailer selects [q.sub.i](j) in the traditional system, and the manufacturer chooses it in the VMI system.

Similarly, given inventory decision-maker i, signal j, and inventory management system k, the retailer's profit is represented by:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The retailer purchases [q.sub.i](j) from the manufacturer. The first integral reflects the retailer's expected profit if the inventory on hand exceeds consumer demand. The retailer meets demand and incurs a holding cost, h, on each unit remaining. The second integral represents the retailer's expected profit when consumer demand exceeds the quantity on hand. The retailer sells current inventory and incurs a stockout cost on each unit order that remains unfilled.

I assume that the wholesale price is determined prior to any information transmission or quantity decision. The contract cannot be renegotiated. Refer to Baiman (1990) for a discussion of renegotiation research in both complete and incomplete contract settings. (9)

Traditional System

In the traditional system, the retailer receives the consumer demand signal and indirectly transmits the signal to the manufacturer via her order, [q.sub.r](j). Because the retailer's cost and information structure are common knowledge, the manufacturer can compute the retailer's order, given each of the J signals. Thus, the manufacturer faces a discrete retailer demand distribution with J points and a variance of 1/J [[SIGMA].sup.J.sub.j=1] [q.sub.r][(j).sup.2] - [[1/J [[SIGMA].sup.J.sub.j=1] [q.sub.r][(j)].sup.2] . After she receives the signal, the retailer faces consumer demand with a variance of [[sigma].sup.2]/12[J.sup.2]. The manufacturer's problem is:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to:

(4) E[E[[[PI].sup.Trad.sub.r]([q.sub.r](j),w)|j]] [greater than or equal to] 0

(5) [q.sub.r](j) maximizes E[[[PI].sup.Trad.sub.r]([q.sub.r](j),w)|j] [for all] j [member of] {1,2,...,J}.

Based on his cost structure and the retailer demand distribution, the manufacturer selects a production quantity to maximize expected profits (Equation (3)). Equation (4) represents the retailer's participation constraint. The manufacturer must ensure that the retailer earns at least her reservation level of profits in expectation. Finally, the retailer selects an order quantity to maximize her expected profits (Equation (5)).

Proposition 1: With J = 2, the results of the traditional system are:

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(7) w = [[sigma](p + 2c - h + s) + 4[mu](p + h + s)]/4[sigma] [equivalent to] [w.sup.Trad]

(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Proof. All proofs are presented in the Appendix.

The retailer selects an order quantity (Equation (6)) based on both parties' cost structures and the consumer demand signal. The retailer bases the order quantity on expected demand, [mu]/2, and adjusts this estimate up or down based on the signal observed. As shown in the proof of Proposition 1 in the Appendix, in selecting the production quantity, the manufacturer minimizes his production costs and produces at the lower bound. The absence of communication means the manufacturer must produce before receiving the order. This results in a potential mismatch between the production and order quantities and an increased probability of a shortfall at the production site. The wholesale price, reflected in Equation (7), serves two purposes: it both induces the correct quantity choice and allocates profits between the two parties. Because it cannot do both tasks perfectly, the manufacturer decides which task w should emphasize, given the parameter values. For example, if the supply-chain profit margin is high, the manufacturer may use the wholesale price to influence the retailer's order quantity. In this case, the manufacturer would sacrifice a portion of his expected profits (Equation (8)) to induce the retailer to order the desired quantity. (10) Consequently, the retailer earns expected profits equal to the expression in Equation (9).

VMI System

VMI delegates the inventory decision to the manufacturer. The retailer truthfully communicates the consumer demand signal prior to production. With probability [alpha], the manufacturer receives full information and uses it in his quantity choice. With probability 1 - [alpha], information is lost in transmission (j = ()), and the manufacturer bases production on his initial priors. The probability proxies for information reliability and is public knowledge. The manufacturer's problem is:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to:

(11) [alpha](E[E[[[PI].sup.VMI.sub.r]([q.sub.m](j),w)|j]]) + (1 - [alpha])E[[[PI].sup.VMI.sub.r]([q.sub.m](),w)] [greater than or equal to] [[PI].sup.T.sub.r].

The manufacturer selects an order and a production quantity to maximize his expected profits (Equation (10)). The participation constraint (Equation (11)) ensures that the retailer expects to earn at least as much as she would earn in the traditional model. The retailer will not agree to use a VMI system unless the manufacturer guarantees the retailer will be at least as well off as in the traditional system.

Proposition 2: With J = 2, the results of the VMI system are:

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(13) [q.sub.m]() = [Q.sub.m]() = [mu] + [[sigma](p - 2c - h + s)]/[2(p + h + s)]

(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(16) E[E[[[PI].sup.VMI.sub.r]([q.sub.m](j),[Q.sub.m](j),w|j]] = [[PI].sup.T.sub.r].

When delegated the inventory decision, the manufacturer selects the production and order quantity that optimizes the entire supply-chain, given the demand information received from the retailer. (11) Equations (12) and (13) represent the manufacturer's quantity choice, given the signal received from the retailer. The production and order quantities are equivalent in the VMI system; these quantities weigh the supply-chain's stockout costs against its holding costs. The wholesale price and manufacturer's expected profit, Equations (14) and (15), respectively, depend on the reliability of the information received from the retailer, the exogenous parameters, and the profit earned by the retailer in the traditional system. The retailer earns the amount that she would have earned in the traditional system (Equation (16)).

Model Comparisons

The following propositions, which form the basis for specifying the empirical hypotheses, characterize the differences between VMI and traditional systems.

Proposition 3:

(17) [q.sub.m](j) [greater than or equal to] [q.sub.r](j) [w.sup.VMI] [less than or equal to] [w.sup.Trad].

In the VMI system, the manufacturer delivers a quantity to the retailer that exceeds the amount the retailer would have ordered in a traditional system. The manufacturer makes this quantity decision based on the higher supply-chain unit margin of p - c rather than on the (smaller) retailer's margin of p - w. This higher supply-chain margin results in a more expensive cost of a stockout, so the manufacturer delivers a larger amount to the retailer to avoid a stockout.

The manufacturer charges the retailer a lower wholesale price in the VMI system than he charges in a traditional system. The amount the manufacturer delivers to the retail store exceeds the amount the retailer would order if given the decision rights. To induce the retailer to switch to VMI, the manufacturer guarantees that the retailer's expected profit will remain the same. The information gains derived from a VMI system enable the manufacturer to lower the wholesale price, increase profits, and yet still ensure that the retailer earns at least as much as she would have earned in a traditional system.

Proposition 4: Holding p, c, h, s, and E[D] constant and letting [DELTA][PI] equal the difference in the manufacturer's profits between the VMI and traditional systems ([[PI].sup.VMI.sub.m] - [[PI].sup.Trad.sub.m]), [DELTA][PI] is:

1. Increasing in information reliability ([alpha]);

2. Ambiguous in consumer demand variability ([sigma]; and

3. Larger with higher information precision (J), for J = {2,3}.

In selecting a system, the manufacturer trades off an order that is based on full information, but that does not reflect his cost structure, against one that considers total supply-chain costs but is based on potentially incomplete information. The greatest benefits of VMI occur when the demand signal is reliable (high [alpha]). High information reliability corresponds to low information asymmetry. The more accurate manufacturer forecast results in higher manufacturer profits, stable retailer profits, and, thus, increased total supply-chain profits. Increases in consumer demand variability lead to ambiguous effects on the difference between the two systems. The direction of this comparative static depends on the values of the exogenous parameters. Finally, more precise information (higher J) leads to greater benefits from VMI because the manufacturer can predict consumer demand more accurately.

IV. HYPOTHESES DEVELOPMENT

Comparisons between the VMI and traditional systems lead to the following empirical predictions.

Relationship between Information, Product Characteristics, and VMI Use

I expect manufacturers to use VMI when the expected profits under VMI exceed those under the traditional system (i.e., when the consumer demand information is reliable and precise). Proposition 4 posits that the benefits of VMI depend partially on the reliability and precision of information about consumer demand. VMI users require sophisticated information linkages to ensure accurate data transfers to the manufacturer, and the retailer must reveal precise sales and inventory information in order for the information to benefit the manufacturer. Proposition 4 shows that the difference in profits between the VMI and traditional systems increases as the information reliability ([alpha]) and information precision (J) increase. (12) Furthermore, as the difference between the expected profits under the two systems increases, I expect the manufacturer to use VMI to a greater extent (i.e., with a higher percentage of volume). (13)

The theoretical results in Proposition 4 also imply an ambiguous relation between consumer demand variability and VMI use. Prior research also finds conflicting results about the relation between VMI use and consumer demand variability. Xu (1996) argues that manufacturers find it difficult to forecast when consumer demand is variable, so information sharing provides more accurate information on consumer demand and allows the manufacturer to plan more effectively. In contrast, Fisher (1997) contends that manufacturers should use VMI for products with more stable demand. Given the ambiguous sign in Proposition 4 and the conflicting results from prior research, I make no prediction about the direction of the relation between consumer demand variability and the extent of VMI use.

To summarize, I test the following hypotheses (stated in alternative form):

H1a: Manufacturers use VMI systems to a greater extent when the retailer transfers more reliable and precise information.

H1b: Manufacturers use VMI systems to either a greater or a lesser extent when consumer demand variability is high.

Effect of VMI Use on Wholesale Price

Proposition 3 states that the manufacturer charges a lower wholesale price in the VMI system than in the traditional system. The lower wholesale price represents the retailer's information rents and her portion of the efficiency gains. I expect more intensive use of VMI to increase efficiency gains, thereby leading to further reductions in the wholesale price. This leads to the following hypothesis:

H2: The more intensively the manufacturer uses VMI, the lower the wholesale price.

V. EMPIRICAL RESEARCH DESIGN

Research Setting

The empirical analysis focuses on the food and consumer packaged goods (F&CPG) industry. This highly competitive industry has been an early developer and adopter of information sharing and collaboration among supply-chain members. Accordingly, the F&CPG industry provides fertile ground for exploring manufacturer-retailer logistic partnerships. However, the results might not generalize to other industries.

Research Procedure

Survey Instrument

Written jointly with Andersen Consulting, the Stanford University Supply-Chain Management Forum, and Research, Inc., the survey encompasses a broad range of supply-chain management initiatives and is based on conversations with executives about collaborative techniques and performance measurement in the industry. During pre-survey interviews, we found that most companies/divisions do not track the financial impact of collaborative partnerships; managers can only approximate the financial effect of, say, a switch to VMI. Therefore, the survey uses ordinal scales. The survey comprised six parts: business strategies and characteristics, new product collaboration, information linkages, material linkages, outsourcing and distribution, and inventory collaboration. We asked respondents to answer the questions as they related to the primary products in the respondents' divisions. I specifically formulated a subset of questions related to VMI that included the company's use of VMI, the type and extent of information sharing, and the sophistication of the manufacturer's information linkages. We mixed the VMI questions with other questions to mitigate any bias that might occur were a single section to ask questions only about VMI.

An external market research firm conducted a 30- to 45-minute phone interview with each executive responsible for collaboration and/or logistics at the division level. Telephone inquiries result in fewer nonresponses and allow interaction between the interviewer and interviewee. One-on-one contact allows the interviewer to define various terms in the survey consistently.

Sample

The sample consists of 100 divisions of manufacturers in the F&CPG industry. Sixty-one respondents are divisions of public companies, and many are different divisions of the same entity. Due to incomplete responses to the VMI questions, I analyze only 53 divisions. Ideally, I would use financial data to analyze the effect of VMI adoption and link manufacturers to their retail partners to assess individual and total supply-chain changes. However, it would be difficult to assess any relationship between a company's consolidated financial statements and initiatives adopted at the division level. Additionally, because the data are cross-sectional rather than longitudinal, I am unable to test the effects of VMI on division performance over time. Thus, the empirical analysis is based solely on the survey responses and relies on self-reported assessments of costs, benefits, information sharing, and collaboration. The estimates offer insight into the information and division characteristics associated with VMI use.

Empirical Variables

The hypotheses suggest that manufacturers' use of VMI depends on the precision and reliability of the information the retailer shares, and possibly on consumer demand variability. I also expect manufacturers' use of VMI to lead to lower wholesale prices. The following sections describe the empirical variables used to test these theoretical predictions.

Dependent Variables

The dependent variable used to test H1a and H1b is the extent of VMI use. Each responding manufacturer division indicated whether the division uses VMI and, if so, the percent of sales that flow through the VMI system. Extent_VMI categorizes the divisions based on their response to a six-point scale ranging from "no VMI" to "VMI with 91 percent or more of your sales."

To test the relation between VMI and the wholesale price transferred between the manufacturer and the retailer (H2), I use the wholesale price (wholesale_price) the manufacturer charges the retailer as the dependent variable. The related question asked the responding manufacturer division to rate the price the company charges the retailer on a five-point scale ranging from "much lower than the industry average" to "much higher than the industry average."

Independent Variables

Precision and reliability of information the retailer shares with the manufacturer. The survey asked a series of questions about the type of internal accounting information the retailer shares with the manufacturer, the percent of sales volume for which the manufacturer receives this information, and the information system's sophistication (i.e., the use of an EDI system and the amount of data that can be seamlessly transferred via the system). Because many of the question responses are correlated, I use principal components analysis to identify the underlying constructs and the specific questions underlying each construct. The first construct, precision, reflects the fineness of the information the retailer shares with the manufacturer, and corresponds to information precision in the model (J). It comprises four items detailing the extent to which retailers share information with the manufacturer, each measured on a six-point scale. Specifically, the items detail the percent of volume for which the retailer provides the manufacturer information on store inventory levels, warehouse inventory levels, warehouse withdrawals, and point-of-sales data. The second construct, reliability, relates to the manufacturer's information linkages (i.e., quality of the information transfer) and proxies for information reliability ([alpha]. It includes seven yes/no responses about the use of an EDI system and the information available through the division's EDI system, including purchase orders, invoices, warehouse inventory data, and production schedules. The more information that flows seamlessly through the system, the more accurate the information that the manufacturer receives and, thus, the more reliable the information.

Consistent with prior literature (Burke 1984), I identify the constructs (described above) via principal components analysis and form indices by adding the scores on the individual components of the constructs. (14) Adding the scores gives each question an equal weight rather than a weight based on the variability in the response. (15) The resulting constructs, precision and reliability, have Cronbach's coefficient alphas of 0.8091 and 0.8335, respectively.

Consumer demand variability. Fisher (1997) argues that consumer demand variability depends on the product life-cycle stage. Early-stage products have unstable and/or unknown consumer demand. Therefore, I use the percentage of products in the introduction and growth stages (life_cycle) to proxy for consumer demand variability.

Control variable. I also control for another variable that may affect a division's use of VMI. (16) Companies adopt VMI if the related gains exceed the costs. Larger companies are more likely to have the resources to afford the high set-up and maintenance costs of adopting VMI in their various divisions. Consequently, the company size, rather than the division size, affects the adoption of large initiatives such as VMI. I use the company sales level (sales) as a proxy for size. The survey asked respondents into which of six groups their companies' sales levels fell. Thus, the companies are grouped categorically rather than continuously on this dimension.

Data Limitations

Similar to other survey research, virtually all the measures I use contain measurement error because respondents used an arbitrary response scale. The respondents rated the levels of information sharing and collaboration on a six-point scale, and their divisions' performance relative to that of the industry on a five-point scale. The answers may be prone to interpretation error. For example, respondents may interpret the phrases "above the industry average" and "significantly above the industry average" differently. As long as these errors are unsystematic, this biases coefficients in the statistical analyses toward zero. Using a phone survey helps alleviate these problems because the interviewer consistently defines terms. To further diminish the measurement error and to simultaneously capture the multidimensional quality of the data, I group related responses into the two constructs identified previously, precision and reliability.

Another limitation is that some respondents may have systematically biased their answers. For example, an upward bias would result if respondents do not reveal that their divisions' performances are lower than the industry average. As long as VMI respondents do not bias their answers in a manner systematically different from those of non-VMI respondents, this should not affect the results.

The empirical analyses test only for associations between information properties and VMI; I do not make any inferences about causality. The hypotheses, as stated, imply that information precision and reliability lead to VMI use. However, companies that have precise and reliable information already may be more inclined to use VMI. Alternatively, adopting VMI may have led the manufacturer to demand more precise and reliable information from the retailer. Without time-series data, one cannot determine the direction of causality between information properties and VMI use.

Empirical Model Specification

Hypotheses 1a and 1b predict the extent of VMI use will increase with the precision and reliability of the information the retailer shares and will be ambiguous in consumer demand variability. Because my measure of the extent of VMI use is an ordered, categorical variable, I use the following ordered PROBIT model to analyze the relation between the independent variables and the extent of VMI use. Multinomial LOGIT and standard linear regression result in similar qualitative inferences.

(18) Prob(Extent_VMI = i) = F([alpha] + [[beta].sub.1]precision + [[beta].sub.2]reliability + [[beta].sub.3]life_cycle + [[beta].sub.4]sales)

where

F(*) = the normal cumulative distribution function;

Extent_VMI = extent of VMI use;

precision = index for precision of information the retailer shares;

reliability = index for reliability of manufacturer's information linkages;

life_cycle = percentage of products in introduction or growth stages (a proxy for consumer demand variability); and

sales = sales of the entire firm.

I test H1a and H1b through the variables precision, reliability, and life_cycle.

Hypothesis 2 predicts that the wholesale price transferred from the retailer to the manufacturer will decrease with the extent of VMI use. The dependent variable, wholesale_price, is ordered and categorical. Therefore, I test H2 using the following ordered PROBIT model:

(19) Prob(wholesale_price = i) = F([alpha] + [[beta].sub.1]Extent_VMI)

where:

F(*) = the normal cumulative distribution function; and wholesale_price = wholesale price charged by the manufacturer.

VI. EMPIRICAL RESULTS

Descriptive Statistics

The descriptive statistics for the empirical variables and the related survey questions appear in Table 2. To be included in the test sample, a respondent must answer all of the related questions. Thus, the number of observations in the test sample is lower than the number in the overall sample. (17) The standard deviations indicate reasonable variation among respondents' answers to each survey question. This alleviates the concern that respondents simply answered that their divisions were "average" on all dimensions. Most of the univariate correlations among the independent variables are not significant at conventional levels (not tabulated). However, reliability is significantly positively correlated with precision and significantly negatively correlated with life_cycle at the 5 percent level.

Average firm-wide sales for the manufacturers in the empirical analyses appear in Table 3. The food industry comprises 68 percent of the test sample, with average (median) company sales of $760 ($500) million. The sample also includes companies specializing in beverage, health and beauty aids, and household products. Annual sales range from less than $100 million to more than $10 billion, with a mean (median) of $849 ($999) million for the sample manufacturers. (18) Untabulated results also show that 49 percent of the respondents use VMI, and they have been using the system for an average of three to four years.

Relation between VMI Use and Information Precision, Information Reliability, and Consumer Demand Variability

The ordered PROBIT model results of tests of H1a and H1b for 53 manufacturer divisions appear in Table 4. Positive coefficients mean that higher values of the independent variable are associated with more extensive VMI use. (19) Consistent with the hypothesis that manufacturers use VMI to a greater extent when the retailer shares more precise and more reliable information (H1a), information precision (p = 0.001) and information reliability (p = 0.06) are significantly positively related to the extent of VMI use. (20) By contrast, the proxy for consumer demand variability, life_cycle, is not significant at conventional levels (p = 0.21). Thus, the empirical analysis does not support H1b. Company size (proxied by sales) is associated with more extensive VMI use (p = 0.02). (21) In sum, the extent of VMI use increases with information precision, information reliability, and company size. (22)

Effect of VMI Use on Wholesale Price

Table 5 presents the results for the ordered PROBIT of wholesale price on the extent of VMI use. The analysis reveals that the extent of VMI use is marginally associated with the wholesale price transferred between the retailer and the manufacturer (p = 0.097). Manufacturer divisions that use VMI to a greater extent charge their retailer partners a lower wholesale price. (Controlling for the independent variables associated with the extent of VMI use leads to identical inferences, and the control variables are not statistically significant at conventional levels.)

VII. CONCLUSION AND FUTURE RESEARCH

Supply-chain management requires partners to share information, typically including internal accounting sales and inventory information. However, little evidence exists on the effect of information sharing on supply-chain management contracts and the resulting firm performance. This study models the effects of information structure and demand variability on two alternative inventory management systems that differ in the delegation of decision rights: (1) a traditional system where the retailer makes the inventory decision and (2) a vendor managed inventory (VMI) system where the retailer delegates the inventory decision to the manufacturer. In selecting between the traditional and VMI systems, the manufacturer weighs the use of potentially unreliable information to determine quantity based on total supply-chain costs against allowing the retailer to use reliable information to make a strategic quantity decision based only on her own cost structure.

The model suggests that the extent of VMI use increases with the amount of internal accounting information the retailer reveals to the manufacturer (i.e., precision) and the manufacturer's ability to capture this information (i.e., reliability). The model also suggests that the extent of VMI use leads to lower wholesale prices because the manufacturer must share some of the efficiency gains that result from VMI with the retailer.

I test these theoretical predictions using survey data from manufacturer divisions in the food and consumer packaged goods industry. The results support the first theoretical prediction that the extent of VMI use increases with precise and reliable flows of internal accounting information from the retailer to the manufacturer. I also find that VMI use increases with the size of the manufacturer. The evidence suggests that the extent of VMI use is only marginally associated with a lower wholesale price.

This study shows that the precision and reliability of internal accounting information, and the retailer's willingness and ability to share this information, should affect the way manufacturers and retailers structure their relationship, and the inventory management decision rights in particular. The results suggest that VMI is more likely to lead to higher supply-chain profits if both companies commit to sharing precise internal accounting information and reliably transmitting, receiving, and using this information for inventory decisions.

APPENDIX PROOFS

Proof of Proposition 1

The solution to the traditional system is found by solving the following problem with J = 2:

(20) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to:

(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The incentive compatibility constraint (22) is solved to determine the quantity ordered given each of the two signals. Taking the derivative of the constraint with respect to [q.sub.r](j), setting it equal to zero, and solving for [q.sub.r](j) gives:

(23) [q.sub.r](1) = [mu] - [sigma](w + h)/2(p + h + s)

(24) [q.sub.r](2) = [mu] + [sigma](p - w + s)/2(p + h + s).

When the participation constraint (21) is not binding, the derivative of Equation (20) with respect to [Q.sub.m]() gives:

(25) -1/2 c.

The above expression implies that the manufacturer will produce at the lower bound, [q.sub.r](1).

If Equation (25) is negative, then the manufacturer will produce [q.sub.r](1); if positive, then [q.sub.r](2).

I substitute the solutions to the order and production quantities into the original optimization problem. Taking the derivative with respect to w and setting the equation equal to 0, one can solve for w. The retailer's participation constraint may or may not be binding.

When the constraint is not binding, the first-order condition on w is:

(26) [sigma](p + 2c - 4w - h + s) + 4[micro](p + h + s)/4(p + h + s) = 0.

Solving the first-order condition for the wholesale price gives:

(27) w = [sigma](p + 2c - h + s) + 4[micro](p + h + s)/4[sigma].

Substituting the wholesale price into the quantity decisions gives:

(28) [q.sub.r](1) = [mu]/2 - [sigma](p + 2c + 3h + s)/8(p + h + s)

(29) [q.sub.r](2) = [mu]/2 + [sigma](3p - 2c + h + 3s)/8(p + h + s).

Substituting the wholesale price and the quantity decisions into the expected manufacturer and retailer profits (Equations (20) and (21), respectively) gives:

(30) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(31) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

When the participation constraint is binding, the manufacturer sets the constraint equal to 0 and solves for the wholesale price:

(32) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Substituting the wholesale price into the order quantity formulas ((23) and (24)) and the objective function (20) gives the following:

(33) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(34) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(35) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Q.E.D.

Proof of Proposition 2

In the VMI system, the manufacturer solves the following problem:

(36) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to:

(37) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The manufacturer adjusts the wholesale price to make Equation (37) binding. After solving Equation (37) for w, I place the solution back into the objective function. I then take the derivative of the objective function with respect to [q.sub.m](1), [q.sub.m](2), and [q.sub.m](). I set the derivative equal to 0 and solve for the variables. The solution to the entire problem is as follows:

(38) [q.sub.m](1) = [mu] - [sigma](c + h)/2(p + h + s)

(39) [q.sub.m](2) = [mu] + [sigma](p - c + s)/2(p + h + s)

(40) [q.sub.m]() = [mu] + [sigma](p - 2c - h + s)/2(p + h + s)

(41) w = 4([micro]p - [[PI].sup.T.sub.r])(p + h + s) + [sigma]([alpha] - 2)([c.sup.2] + h(p + s))/[sigma]([alpha] - 2)(2c - p + h - s) + 4[micro](p + h + s)

(42) [[PI].sup.VMI.sub.m] = -[[PI].sup.T.sub.r] + [mu](p - c) + [sigma]([alpha] - 2)(p - c + s)(c + h)/4(p + h + s)

(43) [[PI].sup.VMI.sub.r] = [[PI].sup.T.sub.r].

Q.E.D.

Proof of Proposition 3

Comparing the quantities selected in the traditional and VMI models, the difference is:

(44) [q.sup.VMI.sub.m](1) - [q.sup.Trad.sub.r](1) = [q.sup.VMI.sub.m](2) - [q.sup.Trad.sub.r](2) = [sigma](p - 2c - h + s) + 4[mu](p + h + s)/8(p + h + s).

In the VMI system, [q.sub.m]() = ([mu] + [sigma](p - 2c + s - h))/2(p + h + s) = (2[micro](p + h + s) + [sigma](p - 2c + s - h))/2(p + h + s). The denominator is always positive. Assuming that the quantity ordered must be nonnegative, the numerator must be positive also; but 2[mu](p + h + s) + [sigma](p - 2c + s - h) < [sigma](p - 2c - h + s) + 4[mu](p + h + s). Therefore, the numerator in Equation (44) is positive. The quantity produced and ordered in the VMI system exceeds that ordered in the traditional system.

The difference between the wholesale price in the VMI and traditional systems is:

(45) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In simplifying and expanding the numerator, all but two terms are negative. These terms are less than the other terms in absolute value, making the numerator negative. Again:

2[mu](p + h + s) + [sigma](p - 2c + s - h) [greater than or equal to] 0 [??] 4[mu](p + h + s) + 2[sigma](p - 2c + s - h) [greater than or equal to] 0.

Since 2 - m [less than or equal to] 2 and 4[mu](p + h + s) > 0, the denominator is positive and the difference is negative. The wholesale price charged in a VMI system is less than that charged in a traditional system.

Q.E.D.

Proof of Proposition 4

Let:

(46) [DELTA][PI] = [[PI].sup.VMI.sub.n] - [[PI].sup.Trad.sub.m].

Taking the derivative of Equation (46) with respect to information reliability, [alpha], gives the following:

(47) [differential][DELTA][PI]/[differential][alpha] = [sigma](c + h)(p - c + s)/4(p + h + s) > 0.

Turning now to the effect of consumer demand variability, [sigma], I use proof by construction to show that the relationship between the change in the difference in expected profits between the two systems is ambiguous in [sigma]. Suppose that p = 10, c = 5, h = 1, s = 1, [mu] = 50, [alpha] = 0.5. When [sigma] = 5,10,15, the values for [[PI].sup.VMI.sub.m], [[PI].sup.Trad.sub.m], and [DELTA][PI] are as follows:

                        [sigma] = 5   [sigma] = 10   [sigma] = 15

[[PI].sup.VMI.sub.m]      244.37         238.75         233.13
[[PI].sup.Trad.sub.m]     243.67         237.39         231.16
[DELTA][PI]                 0.70           1.36           1.97

For the above example, [differential][DELTA][PI]/[differential][sigma] < 0.

Now suppose that p = 100, c = 5, h = 1, s = 1, [mu] = 50, [alpha] = 0.5. When [sigma] = 45,50,55, the values for [[PI].sup.VMI.sub.m], [[PI].sup.Trad.sub.m], and [DELTA][PI] are as follows:

                        [sigma] = 45   [sigma] = 50   [sigma] = 55

[[PI].sup.VMI.sub.m]      6073.24        5663.33        5330.68
[[PI].sup.Trad.sub.m]     4070.00        3799.08        3579.67
[DELTA][PI]               2003.24        1864.25        1751.01

For the above example, [differential][DELTA][PI]/[differential][sigma] < 0.

Based on the two examples above, [differential][DELTA][PI]/[differential][sigma] is ambiguous.

Finally, I show that [DELTA][PI] is increasing in information precision. That is, [DELTA][PI] is higher when J = 3 than when J = 2.

Solving the above models when J = 3 and comparing [DELTA][PI] between J = 2 and J = 3 gives the following:

(48) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Because 1/576[sigma] > 0, the sign of the above equation depends on the sign of the numerator. Rearranging the terms in the numerator gives the following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Based on the following assumptions, it can be shown that the above expression is nonnegative and, therefore, that the difference is higher when J = 3 than when J = 2.

Assumptions

p > c, 0 [less than or equal to] [alpha] [less than or equal to] 1, and that demand must be positive: E[D] [greater than or equal to] 3 * SD[D] where SD[D] is the standard deviation of the consumer demand distribution. The retail price must exceed the unit production cost or the product would not be produced and sold. The probability that the manufacturer receives the information, [alpha], must be between 0 and 1 by definition. Finally, it seems intuitive that consumer demand is positive. Therefore, I assume that three standard deviations below expected demand is also positive; the probability of negative demand given this assumption is extremely low.

Q.E.D.

TABLE 1
Glossary of Notation

Endogenous Variables

[q.sub.i](j)           Quantity ordered by party i where i [member of]
                         {r,m}, j [member of] {1,2,...,J}
[Q.sub.m](j)           Quantity produced by the manufacturer where
                         j [member of] {1,2,...,J}
w                      Wholesale price per unit
[[pi].sup.k.sub.m]     Expected manufacturer profit given system k
                         where k [member of] {Trad, VMI}
[[pi].sup.k.sub.r]     Expected retailer profit given system k where
                         k [member of] {Trad, VMI}

Exogenous Variables

p                      Retail price per unit
c                      Manufacturer's production cost per unit
h                      Holding cost per unit for the retailer
s                      Stockout cost per unit for the retailer
[mu]                   Expected consumer demand
[sigma]                Length of the initial consumer demand
                         distribution
D                      Initial priors about consumer demand,
                         D ~ U [[mu] - [[sigma]/2], [mu] + [[sigma]/2]]
[alpha]                Probability that the signal is reliable
J                      Number of partitions offered by the information
                         system; information precision
[U.sub.r]              Reservation utility of the retailer
TABLE 2
Descriptive Statistics for the Extent of VMI Use, Wholesale Price,
Precision and Reliability of Information Shared, Consumer Demand
Variability, Control Variable, and Questions that Comprise the
Factors (precision and reliability)

Variable (a)               n    Mean   Std. Dev.   Min.   Median   Max.

Extent_VMI                53    2.38      1.61      1        2        6
Wholesale_price           52    2.98      0.75      1        3        4
Precision                 53    9.66      5.38      4        8       24
Reliability               53    3.25      2.13      0        4        7
Life_cycle                53   32.26     28.95      0       25      100
Sales                     53    3.70      1.46      1        4        6

Questions Measuring
Precision of
Information Shared
Factor (b)

Sharing Store Inventory   53    2.32      1.37      1        1        6
  Levels
Sharing Retail            53    2.77      1.86      1        2        6
  Warehouse Inventory
  Levels
Sharing Warehouse         53    2.32      1.73      1        1        6
  Withdrawals
Sharing Point-of-Sale     53    2.24      1.51      1        2        6
  Data

Questions Measuring
Reliability of
Information
Transmission Factor (c)

Basic EDI system          53    0.81      0.39      0        1        1
Transmit purchase         53    0.73      0.45      0        1        1
  orders via EDI
Transmit invoices via     53    0.66      0.48      0        1        1
  EDI
Transmit advance ship     53    0.43      0.50      0        0        1
  notices via EDI
Transmit warehouse        53    0.17      0.38      0        0        1
  inventory data via
  EDI
Transmit production       53    0.16      0.36      0        0        1
  schedules via EDI
Transmit transportation   53    0.30      0.46      0        0        1
  information via EDI

(a) Variable definitions:

     Extent_VMI = the extent that the manufacturing division uses
                  VMI on a six-point scale where 0 = no VMI and
                  6 = use VMI for more than 91 percent of sales;

Wholesale_price = measure for the price the manufacturer charges the
                  retailer. The related survey question asks, "Would
                  you characterize the prices your company charges
                  the retailer as ..." The answer is categorical,
                  ranging from "much lower than the industry average"
                  to "much higher than the industry average";

      Precision = index for the precision of the information the
                  retailer shares (J). The index is the sum of scores
                  from a series of questions regarding the extent to
                  which retailers share information with the
                  manufacturer, based on a six-point scale. Higher
                  numbers indicate the retailers share more precise
                  information;

    Reliability = index for the reliability of the manufacturer's
                  information linkages ([alpha]), The index is the
                  sum of scores from a series of yes/no questions
                  about the information available through the
                  manufacturer's system. Higher numbers indicate
                  more reliable information systems.

    Life_cycle = percentage of products in the introduction and
                 growth stages ([sigma]). The related survey
                 question asks, "About what percentage of your
                 products are in the introduction and growth
                 stages?" This variable proxies for variability
                 in consumer demand; and

         Sales = company sales, based on the answer to the survey
                 question "Company Sales." The categorical answer
                 uses a six-point scale; higher numbers correspond
                 to higher sales.

(b) These items are measured on a six-point scale where 0 = no
information sharing and 6 = share the given information for
91 percent or more of sales.

(c) Items are measured through yes/no questions: 0 = no and 1 = yes.
TABLE 3
Sales Levels for the Sample Manufacturer Firms (n = 53)

                                   Mean Sales     Median Sales
Sector                   Number   (in millions)   (in millions)

Food                       36           $760            $500
Beverage                   12         $4,780         $10,000
Health and Beauty Aids      2           $999            $999
Household Products          3           $200            $200
TABLE 4
Results of Ordered PROBIT Analysis of the Extent of VMI Use on the
Precision and Reliability of Information, Consumer Demand Variability,
and Control Variable for 53 Manufacturer Divisions

Prob(Extent_VMI = i) = F([alpha] + [[beta].sub.1]precision +
[[beta].sub.2]reliability + [[beta].sub.3]life_cycle +
[[beta].sub.4]sales)

              Predicted
Variable        Sign      Coefficient   Std. Error   p-value (a)

Intercept                    3.11          1.01      0.002 ***
Precision         +          0.11          0.04      0.001 ***
Reliability       +          0.13          0.09      0.063 *
Life_cycle        ?         -0.01          0.01      0.205
Sales             +          0.22          0.11      0.025 **

*, **, *** Indicate significance at the 10, 5, and 1 percent levels or
better, respectively.

(a) The p-value for the variables are one-tailed probabilities, except
for the intercept term and life-cycle, which are two-tailed
probabilities.
TABLE 5
Results of Ordered PROBIT Analysis of the Wholesale Price on the Extent
of VMI Use for 52 Manufacturer Divisions

Prob(wholesale_price = i) = F([alpha] + [[beta].sub.1]Extent_VMI)

              Predicted
Variable        Sign      Coefficient   Std. Error   p-value (a)

Intercept                    2.47          1.23       0.043 **
Extent_ VMI      --         -0.13          0.10       0.097 *

*, ** Indicate significance at the 10 and 5 percent levels or better,
respectively.

(a) The p-value for the Extent_ VMI variable is a one-tailed
probability.

Q.E.D.

This paper is based on my dissertation at Stanford University, I thank my dissertation committee, Richard Lambert, Srikant Datar, and Jin Whang, for their helpful comments. I also acknowledge the suggestions of an anonymous referee, Mark Bradshaw, Tom Cameron, Shane Dikolli, George Foster, Raffi Indjejikian, Bjorn Jorgensen, Robert Kaplan, Laura Kopczak, Hau Lee, Greg Miller, V. G. Narayanan, Elie Ofek, Paddy Padmanabhan, James Patell, Madhav Rajah, Ratna Sarkar, Michael Smith, Erik Steiner, and workshop participants at the Boston Accounting Research Consortium; Carnegie-Mellon University; University of Chicago; Harvard University; New York University; Northwestern University; University of Rochester; Stanford University; University of California, Berkeley: University of Washington; and the 2000 American Accounting Association Annual Meeting in Philadelphia. I thank Andersen Consulting for assisting in the data collection. The financial support of the Andersen Foundation is greatly appreciated.

Submitted January 2000 Accepted November 2001

(1) Baiman and Rajan (2002) review the incentives literature related to buyer-supplier transactions.

(2) Refer to Lambert (2001) for a comprehensive review of research on transfer pricing and information sharing.

(3) If I reverse the principal and the agent (i.e., if the retailer becomes the principal), then the traditional system will achieve first-best profits; the retailer will have both precise information and decision rights. The addition of manufacturer moral hazard and/or asymmetric information generates less than first-best profits. The empirical tests focus on the manufacturer's use of VMI and the information flow between the parties rather than on manufacturer or retailer effort. Accordingly, I model the manufacturer as the principal and omit moral hazard from the model.

(4) A solution to the first-best, full information setting is available from the author upon request.

(5) The reservation level of profit reflects the retailer's bargaining power, the opportunity cost of shelf space, and manufacturer competition. See Cohen (2000) for further analysis without assuming zero reservation level of profits.

(6) I model only the retailer as possessing private information. I expect greater gains if the manufacturer also possesses private information and combines the two sets in his estimation of expected demand.

(7) E[D] = [mu], Var[D] = [[sigma].sup.2]/12.

(8) If the retailer sells a substitute product, then s represents the difference in the selling prices of the two products. A negative h implies that excess inventory has a positive value.

(9) I omit some distinguishing features of VMI, including more frequent deliveries, transportation costs, and system set-up and maintenance costs. The survey I use in the empirical analysis does not encompass these issues. Because the related hypotheses are not currently testable, I exclude these features from the theoretical model.

(10) There are parameter values for which the wholesale price primarily allocates profits, and the retailer's participation constraint binds. The retailer does not internalize total supply-chain costs in this scenario; w and [q.sub.r](j) depend only on the retailer's costs. Because this scenario produces similar qualitative results, I do not present it in the text.

(11) If [alpha] = 0, then this model reduces to a fully collaborative model given no signal, and if [alpha] = 1, then this model reduces to a full-information, fully collaborative model.

(12) This hypothesis does not reflect the additional cost of gathering and communicating more precise information.

(13) This expected effect of the benefits of VMI on the volume flowing through the VMI system is consistent with Clark and Hammond (1997).

(14) Labovitz (1970) shows that the correlation between almost any ordinally scaled measure (such as the scale I derive using equal weights) and the "correct" intervally scaled measure is very high as long as the number of levels in the ordinal scale exceeds 15 or 20, as is the case with the current measures.

(15) I repeated the analysis using principal components and factor analysis scores to form the constructs. The empirical results are qualitatively similar.

(16) The analytical results assume the retailer earns equal profits in the two systems. The survey did not ask about retail partners, their power, or their performance. Thus, my empirical analysis cannot control for retailer profits.

(17) Note that only 52 divisions responded to the question about the wholesale price. Consequently, further tests related to H2 will only analyze 52 observations.

(18) The composition of the test sample is similar to that of the entire sample of 100 respondents.

(19) One should interpret the coefficients carefully. If a given variable increases the VMI use "rating," then the probability of extensive VMI use increases and the probability of no VMI use decreases. However, the probability of being in the intermediate categories could move in either direction (Greene 1993, 672-676).

(20) One can interpret reliability as the minimal technology that the manufacturer possesses. However, VMI also may depend on the manufacturer's ability to interpret the information. Unfortunately, the survey does not measure this variable. The study's inferences should not be affected by this omission unless the manufacturer's ability to interpret the data is correlated with the included independent variables.

(21) Lee et al. (1997) find that the demand variability that the manufacturer faces from its retailer partners differs from the underlying consumer demand variability. High variability of retailers' demand often leads to supply-chain management collaboration, such as VMI. I also run the empirical analyses with a variable that proxies for retailer demand. The related question asked respondents to rank the demand variability they experience with their retailer partners on a three-point scale. The inferences do not change when this variable is included in the analysis.

(22) I also test the hypothesis using an alternative dependent variable where 1 = VMI adopters, and 0 = nonadopters. The results are qualitatively similar except that the information precision variable only marginally affects the probability of using VMI (p = 0.12).

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Susan Cohen Kulp
Harvard University