Dynamic Targeted Pricing in B2B Relationships all commerce within the United States ... and it incorporates internal and ... Dynamic Targeted Pricing in B2B Relationships Marketing

Vol. 33, No. 3, May–June 2014, pp. 317–337ISSN 0732-2399 (print) � ISSN 1526-548X (online) http://dx.doi.org/10.1287/mksc.2013.0842

© 2014 INFORMS

Dynamic Targeted Pricing in B2B Relationships

Jonathan Z. ZhangMichael G. Foster School of Business, University of Washington, Seattle, Washington 98195, [email protected]

Oded Netzer, Asim AnsariColumbia Business School, Columbia University, New York, New York 10027 {[email protected], [email protected]}

We model the multifaceted impact of pricing decisions in business-to-business (B2B) relationships that aregoverned by trust. We show how a seller can develop optimal intertemporal targeted pricing strategies to

maximize profits over time while taking into consideration the impact of pricing decisions on short-term profitmargin, reference price formation, and long-term relationships. Our modeling framework uses a hierarchicalBayesian approach to weave together a multivariate nonhomogeneous hidden Markov model, buyer heterogene-ity, and control functions to facilitate targeting, capture the evolution of trust, and control for price endogeneity.We estimate our model on longitudinal transactions data from a retailer in the industrial consumables domain.We find that buyers in our data set can be best represented by two latent states of trust toward the seller—a“vigilant” state that is characterized by heightened price sensitivity and a cautious approach to ordering anda “relaxed” state with purchase behaviors that are consistent with high relational trust. The seller’s pricingdecisions can transition buyers between these two states. An optimal dynamic and targeted pricing strategybased on our model suggests a 52% improvement in profitability compared with the status quo. Furthermore,a counterfactual analysis examines the seller’s optimal pricing policy under fluctuating commodity prices.

Keywords : business-to-business marketing; pricing; customer relationship management; hidden Markovmodels; channel relationships

History : Received: February 19, 2011; accepted: November 19, 2013; Preyas Desai served as the editor-in-chiefand Peter Fader served as associate editor for this article. Published online in Articles in Advance April 1, 2014.

1. IntroductionThe business-to-business (B2B) sector plays a majorrole in the United States and world economy. B2Btransactions command more than 50% market shareof all commerce within the United States (Dwyer andTanner 2009, Stein 2013). Despite their obvious impor-tance, B2B issues have received scant attention in themodeling literature within marketing. Only a smallfraction (approximately 3.4%) of the articles pub-lished in the top four marketing journals deal withB2B contexts (LaPlaca and Katrichis 2009). Comparedwith other marketing decisions, the topic of pricingin B2B environments is particularly underresearched(Liozu 2012, Reid and Plank 2004). In this paper,we address this imbalance by developing an inte-grated framework for modeling the multiple impactsof pricing decisions in a B2B context and illustratehow our framework can aid sellers in implement-ing first-degree and intertemporal price discrimina-tion for long-run profitability.

Pricing decisions in B2B contexts differ from thosewithin business-to-consumer (B2C) environmentsacross multiple dimensions. First, B2B settings areoften characterized by product and service customiza-tion and by the reliance on personal selling to forge

and cement transactions. In many B2B situations, sell-ers can easily vary prices across buyers and can evenchange prices between subsequent purchases of thesame buyer. In contrast, B2C retailers are often lim-ited in their ability to fully target prices for individualconsumers because of logistical and ethical concerns(Khan et al. 2009).

Second, B2B environments are generally character-ized by long-term relationships between buyers andsellers (Morgan and Hunt 1994). The development oftrust, commitment, and norms over repeated inter-actions can impact buyers’ attitudes, comfort levels,and price sensitivities over time (Dwyer et al. 1987,Morgan and Hunt 1994, Rangan et al. 1992). Pricingdecisions, in turn, can play a vital role in develop-ing, transforming, and sustaining such relationships(Kalwani and Narayandas 1995).

Third, transactions in B2B markets are more com-plex than those in B2C markets as business buy-ers typically make several interrelated decisions ona given purchase occasion. Specifically, B2B buyersnot only choose what, when, and how much to buybut also decide how to buy. In B2B settings, buy-ers choose whether to ask for a price quote (offeringthe seller the opportunity to provide a price quote)or to order directly from the seller, without asking

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Zhang, Netzer, and Ansari: Dynamic Targeted Pricing in B2B Relationships318 Marketing Science 33(3), pp. 317–337, © 2014 INFORMS

for a price. Requests for price quotes allow sellers toobserve demand and price sensitivity even when asale is not made (i.e., when the seller makes a bidand the buyer rejects the bid). Such data are rarelyobserved in B2C settings (Khan et al. 2009).

Fourth, situational triggers can influence the deci-sions of buyers. For instance, price changes in com-modity markets can impact purchasing decisions,thus necessitating the use of such external factorsin modeling demand. Finally, decision makers (buy-ers and sellers) in B2B settings are often assumed tobehave rationally (Reid and Plank 2004). Thus, oneneeds to consider whether behavioral pricing effectsregarding reference prices and loss aversion (Kalya-naram and Winer 1995) are operant in the B2B domain(Bruno et al. 2012).

In summary, the above distinguishing features ofB2B settings offer sellers significant pricing flexibil-ity. In particular, the reliance on salespeople, the needfor product/service customization, and the volatilityof commodity prices make targeting and intertempo-ral customization of prices feasible and desirable. Theadoption of sophisticated customer relationship man-agement software and database capabilities is makingsuch customization increasingly possible.

In this paper, we develop a modeling frameworkthat incorporates the unique facets of B2B contextsand models the multiple buyer decisions on each pur-chasing opportunity in an integrated fashion. Specif-ically, we posit that the different aspects of buyerbehavior are governed by a common latent statethat represents the trust between the buyer and theseller. This latent state creates dependencies across thebuyer’s decisions (when to buy, how much to buy,whether to request a quote or order directly withouta quote, and whether to accept or reject the quote).The level of trust can evolve over time as a functionof the nature of interactions between the buyer andthe seller and via the seller’s pricing decisions. Weuse a multivariate nonhomogeneous hidden Markovmodel (HMM) to model how trust governs buyerdecisions and how it evolves over the duration of therelationship as a function of pricing. In addition, ourHMM framework accounts for buyer heterogeneity,and it incorporates internal and external (commodity)reference price effects and price endogeneity usinga Bayesian version of the control function approach(Park and Gupta 2009, Petrin and Train 2010).

We apply our framework on longitudinal trans-action data from an aluminum retailer that sells toindustrial buyers. We identify two latent states oftrust that are consistent with conceptual frameworksof buyer segmentation in the B2B literature (e.g.,Rangan et al. 1992, Shapiro et al. 1987). These include(1) a vigilant state characterized by high buyer pricesensitivity and a cautious approach toward ordering

and (2) a relaxed state that is characterized by moredirect orders and lower price sensitivity. We also findstrong evidence for asymmetric reference price effectssuch as loss aversion and gain seeking. Consistentwith relationship life-cycle theory (Dwyer et al. 1987,Jap and Anderson 2007) and hedonic adaptation the-ory (Frederick and Loewenstein 1999), we find thatbuyers not only weigh price losses more than gainsbut also take longer to adapt to losses than to gains.We further provide empirical evidence for the rateof buyer–seller relationship migration over time andshow how the seller can use prices to manage theserelationship migrations profitably.

From a managerial perspective, we illustrate howthe seller can use our model to compute optimalprices that are targeted for each transaction of eachbuyer so as to maximize long-term profits. Such anoptimal pricing policy balances different short- andlong-term perspectives. Although it is common tothink of prices as having mainly short-term effects,prices are likely to have long-term effects in B2B mar-kets because of the importance of buyer–seller rela-tionships and because prices can impact trust. We findthat the optimal dynamic targeted pricing policy canincrease the seller’s profitability by as much as 52%over that of the status quo. We also use a counter-factual analysis to examine the nature of the optimalpricing policy in the presence of a volatile aluminumcommodity market. Changing commodity prices alterthe seller’s costs and the external reference prices ofbuyers. We find results that are consistent with thedual-entitlement principle (Kahneman et al. 1986)—itis optimal for the seller to pass on much of the costincrease to buyers when commodity prices increase,whereas it is optimal to “hoard” some of the benefitsof a cost decrease when commodity prices drop.

In summary, our research advances the B2B pric-ing literature in several directions. On the method-ological front, it offers a hierarchical Bayesian frame-work for relationship dynamics that weaves togethera multivariate nonhomogeneous HMM, heterogene-ity, and control functions. More important, on the sub-stantive front, it offers B2B managers an approach todynamically target prices. Our results showcase theeffect of pricing decisions on the evolution of trustbetween buyers and sellers and illustrate how behav-ioral factors such as loss aversion and reference price,which are commonly ignored in what are tradition-ally considered to be “rational” purchasing contextsand in the commonly used cost-plus pricing approachare important for B2B pricing. We also offer insightsabout how the seller should react to volatile commod-ity prices.

The rest of the paper is organized as follows. Sec-tion 2 highlights the challenges and opportunities in

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Zhang, Netzer, and Ansari: Dynamic Targeted Pricing in B2B RelationshipsMarketing Science 33(3), pp. 317–337, © 2014 INFORMS 319

investigating pricing decisions in B2B settings. Sec-tion 3 describes the data from an industrial aluminumretailer. Section 4 outlines our modeling framework.Section 5 applies our modeling framework to the data.Section 6 describes the dynamic targeted pricing opti-mization based on the estimated model, and §7 con-cludes by discussing practical implications, theoreticalcontributions, and future directions.

2. Targeted Pricing Decisionsin B2B Settings

The majority of the research on B2B pricing is con-ceptual and survey based (Johnston and Lewin 1996).Scant attention is given to quantitative pricing mod-els (for an exception, see Bruno et al. 2012), per-haps because of conflicting views about the role andimportance of prices relative to other attributes inB2B contexts (see Hinterhuber 2004, Lehmann andO’Shaughnessy 1974, Wilson 1994). B2B researchers,however, have intensively investigated the role ofbuyer–seller relationships in B2B markets and haveoffered various segmentation and targeting frame-works. We now review this literature and briefly dis-cuss past research on reference prices.

2.1. Relationships in B2B MarketsBuyer–seller relationships can be described using anumber of relational constructs such as trust, com-mitment, and norms (Dwyer et al. 1987). Morgan andHunt (1994, p. 23) posit that trust, “the confidencein an exchange partner’s reliability and integrity,”and commitment, “an enduring desire to maintain avalued relationship” (Moorman et al. 1992, p. 316),are key elements that explain the quality of relation-ships and their impact on behaviors and performance.Palmatier et al. (2006) suggest that a composite con-struct called “relationship quality”—an amalgam oftrust, commitment, and satisfaction—has a strongimpact on objective performance. Similarly, Dwyeret al. (1987) suggest that relational variables such astrust, commitment, norms, and in general relationshipquality increase as relationships progress to more pos-itive states.

Dahl et al. (2005) show that activities that embodyfairness enhance trust, whereas acts of unfairness,opportunism, and conflict negatively influence trustand commitment toward the seller (Anderson andWeitz 1992). Dwyer et al. (1987) and Jap and Ander-son (2007) posit that negative actions, especially thosethat are perceived to be unfair, can cause the rapiddeterioration of a relationship, with a low prospectof a rebound. Apart from seller actions, environmen-tal uncertainty can also moderate relationship perfor-mance (Cannon and Perreault 1999). We rely on thisresearch to model the impact of pricing decisions andthe influence of uncertain commodity markets on theevolution of buyer–seller relationships.

2.2. Segmentation and Targeting in B2B MarketsFirmographics, such as customer size, industry, andcustomer location, are traditionally used for segmen-tation in industrial markets. Researchers, however,have also proposed segmentation based on buyingbehavior and relationship with sellers. Rangan et al.(1992) suggest that the weight given to price (relativeto service) is an important driver of buyer hetero-geneity. They use survey data to identify a segmentof “programmed” business buyers who are less pricesensitive and invest less in the buying process anda segment of “transactional” buyers who are moresensitive to price and are also more knowledgeableabout the product because it is more important totheir businesses. Shapiro et al. (1987) refer to thesetwo segments as “passive” and “aggressive” buyers,and Matthyssens and Van den Bulte (1994) denotethese as “co-operative” and “antagonistic.” Shapiroet al. discuss the merit of using different targetingstrategies for each segment and the possible migra-tion of buyers between these segments as a result ofthe seller’s targeting efforts.

In this research, we use transactional data touncover evidence that supports the above dynamicsegmentation framework. Consistent with the papersdiscussed above, we find that buyers at any giventime can belong to either a relaxed or vigilant state,depending on their sensitivity to past prices, previoustransactional outcomes, and sensitivity to market con-ditions. We then propose a targeting framework thatleverages this information to migrate buyers betweenthese two states.

The growing literature on targeting and customiza-tion is also relevant for our research. The empiricalliterature on targeting has focused mostly on non-price instruments. In B2B settings, marketing actionssuch as face-to-face meetings, direct mail and tele-phone contacts (Venkatesan and Kumar 2004), anddollar expenditure on marketing efforts (Kumar et al.2011) have been investigated. Similarly, in B2C con-texts, researchers have focused on marketing actionssuch as catalog mailing (Simester et al. 2006), coupons(Rossi et al. 1996), digital marketing campaigns(Ansari and Mela 2003), pharmaceutical detailing andsampling (Dong et al. 2009, Montoya et al. 2010),and promotions (Khan et al. 2009). Empirical researchon individually targeted pricing has been relativelysparse, possibly because of the informational, logis-tical, ethical, and legal constraints that impact pricediscrimination in traditional (B2C) settings (Khanet al. 2009).

2.3. Reference Prices inCustomer Buying Behavior

The notion that consumers rely on internal andexternal reference prices is well established within

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marketing (Hardie et al. 1993, Kalwani et al. 1990,Kalyanaram and Winer 1995, Winer 1986). Externalreference prices (e.g., manufacturer’s suggested retailprice and prices of other brands) are generally observ-able and common to all customers, whereas internalreference prices are individual specific and are oftenconstructed using the customer’s observed prices onprevious purchase occasions.

A large literature demonstrates the behavioraland psychological (Kalwani et al. 1990, Wedel andLeeflang 1998) as well as the rational and economic(Erdem et al. 2010) underpinnings of reference priceeffects. In the behavioral pricing literature, prices canbe coded as either losses or gains relative to a refer-ence price and can thus have an asymmetric impacton brand choice (Kalwani et al. 1990, Putler 1992),purchase timing (Bell and Bucklin 1999), or purchasequantity (Krishnamurthi et al. 1992).

Despite the voluminous literature, reference priceshave found little application in B2B pricing mod-els because B2B decision makers are presumed to berational (Kalyanaram and Winer 1995). In a recentexception, Bruno et al. (2012) demonstrate that indus-trial buyers exhibit asymmetric reference price effectsthat are affected by the depth of interactions betweenbuyers and sellers. We add to the sparse literatureon B2B reference pricing and explore both internal(past prices) and external (commodity spot prices)reference prices. We also examine the possible long-term effects of reference prices in a B2B context. Next,we describe our data set and the business context inwhich the seller operates.

3. DataOur data come from an East Coast aluminum retailer(seller) that supplies to industrial clients (buyers)who operate in its geographical trading area. Theseller buys raw aluminum directly from the mills,cuts it according to the specifications provided byits small- to medium-sized industrial clients (e.g.,machine shops, fabricators, small manufacturers), andthen ships the product to them. The buyers use theproduct as a component in their own products or ser-vices. Hence, our seller is a value-add intermediaryin the industrial consumable market, and our data setis typical of what is found in this B2B market.

The data set contains buyer-level information onpurchase events over 21 months from January 2007to September 2008. A purchase event begins with theneed for a certain quantity at a given point in time.Given this need, the buyer either places a direct order,without asking for a price quote, or requests a pricequote (usually via phone or fax). For example, a typ-ical direct order may be received in the morning viaa fax saying, “Send me four aluminum sheets, X inch

by Y inch and thickness of Z inch, by tomorrow after-noon.” Direct orders are generally fulfilled immedi-ately, and the buyer is charged a price determinedby the seller. Alternatively, if the buyer requests aquote (i.e., places an “indirect order”), the firm bidsfor the buyer’s business and can only “win” the busi-ness if the buyer accepts the quoted price. Thus, inour setting, purchase events include not only com-pleted transactions but also lost transactions involv-ing quotes that were not accepted. This allows for abetter understanding of buyer price sensitivity.

The seller keeps a large number of stock-keepingunits (SKUs) that are defined based on the shape,thickness, and customizable size of the aluminum.Furthermore, the wholesale cost of aluminum changeson a daily basis following the London Metal Exchange(LME). Therefore, as is typical in this industry, theseller does not maintain a price list and deter-mines the price to charge or quote on a case-by-casebasis. Because order quantities vary substantially andbecause of the large number of SKUs, the industryuses a common metric, “price per pound,” to whichthe seller adds the cutting and delivery costs to arriveat a price for an order. As is typical of most cus-tomer relationship management data sets in B2B set-tings, our data set does not include information aboutthe competition. However, it is likely that a buyerrequests quotes from multiple vendors. Thus, unful-filled indirect orders provide an indirect signal fora purchase that goes to the competition. Our buy-ing process includes a first-level-auction “take it orleave it” quote process, in which the buyer requests aquote, the seller makes a bid, and the buyer decideswhether to accept the bid. Conversations with man-agement indicate that negotiation beyond the initialquote request, as well as customer returns, are rarein this business. Moreover, in our data, we observethat the price and quantity quoted by the seller areidentical to the price and quantity reported on thefinal invoice for more than 99% of the orders, sug-gesting minimal negotiations. Our model needs to beextended to explicitly capture negotiation processeswhen applying it to other B2B domains in whichnegotiations are common (e.g., Milgrom and Weber1982, Mithas and Jones 2007).

Our sample contains 1,859 buyers for whom weobserve at least seven purchase events (quotes ororders) in the data period (see Tables 1 and 2 for

Table 1 Descriptive Statistics

Number of buyers 1,859Overall number of observations (purchase events) 33,925Proportion of direct purchases 0.53Proportion of quotes that are accepted 0.47

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Table 2 Descriptive Statistics per Buyer

Mean Std. dev. Lower 10% Median Upper 90%

Total number of 2306 2008 800 1600 5200purchase events

Proportion of 5506 2406 2104 5701 8705direct orders

Order amount for 861 1,636 100 402 1,932direct orders (US$)

Order amount for 1,724 3,445 165 667 3,770quote requests (US$)

Purchase event 1,236 1,471 292 808 2,458amount (US$)

Quantity (lb.) 457 553 92 288 968Interpurchase event 6041 4031 1080 5023 12045

time (weeks)

summary statistics of the data).1 On average, a buyerin our sample engaged in 23.6 purchase events dur-ing the span of 21 months. Of these, 53% weredirect orders on which no price quote was requested.The relatively large proportion of direct orders isconsistent with the notion of “programmed” buyersdescribed in Rangan et al. (1992) and Shipley andJobber (2001). It is also consistent with the view thatmany buyers may have developed certain levels oftrust and norms with the seller and would rely onthese norms for speedy order fulfillment.

An average purchase event involves 457 lb. of alu-minum, with an average price of $3.24/lb. Table 2shows that (1) direct orders tend to be smaller, sug-gesting the possibility that buyers are less price sen-sitive when ordering smaller quantities; (2) buyersare heterogeneous in terms of their metal needs andtransactions with the firm; (3) buyers exhibit differentpropensities to order directly, implying variation intheir attitudes and latent relationships with the firm;and (4) about half of the orders are direct, which resultin a sale regardless of the price charged. This suggeststhat the firm may be tempted to charge “any” price onsuch direct orders. However, as we show later, suchexploitative pricing behavior can have negative long-term consequences.

We now look at some model-free evidence to under-stand the relationship dynamics in our data and tomotivate our modeling approach. Figure 1 is basedon the group of buyers for whom we observe thecomplete history of interactions with the seller. The

1 From a substantive point of view, more than 92% of the buyers inour data have at least seven purchase events. Thus, this selectionprocess does not have a significant impact on the representativenessof our sample. From a methodological point of view, we use thiscutoff to ensure that our model is capable of capturing a rich set ofrelationship dynamics. To check for robustness, we also ran modelswith a larger sample that included buyers with three or more pur-chase events. The substantive results and their significance remainsimilar.

Figure 1 Model-Free Evidence—Probability of Quote Request OverTime for New Buyers

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1st 2nd 3rd 4th 5th 6th

Like

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Figure 2 Model-Free Evidence—Buying Behaviors Following a Gainor a Loss on a Direct Order

figure shows the probability of a quote request forthe first six purchase events of these buyers. We seethat, as expected, almost all buyers request a quoteon their first order. However, this probability goesdown for subsequent orders (i.e., buyers are morelikely to order directly over time). This pattern isconsistent with the view that most buyers start outwith an “exploratory” or “transactional-only” attitudetoward buying but then gradually build trust, com-mitment, and norms of interactions with the sellerover repeated interactions.

Figure 2 shows an interesting pattern that cap-tures how current pricing on a direct order impactsbuyer behavior on the next purchase event. The figureshows that charging in a direct order a price that ishigher than the average of the prices the buyer facedin the past2 (interpreted as a loss) increases the like-lihood of a quote request on the next purchase event

2 As we describe later in more detail, we use the quantity-weightedaverage price the buyer observed in past purchase events as a ref-erence price.

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by about 50% (from 42% to 63%) and increases theprobability of losing the next bid. This pattern impliesthat the seller needs to be careful in pricing directorders because charging excessively above the refer-ence price (hence violating the trust that the buyerplaces in the seller) can result in undesirable conse-quences on subsequent purchase events. We capturesuch considerations in our model by allowing thebuyer’s latent trust level to shift over time as a func-tion of the prices received from the seller. We describeour modeling framework next.

4. ModelIn this section, we model a sequence of purchaseevents for each buyer while taking into account therelationship states that evolve over time as a resultof the seller’s pricing decisions. A purchase event ischaracterized by four interrelated buyer decisions:(1) when to buy; (2) how much to buy; (3) whether toorder directly without asking for a price quote, whichalways results in a purchase, or to request a quote,hence allowing the seller to bid for business; and(4) whether to accept the quote if a quote is requested.We can write the vector of observed behaviors forbuyer i at purchase event j as yij = 4qij1 tij1 bij1wij5,where qij is the quantity requested or ordered, tij isthe time (in weeks) since the last purchase event (i.e.,the interpurchase event time), and bij and wij are thebinary quote request and quote acceptance decisions,respectively. The seller observes the marketing envi-ronment and buying and pricing history for buyer iat purchase event j before setting the unit price pij forthe event.

To model buyer dynamics over repeated purchaseevents, we allow the buyer to transition between dif-ferent latent behavior/relationship states of trust3 thatdifferentially impact the four buying decisions. Theseller’s past pricing decisions may affect the buyer’stransition between states. For example, as suggestedby Figure 2, a buyer who is charged a high price maybe more likely to transition from a “relaxed” or trust-ing state that is characterized by a high propensity toorder directly and a low price sensitivity to a “vigi-lant” or evaluative state that reflects a higher propen-sity to request quotes and a higher price sensitivity.

We capture such dynamics using a multivariatenonhomogeneous HMM (Montoya et al. 2010, Net-zer et al. 2008, Schweidel et al. 2011). In the HMM,

3 In what follows, we call the HMM latent states states of trust.However, this latent state could be interpreted more generally as arelationship quality state, which combines trust, commitment, andnorms between the buyer and the seller (Palmatier et al. 2006).Because the states are inferred from secondary data, we remainagnostic about this distinction.

the joint probability of a sequence of interrelated deci-sions up to purchase event j , for buyer i, 8Yi1 =

yi11 0 0 0 1Yij = yij9, is a function of three main compo-nents: (1) the initial hidden state membership prob-abilities Öi; (2) a matrix of transition probabilitiesamong the buying-behavior states, ìi1 j−1→j ; and (3) amultivariate likelihood of the buyer decisions condi-tional on the buyer’s buying-behavior state, Lij � s =

fis4qij1 tij1 bij1wij5. We describe each of these compo-nents next.

4.1. Initial State DistributionLet s denote a buying-behavior state (s = 1121 0 0 0 1 S).Let �is be the probability that buyer i is in state s attime 1, where 0 ≤ �is ≤ 1 and

∑Ss=1 �is = 1. We use S−1

logit-transformed parameters to represent the vectorcontaining the initial state probabilities.

4.2. Markov Chain Transition MatrixRing and Van de Ven (1994) suggest that B2B relation-ships evolve with repeated buyer–seller interactions;the experience from each interaction can either elevateor upset a relationship. Consistent with this notion,we model the transitions between states as a Markovchain. Each element of the transition matrix (ìi1 j−1→j )can be defined as �ijss′ = P4Sij = s′ � Sij−1 = s5, which isthe conditional probability that buyer i moves fromstate s at purchase event j − 1 to state s′ at purchaseevent j , and where 0 ≤�ijss′ ≤ 1 ∀ s, s′, and

∑

s′ �ijss′ = 1.Because the transition probabilities are influenced bythe seller’s pricing decisions at the previous purchaseevent j − 1, we define

�ijss′ =ex′

j−1Ãis

1 +∑S−1

s=1 ex′ij−1Ãis

1 (1)

where xij−1 is a vector of covariates (e.g., price or ref-erence price) affecting the transition between states,and Ãis is a state- and buyer-specific vector of responseparameters.

4.3. State-Dependent Multivariate InterrelatedDecisions

The buyer makes the four interrelated decisions con-ditional on being in state s at purchase event j . Thesedecisions, however, are unconditionally interrelatedbecause they all depend on the buyer’s latent state.

Given that buyer i is in a latent state Sij = s onpurchase event j , we can factor the state-conditionaldiscrete-continuous joint likelihood, Lij � s , for the fourinterrelated behaviors as4

Lij � s = fis4qij1 tij1 bij1wij5

= fis4qij1 tij5Pris4bij1wij � qij1 tij50 (2)

4 To avoid clutter, we describe first the model in the general dis-tribution form and then outline the particular distributions andparameterizations that we used.

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In the above, we assume that the joint decisions ontiming and quantity stem primarily from the buyer’sneed for the product. Because these decisions occurprior to the decision to request a quote or orderdirectly, they impact the latter set of decisions. Thedecision to accept or reject a quote (wij) occurs onlywhen the buyer decides to request a quote rather thanorder directly from the seller (bij = 1), so we specifythe joint probability of bij and wij as follows:

Pris4bij1wij � qij1 tij5

= Pris4bij = 0 � qij1 tij51−�bij

· 6Pris4wij � bij = 11 qij1 tij5Pris4bij = 1 � qij1 tij57�bij1 (3)

where �bij equals 1 if purchase event j for buyer i is a

quote request and 0 otherwise.In modeling the time between purchase events, tij,

the last observation for each buyer, t∗ij, is censoredbecause of the fixed time horizon of the data set.5

Let S4t∗ij5 be the survival function for the censoredobservation, and let �c

ij be a censoring indicator, whichequals 1 if observation j for buyer i is censored and0 otherwise. Accordingly, accounting for censoringand inserting Equation (3) into Equation (2), we canrewrite Equation (2) as follows:

Lij � s = fis4qij1 tij1 bij1wij5

= Sis4t∗

ij5�cij[

fis4qij1 tij5Pris4bij = 0 � qij1 tij51−�bij

· 6Pris4wij � bij = 11 qij1 tij5

· Pris4bij = 1 � qij1 tij57�bij]1−�cij 0 (4)

Next, we describe the distributional assumptions foreach of the four decisions.

4.3.1. Modeling Quantity and Time BetweenEvents. We assume that the purchase event times fol-low a two-parameter log-logistic distribution (Kumaret al. 2008; Lancaster 1990, p. 44) because it flex-ibly accommodates both monotonic and nonmono-tonic hazards. The probability density function (p.d.f.)and cumulative distribution function (c.d.f.) of thelog-logistic are given by

fis4tij5=ex′

ijÂtsi+�tij�st�s−1ij

41 + ex′ijÂtsi+�tij t

�sij 5

21

Fis4tij5=ex′

ijÂtsi+�tij t�sij

1 + ex′ijÂtsi+�tij t

�sij

1

(5)

5 We do not model the first purchase event for each buyer and useit as an initialization period to account for left truncation and ini-tialize the dynamics.

where �s > 0 is a shape parameter; Âtsi is a vectorof coefficients for buyer-level, purchase event-specificcovariates such as prices or reference prices; and �t

ijrepresents an unobserved shock associated with theinterpurchase event time. We assume that the randomshock �t

ij is correlated with the unobserved shock inthe pricing equation to account for possible endogene-ity (see §4.4).

We assume that quantities requested and/orordered follow a log-normal distribution with p.d.f.and corresponding c.d.f. given by

fis4qij5=�44log qij − x′

ijÂqsi − �qij5/�5

�qij1

Fis4qij5=ê

( log4qij5− x′ijÂqsi − �

qij

�

)

1

(6)

where Âqsi is a vector of coefficients for a set of buyer-level and purchase event-specific covariates that affectthe mean quantity, �

qij is an unobserved random

shock that is correlated with the unobserved shock inthe pricing equation discussed below, � is the scaleparameter, and � and ê represent the p.d.f. and c.d.f.of the standard normal distribution, respectively.

4.3.2. Modeling Buyer Quote Request andAcceptance Decisions. Buyer i’s binary quote re-quest decision on purchase event j , (bij) is governedby an underlying latent utility b∗

ij such that

bij =

{

1 if b∗ij > 0 (indirect)1

0 otherwise (direct)0

Similarly, conditional on a price quote, buyer i’sbinary decision to accept or reject the quote on pur-chase event j , (wij), is driven by the latent utility w∗

ijsuch that

wij =

1 if b∗ij > 0 and w∗

ij > 010 if b∗

ij > 0 and w∗ij ≤ 01

unobserved otherwise0

We assume that each of the latent variables, b∗ij and

w∗ij, are distributed logistic. Thus,

Pris4b∗ij < 05=

1

1 + ex′ijÂbsi+�bij

and

Pris4w∗ij < 05=

1

1 + ex′ijÂwsi+�wij

0

(7)

The vector of parameters Âbsi and Âwsi relate the quoterequest and quote acceptance latent utilities, respec-tively, to a set of covariates such as price, referenceprice, and time since the last order. The unobservedshocks �b

ij and �wij are associated with the quote request

and quote acceptance decisions, respectively. Theseare correlated with the unobserved shock of the pric-ing equation, which is discussed subsequently.

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4.4. The Control Function Approachto Price Endogeneity

We need to account for two potential sources of endo-geneity. First, it is possible that the seller’s pricingdecisions are based on unobserved random shocksthat also impact the buyers’ decisions. For example,demand boosts and supply shortages can increase theprices that sellers charge. Such common economicshocks to both pricing and demand may be observedby buyers and the seller but remain unobserved to theresearcher. In such a case, price will be correlated withthe unobserved components (the �’s) of the four dis-tributions. Second, the seller may set prices for eachbuyer individually by using its knowledge about eachbuyer’s sensitivity. This again is private informationthat is not observed by the researcher. Ignoring endo-geneity can result in misleading inferences about theprice sensitivities of customers (Villas-Boas and Winer1999). We therefore use a Bayesian analog of the con-trol function approach to account for price endogene-ity (Park and Gupta 2009, Rossi et al. 2005).

We express price as a function of an observedinstrumental variable, zij, that is correlated with pricebut is uncorrelated with the unobserved factors thatimpact the four decisions. Specifically, we use theseller’s wholesale cost (that is, the cost that the sellerpays to the mills for the metal) as the instrumen-tal variable zij to address the first source of potentialendogeneity resulting from common unobserved eco-nomic shocks. This cost is observed by the seller butnot by buyers. Conversations with the managementteam reveal that the salespeople observe the whole-sale cost on their computer screens and rely heavilyon it when setting the price. Wholesale prices havebeen commonly used as instruments for price (e.g.,Chintagunta 2002). To address the second potentialsource of endogeneity, individual targeting, we use abuyer-specific random intercept in the pricing equa-tion below. Formally stated, we have

pij = �1i +�2zij +�ij1

where �ij represents unobserved factors that influencethe pricing decision. We assume that �ij is distributedjointly bivariate normal with each of �l

ij, l ∈ 8t1 q1 b1w9in Equations (5)–(7).

The bivariate normal distribution for each of thefour decisions can be written as

f 4�ij1 �lij5∼ MVN

((

00

)

1

(

�2p �pl

�pl �2l

))

l ∈ 8t1 q1 b1w91 (8)

where �2p is the variance of �ij, �2

l is the variancefor the random shock �l

ij, and �pl is the covariancebetween �ij and �l

ij.

Inserting Equations (5)–(8) into Equation (2), weobtain the likelihood of the four interrelated buyerdecisions and the observed price, conditional on thebuyer’s state and the random shocks �ij and �l

ij:

Lij � s = fis4qij1 tij1 bij1wij1 pij5

= fis4qij1 tij � pij5Pris4bij1wij � qij1 tij1 pij5f 4pij50

4.5. The HMM Likelihood FunctionThe likelihood of observing the buyer’s decisionsover J purchase events (Yi11Yi21 0 0 0 1YiJ1) can be suc-cinctly written as (MacDonald and Zucchini 1997)

LiJ = P4Yi1 = yi11 0 0 0 1YiJ = yiJ5

= �iMi1ìi11→2Mi21 0 0 0 1ìi1 J−1→JMiJ1′1 (9)

where ëi is the initial state distribution described in§4.1, ìi1 j−1→j is the transition matrix described in §4.2,Mij is a S × S diagonal matrix with the elements Lij � s

from Equation (4) on the diagonal, and 1′ is a S × 1vector of ones.

We restrict the probability of a quote request tobe nondecreasing in the trust states to ensure theidentification of the states. We impose the restric-tion �̃b01i ≤ �̃b02i ≤ · · · ≤ �̃b0Si by setting �̃b0si = �b01i +∑s

s′=2 exp4�0s′i5, s = 21 0 0 0 1 S. As both the interceptsand the response parameters are state specific, weimpose this restriction at the mean of the vector ofcovariates by mean centering xij. Finally, we scalethe likelihood function in Equation (9) followingthe approach suggested by MacDonald and Zucchini(1997, p. 79) to avoid underflow.

4.6. Recovering the State MembershipDistribution

We use filtering (Hamilton 1989) to determine theprobability that buyer i is in state s at purchase event jconditioned on the buyer’s history:

P4Sij = s � Yi11Yi21 0 0 0 1Yij5

= ÖiMi1ìi11→2Mi21 0 0 0 1ìi1 j−1→j·sLij � s/Lij1 (10)

where ìi1 j−1→j·s is the sth column of the transi-tion matrix ìi1 j−1→j , and Lij is the likelihood of theobserved sequence of joint decisions up to purchaseevent j from Equation (9).

5. Model Estimation and ResultsIn this section, we describe how we instantiate theabove model in our application. We first present therationale for our choice of variables and then interpretthe parameter estimates.

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5.1. Description of VariablesInternal reference prices and asymmetric reference priceeffects: We define the internal reference price forbuyer i, at purchase event j , as a quantity-weightedaverage of the buyer’s past observed prices (in dollarsper pound)6

reference_priceij =

∑j−1k=1 quantityik × price_lbik

∑j−1k=1 quantityik

1

where price_lbij is the price per pound observed bybuyer i in purchase event j . The quantity weight-ing reflects that buyers attend closely to larger ordersrelative to smaller ones. To examine the differentialeffects of price increases and price decreases on buyerdecisions, we incorporate asymmetric reference priceeffects using “gain” and “loss” variables:

gainij =

reference_priceij − price_lbij

if price_lbij < reference_priceij1

0 otherwise3

lossij =

price_lbij − reference_priceij

if price_lbij > reference_priceij1

0 otherwise0

External reference prices and the commodity market: Cus-tomers often use external reference prices when mak-ing buying decisions (Kopalle and Lindsey-Mullikin2003, Mazumdar et al. 2005). Commodity prices serveas an obvious candidate for an external source ofreference price in our setting. We expect that someindustrial buyers would attend to this external sourceof reference price when making buying decisions.As the seller primarily sells aluminum products, weuse the daily spot prices from the LME aluminumspot market to capture the impact of the fluctua-tions in the commodity market. We define lmeij asthe aluminum spot price (in thousand dollars permetric ton) on the LME at purchase event j forbuyer i.

We theorize that, all else being equal, high LMEprices at the time of purchase will make the seller’soffered price appear relatively lower. This effect islikely to be stronger for buyers who have a low levelof trust for the seller, leading them to consult the LMEprior to purchasing. Additionally, high LME pricesmay result from an overall good market for aluminumand thus reflect increased demand.

6 We tested several alternative specifications of the reference pricevariable including simple average of past prices and time-weightedreference prices. The quantity-weighted reference price resultedin the best model fit. Incorporating time decay to the quantity-weighted reference price formulation did not result in significantimprovement in the model’s fit.

Economic volatility and the volatility in the commod-ity market: The extant literature in B2B relationshipmarketing suggests that buyers rely more heavily onrelationships with sellers during periods of environ-mental uncertainty and volatility because strong rela-tionships provide stability in an unstable environment(Fang et al. 2011, Jaworski and Kohli 1993, Palmatier2008). To assess the impact of economic volatility, wedefine lme_volatilityij as the volatility of the aluminumspot prices, calculated as the standard deviation of theLME daily returns over the seven trading days priorto purchase event j for buyer i.

We theorize that the volatility in the spot mar-ket would have a negative effect on demand. Thisadverse effect of economic volatility will be attenu-ated for buyers who have a higher-quality relation-ship with the seller relative to those with lower lev-els of trust. We now describe how these variables areincluded in each of the buyer decision’s components.

5.1.1. The State-Dependent Decisions. We in-clude the following variables in the state-dependentcomponents for the four decisions:

1. Purchase event times: We expect the timing of thepurchase event to depend on the previous quantitybecause of inventory effects and on past internal ref-erence price effects. Thus, xij in Equation (5) includesthe covariates gainij−1, lossij−1, and quantityij−1.

2. Quantity: We expect that the price gain (loss)experienced on the previous purchase event and thecurrent level and volatility of the commodity mar-ket to impact requested quantity. Thus, xij in Equa-tion (6) includes the covariates gainij−1, lossij−1, lmeij,and lme_volatilityij.

3. Quote request: Given a particular relationshipstate, we expect that buyers in general will have alower propensity to order directly when the quantitydesired is large, when a long time has elapsed sincethe previous purchase, or when the market conditionsare volatile. Furthermore, consistent with Figure 2, aperceived overcharge on the previous purchase eventcould increase the likelihood of requesting a quote.Thus, xij in Equation (7) includes tij, quantityij, gainij−1,lossij−1, lmeij, and lme_volatilityij.

4. Quote acceptance: We predict that the likelihoodof accepting a quote will be higher when the quan-tity ordered is small, purchases are frequent, and thebuyer experiences a price gain on the current pur-chase event. We also expect the gain and loss effects tobe magnified for larger orders. Furthermore, the deci-sion could be affected by the commodity market con-ditions. Thus, xij in Equation (7) includes tij, quantityij,gainij, lossij, gainij ×quantityij, lossij ×quantityij, lmeij, andlme_volatilityij.

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5.1.2. The Nonhomogeneous Transition Matrix.The gain or loss experienced on the previous purchaseevent can affect the buyer’s evaluation (or reevalua-tion) of the relationship with the seller and can triggera transition among relationship states, thereby affect-ing purchases in the long run. Specifically, we pos-tulate that price losses (a perceived overcharge) maytrigger a transition to a lower trust state. Similarly, aprice gain on the previous order may trigger a transi-tion to a higher trust state. Thus, xij−1 in Equation (1)includes gainij−1 and lossij−1.

5.2. Heterogeneity SpecificationCapturing cross-buyer heterogeneity facilitates target-ing and allows for the proper accounting of referenceprice effects (Bell and Lattin 1998). Capturing hetero-geneity is also crucial for empirically distinguishingdynamics from cross-buyer heterogeneity (Heckman1981). Therefore, we allow the initial state member-ship, the transition matrix parameters, the coefficientsin the four equations, and the intercept of the pricingcontrol function equation to vary across buyers.

5.3. Estimation ProcedureWe use a hierarchical Bayesian approach based onMarkov chain Monte Carlo (MCMC) methods forinference. The inherent complexity of the HMM oftenleads to significant autocorrelation among the draws.We therefore use the adaptive Metropolis procedurein Atchadé (2006) to improve mixing and conver-gence. We use proper but diffuse priors for all param-eters. Details of priors as well as full conditionalsare available from the authors upon request. We usethe first 18 months of data for estimation and thelast three months for validation purposes. Our resultsare based on the last 250,000 draws from an overallMCMC run of a million iterations. Convergence wasensured by monitoring the time series of the MCMCdraws.

5.4. Choosing the Number of StatesWe begin by determining the number of HMM states.We use the in-sample log-marginal density (LMD)and the deviance information criterion (DIC) to selectthe number of states. The models with one, two,three, and four states have LMD values of −701652,−621781, −631352, and −641208, respectively, andDIC values of 144,725, 130,516, 133,304, and 135,921,respectively. Thus, the model with two states has thehighest support in terms of both LMD and DIC. Wetherefore move forward with this model.7

7 We also estimated a three-state HMM where the third state isan absorbing state with no purchase activity, capturing permanentdefection. The LMD and DIC of that model were −631764 and133,421, respectively. For completeness, we also tested the fit of atwo-segment latent class model (LMD: −941462, DIC: 187,234) and

5.5. Model Fit and Predictive AbilityWe compare the fit and predictive ability of the pro-posed model (full model) to that of six benchmarkmodels. These differ from the full model with respectto (1) the extent of heterogeneity, (2) the degree ofdynamics as captured by the HMM, (3) the account-ing for price endogeneity, and (4) whether the buy-ing state is modeled as observed or latent. We alsocompare our model to a recency-frequency-monetary(RFM) model (Benchmark 5) that is typically usedin marketing to assess and predict customer rela-tionships. Finally, we compare the full model to alatent class model in which the group membership isallowed to vary over time based on previous pricing(Allenby et al. 1999). The benchmark models are asfollows:

1. Benchmark 1: In this model, all parameters areassumed to be invariant across buyers. A comparisonof this model with the full model allows us to assessthe importance of modeling heterogeneity.

2. Benchmark 2: This model ignores the two sourcesof dynamics present in the full model—i.e., the HMMspecification and the reference price effects. We there-fore estimate a single state (i.e., no HMM) model inwhich the reference prices are replaced with actualprices. In this model, the four decisions are indepen-dent. Comparing this “static” model to the proposedmodel allows us to assess the value of capturing rela-tionship dynamics. Comparing this model with theone-state model from §5.4 allows us to assess thevalue of accounting for reference prices.

3. Benchmark 3: This model assumes that the pricesare exogenous; otherwise, it is identical to the fullmodel in all other aspects. Thus, this model doesnot have the Bayesian control function component.A comparison of this model with the full model canhighlight the extent of price endogeneity and the per-ils of ignoring it.

4. Benchmark 4: This model uses an observed statevariable instead of a latent relationship state. Amongthe four buying decisions, the quote request behavioris the most indicative of the relationship state. Hence,in this “simplified” observed state model, we deter-ministically assign state membership based on eachbuyer’s quote request behavior on the previous pur-chase event instead of using the probabilistic latentrelationship in an HMM.

5. Benchmark 5: This is the RFM model commonlyused in B2C settings, where we model each of the

three-segment latent class model (LMD: −891321, DIC: 179,442) byrestricting the transition matrix to a diagonal matrix. Thus, con-straining the parameters of the transition matrix resulted in worsemeasures of performance.

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four decisions using recency (interpurchase time), fre-quency (the buyer’s historical average number of pur-chases per week), monetary value (the buyer’s histori-cal average of invoice prices), and the other covariatesthat are used in the full model.

6. Benchmark 6: This is a latent class model thatuses time-varying class membership weights to cap-ture dynamics. Instead of using an HMM, this modelcaptures dynamics by specifying the latent state mem-bership as a function of only the reference prices andnot of the previous states.

We compare the fit and predictive ability of theseven models using the LMD and the DIC statis-tics on the calibration sample and the validation log-likelihood on the validation sample. We also assessthe component-specific fit and predictive ability usingthe root mean squared error (RMSE) and the meanabsolute deviation (MAD) between the predicted andobserved values of the four outcome variables. Inaddition, we use hit rates for the binary quote requestand conditional quote acceptance decisions within thecalibration and validation samples. To account foruncertainty in MCMC, the prediction measures areaveraged across MCMC runs, rather than using pointestimate. We also assessed the performance of themodel using posterior predictive checks (details ofthis analysis is available in the Web appendix avail-able as supplemental material at http://dx.doi.org/10.1287/mksc.2013.0842).

Table 3 presents the model comparison statistics forthe seven models. We see that the full model outper-forms the benchmark models on both the component-specific and overall measures both in and out ofsample. First, the relatively poor performance of theno-heterogeneity model results from the substantialbuyer heterogeneity and suggests an opportunityfor individually targeted pricing. Second, the resultspoint to significant and latent relationship dynam-ics. Accounting for such dynamics in a holistic, latentfashion using an HMM, instead of using an observedstate, improves the representation and prediction ofbuying behavior. We also find that accounting forprice endogeneity results in only a marginal improve-ment in model performance. This is consistent withthe reported use of a “cost-plus” pricing strategy bythe seller and with the finding that a regression ofprice on wholesale cost yields an R2 of 0.84. Althoughthe RFM model has a reasonable fit and predictiveability in our application, it fits and predicts the datasignificantly worse than the proposed HMM. Fur-thermore, unlike the HMM, the RFM model cannotinform us about the impact of pricing decisions onthe dynamics in buying behavior.

From a managerial perspective, the seller can rel-atively easily implement the Benchmark 4 model

based on the observed states. Although the perfor-mance of this benchmark is inferior to the full model,accounting for reference price effects and observedstate changes based on bidding behavior is alreadya major step forward for most industrial consum-able B2B companies (our company included) that stillengage in cost-plus pricing and do not have any sys-tematic way to perform individual price targeting. Weexplore this model further in §6.

5.6. Parameter EstimatesIn this section we discuss the parameter estimates ofthe full model with two latent relationship states.

5.6.1. The HMM States. Table 4 contains the pos-terior means, standard deviations, and the 95% pos-terior intervals for the parameters of the full model.Recall that all covariates are mean centered, sothe intercept of each equation captures the averageresponse tendency. A comparison of the parametersacross the two states indicates that buyers in State 2are more likely to request a price quote but are lesslikely to accept the quote relative to buyers in State 1.Buyers in State 2 are more sensitive to reference priceeffects and exhibit stronger loss aversion in the inter-purchase event time, quote request, and quote accep-tance decisions. As we have theorized, buyers whoare in State 2 at a given purchase event also tend tobe more responsive to the commodity market (LME)as an external reference price. Interestingly, whereaseconomic volatility (as measured by the volatility ofLME) has a negative impact for buyers in State 2, theimpact is mitigated for buyers in State 1.

Overall, this multidimensional view of the two rela-tionship states (see a summary of the two states inTable 5) implies that buyers in State 2 exhibit a morecautious approach toward buying from the seller,whereas buyers in State 1 appear more relaxed in theirrelationship with the seller. We therefore call State 1the relaxed state and State 2 the vigilant state. As buyerstransition to the relaxed state, possibly as a result offavorable past interactions with the seller, they sim-plify their buying decisions, become less focused onprice losses, and are less concerned about the exter-nal economic environment. This simplified buyingprocess is beneficial for both parties. For buyers, itsaves resources on search and transaction costs. Forthe seller, buyers that are in a trusting state are asource of stable cash flow without the uncertainty ofthe quote request process. The relaxed state, therefore,represents a higher level of relationship quality whencompared with the vigilant state. The average orderquantity for customers in the relaxed state is smallerthan in the vigilant state, which indicates that cus-tomers are more likely to be vigilant when the stakesare high.

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Table3

Mod

elSe

lectionan

dPred

ictiv

eVa

lidity

Full

mod

elBe

nchm

ark

1Be

nchm

ark

2Be

nchm

ark

3Be

nchm

ark

4Be

nchm

ark

5Be

nchm

ark

6

Hete

roge

neity

Yes

NoYe

sYe

sYe

sYe

sYe

sDy

nam

ics

Dyna

mic

s(H

MM

Dyna

mic

s(H

MM

Nody

nam

ics

Dyna

mic

s(H

MM

Obse

rved

stat

e(la

stbi

dbe

havi

or)

Dyna

mic

s(R

efer

ence

Refe

renc

epr

ice+

Tim

e-va

ryin

g+

Refe

renc

epr

ice)

+Re

fere

nce

pric

e)+

Refe

renc

epr

ice)

+Re

fere

nce

pric

epr

ice+

RFM

)st

ate

mem

bers

hip

Cont

rolf

unct

ion

Yes

Yes

Yes

NoNo

Yes

NoLM

D–62,78

1–9

0,58

4–7

2,46

1–6

3,00

8–6

8,35

9–6

6,99

8–6

9,12

2DI

C13

0,51

618

1,62

314

8,81

113

1,19

714

0,38

813

7,35

114

1,02

5Co

mpl

exity

pD4,

798

753,

266

4,78

22,

856

3,75

52,

973

Valid

atio

nLL

–16,02

5–2

1,03

1–1

6,85

6–1

6,07

3–1

7,98

5–1

7,04

5–1

7,32

0

InOu

tof

InOu

tof

InOu

tof

InOu

tof

InOu

tof

InOu

tof

InOu

tof

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

sam

ple

Hitr

ate

Quot

ere

ques

t0072

0062

0060

0058

0062

0060

0072

0062

0064

0062

0064

0062

0064

0062

Bid

acce

ptan

ce0069

0057

0057

0055

0064

0058

0069

0057

0066

0057

0067

0057

0066

0057

RMSE Qu

antit

y0091

0099

1066

1067

1005

1004

0091

0099

1004

1003

1003

1003

1001

1001

Inte

rpur

chas

e15057

19023

2403

127

050

2003

32103

91506

019

027

2001

321

018

1909

32009

71905

32005

5tim

eQu

ote

requ

est

0051

0057

0060

0087

0058

0065

0051

0057

0057

0065

0056

0064

0055

0063

Bid

acce

ptan

ce0053

0064

0074

0097

0070

0069

0053

0064

0069

0068

0069

0068

0067

0066

MAD Qu

antit

y0040

0040

0069

0067

0044

0048

0040

0040

0044

0048

0043

0047

0042

0046

Inte

rpur

chas

e11066

14026

1707

518

010

1402

81500

41106

814

028

1401

414

089

1400

01407

51307

21404

5tim

eQu

ote

requ

est

0030

0036

0043

0053

0031

0038

0030

0036

0032

0037

0033

0038

0032

0037

Bid

acce

ptan

ce0039

0047

0060

0073

0039

0046

0039

0047

0039

0046

0041

0049

0040

0048

Notes.

Num

bers

inbo

ldre

pres

entt

hebe

stfit

/pre

dict

ive

abili

tyfro

mam

ong

allt

hem

odel

s.Co

mpl

exity

pD,t

heef

fect

ive

num

ber

ofpa

ram

eter

sof

aBa

yesi

anm

odel

;val

idat

ion

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Table 4 Parameter Estimates for the Four Decisions—PosteriorMeans, Standard Deviations, and 95% Posterior Intervals

Quantile

State Parameter Mean Std. dev. 2.5% 97.5%

(a): Quantity decisionState 1 Intercept −10834 00040 −10912 −10756

gain(j − 1) 00004 00021 −00038 00046loss(j − 1) −00032 00013 −00058 −00006lme (j) 00027 00132 −00231 00285

lme_volatility (j) −00794 00496 −10766 00178State 2 Intercept −10492 00034 −10558 −10426

gain(j − 1) 00127 00019 00089 00165loss(j − 1) −00094 00014 −00122 −00066lme (j) 20947 00550 10869 40025

lme_volatility (j) −30353 10075 −50461 −10245

(b): Interpurchase event time decisionState 1 Intercept 00994 00030 00936 10052

quantity (j − 1) −00010 00030 −00068 00048gain(j − 1) −00067 00014 −00095 −00039loss(j − 1) 00050 00014 00022 00078

State 2 Intercept 00858 00032 00796 00920quantity (j − 1) 00031 00021 −00011 00073gain(j − 1) −00016 00016 −00048 00016loss(j − 1) 00040 00010 00020 00060

(c): Quote request decision (quote request vs. direct order behavior,where quote request = 1)

State 1 Intercept −10103 00035 −10171 −10035quantity (j) 00403 00099 00209 00597

interpurchase 00029 00004 00021 00037time (j)

gain(j − 1) −00085 00027 −00137 −00033loss(j − 1) 00094 00024 00046 00142lme (j) −00980 00896 −20736 00776

lme_volatility (j) 10184 10077 −00928 30296State 2 Intercept 10040 00082 00880 10200

quantity (j) 20119 00587 00969 30269interpurchase 00004 00007 −00010 00018

time (j)gain(j − 1) −00340 00015 −00370 −00310loss(j − 1) 00721 00017 00687 00755lme (j) −10850 00601 −30028 −00672

lme_volatility (j) 30319 10319 00733 50905

Our empirical results are consistent with the theo-retical literature in B2B relationship marketing, whichposits that as relationships improve, buyers in thesupply chain focus holistically on the relationship andon the long-term benefits that such a relationship pro-vides (Dwyer et al. 1987). Relaxed buyers are alsonot easily affected by adverse external environmen-tal changes because the relationship provides a safeharbor and a level of stability in an otherwise unsta-ble business environment (Fang et al. 2011, Jaworskiand Kohli 1993, Palmatier 2008). The two states wehave identified have also been referred to in the B2Bliterature as “programmed” and “transactional” seg-ments of buyers (Rangan et al. 1992), “passive” and“aggressive” buyers (Shapiro et al. 1987), and “co-

Table 4 (Cont’d.)

Quantile

State Parameter Mean Std. dev. 2.5% 97.5%

(d): Quote acceptance decision (quote acceptance vs. rejection behavior,where accept = 1)

State 1 Intercept 00217 0.015 00187 00247quantity (j) −00212 0.033 −00276 −00148

interpurchase 00002 0.017 −00032 00036time (j)gain(j) 00206 0.015 00176 00236loss(j) −00182 0.016 −00214 −00150

quantity (j) 00081 0.018 00045 00117× gain(j)

quantity (j) −00049 0.016 −00081 −00017× loss(j)lme (j) 00212 0.510 −00788 10212

lme_volatility (j) −00351 1.077 −20463 10761State 2 Intercept 00101 0.050 00003 00199

quantity (j) −00525 0.047 −00617 −00433Interpurchase −00031 0.008 −00047 −00015

time(j)gain(j) 00127 0.015 00097 00157loss(j) −00219 0.020 −00259 −00179

quantity (j) 00260 0.015 00230 00290× gain(j)

quantity (j) −10662 0.018 −10698 −10626× loss(j)lme (j) 00719 0.469 −00201 10639

lme_volatility (j) −10311 1.145 −30557 00935

Notes. Posterior means and standard deviations are calculated across theMCMC draws. Estimates in bold indicate a significant effect (that is, 95%posterior interval excludes 0).

operative” and “antagonistic” buyers (Matthyssensand Van den Bulte 1994).

5.6.2. Using Pricing to Drive Buyer Dynamics.Buyers can transition between the two states overtime. The parameter estimates in Table 6 and theirtransition matrix representation in Table 7 illustratethese dynamics. The central matrix in Table 7 showsthe transition matrix when the price equals the refer-ence price (i.e., the buyer’s quantity-weighted averagehistorical prices). One can see that the states are rel-

Table 5 Description of the Two HMM States

Relaxed state Vigilant state

Quote request probability (%) 24 83Quote accept probability (%) 63 54Average quantity ordered (lb.) 432 502Interpurchase event time (weeks) 5.5 8.1Average price elasticitya 1.4 3.1Average loss aversion ratioa 0.89 3.01Average sensitivity to LMEa 0.8 6.2

aPrice elasticity, loss aversion, and LME sensitivity are averaged acrossbuyers and across the four decisions. Because the sign of the effect can varyacross decisions (e.g., price elasticity is negative for quantity but positive forinterpurchase event time), we average the absolute value of these measures.

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Table 6 HMM and Distributional Parameter Estimates

Quantile

Parameter Mean Std. dev. 2.5% 97.5%

Transition matrixState 1 Intercept 10787 0.018 10750 10824

gain(j − 1) 00045 0.013 00019 00070loss(j − 1) −00090 0.013 −00116 −00065

State 2 Intercept 20162 0.037 20091 20231gain(j − 1) −00434 0.015 −00464 −00405loss(j − 1) 00612 0.016 00581 00643

Initial state Vigilant 00683 0.029 00626 00737membership (�)probability

Distributionalparameters

Std. dev. for the quantity model, 00108 0.045 00023 00191log scale (� )

State 1 shape parameter for 00100 0.016 00068 00131interpurchase event time,log scale (�1)

State 2 shape parameter for 00068 0.010 00047 00088interpurchase event time,log scale (�2)

Notes. Posterior means and standard deviations are calculated across theMCMC draws. Estimates in bold indicate a significant effect (that is, 95%posterior interval exclude 0).

atively “sticky.” A somewhat alarming result for theseller is that the likelihood of a buyer dropping fromthe relaxed to the vigilant state (14.3%) is almost twiceas high as the likelihood of moving from the vigilantto the relaxed state (7.7%). However, the seller canuse its pricing policy to affect transitions between thestates.

Comparing the left matrix in Table 7 with the cen-tral matrix, we see that experiencing a 10% pricedecrease (“gain”) in the previous purchase eventincreases the probability of moving from the vigilantto the relaxed state by almost 2% and also increasesthe chance of remaining in the relaxed state by 3%.This suggests that when buyers perceive that theyare treated well, they are more likely to transition toor remain in a state of a more favorable relationshipwith the seller. In contrast, the right matrix in Table 7shows that a 10% price increase (“loss”) on the pre-vious purchase event increases the likelihood that thebuyer will transition to the vigilant state by almost

Table 7 Posterior Mean of the Transition Matrix Across Buyers

10% price Average price 10% pricedecrease (reference price) increase

Relaxed Vigilant Relaxed Vigilant Relaxed Vigilant(j + 1) (j + 1) (j + 1) (j + 1) (j + 1) (j + 1)

Relaxed (j) 0.886 0.114 0.857 0.143 0.789 0.211Vigilant (j) 0.095 0.905 0.077 0.923 0.043 0.957

7% and also increases the likelihood of staying inthe vigilant state by 3.4%. Thus, a price increase mayhave a long-term effect by transitioning the buyer toa (sticky) state of increased price sensitivity. It shouldbe noted that Table 7 presents transition matricescomputed at the posterior mean. Our MCMC estima-tion permits an accounting of posterior uncertaintyfor the transition matrices of each buyer. We leveragethis heterogeneity in developing a targeted pricingpolicy in §6. The average loss aversion in the impactof reference prices on the transition between the statesranges from 1.5 to 2.5, consistent with the loss aver-sion ratios commonly reported in B2C applications.

5.6.3. Investigating Price Endogeneity. To assessthe extent of endogeneity, we look at the correlationsbetween the unobserved error in the price equationand each of the random shocks (�’s) for the four deci-sions. There are mildly negative correlations for thequantity and quote acceptance decisions and mildlypositive correlations for the interpurchase event timeand quote request decisions. These correlations are allin the expected direction and imply that (1) despitethe predominant practice of cost-plus pricing, theseller does occasionally target price-insensitive (sen-sitive) buyers by charging them higher (lower) pricesand that (2) unobserved shocks could influence boththe seller’s pricing decisions and the buyers’ behavior.Although a failure to properly account for price endo-geneity could result in overestimation of the effectsof price gains and an underestimation of the impactof price losses, it should be noted that, overall, thedifferences in the price sensitivity estimates betweenthe two models are relatively small, and accountingfor endogeneity only results in a modest gain in ourapplication. Estimates of the correlations between theunobserved error in the price equation and each ofthe random shocks for the four decisions, and a com-parison of the parameter estimates are available in theWeb appendix.

5.7. Disentangling the Short- and Long-TermEffects of Pricing

Assessing the marginal and integrative impact ofprice is not straightforward from the reference pricecoefficients in Tables 4 and 6 because price enters inour model in multiple places. We therefore numeri-cally compute the short-run and long-run elasticitiesfor each of the four decision components and for theHMM state membership probabilities. The elasticity iscalculated for each decision variable using a one-timeshock (price increase or a price decrease) of 10% in theunit price from the average price. We take a horizon of20 simulated purchase events subsequent to the one-time shock to calculate the short-term and long-termelasticities. Following the one-time price shock, we

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Table 8 Short- and Long-Term Price Elasticities of the DecisionComponents and the Vigilant State Membership

Price increase Price decrease

Short- Long- Short- Long-term term Total term term Total

Quantity −0043 −2073 −3021 1039 3005 4053Interpurchase 1022 2034 3057 −0071 −0062 −1035

event timeQuote request 0073 4091 5072 −0053 −1059 −2016Quote −1019 −3042 −4065 0038 0097 1037

acceptanceVigilant state 0062 5047 6018 −0031 −1038 −1072

membership

set prices to the reference price level for the remain-ing 19 purchase events. The short-term elasticity cap-tures the immediate impact (i.e., on the first purchaseevent), whereas the long-term elasticity captures theeffect over the next 19 purchase events. These short-and long-term elasticities are reported in Table 8. Inaddition, Figure 3 illustrates the asymmetry in thepercentage increases and decreases in each affectedvariable over the simulated 20 purchase events fol-lowing the one-time 10% price increase or decrease.

Several insights can be gleaned from Table 8 andFigure 3. First, all price elasticities are in the expecteddirection. Second, the magnitudes of the long-termelasticities are generally much larger than the cor-responding magnitudes of the short-term elasticities.On average, the short-term price elasticities are only10%–53% of the total price elasticities. The averageshort-term quantity elasticities are consistent withthose reported in the literature (Bijmolt et al. 2005,Jedidi et al. 1999, Tellis 1988). Third, factors that aredirectly related to the buyers’ attitudes and relation-ship with the seller (i.e., quote request and vigilant

Figure 3 Duration of Asymmetric Price Effects on the Four Decision Components

5 10 15 20

02

–2–4–6

468

Time period

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uote

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est (

%)

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–10

–15

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state membership) exhibit stronger long-term elas-ticities relative to other factors. Fourth, consistentwith prospect theory (Kahneman and Tversky 1979),we find that price increases (losses) have a strongerimpact than do price decreases (gains) for all deci-sions, except for quantity. The quantity decision, incontrast, exhibits gain seeking. Previous research inB2C has found gain seeking in the effect of referenceprices on quantity when households face low inven-tory (Mazumdar et al. 2005). This result is consistentwith buyers keeping a low inventory of aluminumand relying on the reseller to stock the material. Thus,consistent with Bruno et al. (2012), we find empir-ical evidence for asymmetric reference price effectsfor B2B buyers. Fifth, and perhaps most interestingly,Figure 3 shows that the negative effects of a pricehike (loss) on all four decisions persist longer thanthe positive effects of price drop (gain). This resultis consistent with the literature on B2B relationshiplife cycles that states that damage to the relationshipis difficult to repair as it leaves “psychological scars”(Dwyer et al. 1987, Jap and Anderson 2007, Ringand Van de Ven 1994). This evidence for the longerpersistence of the effects of negative price experi-ences is also consistent with hedonic adaptation theory,which states that individuals adapt faster to improve-ments than to deteriorations (Frederick and Loewen-stein 1999). To the best of our knowledge, this is thefirst empirical investigation of the long-term effectsof asymmetric reference price effects and the firstdemonstration of the hedonic adaption theory usingactual transactional data.

Overall, these results imply that, in B2B contexts,researchers and managers that consider only theshort-term effects of pricing can significantly and sub-stantially underestimate the overall impact of pricing,

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as they ignore the impact of pricing on referenceprices and on the latent relationships that drive long-term profitability. In the next section, we investigatehow firms can use the model’s parameters and lever-age the resulting behavioral insights to dynamicallytarget individual buyers.

6. Targeted and Dynamic PricePolicy Optimization

In this section, we assess the separate and variedinfluences of the seller’s pricing decisions on thebehavior of buyers and consequently on the seller’smedium to long-term profits. We first define theseller’s profit from purchase event j of buyer i as

Profitij = 4Priceij − Costij5qij641 − �bij5+ �b

ij�wij 71

where �bij is a binary indicator that equals 1 when

buyer i requests a quote on purchase event j and is0 for a direct order. The binary indicator �w

ij equals 1when the quote is accepted and is 0 otherwise. Theseller’s objective is to maximize the medium to long-run profit (over T periods) across buyers. Therefore,for each buyer i, the seller sets the sequence of pricespi to one that maximizes

maxpi

Ji4pi5∑

j=1

Profitij4pi5

41 + r5∑j

k=1 tik4pi5

s.t.Ji4pi5∑

j=1

tij4pi5 < T 1

(11)

where tij4pi5 is the jth interpurchase event time andr represents the discount rate. As the interpurchaseevent times are influenced by the pricing decisionsof the seller, the number of purchase events, Ji4pi5, isendogenously determined by the constraint that thesum of the interpurchase event times does not exceedthe length of the planning horizon (T ). We can obtainthe seller’s overall profit by summing the optimalprofits across all buyers.

We conduct the optimization using a 15-monthhorizon. However, we evaluate the performance ofour approach over the first nine months of the plan-ning horizon to limit the impact of end-of-the horizoneffects in the optimization. We therefore split the datainto a calibration sample covering the duration fromJanuary to December 2007 and a holdout period ofnine months ranging from January 2008 to Septem-ber 2008.8 We then use the parameter estimates from

8 For the purpose of price policy simulation, we reestimate the pro-posed model on the first 12 months of data and perform simulationon the subsequent 9 months. The estimates do not differ substan-tially from those using 18 months of data, as reported in Table 4.

the calibration data set to conduct the price optimiza-tion. The optimization is performed for a representa-tive sample of 300 buyers who experienced between6 and 16 purchase events over the calibration periodand an average of 10 purchase events over the ninemonths of our holdout data.

We discretize the continuous pricing decision onany purchase event and use a set of five buyer-specificprice points that form the quintiles of the distributionof prices that the buyer experienced in the calibrationperiod. We choose to stay within each buyer’s his-torical range of experienced prices to avoid a drasticchange in the price regime observed by each buyer,yet still account for the price variance experienced byeach buyer.

We then use a combination of forward simula-tion and complete enumeration over all feasible pricepaths to obtain the set of optimal prices over the sim-ulated purchase events of the buyer in the 15-monthplanning horizon. The optimization process is initial-ized for each buyer by setting the state membershipprobabilities and the reference price to their values atthe end of the calibration period. The forward sim-ulation then proceeds by generating a sequence ofpurchase events. Given the five feasible price pointsat each purchase event, there are 5Jik possible pricenodes for buyer i within the kth random sequence.We account for different sources of uncertainty incomputing the profits for each buyer. Given a vec-tor of parameters for buyer i, we simulate 200 MonteCarlo sequences of purchase events for the buyer foreach price path. These 200 sequences may differ inthe number of purchase events, with the kth randomsequence containing Jik purchase events in the plan-ning horizon. Each purchase event in the simulatedsequence is characterized by the quantity, interpur-chase event time, quote request decision, associatedreference price, and latent state membership prob-abilities. We also account for parameter uncertaintyby repeating the optimization procedure for each ofthe well-separated 100 draws from the MCMC poste-rior distribution of the parameters for each buyer. Ateach simulated purchase event, profits are computedby weighting the HMM latent state-specific profitsby the state membership probabilities, and they areaveraged over the 200 sequences and over the 100draws from the MCMC posterior distribution to com-pute the average profit of each price path. We assumean annual discount rate of 12% (a weekly discountrate r of 0.22%).9 Full details of the price simulation

9 We tested the improvement in precision that can be gained fromincreasing the number of random sequence draws. We choose 200draws as a good compromise between precision and computationaltime because it offers 8% improvement in profits over 100 draws,but it only underperforms 300 draws by 1%. It should also be notedthat because of the dimensionality of the state space, our simulationserves as a heuristic for the optimal prices.

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Table 9 Policy Performance Comparison Over Nine Months

Policy

Current Individual dynamic Individual static Segment dynamic Aggregate static Individual dynamic Observedpricing pricing pricing pricing pricing pricing (myopic) state pricing

Average profit 3,158 4,809 3,867 3,328 2,467 4,117 4,008per customer ($)

Mean price ($/lb.) 3.24 3.40 3.28 3.44 3.41 3.28 3.44Median price ($/lb.) 2.87 3.30 3.11 3.23 N/A 3.11 3.28

and optimization are available from the authors uponrequest.

6.1. Price Policy Simulation ResultsWe now compare the performance of our proposedindividually targeted dynamic pricing policy to thatof the five competing policies:

1. Individually targeted static pricing policy: In thispolicy, a single price is determined for each buyerfor the entire 15-month planning horizon. This policyleverages the heterogeneity in the model’s estimatesacross buyers but ignores dynamics.

2. Segment-targeted dynamic policy: In this policy,only two optimal prices are determined—one pricefor each of the two states. The price at a given pur-chase event therefore depends on the HMM statemembership at each purchase event.10

3. Aggregate single-price static policy: This policychooses a single price for all buyers for the entireplanning horizon. Thus, this policy ignores both het-erogeneity and dynamics.

4. Myopic individually targeted dynamic policy: Inthis policy, the seller accounts for both the buyers’updated latent state membership and the heterogene-ity in the buyers’ response parameters. However, ateach purchase event, the seller maximizes profits onlyfor the current purchase event, as opposed to theentire planning horizon. Thus, the myopic dynamicpolicy considers only the short-term effect of pricingin each period.

5. Observed state policy: This policy corresponds toBenchmark 4 in §5.5. As it may be computationallydifficult for the seller to infer the buyer’s latent state,we investigate optimization based on observed prox-ies of the latent state—namely, whether the buyerrequested a quote in the previous period. This pol-icy can be thought of as a “simple” heuristic to ourproposed policy.

6. Current policy: This is the seller’s current pricingpolicy for the nine months.

A comparison of the results from the alterna-tive policies highlights the marginal improvements

10 In the segment policies, the latent state membership at each pur-chase event is determined by the state with the highest membershipprobability.

in profitability that stems from individual-level tar-geting, from dynamics pricing, and from adopting along-term perspective. Table 9 shows how the sevenprice policies perform. The proposed policy yields thehighest profits per buyer of $4,809 over nine months.Leveraging heterogeneity, as given by the individu-ally targeted static policy, generates a 57% improve-ment in profits when compared with the aggregatestatic policy ($3,867 versus $2,467). An additional 24%improvement results from dynamic targeting ($4,809versus $3,867). This result is consistent with the find-ings of Khan et al. (2009), who highlight the poten-tial gains from intertemporal targeting. Similarly, theproposed policy improves profits by 17% over themyopic policy by leveraging the dynamic impact ofpricing and by adopting a long-term perspective.The proposed policy yields a 52% improvement inprofit compared with the seller’s current policy. Tak-ing into account the entire customer base of the seller,this translates to a potential profit improvement ofapproximately $4 million annually. Even employingthe easier to use observed state policy can generate a27% profit gain.

To compare the performance of the different poli-cies over time, we plot the average monthly profitsover the first nine months of the planning horizon in

Figure 4 Policy Performance Comparison Over Nine Months

2

200

300

400

500

Ave

rage

pro

fit p

er b

uyer

($)

600

700

800

4

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Dynamic individual targetingStatic individual targetingMyopic targetingCurrent policy

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Figure 4. We see that the proposed policy carefullybalances the interplay between several forces thatgovern buyers’ buying behaviors: (1) charging lowerprices to increase quote acceptance, (2) charging lowerprices to keep buyers in the relaxed state or to transi-tion them to it, (3) charging higher prices to increasemargins, and (4) charging higher prices to keep buy-ers’ reference prices high. The myopic policy, on theother hand, ignores points (2) and (4) and thereforecharges lower prices than the proposed policy, aim-ing to convert quote requests into immediate sales(see Table 9). Although the myopic strategy leads tohigher profits than the proposed policy in the firstfew months, charging lower prices results in lowerreference prices and creates a downward pressure onthe seller to continue offering lower prices, whichresults in a vicious cycle of decreasing prices andhence depressed profits. After the first three months,the proposed policy begins to outperform the myopicpolicy demonstrating the importance of using a long-term perspective when setting prices. These resultssuggest that in the world of B2B, where relationshipsare long term and sticky, myopia in price setting canbe a slippery slope.

With regard to prices charged, the proposed pricepolicy recommends a higher price for buyers in therelaxed state versus those that are in the vigilant state($3.63/lb. versus $3.20/lb.). The current policy thatis used by the seller, however, only mildly differenti-ates between buyers in the two latent states. Charg-ing a higher price for buyers in the relaxed state canincrease both the immediate profits and the referenceprices in the long term. Although a higher price mightincrease the chance of transitioning these buyers intothe vigilant state, the stickiness of the relaxed stateand the already increased reference prices act as a“shield” against perceiving future prices as losses.

In summary, the superior profitability of our indi-vidual dynamic targeted price policy, relative to thecurrent policy, stems from its ability to leverage(1) heterogeneity in price sensitivities, (2) differencesacross the latent states so that higher prices can becharged to the less price-sensitive customers in therelaxed state, and (3) the trade-off between the short-run and long-run dynamic effects of pricing.

6.2. Pricing in a Volatile EconomicEnvironment—The Role ofExternal Reference Price

In this section, we examine the optimal price strate-gies that the seller should use to manage volatile eco-nomic conditions. Specifically, we investigate to whatextent the seller should pass through its cost increaseswhen aluminum prices rise and whether the sellerneeds to reduce its prices when aluminum prices fall.

The aluminum prices on the LME fluctuatedbetween US$2,393 to US$3,318 per tonne over the

Figure 5 Optimal and Current Unit Price per Pound by State, UnderDifferent LME Regimes

2.8

3.0

3.2

3.4

3.6

3.8

4.0

Current LMElevel

20%increase

20%decrease

Uni

t pric

e ch

arge

d ($/lb.)

Price policies

Relaxed state

Vigilant state

duration of our data. A change in the commodityprices can lead to at least two opposing impacts onthe profitability of the seller. On the one hand, alu-minum prices influence the seller’s cost of replenish-ment.11 On the other hand, buyers use the price onthe LME as an external reference price. It is there-fore unclear, a priori, how the seller should changeits pricing strategy in response to such fluctuations inthe commodity market. We investigate this questionempirically by computing and comparing our indi-vidual dynamic price policies under two scenarios:(1) a 20% increase in the LME prices over the actualLME prices in the nine months of the planning hori-zon and (2) a 20% decrease over the same period.12

Figure 5 shows how the seller should differentiallyadjust its prices for buyers in the relaxed and vigi-lant states. When the LME price increases by 20%, theseller should increase the unit prices by 12% for buy-ers in the vigilant state but by only 4.6% for buyersin the relaxed state. This result stems from the highersensitivity to the LME prices for buyers who are inthe vigilant state (see Table 4). Figure 5 also showsthat when LME prices drop by 20%, it is optimal forthe firm to “hoard” most of the cost savings and dropprices by only 2.5%–2.8% for buyers in both states.The rationale here is that lowering the price results

11 The seller in our empirical application keeps as much as sixmonths of inventory, so the relationship between the LME pricesand wholesale prices of currently sold orders is relatively weak(R2 = 0005), but the LME impacts directly the wholesale cost ofreplenishment.12 Our use of a 20% shock in LME falls within the range of fluc-tuations observed during the data period. The maximum daily,monthly, and three-month LME fluctuations in our data were 5.6%,22%, and 31%, respectively.

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in a corresponding lowering of the internal referenceprice, and this can have long-term consequences forthe seller’s profitability.

This price strategy of passing on the cost increaseand “hoarding” the benefit of a cost decrease is con-sistent with the dual-entitlement principle (Akerlof 1979,Kahneman et al. 1986, Okun 1981, Urbany et al. 1989).The dual-entitlement principle is based on the notionof perceived fairness and states that (1) firms are “jus-tified,” in the eyes of customers, to increase priceswhen costs increase, to protect firms’ normal profits;and (2) firms do not need to lower prices when costsdrop as customers’ perceptions are mainly driven bytheir past reference prices. Although we do not modelfairness directly, the external and internal asymmetricreference price effects in tandem with the latent truststate capture similar effects. To the best of our knowl-edge, this is the first paper to empirically demon-strate the dual-entitlement principle and to measureits extent in a B2B transaction setting.

In summary, this analysis demonstrates that theseller should pass on most of the cost increases, espe-cially to buyers who are in the vigilant state and arepaying close attention to external reference prices. Theseller should also make the external reference pricemore salient to buyers (particularly those in the vig-ilant state) during inflationary periods. In contrast,cost decreases present a good opportunity for theseller to enjoy a period of heightened profitabilityby keeping prices at the same level, at least in theshort run.

7. General DiscussionUnderstanding and managing the impact of pricingon buyer behavior and on evolving business relation-ships is critical for the long-run profitability of B2Bsellers. In this paper, we present an integrative empir-ical framework for modeling different buyer decisionsvia a common latent and dynamic state of trust andcapture the long-term effect of pricing decisions via aBayesian nonhomogeneous HMM.

We generate several substantive insights in theunderresearched area of B2B pricing. First, we empir-ically uncover two relationship states (vigilant andrelaxed) and show how pricing decisions can affectthe transition between these two states over time.Specifically, we find that appropriate pricing deci-sions can increase trust and relationship quality (inthe form of the relaxed state). Such a state can, in turn,act as a “relationship shelter” by encouraging a sim-plified buying process and can mitigate the adverseeffects of external volatility. Second, we not onlyfind significant asymmetric reference price effects, i.e.,price “losses” loom larger than “gains,” but that ittakes much longer for buyers to adapt to losses—a result that is in sync with the theoretical research

on B2B relationships life cycles and with the psycho-logical research on adaptation. Third, we find thatstrong relationships facilitate a simplified buying pro-cess and act as a shelter against adverse economicenvironments.

We conduct a series of price policy simulationsand demonstrate that the proposed dynamic targetedprice policy can offer a 52% improvement in long-term profitability over the seller’s current pricing pol-icy. Furthermore, we show that the profitability ofbuyers in the relaxed state is almost twice as high asthose in the vigilant state. The proposed policy bal-ances two forces: (1) lowering prices to win businessand to keep buyers in the relaxed state and (2) increas-ing prices to maximize margins and to avoid loweringof internal reference prices.

Our simulation results regarding the optimal pric-ing policy under volatile commodity prices indicatethat the seller should pass on a part of the increasedcosts to buyers, but it should hoard most of the bene-fit when costs decrease. This active management canhelp the seller maintain existing levels of profitabilityduring inflationary periods and enjoy increased prof-itability during deflationary periods.

More generally, this research offers B2B sellers acomprehensive decision framework to manage theirbuyer base using dynamic price targeting. As manyB2B sellers routinely apply cost-based pricing strate-gies (Anderson et al. 1993), we demonstrate that thereis substantial value in leveraging B2B relationshipsto implement valued-based, first-degree intertempo-ral price discrimination. However, it is important tonote that not all buyers are relationship oriented—some customers will evaluate each deal as a uniquetransaction. The seller needs to realize this hetero-geneity so that it does not overinvest (via its pric-ing actions) in buyers who may have little chance ofmigrating to a higher relationship quality state.

We now highlight some limitations of our workand propose directions for future research. First, weassume that buyers are not forward looking withrespect to the seller’s pricing decisions. One couldextend our framework to incorporate buyers’ expec-tations about future price changes (e.g., Lewis 2005)in applications where such expectations are likelyto be important. Second, as is typical in B2B con-texts, our data set (and the data available to thecompany management) does not include competi-tive information. Although quote requests and unful-filled quotes provide indirect evidence for competi-tion, future researchers can extend our framework tosettings in which competitive pricing data are avail-able. This would potentially uncover richer refer-ence price formation and relationship developmentprocesses.

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Third, given our focus on targeting and dynamics,we use data on buyers with at least seven purchaseevents. These were the vast majority (92% of all buy-ers) in our context. Therefore, our conclusions andresults are most suited to these more frequent buyers.

Fourth, we focus on profit maximization for eachbuyer. Other objective functions that treat certain buy-ers to be of strategic importance (e.g., for consistentcash flow or because of the possible impact on otherbuyers) or objective functions that focus on require-ments such as revenue maximization can be explored.Fifth, we focus on the impact of the pricing decisionon the seller’s profitability. Future research can inves-tigate whether price-induced relationship dynamicsdiffer from those that are triggered by other market-ing actions (Kumar et al. 2011).

B2B and B2C business frameworks are not orthogo-nal to each other—rather, we think of these markets asa continuum with substantial overlap. Although ourpricing framework focuses on B2B relationships, it isalso appropriate for those B2C settings in which thecustomer buying process is composed of several inter-related decisions, where the firm has the opportunityto price discriminate to varying degrees and wherelong-term relationships play a big role.

Finally, in this paper we take an initial step towardstudying the underexplored terrain of B2B pricingusing a specific empirical application within the metalindustry. We encourage future researchers to applyour framework to other B2B environments (e.g., thosewith more involved negotiations or with power asym-metry in the supply chain) to investigate the general-izability of our findings.

Supplemental MaterialSupplemental material to this paper is available at http://dx.doi.org/10.1287/mksc.2013.0842.

AcknowledgmentsThe authors are grateful to the aluminum-trading com-pany who provided the invaluable data and the manage-rial insights to our inquiries. The authors also thank theeditor, the associate editor, the two anonymous reviewers,as well as the participants of seminars and conferences inwhich this work has been presented, for their constructivecomments.

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