Sequential Xsell

8/2/2019 Sequential Xsell

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Cross-Selling Sequentially Ordered Products: An Application to

Consumer Banking Services

Shibo Li, Baohong Sun and Ronald T. Wilcox

Shibo Li is an Assistant Professor of Marketing at Rutgers University. Baohong Sun is an Assistant Professor ofMarketing at Kenan-Flagler Business School of University of North Carolina at Chapel Hill. Ronald T. Wilcox is anAssociate Professor of Business Administration at the Darden Graduate School of Business Administration,University of Virginia. The authors would like to thank Peter Boatwright, Ron Goettler, Frenkel ter Hofstede, AjayKalra, Puneet Manchanda, Charlotte Mason, Alan Montgomery, and Kannan Srinivasan for valuable comments.


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Cross-Selling Sequentially Ordered Products: An Application toConsumer Banking Services

Abstract

In service and consumer technology product industries, we often observe people sequentiallypurchasing multiple products and services from the same provider. These sequential purchases can takeplace over an extended period of time and can often be naturally ordered in terms of complexity andfunctionality, with the purchase of some products or services generally preceding that of others. Thiscommonly observed situation offers significant opportunities for companies carrying multiple productsand services to cross-sell other products and services to their existing customer base.

In this paper, we adopt a multivariate probit model, implemented in a Hierarchical Bayesframework, to investigate how customer demands for multiple products evolve over time and itsimplications on sequential acquisition patterns for naturally ordered products. This paper is the first paper

that formally models customers sequential demands and investigates the behavioral reasons drivingconsumers acquisition patterns for multiple products and services. We also study how the sequentialdemands for naturally ordered products develop differently across customers. This model helps managerspredict which product or service a consumer is likely to buy and in what sequence.

We investigate customer purchase patterns for products marketed by a large Midwestern bank. Inthis process we highlight interesting substantive findings and provide guidance to managers charged withallocating marketing dollars towards customers with the greatest incremental profit potential.

Keywords: Sequentially ordered products; Demand maturity; Cross-selling; Bank and financial products;

CRM; Multivariate probit model; Hierarchical Bayes framework


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1. Introduction

We often observe consumers purchasing multiple products and services from the same provider

over time.1 These products often can be naturally ordered in terms of complexity and

functionality leading to the empirical regularity that the purchase of certain products generally

precedes the purchase of others. For example, we often observe that a person generally

establishes a checking account with a given bank before establishing a brokerage account. A

woman may repeatedly patronize a salon or spa for a haircut only before moving on to

purchasing facial treatments. A consumer may also sequentially purchase local and long distance

telephone service, cable television service, and Internet access from the same company. A person

who purchases a personal digital assistant may acquire Internet access, additional memory, and

software from the same provider in the future. The common thread running through each of these

examples is that consumers are more likely to purchase some products or subset of products

before others. The authors have directly observed this phenomenon in the market for consumer

banking services, but strongly suspect that it is prevalent in many other environments as well.

We term the over-time development of consumers complementary demand for multiple

products and services as natural ordering among these products and services.

Markets especially prone to this empirical regularity include those in which consumer

wants evolve after some preliminary consumption, those in which consumers face some

uncertainty about the quality of the product or service offering or markets in which some

consumer learning is required to receive the full benefit of the product. In such markets,

sequentially purchasing multiple products or services from the same provider can enhance the

relationship with the provider, raise switching costs associated with moving to a new provider,

lower uncertainty with respect to additional product purchases, and, in some cases, ensure proper

technical compatibility with products the consumer already owns (Kamakura, Ramaswami and

Srivastava 1991; Kamakura, Wedel, Rosa and Mazzon 2002).

The existence of sequentially developed demand for naturally ordered products offers

great opportunities for companies carrying multiple products and services to cross-sell other

products and services to their existing customer base. These companies are eager to explore

additional profitable opportunities with their current customer base by cross-selling because it is

1 Throughout this paper we will refer to products and services interchangeably. The model we develop is equallyapplicable to both.


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often cheaper to cross-sell to their existing customers than to attract new ones. Further, customer

retention is enhanced with the cross-selling as customer switching cost increases with more

complex relationships (Kamakura, Ramaswami and Srivastava 1991). Indeed, many companies

have come to realize that their current customers are by far the best prospects for new or existing

products and services.

There have been a few descriptive studies over the past four decades that probe

consumers sequential purchases (e.g. Hauser and Urban 1986; Mayo and Qualls, 1987;

Boulding, Karla, Staelin andZeithaml 1993; Bitner and Zeithaml 2000). This research focuses

on describing the existence of sequential acquisition patterns. To our knowledge, the earliest

paper that formally models cross-selling opportunities is Kamakura, Ramaswami and Srivastava

(1991). This research applies latent trait analysis to position financial services and investors

along a common continuum. Using this approach, they obtain the estimates of the purchase

ordering of financial services as well as the latent financial maturity for each household based on

(only) the current ownership of financial services. Recently, Kamakura and Kossar (2001)

develop a split hazard rate model and focus on predicting each customers (physicians) time of

adopting a new product (drug) based on the timing of their past adoptions of multiple products.

Knott, Hayes and Neslin (2002) present four next-product-to-purchase models (discriminant

analysis, multinomial logit, logistic regression, and neural net) that can be used to predict what is

likely to be purchased next and when. Kamakura, Wedel, de Rosa and Mazzon (2002) develop a

mixed-data factor analyzer that is an extension of factor analysis to incorporate various types of

data (choice, counts, or ratings) and is tailored to identify the best prospects for each product

based on customer transaction data. They are not primarily interested in a behavioral

interpretation of the latent dimensions, but rather in a convenient low-dimensional graphical

display of the structure in the data. Edwards and Allenby (2002) propose a general approach to

handling identifying restrictions for the multivariate binomial probit model and develop an

algorithm that is efficient especially for a large number of response options. One of their three

applications is to survey data on ownership of financial products.2 Applicable to cross-sectional

data, the above papers are aimed at inferring cross-selling opportunities from comparison of one-

time measurements of ownership of other products across customers. The resulting next product

2 The proposed multivariate binomial model can be extended to incorporate time series and reflect a sequential set ofoutcomes.


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to sell is usually consistent with the ranking of their market shares. This approach ignores the

over-time development of individual-level demands in favor of a cross-sectional approach. We

believe that to better understand the acquisition sequence of multiple products it is important to

formally model how customer demands for multiple products evolve over time. This approach

will allow us to predict acquisition sequence that is consistent with the development of consumer

demand maturity.

In this paper, we explicitly model the development of customer demand for multiple

products over time and derive a product acquisition sequence based on consumers individual

level of demand maturity. Using a multivariate probit framework applied to panel data, the

model is implemented in a Hierarchical Bayesian framework. In contrast to previous work in the

area, we seek the behavioral reasons that underpin and drive these purchase patterns. Our

empirical application will demonstrate the value of this approach.

2. An Individual-level Model of Sequential Service Acquisition

Consumers have demands for multiple products at any point in time. Economic theory has shown

that in the presence of finite resources, there is a priority structure among the demand

objectives and that this priority structure can be transformed into a priority structure for products

(Kamakura et. al. 1991). Our modeling approach positions multiple products and consumers

demand for those products along a common continuum in a way that reflects the development of

consumer demand maturity. The closer any individual consumers demand maturity is to the

position of a given product, the more likely this product is to satisfy the current need of the

consumer and the more likely he/she is to purchase the product. This follows the theoretical

foundation laid out by Kamakura et. al. (1991) which positions financial services and investors

financial maturity along the same continuum according to their ownership pattern.3 To formulate

this idea in a random utility framework suitable for our panel-data approach, we adopt the ideal

point model developed by Lehmann (1971) in which choice probability is postulated to be

inversely related to the distance of an object (ratings of the actual brands being analyzed) from

the ideal point (a consumers rating of an ideal brand).4 Formally, we assume that household i =

3 In Kamakura, Ramaswami and Srivastava (1991), a latent trait model is used to position products and consumersalong a common continuum in a way that reflects the ownership of the different services by each consumer. Theyallow the probability that a consumer owns a particular financial service to be a function of the consumers positionin this continuum relative to that particular product. See this paper for more detailed discussion.4 See Lehmann (1971) for detailed discussion.


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1, ,Imakes binary purchase decisions (buy or not buy) on each of the productsj=1, , Jin the

product set J, at each time period t. We specify the latent utility of a given household choosing

productj = 1, 2, , Jat occasion tas:

ijtijtijitjiijt XDMOU ++= '|| 1 (1)

and the periodically realizedJpurchase decision variablesyijtare determined by

yijt= 1 ifUijt>0

0 otherwise. (2)

forall i=1, , I, j=1, , Jand t=1, , Ti. Oj forj=1, J is the positions of product j ranked

along the same continuum as demand maturity DMit-1. These are parameters to be estimated.

DMit-1 denotes the demand maturity of consumeri at the end of time t-1. The term || 1 itj DMO

represents the distance between demand maturity and product j. Thus, the probability of

purchasingj depends on the distance between Oj and DMit-1. i measures how the development

of consumer demand maturity, relative to productj, affects the demand for productj.

The variable DMit-1 is latent. However, demand maturity at time t-1 can be reasonably

proxied by some observed ownership or purchase information of each of the possibleJproducts.

These variables measure the demand currently satisfied for consumer i up to time t-1. For

example, the total number of purchases made in this product class, the total amount of money

spent or invested in these accounts, and the time elapsed since first owning each of the products.

The greater the number of purchases, the greater the amount of money placed in these accounts,

and the longer these accounts have been held the more likely it is that the individuals demand

maturity has reached or surpassed that point in the maturity continuum. This assumption

recognizes the marketplace reality that if a person has not had activity in a given set of accounts

for an extended time period he/she may have built up needs that have not been satisfied simply

because of myopia. On the other hand, if a customer has recently spent the fixed time costs

associated with changing their financial situation it is much more likely that their current account

holdings reflect their current state of demand maturity.

We assume the satisfied demand of product j is a linear function of these variables,

1

'ijtZ , where 1ijtZ is a vector ofL variables. Note that purchase activities of different products

contribute differently to the development of demand maturity. For example, a customer who


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invests $5000 to a brokerage account is more likely to move further along the financial maturity

continuum than a customer who put $5000 to a checking account. In order to take into account

the fact that purchases of different products contribute differently to the development of demand

maturity, we weigh the contribution of the purchase of each product by its corresponding order

(or importance) Oj when constructing demand maturity.5 Formally,

)]([ 1'

1

11 =

= ijtJ

j

ijtjit ZDODM (3)

where Dijt-1is dummy variable indicating whether productj is owned by customeri at time t-1

The vectorXijt (K1) is a vector of product and consumer-specific covariates that affect

customers sequential decisions to purchase multiple products from the same company. It

includes variables designed to measure a customers relationship with the company. ij is a Kx1vector of coefficients forXijt. We allow the unobserved part of the utilities to be correlated.

],0[~ MVNit (4)

The correlations capture the co-incidence among different products as termed in Manchanda

et. al. (1999). It takes into account the contemporaneous purchases of different products at the

same time.

It is important to note here that the application of this model does not require the

managers a priori ordering of the products or services. The estimated coefficient pattern of Oj

will recover the natural ordering inherent in the data. Our model is flexible enough to handle a

situation where no managers initial beliefs about the ordering are available. In that case natural

ordering is inferred directly from the estimated parameters. Of course, if managers have strong

initial beliefs, which certainly may be true in some industries, these beliefs can be incorporated

into the prior distributions of the parameters and as such increase the efficiency of this modeling

approach. In our application, while we do have some initial beliefs, we will use noninformative

priors.

5 Note Equation (3) can also be written as )]([ 1'

1

121 =

+= ijtJ

j

ijtjitit ZDODMDM , where

1 ijtZ represents the change of variables represented by Z during the past period and

= =

1

1

1

t

ijijt ZZ

. This

equation shows that demand maturity evolves over time and is updated by the change inZof all the owned productsduring the past period.


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To mitigate the well-known problems associated with not controlling for consumer-level

heterogeneity (Heckman 1981; Kamakura and Russell 1989; Krishna, Currim, and Shoemaker

1991; Gnl and Srinivasan 1996; Allenby and Rossi 1999) we specify i =(i1, i2, , iJ)and

ki=(ki1, ki2, kiJ) as linear functions of household specific variables.

ki

'

,

'

+=

+=

ikki

iii

W

eW(5)

fork = 1, , K. Wi is a m1 matrix containing m-1 household specific variables. and k are

mJmatrices with each element measuring the effect ofWivariable on i and ki respectively.

We assume eiN[0, 2] andkiMVN[0, ].

To solve the identification problem, we normalize one of Oj to be 1.6 We divide the

utility by its corresponding standard deviation and thus transform

to a correlation matrix. Weuse a hierarchical Bayesian approach to estimate the model. Readers interested in the details of

the estimation procedure are referred to Gelfand and Smith (1990), Allenby and Rossi (1999),

and Manchanda, Ansari and Gupta (1999).7

3. Customers Sequential Acquisition of Banking Services

3.1 Data Description

[Insert Table 1a About Here]

We use this model and household-level data collected from a large Midwestern bank to

explore consumers acquisition of financial services. Specifically, we have holding and

transaction information for 8 products of 1201 randomly selected households whose use this

bank as primary bank from July 1997 to June 1998.8 This data includes monthly observations on

which accounts/products the customer had purchased or held as an investment. We also had

access to demographic information for each of these customers. Finally, the bank provided us

6 For identification purpose, one ofOs needs to be normalized to a non-zero value. We haveJequations to identifyJ

Os. The normalized value affects the scales of without affecting the estimated sequential order.7 We have conducted an intensive simulation to study the identification and statistical properties of this model. Wehave also compared the scale of the estimated product ranking coefficients with the estimated demand maturity

based on both simulated data and our data. The two variables are measured at similar scales and the distancesbetween product positions and demand maturity explain purchases very well. Interested readers can contact theauthors for details on the simulation, prior distributions and the estimation of the model.8 The bank gave us access to holding and transaction information for 20 financial products it offered for 1201households. However, there are 11 products without any purchase or very little purchase information in this shortobservation window. There is also 1 product with only 16 purchase observations. In order to avoid the problem ofdata scarcity, we only focus on products with more than 29 purchases in the observation period.


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with the results of a customer satisfaction survey completed by each of the customers in the

sample just before July 1997. Because our data was at the household level, we also observed

repeat purchases. Because we cannot determine whether these repeat purchases represent true

repeats by the same individual or new purchases by someone else in the household, our analysis

is at household level. A brief description of the variables used in this paper is shown in Table 1a.

[Insert Table 1b About Here]

In Table 1b, we report a conditional table which shows how many purchases of product j

being made during the observation window given previous purchases of all the other products.

We also report the total number of current ownerships and new purchases of each of the 8

products. For example, we observe that owning saving, the customer usually go for CD or

another saving account.

3.2 The Specifics of Consumer Banking Service Acquisition Model

We write the utility function of any household i for banking servicej at time tas:

ijtitijiijiij

itjiijt

SWITOVERSATCOMPET

DMOU

+++

+=

321

1 ||(6)

forj=1,..8. We define COMPETi as a dummy variable equal to one when household i has opened

an account in category j with another bank in the past six months. It controls for competition,

which directly affects the possibility of cross-buying more services from the same company. Wedefine OVERSATi as the overall satisfaction score of household i, as measured by the banks

customer satisfaction survey. This represents the banks efforts in improving service quality and

the relationship with its existing customers. Prior research has concluded that is an effective

marketing strategy for service industry (Boulding et. al. 1993).

We also included household-level switching costs (SWITit) in our analysis. It is defined as

one if the account owners profession is white collar, and the household has at least one non-

adult child, and the household owns more than the average number of accounts with this bank.

The logic of this inclusion follows closely the reasoning of Blattberg, Buesing, Peacock, and Sen

(1978), and more primitively the work of Becker (1965). In short, we believe that households

that have a high cost of time, as evidenced by increasing levels of education or the presence of

children, will tend to spend less time shopping around for banking services. Further, individuals


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that have a relatively complex relationship with the bank (have a large number of accounts there)

will also suffer greater inconvenience if they choose to switch banking service providers. While

switching grocery stores is relatively easy, switching service providers can often entail a

significantly higher degree of discomfort. The reasons for this greater inconvenience are

reasonably self-evident, but include such unpleasantness as filling out all of the paperwork

necessary for opening up a series of accounts at a new bank. Therefore, our measure of switching

cost takes into account both intrinsic time costs as well as extrinsic costs associated with the

customers current level of relationship with the bank.

We define the financial maturity as a function of cumulative ownership, monthly balance,

and holding time of all available accounts weighted by corresponding importance of each

product. That is,

)]([ 1312111

11 =

++= ijtijtijtJ

j

ijtjit HoldingBALACCTNBRDODM

Since the data is collected at household level, multiple purchases of the same account can be

opened under the names of different household members. The term ACCTNBRijt-1 captures the

cumulative number of purchases of productj for household i in the past month. Previous research

has shown the importance of using ownership as a predictor variable (see Knott, Hayes and

Neslin 2002). In addition, we also include the monthly balance (BALijt-1) and time elapsed since

first opening this type of account (Holdingijt-1) as additional explanatory variables to better takeinto account the fulfillment of demand for each product. In order to obtain more easily

interpretable estimates ofOj, we rescale all three variablesto have zero mean and unit variance.

These three variables indicate the purchase experience or satisfied needs for product j and can be

interpreted as the realization of consumer demand forj at the beginning of time t. Cumulative or

satisfied demands for all of the products is then weighted by product order to construct the latent

variable, the financial maturity of household i at time t.

We write the utility coefficients as linear functions of basic demographic information.

This allows for household characteristics to influence the weight certain factors will play in the

utility function. Formally, we specify coefficient heterogeneity as:


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+++++=

+++++=

kiikikikikkki

iiiiii

INCOMEAGEGENDEREDUCAT

eINCOMEAGEGENDEREDUCAT

43210

43210 (8)

fork=1, 2 and 3. The coefficients 1 , 2 and 3 capture how different customers have different

information costs associated with adopting product j. 4 reveals the resource constraint. For

example, we believe that better educated and male household heads believe themselves to be

more knowledgeable and better informed about the financial products. They are also more

confident in managing their investments (See Barber and Odean 2001). Thus, we conjecture that

the adoption speed or movement along the financial maturity continuum may be faster for

households that are better educated and with a male head. Higher income individuals may move

along the continuum more quickly because they are more motivated to pay attention to and find

solutions for their financial needs. Similarly, different households may also respond differently

to competition, satisfaction and switching cost.

In the interest of comparing our model to other plausible specifications, we estimate four

competing models and our own. The first is a nave first order Markov model using the sample

conditional purchase probabilities (see Table 1b). Assuming independence among products, it

predicts purchases in the next period based on current ownership. The second model also

assumes the product choices are independent. This model specification is comprised of product

specific binary probit models, one for each category. This particular model specification ignores

potential unobserved correlation across categories, the allocation of assets, switching costs and

heterogeneity. We include this model because this specification is commonly adopted by the

industry to predict probabilities of cross-selling. This model is also similar to Kamakura,

Ramaswami, and Srivastava (1991) and Knott, Hayes, and Neslin (2002) in the sense that they

assume consumers make independent decisions about the purchase of different products. The

third model is a multivariate probit model that is similar to Manchanda, Ansari, and Gupta

(1999). It captures the contemporaneous (non-over-time) complementary relationship among

products on the same purchase occasion. The fourth model adds to the third model thedifferences in intrinsic preferences. Although not directly comparable, this model can be likened

to Edwards and Allenby (2002) in the sense that the predicted purchase order is derived from the

order of intrinsic preferences. The final model is our proposed model. It adds demand maturity to

the fourth model and thereby allows us to take into account customers previously satisfied


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financial needs. The Independent model was estimated using the Probit procedure in SAS. The

remaining four models were estimated using an MCMC (Gibbs Sampler) approach. We use the

Bayes factor criterion for model comparison.

[Insert Table 2 about here]

We report the Deviance Information Criterion (DIC) which penalizes a complex model for

additional parameters (Spiegelhalter, Best, Carlin, and Linde 2002). A lower DIC indicates

better fit. As shown in Table 2, we find that all models that allow products to be correlated rather

than independently acquired (Model 3, 4, and 5) fit better than those that do not (Model 1 and 2).

Model 5 fits better than Model 3 and 4 indicating that taking into account contemporaneous

complementary demand and/or using brand constants is not adequate in capturing sequential

order in our application. The sequential order of financial products is different from market

share. Our proposed model (Model 5) fits the data better than any of the competing models and

demonstrates that taking into account the development of customer financial demand is

important in determining service adoption.

3.3The Substantive Results of our Consumer Banking Application

[Insert Table 3a About Here]

Now we want to turn our attention to our application itself and the substantive results that

arise from it. We first look at the ordering among products by examining the ranking of Oj

reported in Table 3a. The ranking of the parameters indicate a product sequence of checking-

>saving->debit-card->credit-card->installment loan->CD->money market (MM)->brokerage.

This is consistent with our intuition that customers usually invest more aggressively into

financial instruments promising stable returns (e.g. CD, MM) after they obtain basic financial

services (e.g. checking, saving, debit, credit, loan) and into high risk and high return brokerage

accounts only after they have invested in other very low risk products. The implied order of the

eight financial products is consistent with Kamakura, Ramaswami and Srivastavas (1991) idea

of the development of financial maturity from convenience products to stable income products

and then to risky income products. The ordering that was recovered by our model is exactly what


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we a priori expected. It is also consistent with our conversations with bank managers as well as

the hierarchy suggested by Kamakura, Ramaswami, and Srivastava (1991).

The slope parameter indicates how the distance between the financial maturity and the

corresponding product affects the probability of purchase as the customers latent financial

maturity changes. The sign of the coefficient is negative indicating that the closer the distance to

the product, the more likely the product is to be purchased. This is consistent with the

interpretation of distance model by Lehmann (1971). 1, 2 and 3 are all positive and

significant indicating that the cumulative number of account purchases, cumulative balance and

holding time increase financial maturity.

Now referring to the other parameter estimates presented in Table 3a, notice that all

estimated coefficients are significant in the classical sense. Owning any account with another

financial institution takes away business from the bank. This effect is more powerful for higher-

end products than for lower-end products. This is probably due to the fact that the marketplace

for brokerage and other advanced financial services has grown increasingly competitive in recent

years. Whereas it is possible to purchase products from full services brokerage houses like

Schwab and Fidelity that mimic some aspects of a checking account, it is even easier to purchase

products that substitute, or dominate, the more advanced financial service offerings of a

consumer bank.

Overall satisfaction with the bank increases the banks ability to cross-sell its products toexisting customers, and this service quality has a higher impact on the future demand for

advanced financial services than for lower end products. This result is intuitive in that advanced

financial services, brokerage for example, require much more interaction with the bank than say

a CD account which requires almost no human interaction.

Switching costs, which indicate the customers relationship built over the year as well as

the time value of the households, plays an important role in providing the company with

opportunities to cross-sell their other products. These Becker-type effects are generally important

in markets where changing product or service providers is particularly costly in terms of the time

needed to complete the change. Switching costs play a powerful role in influencing households

in all eight product categories. If time costs are high, customers are unlikely to switch banks even

in the face of some amount of dissatisfaction. Following the logic above, we would expect this

effect to be more potent for convenience and advanced services than for cash reserves and indeed


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it is. This result does raise some interesting questions about which customers are most important

for the bank to satisfy. While conventional wisdom would certainly dictate placing a great deal

of emphasis on satisfying the banks wealthier customers our results indicate that some

customers may be trapped by the bank owing to the substantial implicit costs a given customer

might face in switching from one bank to another.

[Insert Table 3b About Here]

Table 3b provides the estimated correlations among the unobserved components of the

utilities. This is the Co-incidence correlation termed in Manchanda, Ansari, and Gupta (1999).

A positive correlation between two products indicate that there are complementary demands for

these two products at each purchase occasion. For example, a household may open checking and

ask for a debit card together simply because they are bundled by the bank. Similarly, if a bank

can sell a customer a saving account, it is more likely to also sell the customer a brokerage

service. Note that these correlations capture the current inter-product relationship. This is

different from the sequential demand for naturally ordered products driven by financial maturity

and knowledge.

[Insert Table 4 About Here]

We now turn our attention to the consumer heterogeneity expressions and examine how

demographic variables like education, gender of the head of the household, age and income

affect the acquisition pattern of sequentially ordered products. Table 4 reports the effects of these

variables on utility weight heterogeneity. Most of the estimates are significant. These estimates

describe how knowledge, risk bearing, life stage and financial resources characterize the speed of

adoption for financial products. The negative coefficients of education and gender in the

heterogeneity equation fori indicate that, for the same amount of financial maturity (the same

distance between financial maturity and the position of checking), greater education or male

household heads are more likely to move faster along the financial continuum than other

customers. These results show that households with greater education or male-headed

households are more aggressive in pursuing products that are more advanced in the sequential

ranking. These results are consistent with the research findings of Barber and Odean (2001) who

find that men are more confident about their ability of managing risky assets. Similarly, we

found that older customers and higher income customers are also more likely to move faster

along the continuum. This is because they have more resources to purchase multiple products.


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The coefficients of education in the heterogeneity equation for the coefficient of competition

directly suggests that those households are less likely to be cross-sold once they open accounts with the

banks competitors. It appears that highly educated households are, or believe themselves to be,

more knowledgeable and confident about financial products and hence are more likely to take

advantage of these outside opportunities. Interestingly, more highly educated customers seem to

care more about customer service and switching costs as determinants of future purchases. They

are in general more sophisticated customers who are also busier than average customers. Owning

accounts from other institutes does not deter households with male household head from opening

other accounts with this bank except debit card and saving. Male household heads seem to care

less than their female counterparts about both satisfaction and switching cost in determining

future purchases. This result may be at least partially explained by the impact of education and

gender on a customers organizational ability, an ability which would certainly impact theirsensitivity to service quality and propensity to switch, or patronize multiple, financial

institutions. In a completely different application, Narasimhan (1986) showed that the education

of the female head-of-household was critical in determining sufficient organizational skills to

effectively use coupons in grocery settings. While the applications are quite different, we suspect

that the logic that governs behavior may well be the same.

Owning accounts in other financial institutions is more likely to deter older customers

from cross-buying other products from the same bank than average customers due to the fact that

older customers have more time to spend to finding the best financial service provider. These

same customers are much more sensitive to satisfaction and less sensitive to switching cost. This

is a potentially important finding as older customers also have the potential to be some of the

banks best customers. Taken together, these results strongly suggest that making attempts to

satisfy older customers should be important to the bank.

Following the same reasoning and also arising from our estimated model, higher income

customers have less time to spend searching for the best product, service, or the lowest price.

They are more likely to be cross-sold other convenience products once they become customers of

the bank. They are less sensitive to satisfaction and more sensitive to switching costs on these

products. These are customers who are somewhat trapped and seek convenience to save time.

However, for non-convenience products like CDs, money market accounts and brokerage

accounts, these customers are the opposite, they are more sensitive to competition and


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satisfaction. We believe that this is because higher income customers are more sensitive to the

return on investment and to the availability of specific investment choices. They are also more

likely to have better knowledge of the options provided by competing banks.

3.4 Predicting Cross-Selling Opportunities

Because part of the focus of this application is to predict the probability of acquiring new

products in order to help bank managers more efficiently allocate their targeting efforts, we now

compare the predictive ability of our proposed model with the other benchmark models. To

accomplish this we divided our original sample of 1201 households into an estimation sample

and a holdout sample. The estimation sample has three quarters of the households, and the

holdout sample has the remaining quarter.

[Insert Figure 1a and Figure 1b about here]

Figure 1a and Figure 1b depict the mean absolute error between the purchase probability

and the actual purchase realization for each of the five models using the estimation sample and

holdout sample, respectively. The worst predictive accuracy arises from the Independent Model

(Model 2). Including co-incidence to allow for co-purchase of multiple products and

heterogeneity (Model 3) increases the predictive accuracy. Thus, the approach suggested by

Manchanda, Ansari, and Gupta (1999), although developed in studying complementary demands

(shopping basket) for frequently purchased products, does indeed capture unobserved factors that

cause multiple purchases at the same purchase occasion in this setting. Comparing Model 4 with

Model 5, we find that a multivariate probit model with sequential ordering effects provides a

much more accurate description of households future purchase decisions. The predictive

accuracy of our proposed model is fairly remarkable. For example, the mean absolute error rate

of convenience services is less than 0.5 percent. While we do not claim that all applications will

achieve such a high degree of accuracy, we believe that the evidence does weigh in favor of

including order effects in attempts to formally model choice in this type of environment.

[Insert Figure 2 Here]

Given the CRM nature of our application, a gains chart is a common approach in

evaluating predictive performance when there are low response rates. Figure 2 includes gains

charts for each of the tested models. The gains chart approach to model evaluation and

comparison begins by selecting the 10 percent of the customers from our holdout sample who,


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17

according to prediction from the model, are most likely to make a purchase. This is done for each

model. Next we compute the number of accurately predicted responses, relative to the total

number of responses in the entire sample; this percentage is the gain due to using the model and

represents the value of sorting the data via the predictions from the models. The No Model line

depicts a situation in which customers are grouped randomly. So, if we have a randomly drawn

group that constitutes 10% of the sample it will on average contain 10% of the overall number of

purchases etc. Analogous values are computed for each percentile of the holdout sample (top

20%, top 30% etc.). The greater the difference between the gains curve and the baseline model,

the better the model. The results of this analysis systematically support the conclusion that the

predictive accuracy of our proposed model is superior to that of the baseline case and each of the

competing models examined. The results are robust at each percentile.

[Insert Table 5 About Here]

Although our main objective is to derive the natural product order to guide the sequence

of cross-selling, our method also allows us to estimate the predicted purchase probability for

product-next-to-buy for each household. For demonstration purposes, we report the cross-selling

probabilities for the first two periods of five randomly selected households (Table 5). We can see

that the cross-selling probability predictions yielded from our proposed model are quite

consistent with the actual purchase data. These provide managers with information on whom and

when to target in order to cross-sell which products at time t. Note that the purchase predictions

on and beyond t+2 depend on prediction of ownership information on and beyond t+1. This

implies that our model will be more accurate in predicting next-to-purchase rather than purchase

incidence more distant in the purchase sequence.

In summary, the most important things we have learned from our application are:

The sequential purchase of multiple products are driven by a households evolving

financial maturity.

Households with higher education or male household heads move more quickly along the

financial maturity continuum than those with lower education or female household heads.

Households that are older and with higher income also move along this continuum more

quickly.

The switching costs created by owning multiple products creates opportunities to cross-

sell other products to the same customer.


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18

Customer satisfaction or service quality is a significant influencer of a customers future

purchase decisions, especially for more advanced financial products (e.g. brokerage).

This effect is particularly strong for older customers.

A multivariate probit model with heterogeneity, switching cost and sequential ordering

effects provides the most accurate description and prediction of households future

purchase decisions.

4. Discussion, Limitations, and Directions for Future Research

This research explicitly models the development of customer demands for multiple

products over time and derives a product purchase sequence under the assumption that different

products are designed to meet the requirements of customers at different stages of their demand

maturity. Being the first cross-selling model applicable to panel data, this paper provides a

behavioral explanation for the over-time development of consumer demand and for purchasing

multiple products from the same provider. Our research also shows that sequential demands for

naturally ordered products develop differently across different customers and points to some of

the antecedents of these differences. It provides guidance to managers charged with allocating

marketing dollars towards customers with the greatest incremental profit potential.

Our model directly suggests that it is important for a company to collect information to

determine their customers stages of demand maturity before spending money to customers whomay not be ready to adopt a new product or service. In addition, it appears that in this particular

market it is more effective to target customers with higher education, males and those with

higher incomes as these customers move faster along the demand maturity continuum and are

faster in adopting new products. Though not the most important factor, increasing the depth of

the customer relationship significantly enhances the cross-selling opportunities, especially for

customers who need some financial advice (e.g. older customers).

Our banking application uncovered several interesting behavioral findings that may be

instructive of consumers service adoption more generally. We say may here because the

study was limited in several ways. First, we do not have detailed information on competition. In

the future, it would be interesting to consider the ownership information with competitors when

calculating demand maturity. This would allow us to derive a more accurate ordering of the

products. Second, while we were able to obtain relatively detailed information on customer-level


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19

account activity, we did not have access to data detailing the marketing activity that each

individual in our sample was exposed to over this time period. If such information were

available, we could more formally explore the impact of marketing variables (e.g. price,

advertising) on cross-selling tactics and opportunities. This would be a valuable contribution to

our knowledge of these markets. Third, our data only covered a time span of one year. In an

environment such as banking in which a customer relationship may last for many years, but new

service acquisitions are relatively infrequent, one year may not be sufficient to capture the

richness of the phenomenon. We expect that data that covers a longer time span would yield

even greater differences between our modeling approach and those that do not account for

temporal ordering. Finally, a product or service provider is not only interested in whether or not

she is likely to sell an additional service to an existing customer but also in the amount of profit

such a sale is likely to generate. We did not have access to data that would allow such analysis.

Future research should more explicitly model the flow of funds, type of usage and cost to

examine the impact of cross-selling on profit.

The market for services is a huge and growing segment of the U.S. economy. Even the

more narrowly defined market for financial services is a truly enormous segment of the

economy. We have seen the benefits of predictive modeling in the arena of packaged goods. The

state of our knowledge in this market has grown dramatically over the past two decades.

Conversely, disproportionately little attention has been paid to the market for services. There is

no doubt that this neglect is at least partially explained by the relative difficulty of obtaining

quality and timely data from service providers. Data from service providers tends to be more

convoluted than data generated by scanner technology. Yet, in spite of these challenges, the

benefits of exploring this marketplace are truly remarkable. We believe our research is one step

in that direction.


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Table 1a. Operationalization of Variables

Variables Definitions

Mean

or Freq

COMPET 1 if the household opens some accounts in another bank during the last six months,0 otherwise

13.3%

OVERSAT Households overall satisfaction (1 to 7) 4.33SWIT 1 if the account owners profession is white collar and the household has at least on

non-adult child and the household owns more than average number of accounts withbank, 0 otherwise

6.6%

EDUCAT The household heads education measured on a 1-5 scale(1 = some high school , , 5 = post graduate

1.21

GENDER 1 if the account owner is a male, 0 otherwise 82.5%

AGE Account owners age 67.01INCOME Households income (1-7) where 1 -


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Table 2. Model ComparisonDIC Log-Marginal

Density

Model 1 20249.9 -10118.1Model 2 22466.0 -11226.4Model 3 20189.9 -10098.0Model 4 20096.7 -10046.4Model 5 18327.3 -9156.3


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Table 3a. Estimation Results of Proposed Model

Product / Covariate COMPET OVERSAT SWIT D. MATURITYRELATIVE TO

EACH

PRODUCT

ORDER (Oj)

Installment Loan -11.60(0.062)

2.55(0.002)

2.55(0.098)

-0.018(0.003)

0.71(0.030)

Debit Card -9.59(0.026)

2.01(0.003)

2.38(0.100)

-0.018(0.003)

0.57(0.028)

Checking -12.04(0.049)

2.77(0.003)

4.40(0.119)

-0.018(0.003)

-0.09(0.032)

Credit Card -8.92(0.065)

2.49(0.007)

1.39(0.095)

-0.018(0.003)

0.69(0.025)

Saving -11.21(0.079)

2.77(0.006)

2.71(0.176)

-0.018(0.003)

-0.03(0.002)

CD -8.40(0.068)

2.33(0.008)

1.80(0.079)

-0.018(0.003)

0.79(0.108)

Money Market -9.54(0.051)

3.10(0.004)

1.20(0.164)

-0.018(0.003)

0.84(0.030)

Brokerage -14.63(0.064)

3.44(0.005)

5.05(0.061)

-0.018(0.003)

1

Estimates ACCTNBR BAL DURATION

D.Maturity

0.135(0.025)

0.028(0.002)

0.057(0.011)

Table 3b. Unobserved Correlations Across Categories

Installment

Loan

Debit

Card

Checking Credit

Card

Saving CD Money

Market

Brokerage

InstallmentLoan

1 0.005(0.013)

0.045(0.012)

-0.219(0.022)

-0.024(0.011)

0.264(0.034)

-0.075(0.020)

-0.125(0.009)

Debit Card 1 0.199(0.025)

0.135(0.019)

0.194(0.018)

0.108(0.031)

0.098(0.013)

0.119(0.011)

Checking 1 0.170(0.018)

0.246(0.013)

0.097(0.031)

0.099(0.013)

0.092(0.012)

CreditCard

1 0.259(0.012)

-0.063(0.012)

0.176(0.027)

0.217(0.014)

Saving 1 0.100(0.014)

0.093(0.020)

0.088(0.014)

CD 1 0.114(0.021)

0.047(0.007)

MoneyMarket

1 0.343(0.015)

Brokerage 1


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23

Table 4. Estimation Results for Heterogeneity EquationsHeterogeneity Equation -

i : coefficient of DM

Intercept Education Gender Age Income

-0.05(0.014)

-0.03(0.007)

-0.09(0.018)

-0.06(0.001)

-0.01(0.003)

Heterogeneity Equation - i1 : coefficient of COMPET


InstallmentLoan

-9.94(0.053)

-3.04(0.107)

0.20(0.080)

-0.04(0.0010)

1.35(0.016)

Debit Card -10.85(0.047)

-2.46(0.037)

-1.52(0.089)

-0.01(0.0008)

1.46(0.019)

Checking -6.10(0.079)

-2.61(0.040)

2.76(0.127)

-0.10(0.0013)

1.01(0.015)

Credit Card -17.98(0.033)

-0.40(0.080)

0.45(0.116)

-0.02(0.0015)

2.97(0.028)

Saving -1.21(0.061)

-0.73(0.039)

-3.37(0.124)

-0.15(0.0012)

0.10(0.020)

CD 5.28(0.065)

-4.00(0.078)

6.27(0.118)

-0.10(0.0011)

-1.13(0.019)

MoneyMarket

-9.83(0.051)

-1.80(0.055)

0.07(0.150)

0.04(0.0013)

-0.11(0.026)

Brokerage -16.74(0.040)

1.71(0.041)

2.40(0.086)

0.02(0.0007)

-0.52(0.016)

Heterogeneity Equation -i2 : coefficient of OVERSAT


InstallmentLoan

2.48(0.039)

0.71(0.032)

-0.08(0.114)

0.002(0.0011)

-0.21(0.022)

Debit Card 1.11(0.049)

0.46(0.033)

0.09(0.129)

0.007(0.0012)

-0.03(0.022)

Checking 4.23(0.055)

0.17(0.034)

-0.60(0.176)

0.003(0.0009)

-0.39(0.027)

Credit Card 3.22(0.042)

0.03(0.032)

-0.88(0.069)

0.002(0.0006)

-0.23(0.012)

Saving 2.60(0.104) 0.25(0.038) -0.55(0.130) 0.011(0.0013) -0.23(0.031)CD 2.01

(0.061)

0.16

(0.040)

0.39

(0.036)

-0.004

(0.0004)

0.09

(0.011)MoneyMarket

3.51(0.207)

0.16(0.045)

-0.94(0.104)

-0.007(0.0014)

0.02(0.044)

Brokerage 2.99(0.106)

0.22(0.043)

-1.15(0.088)

-0.014(0.0009)

0.25(0.046)

Heterogeneity Equation -i3 : coefficient of SWIT


InstallmentLoan

3.31(0.119)

0.74(0.097)

-7.19(0.113)

-0.022(0.001)

0.38(0.022)

Debit Card 7.53(0.134)

1.30(0.061)

-11.77(0.294)

-0.099(0.001)

3.82(0.030)

Checking 2.43(0.134)

1.32(0.111)

-14.28(0.196)

-0.062(0.002)

0.44(0.030)

Credit Card 7.63(0.055)

0.50(0.063)

-13.92(0.085)

-0.032(0.002)

0.29(0.030)

Saving 6.42(0.148)

0.68(0.083)

-5.85(0.272)

-0.108(0.001)

1.68(0.047)

CD 4.10(0.045)

2.94(0.035)

-15.53(0.100)

-0.028(0.001)

0.62(0.012)

MoneyMarket

2.96(0.103)

1.08(0.067)

-11.67(0.141)

-0.053(0.001)

2.61(0.038)

Brokerage 0.79(0.076)

1.95(0.075)

-12.62(0.209)

0.051(0.001)

2.01(0.013)


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Figure 1a: Mean Absolute Error Across M odels

- Estimation Sample

0

0.01

0.02

0.03

0.04

0.05

0.06

Model 1 Model 2 Model 3 Model 4 Model 5

Figure 1b: Mean Absolute Error Across Models- Holdout Sample

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Model 1 Model 2 Model 3 Model 4 Model 5

Figure 2: Gains Chart for Model Comparison Across All Product Categories

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

% of Customers

Cu

mGains No Model

Model 1

Model 2

Model 3

Model 4

Model 5


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Table 5. Selected 10 Households for Cross-Selling Efforts (Proposed Model)

Actual Data Predicted ProbabilitiesHousehold

t

IL DBC CHECK CRC IL DBC CHECK CRC

1 0*(0)

0(0)

0(0)

0(1)

0.0121 0.0102 0.0001 0.00081

2 0(0)

0(0)

0(0)

0(1)

0.0105 0.0093 0.0001 0.0008

1 0(1)

0(0)

0(0)

0(0)

0.0099 0.0044 0.0079 0.00042

2 0(1)

0(0)

0(0)

0(0)

0.0097 0.0034 0.0067 0.0005

1 0(0)

1(1)

0(2)

0(3)

0.0001 0.1931 0.0147 0.17823

2 0(0)

0(2)

0(2)

1(3)

0.0004 0.1322 0.0334 0.2386

1 0(0)

0(3)

0(3)

0(2)

0.0005 0.0168 0.0061 0.00044

2 0

(0)

1

(4)

0

(3)

0

(2)

0.0001 0.1485 0.0052 0.0001

1 0(0)

0(2)

0(1)

0(2)

0.0002 0.0492 0.0001 0.00695

2 0(0)

0(2)

0(1)

0(2)

0.0016 0.0147 0.0014 0.0017

Actual Data Predicted ProbabilitiesHousehold

t

SAV CD MM BRK SAV CD MM BRK

1 0*(0)

0(0)

0(0)

0(0)

0.0007 0.0173 0.0001 0.00001

2 0(0)

0(0)

0(0)

0(0)

0.0006 0.0168 0.0001 0.0000

1 0(0)

0(0)

0(0)

0(0)

0.0014 0.0079 0.0028 0.00072

2 0(0)

0(0)

0(0)

0(0)

0.0015 0.0065 0.0026 0.0006

1 0(1)

0(0)

0(0)

0(0)

0.0004 0.0223 0.0001 0.00163

2 0(1)

0(0)

0(0)

0(0)

0.0005 0.0301 0.0001 0.0015

1 0(0)

0(0)

0(0)

0(0)

0.0000 0.0008 0.0000 0.00424

2 0(0)

0(0)

0(0)

0(0)

0.0001 0.0005 0.0000 0.0053

1 0

(0)

1

(1)

0

(0)

0

(0)

0.0001 0.5644 0.0000 0.00075

2 0(0)

1(2)

0(0)

0(0)

0.0002 0.5743 0.0000 0.0008

* The number 0 or 1 indicates whether the household purchases (1) some service in the corresponding category ornot (0) during the sample period. The numbers in the parentheses are the numbers of accounts that the householdopened in the corresponding category with the bank before the current period.


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Sequential Xsell