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Why Customers Choose Your Product:
a System Dynamics Approach to Customer Choice Modeling
Drs R.M. Mooy
Drs GJ .E. Valk
TNO Telecom
Business & Network Optimization
PO Box 421
2260 AK Leidschendam
the Netherlands
telephone: +31 70 4460023
fax: +31 70 4463144
e-mail: r.m.mooy@ telecom.tno.nl
g.j.e.valk@ telecom.tno.nl
Abstract
For modeling customer choice in industries in which various suppliers offer a
number of products, we found traditional economic modeling methods
inadequate. We therefore developed a system dynamics model capturing the
important (dynamic) effects. In this paper, the drawbacks of the traditional
method are laid out. Then, the model is presented in two stages: first, a generic
structure; second, a number of useful enhancements .
Keywords: Customer Behavior, Customer Choice, Churn, Market Dynamics,
Telecommunications.
Introduction
The liberalization of the Dutch telecommunications industry and the introduction
of new products and services created a continuous demand for new modeling
techniques that would not be too difficult in daily practice yet would describe
customer behavior in an adequate way. TNO Telecom! has been involved in the
development of these models for about six years now.
Models based on (price) elasticities are straightforward to construct and easy to
explain to our clients, but proved to have shortcomings. This led us to develop
more sophisticated models using the philosphy of system dynamics. This paper
presents the generic structure of these models and discusses a number of useful
enhancements.
Churn and the Goal of the Model
In this paper, we will look at the dynamics of a market in which a number of
suppliers offer a number of products or services. One of the suppliers is
considered to be our client The individual people acting in the market are called
the customers.
TNO Telecom is the telecommunications department of TNO, the Netherlands Organization for
Applied Scientific Research. Before J anuary 1°‘ 2003, TNO Telecom was known as KPN
Research, the Research department of KPN Royal Dutch Telecom, the incumbent Dutch
telecommunications operator.
The specific focus of the client and therefore of the model is customer churn.
Customer churn, or simply churn, is usually defined as the rate of movement of
people within a system. For our purpose, we will consider churn to be the number
of customers switching between suppliers and/or products.
Churn implies large costs for firms. To convince a customer to switch to its
product or service, a supplier needs to make a (marketing) effort, implying costs.
Also, the longer a customer has a relationship with a supplier, the more profit is
generated for the supplier. Therefore, a supplier will want to strike a balance
between maximizing the number of customers it has and minimizing (marketing)
cost by managing churn. To achieve this, the supplier needs to have a clear
picture of the dynamics present in the market. He needs to understand which
variables cause people to switch product or supplier.
The goal of the modeling method described in this paper is to provide the client
with a basis for his market(ing) strategy by capturing the dynamics that relate
directly and indirectly to churn.
Dependency
An important concept in modeling customer choice is the notion of Dependency.
A customer's choice is said to be dependentif he, voluntarily or involuntarily,
bases his choice on previous (historical) choices. Subscribing to a
telecommunications service is an example of a dependent situation. A situation in
which the customer makes a new choice every time he wishes to buy the
product, is called independent A good example of an independent situation is
buying bread at the bakery.
While independent situations can adequately be described by other methods,
the system dynamics approach is very suitable to dependent situations. The
reason for this is that system dynamics can take into account the ‘market legacy’
- the situation at earlier time points, for example existing market shares or firm
image. The system dynamics model in this paper is restricted to products and
services (hereafter used interchangeably) with 'dependent' characteristics.
Fora full understanding of the advantages of such a model, a more traditional
method based on elasticities is discussed first.
Experiences with Elasticities in Customer Choice Modeling’
A well-known and widely used technology for modeling customer behavior is
modeling using elasticities of demand. The elasticity of demand is the relative
change in demand induced by a given relative change in an independent (in most
cases exogenous) variable, e.g. price or income. For example, a price elasticity
of -0.2 implies that demand will decrease 0.2% when price is increased 1%.
Elasticities have many advantages: they are easy to use, easy to estimate, and
easy to explain since they are intuitively clear. For these reasons, we often used
price elasticities in forecasting future demand for products and services. Usually,
the demand for a service before a price change was compared to the demand
? In this paper we will only discuss our experiences with price elasticities. Over the years, we
have used other elasticities, like the income elasticity (the effect of the income on customer
behavior) and cross-elasticities (the effect of the price of product X on the demand for product Y).
Our experiences with these elasticities are comparable to our experiences with price elasticities.
afterwards. Because the demand for telecommunications is heavily dependent on
seasonal effects and is rapidly growing?, we mostly used the adjusted demand,
which was defined as the demand corrected for seasonal effects and an
exogenous growth trend. Typically, such a demand function looks like this:
D, =constant +price effect +seasonal effect +exegeneous trend +other effects
where Dt is the (adjusted) demand for a product or service at time t.
But even with corrections for seasonal effects, exogenous trends, income effects
and so forth, we were confronted with some major drawbacks that eventually led
us to develop new methodologies. The most important ones are briefly discussed
below.
¢ Historical Data. Elasticities are usually estimated with historical data that
should not automatically be extrapolated to the present time or new cases.
For example, we found a case where the price elasticity was estimated
based on an observed change in demand due to a 10 percent decrease in
price, say from 1 Euro to 0.90 Euro per entity. This calculated elasticity
perfectly described how consumers used to react to the 10% price
change. But the marketing department used the same elasticity to
calculate the effects of a second strong decrease in price just a few
months later. This was clearly a bridge too far: the customers, confronted
with a second decrease in price shortly after the first one, did not react in
the same way as they reacted to the first decrease in price. In fact, they
hardly reacted at all. For the marketing department this was a hard lesson
that showed the need for a behavioral model that would take into effect the
possible different effects of two or more successive changes in price.
¢ The Ceteris Paribus Assumption. Elasticities rely heavily on the ceteris
paribus assumption. Ceteris paribus (Latin for “other things being the
same”) is an economic assumption holding all other variables constant in
order to focus on the specified ones (Katz & Rosen (1991)). This works
fine in theory, but in practice many variables influence the relationship
between price and demand. In the telecommunications industry each
week is different from the previous one. New competitors come and go,
new services are introduced, etc. The ceteris paribus condition is far too
strict to make sense in a practical situation. In order to compensate for the
dynamics of the industry, we had to make additional corrections like
adding a time series in the elasticities (i.e. making an assumption about
the change in the value of the price elasticity over time). But we found
these additions to be rather artificial and random. There was no scientific
justification and the assumptions could only be verified afterwards.
¢ Market Transparency. Elasticities assume a fully transparent market, i.e.
all players (Suppliers and consumers) know the exact prices. In real life,
34 rapid growth in the demand of telecommunications services was observed during the
development of most of our models.
this assumption is violated. Market research shows that in many cases
customers have no idea what they are actually paying. We once hada
case in which we had to estimate the demand for international calls after a
price change. Because at that time we had nothing better, we used a price
elasticity that was estimated with historical data. In the same period, a
market research was carried out in which the consumers were asked what
price they believed they had to pay for a one-minute international phone
call. Dramatically, the average price the consumers believed they were
paying was an overestimation of nearly 1000% (!)*. If customers
overestimate or underestimate the actual price of a product or service,
their behavior is based on the price they believe they pay instead of the
price they actually pay. A methodology that adequately simulates
customer behavior should therefore take into account the fact that the
awareness of prices could be very low, especially in industries that are
confronted with major price changes in a short period of time.
¢ Cause and Effect. Elasticities do not take into account the underlying
causes for customer choice. They only estimate the theoretical division of
the market without specifying the causes for this division, or describing the
explicit flow of customers between suppliers and products. This is
sufficient when we are only interested in a numerical estimation of future
demand, but in many cases we want to understand the customer behavior
instead of forecastit.
* Customer Rationality. Elasticities assume rational customers. Thatis, if
one supplier sets its prices slightly below the market average, it should
attract the majority of the customers. However, other (often emotional)
variables are not taken into account. That is why in competitive markets,
no firm can attain 100% market share.
¢ Churn thresholds. Elasticities negate churn thresholds. Even though
another supplier may offer a more attractive product, not all customers are
inclined to switch immediately. These thresholds should be modeled
explicitly.
These drawbacks, combined with the fact that we only considered markets with
‘dependent’ characteristics, led us to develop a new method based on the system
dynamics philosophy.
* Prices had recently declined steeply.
The System Dynamics Approach
The System Dynamics Philosophy
As we have seen, the classic economical estimation method described above
suffers from drawbacks. The ‘bottom-up’ philosophy that is presented here is
based on System Dynamics and explicitly models the flow of customers between
suppliers and products, including the underlying reasons for this behavior.
Working together with market experts, the system dynamicist can use this model
to capture the market dynamics. The various causes and effects should be made
explicit, to provide a basis for a supplier to improve its market position.
A pitfall would be the complexity of such a model compared to the simple
estimation models from economic theory. That is why the simple generic
structure of the model is discussed first. So-called enhancements to the model
can then be added according to the needs of the situation.
The Model
The Customer Behavior Model (CBM) describes customers' choices between m
suppliers (S1,...,5m) who offer n products (Pi,...,P ,). For the sake of simplicity, it
is assumed that each supplier S ; offers all products Pj. This assumption is later
relaxed.
The CBM takes the prices of products as a basis, and then applies the effects of
different variables to these prices. The outcome in turn affects the customers’
behavior on the market.
The CBM consists of two parts. The first part, the Price Cascade, describes the
way in which customers perceive and value prices and related (soft) factors. The
second part descibes the Customer Loop: it is the way in which customers react
to the prices and factors. It also depicts the flow of customers between various
suppliers and products in the market.
The Price Cascade
The first part of the model is called the Price Cascade, since it describes how
customers deal with prices and related factors and does not contain any loops.
The Cascade is made up of different steps, which are set up in such a way, that
they can be examined qualitatively and estimated quantitatively individually. In
the first step, the actual prices of the products P,...,P, are determined for each
supplier S;. Then, in step 2, the prices are adjusted for what the customers think
the price is, to yield perceived prices. In step 3, the perceived prices are adjusted
for factors like quality and service to determine the emotional prices.
Figure 1 shows the Price Cascade. Every variable is actually a multi-dimensional
array of all possible combinations (Sj, P)).
Price H
' Factors
v Weigh
! Factors ;
| Actual i
Prices ————_ :
v Perception
Factors i
' Perceived i
i Prices ——— i
| t
Emotional :
| Factors H
| Emotional i
' Prices — i
The Price i
Cascade
Inflow Outflow
Sieve Sieve
Figure 1- The Price Cascade
The steps in the Price Cascade
Step 1. In this step, the actual prices are set for each combination of (Sj, P)). In
the telecommunications industry a customer usually pays a monthly subscription
rate and an amount based on the usage. In order to reduce the number of prices
in our models, we usually take the average monthly bill as the price. The
average bill is calculated by a weighted average of the different prices with the
average use as weight factors.
Step 2.Ask someone what the price of a certain productis and he will most likely
not give the ‘correct’ answer. Instead, he will report what he thinks the product or
service costs. Firms tend to influence the idea the customer has about the price
of a product - lowering the perception of their own prices and increasing the
perception of competitors' prices. Market research has shown that in the
Netherlands, the incumbent telecom operator is generally regarded as expensive,
where (new) competitors are considered cheap(er), even though the actual price
differences are small or even non-existing.
Step 3. Customers base their behavior not only on price. Factors like quality and
service can play a big role, especially if these factors differ greatly between
suppliers. In this step, an estimation is made for how the customer values the
product, expressed in terms of prices. Hereby, ‘positive' product aspects tend to
lower the so-called emotional price where 'negative' aspects augment the
emotional price.
The Price Cascade can be compared to the situation in which you leave your
house on a cold winter day. When deciding what clothes to wear, you might first
want to check the weather forecast without actually checking or measuring the
actual temperature yourself. This forecast can be considered as your perceived
temperature. When you are outside, the temperature you actually experience
(influenced by variables like the wind speed) is called your emotional
temperature.
Utility
The emotional price has a strong relationship with the concept of utility that is
often used in microeconomics. The utility is defined as the total level of
satisfaction of consuming a particular good or service (Katz & Rosen (1991)).
Originally, we used the utility as a measure for the consumer valuation instead of
the emotional price. The utility calculation function looked like this:
U; =f(pp,, of, )
In other words, the utility for product j is a function of the perceived price (pp;) and
some other factors (of), like quality and service, that influence the utility. Since
utility represents the total level of satisfaction, there should be a positive
relationship between the utility level of a certain product and the level of
consumption.
The first release of the Customer Behavior Model used the utility of a product as
an indication for its desirability. But after working with the CBM for several
months, we found that our clients had difficulties with the interpretation of utilities.
The major problem is that utility is an economic measure that has no logical
interpretation. To show this, consider two products, one with a utility of 10 and
one with a utility of 20. Is the second product twice as good as the first one?
What does it say about the future consumption of the products? Is this case
different from a case of two goods with utility of 5 and 10 respectively? And how
can the utility be calculated anyway?
Dealing with these comments, we introduced the emotional price as a different
measure of consumer valuation. The major difference is that the emotional price
is more intuitively clear. It is easier for our client to ask its customers for their
emotional price than for their utility. In the CBM, there is a negative relationship
between the emotional price and the level of consumption.
Example
To illustrate the Price Cascade, we introduce an example: consider a market in
which three suppliers each offer three products. The weighted prices of the
products are as follows:
Pi P2 P3
Si [100 | 100 100
S2 | 80 70 60
S3| 110 [80 80
Weighted prices
However, a customer survey shows that customers regard supplier 3 as a ‘cheap’
supplier, causing the perceived prices for S 3 to be 10% lower:
Pi P2 P3
Si | 100 | 100 100
S2 | 80 70 60
$3 [99 72 72
Perceived prices
Now, assume the quality and service of supplier 1 are significantly better. Market
research shows that S 1's brand and image are worth 20%. This leads to the
following emotional prices:
Emotional prices
The Customer Loop
After the Price Cascade, the (multi-dimensional) variable ‘emotional price' results,
which is used in the Customer Loop to compare the different combinations (S;,
P;) and determine customer behavior.
The Customer Loop Model is presented below in two stages. First, the basic
model is discussed. This model is simple and robust, and serves as a generic
structure. A single, though multi-dimensional loop, the Closed Market Loop,
describes the customers as they churn between different suppliers and/or
products.
Second, a number of possible enhancements for the basic model are presented.
The enhancements add loops as well as in- and outflow structures to the system.
Depending on the particular case, these enhancements should be used with the
basic model to suit the client's needs.
The basic model is shown in Figure 2.
Emotional
Prices
+{{ + +\| +
Cj} Customers ¥ CP
inflow outflow
The Customer
Figure 2 - The Customer Loop
All variables, except C, are calculated for every (S;, P;) combination.
The main part of the basic model consists of the customer flow through the
system. Customers that are unsatisfied with their supplier and/or product flow out
of the customer base. The outflow is determined by the so-called Outflow Sieve.
These customers (represented by the quantity C) are said to be churning and will
then choose a new combination of supplier and product, flowing into the
customer base again. This inflow is influenced by the Inflow Sieve.
The Outflow Sieve is nothing more than a table with, per (Si, P;) combination, the
fraction of customers abandoning that combination. One reason for which
customers switch away from a supplier or product is that they are unsatisfied with
it. For example, the service may be poor or the bill might contain errors. Another
reason would be the ending of the subscription period. Telecom services are
typically offered with a one-year subscription.
The Outflow Sieve thus captures dissatisfying and cancellation effects.
The Inflow Sieve is a table with the fractions of all churning customers who
choose a particular combination. It captures the choice process of customers
who generally base their choice on positive aspects of a supplier or product. The
Inflow Sieve takes satisfying effects into account.
Tuning the Customer Loop boils down to determining the ‘correct’ values for both
sieves, based on market research where possible.
Example (continued from above)
To compute the effect of the Emotional Price (EP) on the Inflow Sieve (IS), we
use the following formula:
This formula has the advantage that lower prices lead to higher inflow. The
parameter 4 denotes the relative influence of price differences on the customers'
behavior. If 4 =0, they don’t care at all about price differences and will randomly
choose a (S, P) combination. If 4 =-1, the customers are very sensitive to
differences in price and will choose the cheapest combination. Generally, 4
should be set close to 0.
Applying the formula with 4 =-0.05 yields:
Pi P2 P3
$i[0.09 [0.09 | 0.09
S2 [0.09 [0.14 | 0.23
S3 | 0.03 [0.13 | 0.13
Inflow Sieve (IS)
This should be interpreted as: 9% of new customers or churning customers will
choose combination (S1, P1). Note that the sum of all the fractions, barring
rounding differences, is 1.
For the sake of simplicity, assume that in every time period, 5% of the customers
abandon their current (Sj, Pj) combination because their subscription period
ends. This effectively cancels the effect of the emotional price on the outflow, and
the Outflow Sieve becomes:
Pi P2 P3
$1 [0.05 [0.05 | 0.05
$210.05 | 0.05 | 0.05
S3 | 0.05 [0.05 | 0.05
Outflow Sieve
This should be interpreted as: every time period, 5% of the customers who
currently have combination (Si, P1) will abandon it. The numbers in the Outflow
Sieve are independent and therefore need not sum to 1.
If we assume that there are 3000 customers, and that Si possesses a market
share of 100% at t=0 (e.g. S1 is the incumbent operator at the liberalization of the
market) and an equal initial division of the customers between the three products,
we get:
Pi P2 P3
Si | 1000 [1000 | 1000
S210 0) )
S310 ) 0
Customer Base at t=0
Now, assuming that the sieves do not change over time, we now have enough
data to run the model. Using these simple assumptions, the system will convert
to an equilibrium, due to the presence of only balancing loops. In Figure 3, two of
the nine combinations are shown.
1200
-+-@--- S1-P1 —+— $2-P3
1000 fe,
ee
ee
e
800 —
Ta
te,
te
600 te
Pee,
*
400 *eee
200
0
0 5 10 15 20 25 30
Figure 3 - Number of customers for two supplier-product combinations
In the basic model, a few important assumptions are made. First, the market is
assumed to be closed, meaning that no customers enter or leave the system (i.e.
no new customers are ‘born' and none ‘die'). Second, all customers choose
exactly one supplier-product combination. Third, the ‘amount’ of the product or
service that the customer purchases, is ignored, and can be estimated separately
if needed.
Enhancements
We have tailored our model to various specific cases by adding model
enhancements to the basic structure. Each enhancement adds to the model, or
relaxes an assumption. However, adding enhancements makes the model more
complex. That is why itis a good idea to make a checklist of possible
enhancements and to determine together with the client which ones to apply.
In various models, we applied the following enhancements:
1. Allowing Physical Customer Changes. The assumption that no
customers enter or leave the model is relaxed. Customers then leave the
system proportionally. Customers enter the system using the Inflow Sieve.
Adding this enhancement is a good idea if the size of the market varies
over time.
2. Product Churn versus Supplier Churn. In certain markets, thresholds
exist that diminish the chum between suppliers but not the churn between
different products of the same supplier. For example, changing banks
might imply changing your bank account number, which is awkward. To
capture this effect in the model, the variable C should be made multi-
dimensional, and the inflow sieve should take into account where the
customer is churning from.
3. Block entry for certain products and/or suppliers. In certain markets,
regulations prohibit the churning to certain products or suppliers fora
certain time period. For example, the telecom market in the Netherlands
was liberated in 1997. From that moment on, customers were able to
choose their own telecom operator; before that, they were restricted to the
incumbent operator.
4. Multiple products. Here, the assumption that every customer chooses
precisely one supplier-product combination is relaxed. Suppliers might
offer complementary products, perhaps offering a discount or a package
deal. An example of this is the energy market in the Netherlands, in which
many suppliers offers both fuel and electricity services.
5. General effects. It might happen that certain products or suppliers
become more popular or unpopular in time. A product might be ‘hot’
causing more customers to choose that product. A supplier might receive
bad media attention, or be the victim of a boycott. A general parameter
can capture these effects.
6. Seasonal effects. The sales of products or services may be season-
dependent. For example, gas sales are higher in winter than in summer.
Seasonal effects can be represented by an additional factor.
7. Endogenous Prices. If a firm has enough knowledge of its competitors, it
can try to forecast the reactions of competitors by making their (pricing)
decisions endogenous in the model. Loops should be added, increasing
the dynamics in the system.
8. Service Usage. This enhancement takes into account that the better the
deal offered by a supplier, the more a customer will purchase. For
example, a lower price of telecommunications services may cause the
number of calls to go up.
Tailoring and Implementing the Model
The CBM is a generic model. This implies that its structure can be used ina
variety of settings. However, when a specific case is modeled, care must be
taken that the model describes the real situation adequately. To achieve this, the
modeler can tune the individual parts of both the Price Cascade and the
Customer Loop. The client should provide the modeler with qualitative and
quantitative insights and data about the market. For example, the set of
perception factors can be determined in cooperation with the supplier's marketing
department. Or the Outflow Sieve might be tuned according to the outcomes of a
customer survey asking customers why they canceled their subscription.
In any case, the client should be involved in this process. Sterman (2000) states
that "...a main purpose of modeling is to design and test policies for
improvement. To do so, the client must have confidence that the model will
respond to policies the same way the real system would." This is the reason that
the model is designed to capture individual effects that can be understood and
measured by the client.
Final Remarks
The CBM provided us with a relatively simple, but powerful methodology that can
be used in many cases with only small adjustments for each specific case. We
have used it in cases for incumbent operators, but ithas also proved to work for
smaller market players. For TNO Telecom anzd its clients, the CBM is the perfect
compromise between a model that sufficiently captures all relevant effects and a
model that is simple and robust.
References
Katz, Michael & Harvey Rosen. 1991. Microeconomics. Boston: Irwin & McGraw-
Hill.
Sterman, J ohn. 2000. Business Dynamics. Boston: Irwin & McGraw-Hill.
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