An Empirical Analysis of Consumer Purchase Behavior …€¦ · 1 An Empirical Analysis of Consumer...

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An Empirical Analysis of Consumer Purchase Behavior of Base Products and

Add-ons Given Compatibility Constraint

Timothy Derdenger Tepper School of Business Carnegie Mellon University

[email protected]

Xiao Liu Tepper School of Business Carnegie Mellon University [email protected]

Baohong Sun1

Cheung Kong Graduate School of Business [email protected]

December 2012

1 Timothy Derdenger is an Assistant Professor of Marketing and Strategy at Tepper School of Business of Carnegie Mellon University. Xiao Liu is a PhD student of Marketing of the same institute. Baohong Sun is Dean’s Distinguished Chair Professor of Marketing at Cheung Kong Graduate School of Business. All authors have contributed equally and have been listed alphabetically.

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An Empirical Analysis of Consumer Purchase Behavior of Base Products and Add-ons Given Compatibility Constraint

Abstract In the digital camera market, Sony developed the Memory Stick card, which is only compatible with

Sony’s cameras. However, Kodak, Canon, Nikon, and HP all adopted the SD (Secure Digital) memory

card. Despite the common practice of multiple standards, there is lack of knowledge on how

technological compatibility affects consumer purchase decisions on base products and add-ons at the

brand and/or standard level. We recognize the existence of multiple standards and develop a dynamic

model in which a consumer makes periodic purchase decisions on whether to adopt/replace a base

product and/or an add-on product. We take into account the dynamic and interactive inventory effect

by allowing consumers to recognize the long-term financial implications when forward-planning in

switching to a base product that is incompatible with the inventory of memory cards they have

accumulated. Applying the model to consumer purchase history of digital cameras and memory cards

from 2000 to 2004, we demonstrate compatibility makes consumer purchase decisions of base and add-

on products inter-temporally interdependent. Inventory of add-ons significantly affects purchases of

base products. Our model explains the sales trends of the major brands of cameras and quantifies how

much promotion to offer consumers in order to switch standards.

Keywords: Compatibility and standard, base product, add-on product, dynamic structural model, product adoption, product line pricing

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1. Introduction Manufacturers are increasingly relying on selling accessories to raise profits. One natural method in

technology markets is to target consumers who have purchased a “base product” (e.g. printer) with

add-ons (e.g. toner for the printers) that function only with a given base product. Consequently, the

natural linkage between base and add on products, particularly for technology goods, makes consumers’

purchase/upgrade/replacement decisions regarding such products connected.

The add-on product market is non-trivial. For example, for consumer electronics products,

buyers spent an average of 15 percent of the cost of a primary device on that device’s accessories in

2006 as estimated by Consumer Electronics Association.2 In the automobile industry, the market size of

add-ons is $216 billion and it has been growing at an annual rate of 8 percent since 2000.3 This large

market is an appealing piece of the “profit” pie that all manufacturers track. Specifically, consumers

tend to be less price sensitive toward add-on products,4 which leads to a higher margin on add-ons. The

inter-dependence between the base product and its add-ons has several interesting implications for

manufacturers when they make dynamic marketing decisions for all products. Therefore, industry

managers are enthusiastic to understand how to design add-on products in order to boost product line

total sales.

Existing studies on cross-category purchases of durable goods are at a category level, without

recognizing the existence of multiple standards that are regularly observed in practice. There is need to

understand the impact of proprietary standards or incompatibility between base and add-on products

on a consumer’s purchase decisions of the base products and add-ons at the brands and standard level.

An understanding of consumer cross-category choices at the brand/standard level sheds light on why

2 http://www.letsgodigital.org/en/13653/camera_accessories/

3 http://www.autodealermonthly.com/64/2523/ARTICLE/The-Value-Of-The-Accessory-Market.aspx

4 http://technorati.com/business/article/consumers-are-in-the-accessory-market/

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major camera manufacturers compete indirectly in the memory card market by creating incompatible

standards and why Sony chooses to remain separate while others choose to unite.

In this paper, we evaluate the dynamic impact of add-on products on a consumer choice of

base products by deconstructing the impact into the following key issues: First, how or whether prices

of add-ons of one standard affect consumer choice of base products at the brand level. Second, how or

whether inventory of add-ons affects purchase of compatible and non-compatible base products; in

other words, does a compatibility requirement of add-on products create a cost of switching that locks

consumers in to the compatible base product brand? If so, what is the monetary equivalent for the

consumers to switch to a non-compatible brand? Third, is it a good strategy to leverage the switching

cost created by incompatibility of add-ons with base products? Specifically, did Sony gain from

developing its proprietary standard of memory card, the Memory Stick?

We develop a framework in which forward-looking consumers make joint brand choice

decisions regarding the base product and the add-on when several base product brands are compatible

with only one of the several standards of add-on products. Our model assumes sophisticated

consumers take into account price and quality trajectories of add-on products when purchasing a base

product. For instance, if the consumer is faced with an attractive base product that are lowly priced but

add-ons that are highly priced, the consumer will anticipate the potential burden of purchasing

expensive add-on products (Gabaix and Liabson 2006), thus perhaps avoiding the base product.

Forward-looking consumers analyze the total cost of the bundle (the price of the base product and the

expected cost of all add-ons), not just the price of each component. Our model also allows a consumer

to account for his existing utility associated with his compatible base product and inventory of add-ons.

This model allows us to approximate the interesting dynamic decision process regarding inter-

dependent purchases of base products and add-ons: When choosing among camera brands with

compatibility concerns, consumers take into account the accumulated compatible add-ons at hand and

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compare the stream of future consumption utility from the pre-owned memory cards and dis-utilities of

having to purchase compatible memory cards in the future, which we term as dynamic inventory effect.

In this setting, compatibility is the key link between the purchase decisions of the base product and the

add-on. The brand level compatibility further adds interesting consumer choice dynamics.

We find empirical evidence of a strong "add-on-to-base effect" between a camera and memory

cards caused by compatibility—a memory card in inventory can add to the utility of a compatible

camera. Also, we find that a consumer is locked-in by the utility compatible add-ons provide. In

addition to the finding that consumers’ purchase decisions of base products is influenced by the

expected price of the add-on product, we show that the add-on-to-base effect is enhanced when future

prices of add-ons are lower. More specifically, when the expected future price of a memory card

decreases, the purchase probability of the compatible camera increases given the same amount of add-

ons purchased before. In addition, we find the cost for rival firms to steal Sony consumers is larger

($23.055 and $15.196) than for Sony to steal the consumers of competing firms ($8.482).

We also run simulation to study the change of sales under four alternative compatibility policies.

We find that, 1) when incompatibility is removed among standards, the manufacturer of a premium

memory card cannot reap the profit from camera transactions. For instance, if Sony did not create its

proprietary memory card standard, its camera's market share would have been reduced by 6 percentage

points. 2) When adopting an adapter that makes their cameras compatible with the memory cards of

Sony’s, the sales of Standard 3 cameras increase significantly. 3) When manufacturers of Standard 2

cameras lower their camera prices during the initial periods, they benefit more from the dynamic add-

on-to-base effect and increase sales by about 20%. 4) When Sony’s brand equity falls below the industry

average, incompatibility damages Sony’s market share.

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We contribute to the literature on cross-category purchases of durable goods in the following

way: First, our model recognizes the existence of multiple incompatible standards and models

consumer brand choices of base and add-on products. This differs from prior literature that examines

consumer purchases of base and add-on products at the category level. In addition, existing literature

includes a time-invariant constant complementary term to take into account the inter-dependence

between products (Sriram, Chintagunta and Agarwal 2009). We allow forward-looking consumers to

endogenize the purchase quantity of memory cards and to consider the inventory of their memory

cards when determining the purchase of base products and add-ons. In summary, in addition to

incorporating inter-temporal trade-offs regarding inter-temporal pricing effect for the base product as

in the existing literature, our model takes into account two new inter-temporal effects (i) a cross-

category pricing effect and (ii) the cross-category inventory effect. To our knowledge, this is the first

paper to incorporate these effects simultaneously and evaluate how consumers respond to the

purchases of base products and add-ons when multiple standards exist.

2. Literature Review Our paper stems from three streams of literature: durable goods adoption and replacement decision-

making; multi-category purchase analysis; and compatibility. Recent years have seen an increase in

research on empirical examination of durable goods adoption and replacement decision-making. This

stream of research focuses on how consumers take the price and quality evolvement process into

account to make long-term purchase decisions. For example, Melnikov (2001) constructs a dynamic

model that describes consumers' adoption of differentiated durable products as an optimal stopping

problem. By utilizing data from the U.S. computer printer market, the author finds evidence of

forward-looking behavior. Song and Chintagunta (2003) models adoption process of digital cameras,

accounting for both consumer heterogeneity and forward-looking behavior. Applying this model to

aggregate data in the digital camera category from 1996 to 1999, the authors find that Sony's entry

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effects can be decomposed into a market expansion and brand switching effects. Gowrisankaran and

Rysman (2007) build a dynamic model of consumer preferences with heterogeneity, rational expectation

of future products and repeat purchases over time. Nair (2007) studies the optimal pricing strategy for a

firm to sell video-games to forward-looking consumers who strategically delay purchase to benefit from

lower prices in the future. Gordon (2009) models both product adoption and replacement process.

Using aggregate data in the PC processor industry together with micro-level survey data, the author

infers ownership and replacement behavior. The paper reveals substantial variation in replacement

cycles with consumers' forward-looking behavior and heterogeneity. However, this stream of research

focuses on single product category and does not examine multi-category purchases.

Recently, there have emerged a few papers investigating the complementarity relationship

between a base product and some add-on components. Seetharaman et al. (2005) provides an excellent

review of models of multi-category choice behavior, including three outcomes: purchase incidence,

brand choice, and quantity consideration. Sriram, Chintagunta and Agarwal (2009) present a framework

for measuring complementarity effect across personal computers, digital cameras, and printers. The

complementarity term captures the additional per-period utility that the consumer derives from owning

products from both categories. Gentzkow (2007) as well as Liu, Chintagunta and Zhu (2010) develop

similar models to identify the complementarity term, which is modeled as a constant synergy coefficient

times an indicator that takes a value of one when a consumer purchases in both categories and zero

otherwise. Constrained by data, none of them have fully discovered the dynamic impact of one category

on the other. In the interesting work by Gabaix and Laibson (2006), the joint decisions of a focal

product and its add-on are studied by relaxing the rational expectation assumption. Assuming a

heterogeneous discounting factor (hyperbolic discounting), they show that in managing high-tech

products (e.g., printers) with add-ons (e.g., toner), firms exploit myopic consumers through marketing

schemes that shroud high-priced add-ons. Though recognizing the complementary relationship

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between base products and their add-ons, these models use a time-invariant constant term to capture

the relationship. Our paper takes a different perspective. We design a more intuitive model where the

cross-category dependence relies on compatibility of base products and add-ons. We further look at

how consumers' forward-looking tendency determines their purchase sequence of base products and

add-ons. The cross-category dynamic influence is our emphasis.

Finally, our paper is related to the literature on the compatibility problem of base products and

add-ons. Standard economics literature claims that if products are incompatible, switching costs bind

customers to vendors. Such not only involves direct efficiency losses but also softens competition and

magnifies incumbency advantages (see Farrell and Klemperer (2005) for a good review). Therefore,

consumers as well as economists favor compatibility, or in other words standardization (see Farrell and

Simcoe (2012) for benefits of compatibility). However, on the supply side, firms have incentives to

create incompatibility constraints. Matutes and Regibeau (1988) used a “mix and match” model to show

that compatibility leads to higher pricing. Katz and Shapiro (1985) found that firms with good

reputations or large existing networks tended to be against compatibility while firms with weak

reputation tended to favor product compatibility. There is also a large body of marketing literature

focused on compatibility with network externality. However, our paper does not consider this network

effect.

3. Industry Background and Data Description

3.1. Digital Camera and Memory Cards Industries

Since 1994, technology for the digital camera has constantly improved: higher pixel counts, larger

sensors, shorter shutter lag, smaller and lighter bodies, and more optical zoom options. The camera

industry saw a substantial increase in brands and models of digital cameras, with Canon, Casio, Fujifilm,

Kodak, Nikon, Olympus, and Sony as the major brands with long product lines.

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As digital cameras began taking higher quality pictures, consumers demanded larger storage

devices on which to save photos. In the early 1990's, the PC Card (PCMCIA) was the first commercial

memory card format. It was followed by CompactFlash, SmartMedia, and Miniature Card.

Accompanying Sony’s first digital camera in the market was a 3.5” floppy disk storage device.

The desire for smaller cards in digital cameras led Sony to invest research and development resources to

create its own memory card format, the Memory Stick, which was launched in October 1998. Since

then, Sony has continued to use its proprietary standard and its extensions, such as Memory Stick PRO,

Memory Stick Duo, and Memory Stick PRO Duo, as the compatible storage add-ons for its cameras.

In January 2010 it began to support two memory formats, the SD and Memory Stick..

Olympus and Fujifilm, on the other hand, employed SmartMedia cards as the compatible

storage device until July 2002 when they jointly invented another format, the xD card5. After July 2002,

xD cards were used in a select number of Olympus and Fujifilm digital cameras.

The success of the Sony Memory Stick intrigued SanDisk, Matsushita, and Toshiba to develop

and market the SD (Secure Digital) Memory Card to compete against Sony6. Early samples of the SD

Card became available in the first quarter of 2000. Later in March 2003, SanDisk Corporation

announced the introduction of the miniSD, a variant of the original SD Card. Because SD cards are

ultra-compact, reliable, interoperable, and easy to use, a lot of leading digital camera manufacturers,

including Canon, Kodak, Nikon, and HP, which originally used CompactFlash, switched to SD cards in

their consumer product lines in 2002. The timeline of adoption of memory cards is shown in Table 1.

[Insert Table 1 about Here]

5 http://en.wikipedia.org/wiki/XD-Picture_Card

6 http://en.wikipedia.org/wiki/Secure_Digital

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To facilitate model setup in the following sections, we categorize memory cards into three

standards. PCMCIA (PC) and Memory Stick (MS) are labeled as “Standard 1” and only Sony cameras

are compatible with the Standard 1 cards. SmartMedia cards (SM) and xD cards (XD) are grouped as

“Standard 2” with Olympus and Fujifilm cameras compatible with Standard 2 cards. CompactFlash (CF)

and SD cards are called “Standard 3” cards with Kodak, Canon, HP, and Nikon cameras all adopting

Standard 3 memory cards.

We are able to group two formats (for example, PCMCIA and Memory stick) as the same

standard because when the new memory stick was launched, Sony’s cameras were designed to use both

formats (e.g. Sony’s Cyber-shot DSC-D700). Moreover, adapters existed to transfer data from both

formats of memory cards to the computer. In the case of Sony, although there were constantly new

introductions (later versions of Memory Stick) to the market, i.e. Memory Stick Select and Memory

Stick Pro, most devices that use the original Memory Sticks support both the original and PRO sticks

since both formats have identical form factors7. Therefore, during our observation period, we assume

no introduction of new formats and hence the choice set of consumers is identical throughout time.

3.2. Data Description

The data is an individual level scanner panel provided by an anonymous major electronic retailer in the

United States. Our sample consists of the complete purchase records of 828 randomly selected

households that purchased at least one camera in six years, from December 1998 to November 2004.

The transaction record includes detailed information about purchases of products, such as brand name,

product type, price paid, time and location of purchases. In addition, we collected information on

digital cameras at the brand level from a camera database website that tracks detailed information of all

camera models8. The quality information on memory cards is obtained from annual reports of major

7 http://www.dpreview.com/products/sony/compacts/sony_d770

8 www.dpreview.com/products

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memory card manufacturers at the standard level9. Due to data limitation, we do not know product

specifications such as model name of each camera and size of each memory card. Following Song and

Chintagunta (2003), we use size (megabytes) of a memory card as a proxy of quality because it is the

most important factor in determining the performance of a digital camera.

[Insert Tables 2A, 2B, and 2C about Here]

We prepare the data in the time frequency of a quarter because consumers seldom purchase

cameras and memory cards more frequently than that. We use the first five quarters to obtain each

household’s initial conditions and the remaining twenty quarters to estimate the model. During the five-

year sample period, the 828 households made 934 transactions of cameras and 890 purchases of

memory cards. Table 2A presents market shares of different brands of cameras and memory cards. In

the digital camera market, Sony had the largest market share of 29.34%. Olympus and Fujifilm together

took up 22.81%, and left the remaining 47.85% to other brands. Consistently, Standard 1 memory cards

(compatible with Sony cameras) took up a market share of 28.99%, Standard 2 memory cards

(compatible with Olympus and Fujifilm cameras) had a market share of 21.24% and Standard 3

memory cards (compatible with Kodak, Canon, HP, and Nikon cameras) occupied the rest, 49.78%.

Table 2B reports the total purchase incidences for 828 consumers. The majority (77.78%) of

consumers purchased only one camera and one memory card; 12.98% of consumers had replaced

cameras; 11.84% of consumers purchased more than one memory card. The maximum number of

camera purchase incidences is three and the maximum number of memory card purchase incidences is

four. These numbers are consistent with the nature of cameras as durable goods.

Table 2C reports the summary statistics of price and quality information. On average, the price of

the Sony camera is the highest and that of the HP camera is the lowest. Interestingly, the quality

9 www.dpreview.com/products

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measure is not quite aligned with price because Nikon, rather than Sony, has the highest average quality.

In terms of memory, Standard 2 is the highest priced with lowest average quality while Standard 3

charges the lowest price with the highest average quality.

3.3. Model Free Evidence of Inter-temporal Dependence

Cross Category Inter-interdependence

[Insert Figures 1 and Figures 2 about Here]

Figures 1A illustrates how demand of cameras evolved over time whereas Figure 1B shows the price

trends for each camera brand. We also present demand and price trends of memory cards in Figures 2A

and 2B. There are three things to note from these figures that show a price trend alone cannot explain

the sales trend (as in previous literature). First, the price gap between Sony and most Standard 3

cameras became smaller over time--Sony’s price fell over the entire time period whereas Kodak’s fell

during the beginning but slightly increased in the remainder. Yet, Kodak’s sales of cameras increased

faster than that of Sony’s. We conjecture this can be explained by the lower camera price charged by

Kodak at the beginning of the data period to encourage purchases of camera and, hence, memory cards.

We can see that even though the price gap of memory cards remains quite stable, the sales of Standard

3 memory cards increased significantly over the years. It also takes advantage of the add-on effect

where the price of Kodak standard memory cards fell faster than that of the competing standards.

Second, between 1998 and 2004, the market share of Sony's digital cameras increased from 17

percent to 23 percent10 despite having a highly priced camera and the highest-priced memory cards

among all the competitors. Given the fierce competition in the digital technology product market, the

fact that Sony gained market share over time is surprising. Sony’s unique strategy of creating a

proprietary add-on product (memory card) standard to contribute to sales of the base product (camera)

10http://www.pcworld.com/article/114711/sony_unveils_digicams_photo_printer.html

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raises an interesting research question: what is the dynamic impact of the add-on product on consumer

choices of the base product?

Third, although Olympus and Fuji cut camera prices aggressively after the second half of 2003,

it did not help save their camera sales. Perhaps such a limited response is a consequence of the price of

memory cards compatible with their cameras rising and of forward-planning customers realizing the

long-term financial burden of having such a bundle of products. These figures provide some evidence

for a cross-category pricing effect. More specifically, if consumers anticipate the price of future add-on

products as going up, they will switch brands in the base product category to minimize the total

financial burden of the product portfolio.

Add-on-to-base Effect

[Insert Figure 3 about Here]

In addition to the above memory price effects on camera purchase incidence, perhaps inventory of

memory cards (our add-on-to-base effect) also plays an important role in camera purchases. We assume

memory cards do not become obsolete, and with this a consumer who owns a memory card should be

more reluctant to switch to a camera that is incompatible with her existing stock of memory inventory.

On the other hand, a consumer who has zero stock of memory card inventory is not as relatively

“locked-in” to a particular camera brand than the previous consumer type. Figure 3 illustrates the

purchase incidences for each camera brand conditional on consumer inventory levels of compatible

memory cards. We see that for all camera brands, purchase incidence increases as inventory levels of

compatible memory cards increase. This is particularly true for Sony where it appears a Sony consumer

is locked-in and perhaps faces higher switching costs or add-on-to-base effects associated with existing

memory card inventory than consumers who own other standards.

In summary, the data pattern shows the inter-temporal interdependence between purchases of

base and add-on products. It is evident that forward-planning consumers take into account the financial

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implications of discarding their existing add-ons when comparing long-term utilities of alternative

choice sequences. In the next session, we develop a model to explicitly describe this decision process.

4. Model

4.1. Assumption

Consumer purchase behavior of high-tech and durable goods is distinguished from that of fast-moving

goods on several fronts. First, prices of technology products decline while quality improves over time.

Thus, a model of consumer adoption of products needs to account for the fact consumers anticipate

these future price and quality trajectories while deciding when to purchase. Second, since products are

durable in nature and add-on products can be purchased subsequently, consumers tend to look into the

future when making purchasing decisions. Finally, the forward-looking behavior of consumers and the

issue of compatibility between camera and memory card imply that a consumer's decision of purchasing

the base product is likely to depend on when she anticipates the purchase of the add-on products.

Therefore, the purchase decision for the base product would depend not only on the expected price

and quality trajectories of that product, but also on the anticipated price and quality of the add-on

product. To approximate this decision calculus, we develop a model of consumer purchase (adoption

and replacement) decisions of base products and add-ons as a dynamic optimization problem under

price and quality uncertainty.

In light of the data on hand and the specific industry we study, we make several assumptions

regarding consumer behavior for model parsimony. First, we assume consumers can buy only at the

focal store. This assumption may seem quite restrictive as consumers sometimes purchase at several

electronic stores. However, this concern is mitigated because all households in our sample are holders

of loyalty cards and most of them have purchased at least one camera during the observation period.

Next we treat a consumer who buys multiple cameras or memory cards on a single trip as only one

purchase incidence. This assumption is reasonable because only a very small portion (0.6%) of the

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purchases in our sample involves multiple items. Third, we assume there is no resale market for

cameras and a discarded camera cannot be exchanged for its residual value. This implicitly assumes

consumers only derive utility from their most recently purchased camera.

4.2. Consumer Choices and Flow Utility

Assume the consumer �(� = 1,2, … , ) makes purchase decisions of both the base product (camera �)

and the add-on (memory �) jointly at time period ( = 1,2, . . , �). There are multiple brands of

cameras and multiple standards of memory cards to choose from. We denote a consumer’s choice of

both product categories as a pair (�,�) in which the base product is �(� ∈ �0,1,2, … , ��),where 0

denotes no purchase, and � is the total number of camera brands. The choice of the add-on product is

�(� ∈ �0,1,2, … ,��),where again 0 denotes no purchase and � is the total number of memory

card standards. In our data, � = 1,2,3,4,5,6,7 represents Sony, Olympus, Fujifilm, Kodak, Canon, HP

and Nikon respectively while � = 1,2,3 corresponds to Standard 1 (Memory Stick), Standard 2

(SmartMedia/xD card), Standard 3 (CompactFlash/SD card) respectively. Thus, during each time

period, a consumer faces four types of choice alternatives: (1) purchase (adopt or replace) a camera of

brand � only, (2) purchase a memory card of standard � only, (3) purchase one camera and one

memory card together and (4) purchase neither product. There are altogether 18 choice alternatives.

Our model follows the large literature pertaining to choice models (Guadagni and Little 1983)

and assumes the per-period utility function can be decomposed into a deterministic part and an

idiosyncratic error term.

��,� = � ��,� + "��,� (1)

Superscripts of � and � denote choice of camera � and memory card �. We now discuss in

detail the deterministic components of the four different choice alternatives.

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Case 1: Purchase Camera Only

When a consumer buys only a camera, she can derive utility from the attributes of the camera,

summarized by the brand-specific constant and quality. She also pays a price to purchase the camera.

Moreover, she can enjoy consumption utility from using the compatible memory cards in inventory for

storing pictures. The utility function for purchasing a camera and no memory cards takes the form:

� ��,# = $�� + %��&�� + ' (��(�~�)*+��,

�-.+ /�0�� (2)

for all � ∈ �0,1,2, … , ��.The first term $�� in (2) is the brand-specific fixed effect, which comprises any

intrinsic utility of purchasing camera of brand �. &�� is the quality of the camera �, which is measured

by megapixels in our data set. Its coefficient %�� is the marginal utility for a single unit of quality

increment.

The third term captures the inventory effect of compatible memory cards at hand. Because

memory cards in inventory can be used to store photos and multiple memory cards provide

convenience and flexibility, consumers still derive utilities from them. Indicator (�~�) denotes that

only compatible memory cards can enhance the utility of a camera. From the data description section

we know that (� = 1)~(� = 1); (� = 2,3)~(� = 2); (� = 4,5,6,7)~(� = 3). In order to account for the fact that all previously purchased compatible memory cards adds to

the utility of a compatible camera we multiply the indicator (�~�) by the term *+�� which is the

inventory of memory card � at time hold by consumer �. The coefficient (�� measures the marginal

utility one compatible memory card � in inventory can add to the purchased camera. We name the

coefficient (��as "add-on-to-base effect". If a consumer decides to purchase a camera incompatible

with the memory cards in inventory, she chooses to let the memory cards in inventory go obsolete. The

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fourth term of Equation (2) represents the price effect, with0�� as price for camera of brand � and

coefficient /� as the price sensitivity.

Case 2: Purchase Memory Only

When a consumer buys only a memory card, she obtains utility from consuming the memory card and

using it as storage for the compatible camera she possesses. Thus, the utility function takes the form:

� ��#,� = 2�� + %�� ∗ &�� + /�0�� (3)

The first two terms in equation Error! Reference source not found. consist of the utility

associated with the physical characteristics of memory, where 2�� is the standard-specific fixed effect of

memory card �, &�� is the quality of the memory card measured by megabytes and its coefficient

%�� measures consumer �’s sensitivity to quality or storage capacity. 0�� is the price of memory card

� and /� denotes price sensitivity.

Case 3: Camera & Memory

Assuming the purchased camera is compatible with the memory card (no consumer purchased

incompatible base product and add-on at the same time in our data), when a consumer simultaneously

purchases camera � and memory card � the utility function is a combination of those in the previous

two cases.

� ��,� = $�� + %��&�� +'(��(�~�)*+��4,

4-.+ 2�� + %��&�� + /�0�� + /�0�� (4)

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Case 4: No Purchase

If a consumer does not own a camera and she decides not to make a purchase of any product at time t,

we normalize the utility to zero.That is,

� ��#,# = 0. Moreover, we assume when purchasing only a memory card, consumers simply determine

whether the net utility is greater than zero, not the sum of all memory cards at hand. Thus, the no

purchase utility associated with only memory is also normalized to zero. This is due to the manner in

which we treat memory cards: while cameras are upgraded and replaced, memory cards are not.

However, if a consumer owns a camera and decides not to replace it with a new one, she continues to

receive utility from the camera and the compatible memory cards in inventory (if there is any) without

paying additional cost. Thus, the utility function has two components: possession of a camera, and the

add-on-to-base effect provided by inventory of compatible memory cards. Consequently, the per period

utility for a consumer who owns a camera and/or memory cards is

� ��#,# = 5� ∗'(*+�� = 1)6

�-.+ ' '(��[(*+�� = 1, �~�) ∗ *+��

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�-.]

,

�-. (5)

We determine the utility of the outside option with a “reduce form” approximation. Ideally, we

would include the gross utility of the camera or memory in inventory. Instead we capture the utility of a

camera with the parameter 5�, which is not camera-specific, and memory utility with parameter (�� ,

which is standard-specific due to the computational complexity associated with tracking which brand

and quality camera a consumer holds in inventory as well as the memory card standard and its quality.

Implementation of a more precise specification would increase the state space from 590513 to

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4.7890e+052 generating even more of a computational burden than the specified model.11 We therefore

approximate the outside option but realize that doing so incorporates a slight bias in our parameter

estimates from a model that more precisely tracks memory and camera utility. Utility functions for each

of the 18 choice alternatives are shown in Table A1 of the Appendix. In summary, this specification

demonstrates the fact that a consumer's existing product represents her state-specific outside option.

The utility of the outside option is a function of endogenously determined past choice. Lastly, we

assume the error term associated with each of the above deterministic components of utility above is

"9��,� and is independent and identically distributed with the Type I Extreme Value.

Note the memory inventory term links a consumer purchase decision of a camera and that of

memory cards into a single framework, i.e., a forward-looking consumer who makes a purchase

decision of a camera at time t will consider not only the extra utility generated by the compatible

memory cards in inventory, but also the effect of future price and quality of the memory cards. Without

this term, the purchase decisions of the two categories will be separated as in most existing literature

with the exception of Sriram, Chintagunta and Agarwal (2009) and Liu, Chintagunta and Zhu (2010) in

which the complementarity between the two categories is captured by a time-invariant term in the

utility function.

Our approach is fundamentally different from existing literature on cross-category purchases of

durable goods for the following reasons: First, we recognize the compatibility at the brand (for camera)

and standard level (for memory cards). This allows us to study how brand choices of base products are

driven by past, current, and future choices of standard of the add-on products. Second, we allow the

add-on-to-base effect to depend on the number and quality of the add-on products owned. Therefore,

the add-on-to-base effect can vary across time and affect the inter-temporal decision-making of

forward-looking consumers--since the more compatible memory cards accumulated, the higher the per-

11 With our current specification, the estimation procedure takes around 140 hours on an Intel Core i7-2640M PC.

,

20

period add-on-to-base effect. This implies that the accumulation of add-on products creates a higher

cost of switching for consumers to abandon the compatible base product. This allows us to provide

some explanation on the observation of consumers latching on to a particular brand of camera.

4.3. State Transitions

Inventory Process

According to our assumptions above, a consumer uses only the latest purchased camera. So when

camera � is purchased at time , its inventory becomes 1. When no camera is purchased at time , the

inventory for each brand � remains the same as in the last period. And if a different camera �′ is

purchased, the inventory of camera � is reset to zero because it is replaced by the new camera.

So the inventory process for camera is (after dropping the consumer index �)

*+��:.� =;<= 1 �>?��,. = 1*+�� >?��′,. = 0>@ABCC�′∈ �1,2, … , ��0 �>?��′,. = 1>@AB*D�′≠ � FG

H (6)

where ?��,.is the indicator of consumer's choice, with ?��,. = 1 meaning the consumer purchasing

brand �(� = 1,2,3,4,5,6,7) as the base product and any memory card (including no purchase) as add-

on product. *+�� is the beginning inventory of camera � at time . On the other hand, since memory cards do not become obsolete, the inventory process of

memory cards is the purchases accumulated through time.

*+��:.� = *+�� + ?�.,� (7)

Where *+�� is the beginning inventory of memory card �at time and ?�.,� is new purchase

during period . If no purchase is made at time , ?�.,� = 0. This process is in contrast to that of fast-

moving packaged goods, for which inventory is cumulative purchases minus consumption throughout

21

time. The transition matrix of inventory process from period to period +1 for the 18 choice options

is shown in Table A2 of Appendix 1.

Price and Quality Process

We assume that consumers have rational expectations about the stochastic processes governing the

evolution of price and quality, which follow a first-order Markov process. We also take into account

competitive reaction. Thus,

�B�IAB: KLlnOPQ RΩ�S.T = UV + WX ln OPQSY + ZVQ

�I�@AD:KLln O[Q RΩ�S.T = \V + ]X ln O[QSY + ^VQ

�B�IAB: KLln_PQ RΩ�S.T = U` + Wa ln _PQSY + Z`Q

�I�@AD:KLln_[Q RΩ�S.T = \` + ]a ln_[QSY + ^`Q

(8)

(Letters in bold denote vectors of all choice alternatives

( OPQ = (0��., 0��b, 0��c, 0��d, 0��e, 0��f, 0��g), ZVQ = hij�. , ij�b , ij�c , ij�d , ij�e , ij�f , ij�g k, O[Q =(0��., 0��b, 0��c), ^VQ = hlj�. , lj�b , lj�c k, _PQ = (&��., &��b, &��c, &��d, &��e, &��f, &��g), Z`Q =him�. , im�b , im�c , im�d , im�e , im�f , im�g k, _[Q = (&��., &��b, &��c), ^`Q = hlm�. , lm�b , lm�c k).UV, \V, U`B*n\`

are vectors of coefficients and Wop×p

and ]ot×t

are matrices that capture the influence of competitors’

price. KL. RΩ�S.T is conditional expectation given set of state variables Ω�S.. The variable ZVQu (^VQv )

are random price shocks of brand �(�) at time and Z`Qu (^`vQv ) are random quality shocks of brand

�(�) at time . We assume random shocks in prices of all �(�) brands, ZQ(^Q), follow a multivariate

normal distribution:

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22

ZVQ~w(0,Σxj)

^VQ~w(0,Σyj)

Z`Q~w(0,Σxm)

^`Q~w(0,Σym)

(9)

The diagonal elements in Σxj (Σyj,Σxm ,Σym ) denote the corresponding variance of ZVQ (^VQ, Z`Q, ^`Q) and the off-diagonal elements denote the covariance between prices (qualities) of different

brands. Allowing random shocks to be correlated can further capture the co-movement of prices

(qualities) of the competing brands. The price (quality) process parameters are estimated using the price

(quality) data prior to the estimation of the model. They are then treated as known in the model

estimation when we solve the consumer's dynamic optimization problem.

Notice here that our assumption of rational expectation is strong. In reality, prices (qualities) are

endogenously determined by the interaction of firms and consumer demands. As we do not have firm

level data, we make the assumption that prices (qualities) are exogenously set by firms, and consumers

are able to rationally anticipate the price (quality) trajectories based on historical prices (qualities) of the

focal firm and all competitors.

4.4. Dynamic Optimization Problem and Inter-temporal Tradeoffs

Given the base products and add-ons are durable in nature, we follow the standard literature and

assume the objective of the consumer �is to maximize the expected present value of utility over the

(finite) planning horizon = 1,2, … , �

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max|}~�,� �K['' ' ��?��,��,�|Ω��,

�-#

6

�-#

�

�-�]� (10)

where � is the discount factor. ?��,� is the choice indicator with ?��,� = 1 indicating alternative (�,�)

is chosen by the decision maker � at time and ?��,� = 0 indicates otherwise. Choice options are

mutually exclusive, so that ∑ ∑ ?��,� = 1,�-#6�-# . The state space for the dynamic optimization

problem at time for consumer �is Ω�� which consists of the set of inventory of camera and memory

cards, their prices, quality and the vector of unobserved taste shocks, so

Ω�� = ��u�Q, ��v�Q, OP�Q, O[�Q, _P�Q, _[�Q, ��Q� (11)

with letters in bold denoting vectors of all choice alternatives.

The timing of a representative consumer’s decision is as follows. A consumer in the model

makes purchase decisions for both base products and add-ons. She can choose cameras of seven

different brand groups and three compatible standards of memory cards. The adoption behavior of a

camera and a memory card may be at the same time or in a sequential order. A typical purchase pattern

is that a consumer first buys a camera and in a later period, she hopes to enhance functionality of the

camera, thus purchasing a memory card for greater storage space. The trade-off for consumers in this

adoption period is two-fold. First, when she chooses between standards of memory cards, some

standards are of high quality at the expense of high price while others are mediocre but less expensive.

Second, a consumer has to decide whether to adopt early or late. An early adopter of either base

products or add-ons sacrifices the high prices soon after product launch to gain the stream of

consumption utilities in the product life cycle, whereas a late adopter strategically waits for prices to

decline. The state variables that determine a consumer’s choice are expected prices of base products

and add-ons and their quality. After some time, new products (e.g. a camera with more pixel counts or a

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memory card of larger size) are introduced to the market, and the consumer becomes tired of using the

old camera and looks to upgrade her camera. The state variables in her consideration set now include

price, quality as well as inventory of cameras and memory cards at hand. The choice alternatives with

respect to the base product for her are (1) buy only a new camera of the same standard (2) switch to

another brand of camera. For the first alternative, she not only gains utility from the new camera itself,

but also she can continue using the memory card previously purchased. This add-on-to-base effect can

justify a consumer’s choice to stay with the existing standard; i.e. a consumer is locked-in by the add-

ons. In other words, the willingness to continue using the add-on products creates a switching cost for

consumers. In contrast, if a consumer finds another standard sufficiently attractive, she could forgo the

inventory of all memory cards and start with the new standard. She makes this switching behavior

because the competitor’s camera/memory card bundle provides higher total present value (discounted

future values) for her. For example, a competitor’s camera could be of high quality, or a competitor

develops a memory card of larger storage, or she anticipates price of a competitor’s memory card will

drop rapidly, etc.

The choice alternatives with respect to the add-on product are (1) add one more add-on

product compatible with the base product on hand to enhance usability and (2) stay with the current

inventory. As we can see here, consumers face tradeoffs in both the price (adjusted by quality)

dimension and the inventory dimension. The former tradeoff implies a sophisticated consumer take

into account price trajectories of add-on products when purchasing a base product. Even if facing an

attractive base product with a lower price, the consumer will anticipate the potential high burden of

purchasing add-on products (Gabaix and Laibson 2006), thus avoiding it. So a consumer needs to

sacrifice the price loss of base products to achieve an optimal strategy of purchasing the whole bundle

if the add-on prices are sufficiently lower. Whereas the latter tradeoff implies that, a standard switcher

sacrifices the utilities provided by compatibility of the existing base product and add-ons to obtain

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higher net utility from the other brand. On the other hand, a loyal consumer sacrifices higher net utility

from other standards to maintain continuous utility from previously purchased add-ons; in other words,

she would be locked in by the add-ons. In summary, our model incorporates trade-offs regarding own-

product inter-temporal price and quality effect, cross-category price and quality effect and cross-

category dynamic inventory effect. To our knowledge, this is the first paper to study these three effects

at the same time.

4.5. Heterogeneity, Initial Value, and Identification and Estimation

We adopt the latent class approach (Kamakura and Russell 1989) to incorporate unobserved

heterogeneity for quality preference, add-on-to-base effect, and price sensitivity.

Inventory of camera and memory card is an important state variable that plays a role in a consumer’s

decision process. As our sample starts in late 1998, we do not know the purchase history of consumers

before this time, which gives rise to an initial condition problem. Fortunately, we know that the first

series of digital cameras for the consumer-level market was launched after 1994. According to the

dataset of dpreview.com12, only 17 models of camera were launched before 1998. Therefore, at the

beginning of our sample period, very few consumers could have adopted cameras. We carefully

examine the data for the first two purchase occasions. For consumers who buy memory cards first and

an incompatible camera in a subsequent purchase occasion, we assume they adopted a compatible

camera before the start of the observation period. These consumers amount to roughly 1.09% of the

total sample. Specifically, we randomly assign a compatible camera purchase to one of the five periods

and in the case where multiple brands of cameras are compatible for a certain standard of memory card

we randomly assign a brand. Further, we use the first five quarters (1998 4th quarter to 1999 4th quarter)

12 http://www.dpreview.com/products/timeline?year=all&brand=&category=

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as a training period to determine consumers’ initial inventory level. Needless to say the concern from an

initial condition problem is minimal and we have attempted to minimize its effect.

The maximization of (10) is accomplished by choosing the optimal sequence of control

variables �?��,�� for � ∈ �0,1, … , ��,� ∈ �1,2, … ,�� and � ∈ �1,2, … , �� . Define the maximum

expected value of discounted lifetime utility as

��LΩ��T = max�|}~�,��?��,��,�

+ �K[ ' ' ' max|}~�′,�′

��?��′,�′��′,�′|Ω�� , ?��,�,

�′-#

6

�′-#

�

�-�:.]�

(12)

The value function � depends on the state at . Given takes values from an interval of finite length,

the value function can be written as

��LΩ��T = max�,�(��,�(Ω��)). (13)

Based on the Bellman equation (Bellman 1957),

��,�(Ω��) = ��,� + "��,� + �K max|}~�′,�′

[?��′,�′��′,�′LΩ��:.T|Ω�� , ?��,� = 1] (14)

at time T,the choice-specific value function is simply ��,�(Ω��) = ��,� + "��,� . We assume the

error terms are iid Gumble. The choice probability for consumer � to choose alternative (�, �) at time

has a closed-form solution:

0��,� = exp(��,�)∑ ∑ exp(��′,�′),�-#6�-#

(15)

,

27

where ��,� is the deterministic part of the choice-specific value function, i.e. ��,� = ��,� − "��,�. The corresponding log-likelihood function to be maximized is

LL = ''[''?��,�log(0��,�)��]

�

�-.

�

�-. (16)

To estimate the dynamic model, we follow the convention and fix the discount factor � at 0.95,

same for all consumers. Given there are 8 dimensions of state variables we encounter the problem of a

large state space. We adopt the interpolation method developed by Keane and Wolpin (1994) and

calculate the value functions at a subset of the state space, and then use these values to estimate the

coefficients of an interpolation regression to correct for such a problem. More specifically, we draw 100

state-space points and adopt a linear interpolation function of the state variables. Next, we use the

interpolation regression function to provide values for the expected maxima at any other state points

for which values are needed in the backward recursion solution process. We also assume the planning

horizon is 35 quarters (≈8.75 years, 1.75 times longer than our observation period).

5. Results and Discussion

5.1. Model Comparison

To evaluate the importance of incorporating the dynamic add-on-to-base effect, we compare the data

fitting performance of our proposed model with several alternative benchmark models. The first

benchmark model assumes zero discount factor, no add-on-to-base effect, and homogeneous

consumers. This is a myopic model, in which homogenous consumers are assumed to make

independent purchase decisions of base and add-ons to maximize current utility--consumers do not

consider the inter-temporal dependence between base product and add-ons. The second model adds to

the first benchmark model forward-looking consumers. Even though customers are allowed to take

into account future trends of prices and quality, their purchases of base product and add-ons are

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assumed to be independent since this model does not recognize compatibility. The third benchmark

model adds the add-on-to-base effect but assumes it is a constant. This model is similar to Sriram,

Chintagunta and Agarwal’s (2009) estimated model. We replace our add-on-to-base effect term, which

is a function of memory inventory, with a constant. It is important to note this model implicitly

assumes that the add-on and base products are not required to be purchased simultaneously like that of

Sriram et. al. for consumers to recover the constant term. The fourth benchmark model is the

aforementioned model without heterogeneous consumers. The fifth model adds heterogeneous

consumers and is our proposed model.


We estimate our proposed model with one to four segments. Comparison of BIC suggests the

two-segment model is the most preferred and that of AIC suggests the three-segment model. For ease

of interpretation, we pick the two-segment model as our proposed model and report model

performance of the two-segment model in the following discussion. Table 4 presents the log-likelihood,

AIC and BIC of the five alternative models. All of our dynamic models (Models 2-5) outperform the

myopic model (Model 1). This implies dynamic models have an advantage in explaining data that an

inherently dynamic process generates. Similarly, models recognizing the add-on-to-base effect (Models

3-5) outperform the ones that treat purchase decisions of base products and add-ons independently

(Models 1 and 2). AIC and BIC further improve when we replace the constant add-on-to-base effect in

Model 3 with cumulative inventory term of memory cards in Model 4. It shows that a model taking into

account all previously purchased memory cards better approximate the dynamic decision process of

making a new camera replacement decision.

5.2. Parameter Estimates

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Table 5. Estimation Results


In Table 5, we report the estimated coefficients for the proposed model. All the parameter estimates are

statistically significant at the 0.05 level. The intercept terms represent consumer intrinsic preference for

the seven brands of camera and three standards of memory cards. Comparison of these intercepts

reflects the relative attractiveness of different brands within each category, after accounting for the

other factors included in the utility function. For example, consumers in segment 1 prefer Sony and

Olympus, followed by Kodak, Canon, Fuji, Nikon, and HP in sequential order for cameras and

Standard 3, Standard 2, and Standard 1 for memory cards. However, the preference order is Sony,

Nikon, Kodak, Olympus, Canon, HP, and Fuji for cameras and Standard 2, Standard 3, and Standard 1

for memory cards for segment 2 consumers.

The coefficients of quality for camera and memory cards are both positive for both segments,

implying consumers care about the quality of the products. Not surprisingly, the coefficients of camera

inventory are positive for both segments, which suggests consumers are more likely to purchase

memory cards compatible with the camera they have in hand. As expected, the price coefficient is

estimated to be negative, showing consumers are price sensitive to the base and add-on products.

For all consumers, there is a significant add-on-to-base effect for all three standards of memory

cards. This confirms our conjecture that consumers with a higher number of memory cards

accumulated in the inventory display a higher probability of purchasing a camera that is compatible

with the memory cards. It is interesting to compare the magnitude of add-on-to-base effect across

standards. The add-on-to-base effect is highest for Standard 1, followed by Standard 3, and Standard 2

has the lowest effect. This implies that consumers value their previously purchased Sony memory cards

most. Given everything else equally, an owner of Sony memory cards is much more likely to purchase

another Sony camera, evident from Table 3, which presents a consumer’s probability of switching

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standards. More generally, the larger the add-on-to-base effect, the greater the cost of switching to a

new standard the consumer faces.

Comparing the estimates across the two segments, we find segment 1 consumers are defined

more by higher price sensitivity (-1.904 vs -0.487) and low quality sensitivity (0.428 vs. 1.122 for camera

and 0.111 vs. 1.488 for memory card). Consumers in segment 2 are characterized as being sensitive to

quality but less sensitive to price. For the remainder of the discussion, we refer to the first segment as

the price-sensitive segment and the second segment as the quality-sensitive segment. The price-sensitive

segment constitutes the majority of the population (91.7%). Interestingly, price-sensitive consumers are

found to have higher add-on-to-base effects. This is not surprising because price-sensitive consumers

are relatively more concerned about the future financial burden of purchasing memory cards. Thus,

they value more the memory cards in inventory.

5.3. Dynamic Add-on-to-Base Effect and Interaction with Future Prices of Add-ons

[Insert Figure 4 about Here]

Figure 4 characterizes a consumer decision rule describing how forward-looking consumers

make a dynamic choice of base products based on current inventory and the expected future price

sequence of compatible memory cards. Purchase probability of the compatible camera increases with

inventory of compatible memory cards. This is because when planning her purchase sequence in the

future, a consumer with higher inventory of memory cards, and thus extra storage space already in

possession, not only enjoys a long-term consumption utility stream, but also avoids a stream of future

spending on new memory cards. This is the dynamic add-on-to-base effect captured by our model.

Interestingly, the dynamic add-on effect is most prominent for Standard 1 (Sony’s) and Standard 3

cameras, in the sense that the purchase probability increases faster for the same amount of

accumulation in memory card inventory. This is because when compared with those of Standard 2,

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Sony’s memory card offers a higher consumption utility stream while Standard 3 memory cards offer

lower financial commitment. This implies that switching to an incompatible camera means not only

incurring a purchase price, but also a loss of long-term consumption utility as well as a future of

purchasing additional memory cards of another standard.

Figure 4 also presents how a current purchase decision of a camera is driven by the future price

trend of compatible memory cards. As expected, for all brands, when the expected future price of a

memory card decreases, the purchase probability of the compatible camera increases because the

financial commitment related to the planned purchase sequence for owning a composite of camera and

memory card(s) is lower compared with other brand bundles.

It is interesting to discuss how the future price expectations interact with the aggregate dynamic

add-on-to-base effect. The model determines and we illustrate in Figure 4 that the add-on-to-base

effect becomes more prominent when consumers expect future prices of compatible memory cards to

be lower. This is because when expecting lower future prices of memory cards, consumers holding the

same amount of memory cards in inventory can save more financial resources when purchasing new

memory cards in the future, thus making them even more likely to purchase the compatible camera. Put

in other words, the lower future prices of memory cards can enhance the dynamic add-on-to-base

effect for the compatible camera. Note, the interactive effect between the how inventory and price

affect purchase probability cannot be easily captured by reduced form models.

5.4. Quantify Purchase “Lock-In” due to Compatibility

Our dynamic model allows us to quantify the cost of switching consumers to an incompatible camera

when they have different inventory levels of memory cards. Our definition of the cost of switching is

the minimum lump-sum payment that a manufacturer needs in order to compensate a consumer to get

her to switch to its brand of camera. As the consumer is forward-looking, this cost of switching

measures the difference between total discounted values of two streams of utilities stemmed from

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purchasing two different cameras. More specifically, it is the difference between the continuation value

of purchasing a compatible camera and the continuation value of switching to an incompatible brand

divided by the price sensitivity coefficient. Given our way of defining the cost of switching, it is time

and state-dependent. Thus, we arbitrarily selected period ten, with which we calculated the monetary

equivalent of switching using the scenario of one representative consumer who has one compatible

memory card in inventory during this period.


We report the monetary value of the cost of switching for the two segments as well as for the

three brand groups in Table 6. On average, Olympus or Fujifilm needs to offer a $23.055 discount and

Kodak/Canon/HP/Nikon need to offer $21.024 to induce consumers to switch from Sony. Sony has

to offer only $8.482 to steal a consumer from Olympus/Fujifilm and $15.196 to induce brand switching

from Kodak/Canon/HP/Nikon.

From the above comparison, we see that Sony (the first row) has the highest cost of switching.

This means that for the same amount of inventory of memory cards, it is more costly to attract

consumers from Sony to other brands than vice versa. Thus, Sony enjoys the highest rates of “lock-in”

or loyalty because of the incompatibility: consumers tend to stick with the same standard, or choose the

brand names that are compatible with their inventories of memory cards. It is followed by Standard 3

cameras. This can be explained by the higher dynamic add-on-to-base effect modified by the price

expectation: having the same amount of memory cards on hand, Sony owners enjoy higher total

discounted future consumption utility from purchasing a compatible camera than purchasing a non-

compatible camera (the coefficient of add-on-to-base effect is highest for Sony). However, this is

mitigated by the higher expected future financial commitment in purchasing new memory cards

because we have shown that higher future prices lower the dynamic add-on-to-base effect. By this

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means, the introduction of the Memory Stick assists Sony in building strong brand loyalty because

consumers are tied to the standard by a high cost of switching. When product replacement becomes

more frequent as product quality improves over time, such lock-in effect creates continuous sales for

Sony.

The comparison of switching costs also indicates that it takes nearly double the amount of

discount to coerce consumers to switch from Standard 3 cameras than from Standard 2 cameras. This

is not only because Standard 3 cameras have higher -base effect, but also because the future prices of

Standard 3 memory cards are lower than those of Standard 2 cameras. This enhances the dynamic add-

on-to-base effect and competitiveness of Standard 3 cameras, which is not as high as that enjoyed by

Sony.

We also notice (present in Table 6) the cost of switching is higher among consumers in segment

1 (price-sensitive consumers) than consumers in segment 2 (quality-sensitive consumers). Recall that

price-sensitive consumers also have larger add-on-to-base effects and thus have the most utility to lose

by eliminating their current memory card inventory when switching standards.

5.5. Price Elasticity

Unlike those in the existing literature, our model is built at the brand and standard choice level, allowing

us to examine how price affects brand or standard switching decisions. In addition, our model takes

into account the inter-temporal dependence of base and add-on products, permitting us to study how

price affects brand or standard switching across categories. In Table 7, we report the percentage

changes in sales when the price increases by 10% for both camera brands and memory standards. There

are many notable results; however, we focus on the most interesting ones related to cross-category

elasticities.

,

34


First, it is interesting to note that own-category price effect dominates cross-category price

effect for all brands with the exception of Sony. When the price of Sony memory chips increases by

10%, purchase probability of the Sony camera decreases by 12.10%. With the same 10% increase in the

price of the Sony camera, however, purchase probability of Sony camera decreases only by 9.74%. In

other words, the change of purchase probability for the Sony camera decreases more when the price of

the compatible Standard 1 memory card decreases than when its own price decreases. This is because

the high price charged by Sony for its memory card prevents consumers from purchasing more

memory cards, thus eroding the dynamic add-on-to-base effect to a point that consumers become

highly sensitized to the price of memory cards.

Furthermore, when examining the cross-category elasticities listed in the last three columns, we

find that when the price of a Standard 1 or 2 memory card increases, most sales transfer to Standard 3

cameras. For example, when Sony increases the price of its memory card the sales of Standard 3

cameras (Canon, HP and Kodak) increase more than those of Olympus and Fuji. Similarly, when the

price of a Standard 2 memory card increases by 10% the sales of Standard 3 cameras also increase more

than Sony. This means that charging higher prices for memory cards drives consumers to a more open

standard in which more cameras can share the same memory card. It is also important to note that

competition among camera brands is most fierce within standards.

6. Policy Simulations We calibrated our dynamic model in order to conduct counterfactual analysis to examine the following

research questions: 1) How does the market change when we eliminate compatibility constraints? 2)

What if the inferior standard tries to be compatible with the superior standard? 3) Can a firm improve

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its market position by adopting a pricing strategy to take more advantage of the add-on-to-base effect?

4) Is incompatibility design beneficial for all firms?

6.1. Compatibility

To investigate the implication of compatibility, we carry out a simulation wherein we estimate average

choice probabilities of cameras and memory cards of different standards when the add-on-to-base

effect exists regardless of standards. For instance, a previously purchased Sony Memory Stick can be

used on any newly purchased cameras from Olympus, Fujifilm, Kodak, Canon, HP, and Nikon in

addition to Sony. Thus, all memory cards in inventory will exert the add-on-to-base effect to the

purchased camera, though in various magnitudes determined by the coefficient of add-on-to-base-

effect. To approximate this scenario, we set the standard-specific add-on-to-base effect to be the sum

of inventory of all memory cards as if no compatibility constraints exist across standards.


The second and third columns in Table 8 compare the purchase probabilities using original

parameter estimates with those generated by counterfactual simulation; from this we can understand

the extent to which compatibility changes purchase probabilities of base products. The results suggest if

Sony made its Memory Stick compatible with the products of all competitors, its market share would

have dropped by 7.04 percentage points (from 30.38 percentage points to 23.34 percentage points) in

the camera market, and the share of Memory Stick would have dropped by 5.51% (from 30.66% to

25.15%). This occurs because consumers are no longer locked-in by the Memory Stick. Without the

compatibility constraint, consumers are free to choose whatever brand of new camera they like for their

next purchase, which undermines Sony's brand equity, or brand synergy effect.

On the other hand, if Kodak, Canon, HP, and Nikon did not fight back by adopting their

distinct format (SD card) the camera market share for this brand group would have jumped by 8.11

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36

percentage points (from 47.49 percentage points to 55.60 percentage points), and the share for

Standard 3 memory cards would have increased by 8.19 percentage points (from 48.33 percentage

points to 56.52 percentage points). However, removing the incompatibility across standards has

marginal impact on the market shares of camera and memory cards of Standard 2.

6.2. Partial Compatibility

The first simulation shows that Sony’s proprietary standard of memory card (Standard 1) exerts strong

pressure on the market share of Standard 3 memory cards. One defending strategy for Standard 3

might be to create an adapter that allows its compatible cameras to read Standard 1 cards. By this

means, Kodak, Canon, HP, and Nikon can break down the lock-in effect of Sony’s memory card, thus

making their cameras more attractive. More specifically, we allow all cameras that are compatible with

Standard 3 memory cards, i.e. Kodak, Canon, HP and Nikon, to be compatible with Standard 1

memory cards. Therefore, we increase the size of the choice set from 18 to 22 by adding four new

choice alternatives, ��, �� = �(4,1), (5,1), (6,1), (7,1)� , because under this situation Kodak (c=4),

Canon (c=5), HP (c=6), and Nikon (c=7) can use the Sony Memory Stick (m=1). Moreover, the add-

on-to-base effect term is modified accordingly because Sony, Kodak, Canon, HP, and Nikon are now

all compatible with a Standard 1 memory card. So in the occasion of purchasing any of these five

cameras, a Standard 1 memory card in inventory will contribute to utility through the add-on-to-base

effect term.

Our simulation result reported in the second and fourth column shows that all Standard 3

cameras can steal market share from Sony cameras. For example, Kodak can increase its market share

by 3.54 percentage points and Canon can increase sales by 2.02 percentage points. This is because Sony

memory cards can be used with a third group of cameras, thus avoiding Sony’s add-on-to-base effect.

Consequently, the market share of Olympus and Fujifilm is smaller because of the added choice

alternatives leading to more fierce competition in the market.

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37

6.3. Alternative Dynamic Pricing Strategies

As mentioned in the data description session, Olympus and Fujifilm employed a pricing strategy for

cameras that was high in the first two years (2000 and 2001) and lowered later. The consequence of

such pricing is that consumers delay purchase. The low sales and hence fewer inventory of memory

cards during the first two years did not help these brands harvest the add-on-to-base effect. An

opposite strategy would be to start with a low price to attract consumers in purchasing both the camera

and memory cards and later exploit the high add-on-to-base effect from consumers’ high inventory of

memory cards by upping prices.

In the next policy simulation, we allow the prices of Olympus and Fujifilm to keep falling by 10%

each quarter during the first two years and then increase by 1% each quarter from 2002 to 2004.

Comparing the second and fifth columns of Table 8 shows that under the new pricing scheme, the

market share of Olympus and Fujifilm cameras would increase by 3.33 percentage points and 1.17

percentage points, respectively. Correspondingly, the overall market share of Standard 2 memory cards

would rise by 1.91 percentage points.

Olympus’s initial low price triggers consumers to adopt the camera early and enjoy the stream

of utility from the camera and memory cards onwards. With Standard 2 memory card in hand,

consumers are also more willing to buy Olympus cameras in later periods. In summary, we can think

of this new pricing policy as one that is more consistent with penetration pricing and product line

pricing, where lower initial prices boost camera and hence memory card sales. This increase for

memory cards permits the manufacture of cameras to generate higher consumer dynamic add-on-to-

base effect and lock in consumers to purchases of compatible cameras in later periods.

6.4. Incompatibility and Brand Equity

Recall in section 5.2 that Sony has the largest brand-intrinsic preference, or in other words, the

strongest brand equity in the camera market. Such lays the foundation for its success. If its brand equity

쪠Ҟ

38

were not as strong, the aid of the add-on-to-base effect stemming from incompatibility might be

marginalized and thus have less influence on the market for base products. So we find it necessary to

examine how brand equity and incompatibility are related. Does strong brand equity lead to greater or

lesser impact from incompatibility between base and add-on products? We run a series of policy

simulations where Sony’s brand-specific intercept is set to that of the brand that ranks 2nd to 7th in the

market. We compare the market share of Sony before and after eliminating incompatibility between

memory cards and cameras (as done in section 6.1). Figure 5 depicts how the effect of incompatibility

varies with Sony’s brand equity rank. As we can see, when Sony had the strongest brand equity, creating

incompatibility with other standards had a significant impact on its market share a decrease of 7.04

percentage points. This effect of incompatibility diminishes as Sony’s brand equity advantage vanishes

(from rank 1 to rank 4). Strikingly, when Sony’s brand equity falls below the industry average (rank 5 to

rank 7) its market share would have increased if it created a memory card format compatible with all

cameras. In other words, a market follower should not set up a compatibility constraint to bind itself.

This policy simulation can rationalize a well-known case of Betamax. In 1975, Sony introduced

the Betamax video standard and a year later JVC launched the competing standard VHS. For around a

decade the two standards battled for dominance, with VHS eventually emerging as the winner. Why did

Sony lose the video tape standard war but win the memory card standard war later? One possible

reason is that Sony didn’t have as strong brand equity in the VCR market as it did in the digital camera

area. Technically, (due to its solution to the recording head drum miniaturization,) Sony made its Beta

camcorders only record while VHS camcorders could review footage in the camcorder and copy to

another VCR for editing. With this limitation, Sony’s Betamax failed even though it was the market

pioneer and tried to take advantage of the lock-in effect of video tape format.

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7. Conclusions and Future Research High-technology durable products often comprise base products and add-ons. When making purchase

decisions, forward-looking consumers take into account price, quality, and compatibility and make joint

inter-temporal decisions. This paper provides a framework to explicitly model consumer brand and

standard choices of base and add-on products and investigate the dynamic dependence between two

product categories, when multiple standards exist. Distinguishing ourselves from prior literature, which

accounts for complementarity between product categories with a time-invariant constant term, we allow

forward-looking consumers to endogenize the purchase quantity of memory cards and to consider the

inventory of their memory cards when determining the purchase of base and add-on products. To our

knowledge, this is the first paper to incorporate the cross-category pricing and the cross-category

dynamic inventory trade-offs simultaneously. Furthermore, our analysis is at brand and standard level,

which enables us to calibrate cross-brand, cross-standard, and cross-category price elasticity and

compare the relative magnitude of each. Once given these elasticities, we further examined consumers’

switching propensity in brand and standard, as well as interdependence across categories. Our results

enrich the current literature by further probing competition at the standard and category level.

We found the dynamic add-on-to-base effect locks-in consumers to the base product brand and

becomes stronger with greater inventory levels of add-ons. Among three standards, Sony’s Memory

Stick enjoys the highest add-on-to-base effect, which further leads to highest cost of switching and

greatest lock-in effect. Following this, we demonstrated that Sony gained profits from developing its

proprietary standard of memory card (the Memory Stick). We also found such a strategy might not be

as profitable for a manufacturer with lower brand equity. On the other hand, we showed that when

making a purchase decision for the base product, consumers take into account future prices of the add-

on product because the financial commitment is related to the planned purchase sequence of both

categories. Furthermore, the dynamic add-on-to-base effect can be enhanced by lower future prices of

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40

add-ons. For example, if Standard 2 drops its initial price of memory cards, consumers will be triggered

to adopt the camera early and the market size of Olympus will be expanded.

Insights from this stream of research will offer managers more comprehensive product

strategies. For example, managers can employ pricing and promotion strategies for add-ons to improve

base product market performance by taking advantage of the cross-category pricing effect and cross-

category dynamic inventory effect. A cheaper price of add-ons in the early period of new product

introduction may encourage adoption and lock consumers in. On the other hand, market leaders may

consider designing exclusive add-ons, which can lead to greater market share of the base product.

Followers though should elect to either be compatible with the leading brand or create a union with

other players in the market to diminish the market power of the leading brand. Furthermore, pricing or

promotion strategies of add-ons should be targeted heavily at price-sensitive consumers than quality-

sensitive consumers.

Our research is subject to limitations that open areas for future research. First, with lacking

product attributes in our data, we can't estimate intrinsic preference for various models of cameras and

memory cards in a more refined fashion. Future works can further examine whether the documented

add-on-to-base effect is more prominent for a high-end product or low-end product. Second, the

current paper assumes price and quality are exogenously given. A very interesting topic to explore is

how firms design the full product line by deciding price trajectories for both base products and add-ons

taking consumers' dynamic decision-making processes into consideration. A full equilibrium model is

needed to solve this problem from both sides of supply and demand. Third, Gabaix and Laibson (2006)

reveal a very interesting phenomenon regarding base product and add-ons where firms shroud

information about add-ons to consumers. Only sophisticated consumers take advantage of the firm that

shrouds information by avoiding add-on purchases; the unsophisticated fall into the trap of high add-

on prices. Our paper supports the decision-making process of sophisticated consumers with evidence

41

of their consideration of base products and add-ons at the same time. Future research can modify our

model to allow only part of the consumers to be forward-looking with the rest short-sighted. Fourth,

we keep other firm strategies, for example product design, pricing, cost structure, exogenous. But in

reality, making add-on products compatible with base products involves engineering design, which will

affect other firm decisions as well.

References Bass, F. M. 1969. A new product growth model for consumer durables. Management Sci. 15(5) 215--227. Bellman, Richard (1957), Dynamic Programming, Princeton, NJ: Princeton University Press. Erdem, T., M. P. Keane, T. S. and J. Strebel. 2005. Learning about computers: An analysis of information search and technology choice. Quant. Marketing Econom. 3(3) 207--246. Farrell, Joseph, and Paul Klemperer, “Coordination and Lock-In: Competition with Switching Costs and Network E�ects,” in M. Armstrong and R. Porter, eds., Handbook of Industrial Organization, Volume III (Amsterdam: North-Holland, 2005). Farrell, J. and Simcoe, T. 2012. Four Paths to Compatibility. Oxford Handbook of the Digital Economy. Oxford University Press. Gabaix, X., Laibson, D. 2006. Shrouded Attributes, Consumer Myopia, and Information Suppression in Competitive Markets. Quart. J. of Econom. 121 (2): 505-540. Gentzkow, M. 2007. Valuing new goods in a model with complementarity: Online newspapers. Amer. Econom. Rev. 97(3) 713--744. Gordon, B. R. 2009. A dynamic model of consumer replacement cycles in the PC processor industry. Marketing Sci. 28(5) 846--867. Gowrisankaran, G., M. Rysman. 2007. Dynamics of consumer demand for new durable consumer goods. Working paper, Boston University, Boston. Guadagni, P. M., J. D. C. Little. 1983. A logit model of brand choice calibrated on scanner data. Marketing Sci. 2(3) 203--238. Liu, H., P. Chintagunta and T. Zhu 2010. Complementarities and the demand for home broadband internet services. Marketing Sci. 29(4) 701--720. Kamakura, Wagner and Gary Russell (1989), "A Probabilistic Choice Model for Market Segmentation and Elasticity Structure," J. of Marketing Res. 26 (November), 379-90. Katz, M. L., C. Shapiro. 1985. Network externalities, competition, and compatibility. Amer. Econom. Rev. 75(3) 424–440. Matutes, Carmen, and Pierre Regibeau, (1988), "Mix and Match: Product Compatibility Without Network Externalities," Rand J. Econom, vol. 19 (2), pp. 219-234. Melnikov, O. 2001. Demand for differentiated durable products: The case of the U.S. computer printer industry. Mimeo, Yale University, New Haven, CT. Nair, H. 2007. Intertemporal price discrimination with forward looking consumers: Application to the U.S. market for console video games. Quant. Marketing Econom. 5(3) 239--292. Norton, J. A., F. M. Bass. 1987. A diffusion theory model of adoption and substitution for successive generations of high-technology products. Management Sci. 33(9) 1069--1086. Rust, J. 1987. Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica. 55(5) 999--1033. Seetharaman, P. B., S. Chib, A. Ainslie, P. Boatwright, T. Chan, S. Gupta, N. Mehta, V. Rao, A. Strijnev. 2005. Models of multicategory choice behavior. Marketing Lett. 16(3--4) 239--254. Sethuraman, R., Srinivasan, V., Kim, D. 1999. Asymmetric and neighborhood cross-price effects: Some empirical generalizations. Marketing Sci. 18(1) 23-41.

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Song, I., P. K. Chintagunta. 2003. Measuring cross-category price effects with aggregate store data. Management Sci. 52(10) 1594--1609. Sriram, S., P. K. Chintagunta, M. K. Agarwal. 2009. Investigating consumer purchase behavior in related technology product categories. Marketing Sci. 29(2) 291--314. Train, Kenneth. 2003. Discrete Choice Methods with Simulation. Cambridge, UK: Cambridge University Press

Table 1 Memory Card Timeline13

Std. 1(SON) Std. 2(OLY/FUJ) Std. 3(KOD/CAN/HP/NIK)

1996 PCMCIA

1997

1998 DISK

SM CF 1999 DISK/MS

2000

MS 2001 CF/SD

2002 SM/XD

SD 2003 XD

2004

Table 2A. Summary of Purchase Incidences of Cameras and Memory Cards

Camera Purchases Memory Purchases Brand Frequency Percentage Standard Frequency Percentage Sony 274 29.34% 1 (Sony) 258 28.99% Olympus 154 16.49% 2 (Olympus, Fuji) 189 21.24% Fuji 59 6.32% 3 (Kodak, Canon, HP, Nikon) 443 49.78% Kodak 196 20.99% Canon 99 10.60% HP 70 7.49% Nikon 82 8.78%

Table 2B. Total Purchase Incidences

Camera\Memory 0 1 2 3 4 Total 0 1 2 0 0 0 3 0.12% 0.24% 0.00% 0.00% 0.00% 0.36% 1 19 644 54 6 2 725 2.29% 77.78% 6.52% 0.72% 0.24% 87.56% 2 29 30 29 3 0 91 3.50% 3.62% 3.50% 0.36% 0.00% 10.99% 3 1 4 3 1 0 9 0.12% 0.48% 0.36% 0.12% 0.00% 1.09% Total 50 678 86 10 2 828 6.04% 82.13% 10.39% 1.21% 0.24% 100.00%

13DISK: 3.5 floppy disk, MS: Memory Stick, SM: SmartMedia card, XD: xD card, CF: CompactFlash, SD: SD card

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Table 2C. Summary Statistics of Price and Quality

Sony Olympus Fuji Kodak Canon HP Nikon M 1 M 2 M 3 Price 521.577 429.172 339.028 387.213 504.043 256.239 342.537 65.182 72.989 62.230 Quality 3.898 3.895 3.547 3.889 4.082 3.316 4.444 3.058 2.900 3.089

Table 3. Brand (Standard) Swithing Matrix

Son C Oly C Fuj C Kod C Can C HP C Nik C M 1 M 2 M 3

Son C 60.526 5.263 0.000 21.053 5.263 2.632 5.263 67.692 3.077 29.231

Oly C 8.696 39.130 4.348 30.435 13.043 4.348 0.000 12.121 42.424 45.455

Fuj C 27.273 0.000 27.273 27.273 9.091 0.000 9.091 6.250 43.750 50.000

Kod C 33.333 9.524 0.000 33.333 4.762 0.000 19.048 20.833 8.333 70.833

Can C 16.667 16.667 0.000 0.000 33.333 33.333 0.000 8.333 8.333 83.333

HP C 18.750 6.250 6.250 25.000 12.500 18.750 12.500 13.043 4.348 82.609

Nik C 20.000 40.000 0.000 20.000 0.000 0.000 20.000 0.000 25.000 75.000

M 1 70.370 3.704 3.704 7.407 7.407 3.704 3.704 66.667 4.167 29.167

M 2 22.222 16.667 16.667 33.333 11.111 0.000 0.000 22.222 27.778 50.000

M 3 31.667 10.000 3.333 25.000 16.667 10.000 3.333 18.182 7.576 74.242

Table 4. Model Comparison

Model 1 Model 2 Model 3 Model 4

Proposed Dynamic Model

Two Seg. Three Seg. Four Seg.

-LL 8110.21 8225.81 8187.64 8077.33 6693.44 6519.36 6663.18 AIC 16250.43 16479.62 16407.27 16188.65 13456.88 13144.71 13468.36 BIC 16511.87 16723.63 16686.14 16484.95 14066.91 14068.48 14705.85

Table 5. Estimation Results

44

Table 6. Switching Cost

Average Sony Olympus/Fuji Kodak/Canon/HP/Nikon Sony $0.000 $23.055 $21.024 Olympus/Fuji 8.482 0.000 8.124 Kodak/Canon/HP/Nikon 15.196 17.397 0.000 Segment1 Sony Oly/Fuji Kodak/Canon/HP/Nikon Sony $0.000 $24.240 $22.004 Olympus /Fuji 8.845 0.000 8.474 Kodak/Canon/HP/Nikon 15.941 18.261 0.000 Segment2 Sony Oly/Fuji Kodak/Canon/HP/Nikon Sony $0.000 $9.961 $10.198 Olympus /Fuji 4.465 0.000 4.256 Kodak/Canon/HP/Nikon 6.966 7.847 0.000

Table 7. Price Elasticities

SonC OlyC FujC KodC CanC HPC NikC M1 M2 M3

SonC -0.974 0.312 0.126 0.457 0.243 0.139 0.178 -1.210 0.107 0.593

OlyC 0.525 -2.898 0.039 0.475 0.271 0.088 0.207 0.338 -1.718 0.643

FujC 0.493 0.490 -14.014 0.996 -0.002 0.501 0.501 0.219 -6.991 0.978

KodC 0.628 0.218 0.061 -1.398 0.165 0.082 0.147 0.364 0.186 -1.054

CanC 0.446 0.445 0.093 0.472 -3.538 0.267 0.176 0.633 0.311 -0.621

HPC 0.177 0.461 0.249 0.270 0.185 -4.457 -0.013 0.441 0.443 -0.904

NikC 0.186 0.450 0.053 0.306 0.201 0.097 -3.741 0.245 0.368 -1.793

OutC 0.006 0.000 0.005 -0.003 0.014 -0.007 0.008 0.016 -0.013 0.000

Model 1 Proposed Dynamic Model

One Segment Two Segments

Seg.1 (91.7%) Seg.2 (8.3%)

Parameters Est. SE Est. SE Est. SE Est. SE

Intercept: Sony (�Y) 1.341 (0.013) 1.112 (0.011) -0.557 (0.011) 2.731 (0.063)

Intercept: Oly (��) 0.389 (0.065) 0.207 (0.050) -0.559 (0.013) 0.327 (0.049)

Intercept: Fuji (��) -0.433 (0.090) -0.878 (0.043) -1.222 (0.023) -0.673 ((0.026)

Intercept: Kodak (��) 0.481 (0.014) -0.194 ((0.008) -0.608 (0.008) 0.665 (0.019)

Intercept: Canon (��) 0.004 (0.019) -0.572 (0.010) -0.671 (0.014) 0.302 (0.025)

Intercept: HP (� ) -0.722 (0.092) -0.682 ((0.077) -2.122 (0.045) 0.149 (0.066)

Intercept: Nikon (�¡) -0.921 (0.102) -1.614 (0.085) -1.946 (0.033) 0.799 (0.062)

Intercept: Std1 (¢Y) -0.299 (0.046) -1.589 (0.035) -2.327 (0.019) -0.221 (0.066)

Intercept: Std2 (¢�) -0.508 (0.060) -1.487 (0.059) -0.422 (0.025) 0.434 (0.095)

Intercept: Std3 (¢�) -0.346 (0.039) 0.084 (0.033) 5.240 (0.017) -0.024 (0.045)

Cquality (Uu) 0.685 (0.026) 0.707 (0.011) 0.428 (0.012) 1.122 (0.037)

Mquality (Uv) 0.929 (0.033) 0.709 (0.031) 0.111 (0.007) 1.488 (0.004)

Cinventory (£) 0.925 (0.076) 0.170 (0.078) 0.074 (0.011) 0.314 (0.010)

A-to-B: Std1 (¤Y) 0.803 (0.098) 0.790 (0.075) 1.076 (0.005) 0.654 (0.014)

A-to-B: Std2 ¤� 0.498 (0.103) 0.785 (0.096) 0.522 (0.006) 0.322 (0.010)

A-to-B: Std3 ¤� 0.726 (0.080) 0.173 (0.061) 0.644 (0.004) 0.604 (0.011)

Price (¥) -1.145 (0.010) -1.478 (0.008) -1.904 (0.000) -0.487 (0.000)

45

M1 -1.189 0.285 0.151 0.425 0.226 0.202 0.237 -3.448 0.313 0.742

M2 0.486 -2.682 -0.698 0.314 0.347 0.010 0.297 0.156 -4.425 0.719

M3 0.243 0.322 0.117 -0.675 -0.134 -0.116 -0.204 0.427 0.254 -2.512

OutM -0.011 -0.006 -0.018 0.023 -0.001 0.002 -0.003 0.005 0.001 0.035

Table 8. Policy Simulations

Market share of camera

Benchmark No Incompatibility Adapter Change Pricing Brand Equity

Sony 30.38% 23.34% (-23.17%) 26.54% (-12.64%) 30.00% (-1.25%) 18.37% (-39.53%)

Oly 16.13% 15.72% (-2.54%) 14.42% (-10.60%) 19.46% (20.64%) 18.62% (15.44%)

Fuji 6.00% 5.34% (-11.00%) 5.31% (-11.50%) 7.17% (19.50%) 7.52% (25.33%)

Kodak 22.44% 25.49% (13.59%) 25.98% (15.78%) 21.82% (-2.76%) 25.94% (15.60%)

Canon 10.52% 12.62% (19.96%) 12.54% (19.20%) 9.63% (-8.46%) 12.52% (19.01%)

HP 7.79% 9.58% (22.98%) 8.13% (4.36%) 7.00% (-10.14%) 9.08% (16.56%)

Nikon 6.74% 7.91% (17.36%) 7.08% (5.04%) 4.87% (-27.74%) 7.95% (17.95%)

Market share of memory cards

Benchmark No Incompatibility Adapter Change Pricing Brand Equity

Std1 30.66% 25.15% (-17.97%) 27.52% (-10.24%) 29.83% (-2.71%) 19.17% (-37.48%)

Std2 20.91% 18.33% (-12.34%) 19.56% (-6.46%) 22.82% (9.13%) 26.31% (25.82%)

Std3 48.33% 56.52% (16.95%) 52.83% (9.31%) 47.26% (-2.21%) 54.52% (12.81%)

Figures 1A and 1B. Purchase Incidences and Price Trend of Camera by Quarter

Figures 2A and 2B. Purchase Incidences and Price Trend of Memory Card by Quarter

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Figure 3. Percentage of Camera Purchases at Memory Card Inventory at 0 vs. 1

Figure 4. Purchase Probability of Camera is Driven by the Expected Future Price and Current Inventory of Memory Card

Figure 5. Sony's Market Share Loss of Eliminating Incompatibility at Different Brand Equity Ranks

0%

10%

20%

30%

40%

50%

60%

70%

Son Oly Fuj Kod Can HP Nik

Brand

Invm=0

Ivm=1

-8.00%

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

rank

1

rank

2

rank

3

rank

4

rank

5

rank

6

rank

7

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Appendix 1

Digital cameras became available to common consumers on February 17, 1994, when Apple, the creator of the Macintosh computer, introduced the Quick Take 100, a color digital camera with a 640x480 pixels14. Later in 1994, Olympus, another leader in the camera industry, introduced their Deltis VC-1100, the world's first digital camera with built-in transmission capabilities, allowing users to connect to a modem and upload digital photos over cellular and analog phone lines to another camera or a computer. Other pioneers in the market include the Kodak DC40 camera (March 28, 1995), the Casio QV-11 (with LCD monitor, late 1995), and Sony's Cyber-Shot Digital Still Camera (1996). Afterward, the industry saw a substantial boom of various models of digital cameras. The quality (measured by megapixels) of all brands of cameras gradually increased over time and there was no dominating brand of highest quality throughout the sample periods. The quality of memory cards (measured by megabytes) also rose as time went by. Standard 3 took a leading position until Standard 1 (Sony’s Memory Stick) caught up after 2003.

Table A1 Summary of Mean Utility Functions

1.only c1:��.,# = $.� + %��¦�.� + (.�*+�§�� + /�¨�.� 2.only c2:u9ªb,# = $b� + %��¦�b� + (b�*+�«�� + /�¨�b� 3.only c3:u9ªc,# = $c� + %��¦�c� + (b�*+�«�� + /�¨�c� 4.only c4:u9ªd,# = $d� + %��¦�d� + (c�*+�¬�� + /�¨�d� 5.only c5:��e,# = $e� + %��¦�e� + (c�*+�¬�� + /�¨�e� 6.only c6:��f,# = $f� + %��¦�f� + (c�*+�¬�� + /�¨�f� 7.only c7:��g,# = $g� + %��¦�g� + (c�*+�¬�� + /�¨�g� 8.only m1:��#,. = 2.� + %�� ∗ ¦�.� + 5� ∗ (*+�.�� = 1) + (.�*+�.�� ∗ *+�§�� + /�¨�.� 9.only m2:��#,b = 2b� + %�� ∗ ¦�b� + 5� ∗ ∑ L*+�� = 1Tc®-b + (b�*+�«�� + /�¨�b� 10.only m3:��#,c = 2c� + %�� ∗ ¦�c� + 5� ∗ ∑ L*+�� = 1Tg®-d ++(c�*+�¬�� + /�¨�c� 11.c1 & m1:��.,. = $.� + %��¦�§� + 2.� + %��¦�.� + (.�*+�§�� + /�(¨�.� + ¨�.�) 12.c2 & m2:��b,b = $b� + %��¦�«� + 2b� + %��¦�b�+(b�*+�«�� + /�(¨�b� + ¨�b�) 13.c3 & m2:��c,b = $c� + %��¦�¬� + 2b� + %��¦�b� + (b�*+�«�� + /�(¨�c� + ¨�b�) 14.c4 & m3:��d,c = $d� + %��¦�¯� + 2c� + %��¦�c� + (c�*+�¬�� + /�(¨�d� + ¨�c�) 15.c5 & m3:��e,c = $e� + %��¦�°� + 2c� + %��¦�c� + (c�*+�¬�� + /�(¨�e� + ¨�c�) 16.c6 & m3:��f,c = $f� + %��¦�±� + 2c� + %��¦�c� + (c�*+�¬�� + /�(¨�f� + ¨�c�) 17.c7 & m3:��g,c = $g� + %��¦�²� + 2c� + %��¦�c� + (c�*+�¬�� + /�(¨�g� + ¨�c�) 18.no purchase:��#,# = 5� ∗ ∑ L*+�� = 1Tg®-. + (.�*+�.�� ∗ *+�§�� + (b�(*+�b�� + *+�c��) ∗*+�«�� + (c�(*+�d�� + *+�e�� + *+�f�� + *+�g��) ∗ *+�¬��

Table A2 Transition Matrix of Inventory Process

Choice invc.ª:. invcbª:. invccª:. invcdª:. ivceª:. ivcfª:. invcgª:. invm.ª:. invmbª:. invmcª:.

(0,0) invc.ª invcbª invccª invcdª invceª invcfª invcgª invm.ª invmbª invmcª (1,0) 1 0 0 0 0 0 0 invm.ª invmbª invmcª (2,0) 0 1 0 0 0 0 0 invm.ª invmbª invmcª

14http://www.thehistoryof.net/the-history-of-digital-cameras.html

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(3,0) 0 0 1 0 0 0 0 invm.ª invmbª invmcª (4,0) 0 0 0 1 0 0 0 invm.ª invmbª invmcª (5,0) 0 0 0 0 1 0 0 invm.ª invmbª invmcª (6,0) 0 0 0 0 0 1 0 invm.ª invmbª invmcª (7,0) 0 0 0 0 0 0 1 invm.ª invmbª invmcª (0,1) invc.ª invcbª invccª invcdª invceª invcfª invcgª invm.ª+1 invmbª invmcª (0,2) invc.ª invcbª invccª invcdª invceª invcfª invcgª invm.ª invmbª+1 invmcª (0,3) invc.ª invcbª invccª invcdª invceª invcfª invcgª invm.ª invmbª invmcª+1

(1,1) 1 0 0 0 0 0 0 invm.ª+1 invmbª invmcª (2,2) 0 1 0 0 0 0 0 invm.ª invmbª+1 invmcª (3,2) 1 0 0 0 0 invm.ª invmbª+1 invmcª (4,3) 0 0 0 0 0 0 0 invm.ª invmbª invmcª+1

(5,3) 0 0 0 0 1 0 0 invm.ª invmbª invmcª+1



Appendix 2 Identification Simulation

We demonstrate the ability of our model to recover model parameters via a simulation study. Our simulation scheme is as follows: First, we simulate price and quality series data, based on the following transition probability VQ = 0.95 ∗ V·SY + ¸Q, ¸Q~w(0,0.25 ∗ ) `Q = 1.1 ∗ `·SY +¹Q, ¹Q~w(0,0.25 ∗ ) . The market structure is set to be the same as the real data where seven brands of cameras belong to three groups and three memory card standards are associated with each of the three groups. We generate the price series for 4 time periods. We use the utility specification as in part 4.2. Given the price series, we compute the observable part of

the value functions. We then generate the value function by simulating the Type I extreme value error term "��,�.

We simulate the purchasing behavior of 1200 individuals. Using the computed values of the ��′º, we decide

the timing of purchase by comparing ��,� with ��#,# (outside option of no purchase). We generate 50 data sets for the same values of the parameters. The results are shown in Table A14. All estimates are within two standard deviations from the true values. This result demonstrates the ability of our model to recover the quality, inventory, and price coefficients.

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Table A3 Simulation Results

Parameters True Value Estimates Std Camera Intercept: Sony 1.8 1.775 0.640 Camera Intercept: Olympus 1.6 1.441 0.551 Camera Intercept: Fujifilm 1.5 1.436 0.660 Camera Intercept: Kodak 1.4 1.239 0.545 Camera Intercept: Canon 1.6 1.490 0.701 Camera Intercept: HP 1.8 1.672 0.515 Camera Intercept: Nikon 1.5 1.500 0.542 Memory Intercept: Standard1 1.5 1.518 0.639 Memory Intercept: Standard2 2.7 3.050 1.111 Memory Intercept: Standard3 1.9 1.669 0.784 Camera Quality 0.6 0.478 0.522 Memory Quality 0.5 0.491 0.371 Camera Inventory 1.1 1.105 0.516 Memory Inventory 0.5 0.556 0.495 Price -1.0 -0.937 0.305

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