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Essays on the luxury fashion market

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Essays on the Luxury Fashion Market
by
Yao (Alex) Yao

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OR PHILOSOPHY
(BUSINESS ADMINISTRATION)

May 2019

i

Acknowledgements
I would like to thank my advisor, Dr. Sha Yang, whose guidance has helped me complete
my dissertation. My study in the program would have been much harder without her help. I am
very grateful for her patience and support. It is an honor to be her student and to work with her. I
also appreciate the help from my committee members and coauthors, Yu-Wei Hsieh, Lan Luo,
Sivaramakrishnan Siddarth, and K. Sudhir.
I have learned a lot from very supporting faculty members at the Marshall School of
Business. I would especially like to thank Gerry, CW, Anthony, Dina, Botao, Max, Davide, and
Dinesh, for their generous help. Another important asset from Marshall is my dear colleagues
and alumni. Linli, Yi, Lin, Shijie, Michael, Zibin, Wayne, Ari, Bora, and especially Xiaoqian Yu,
kindly helped me with my research. I have had a great time with my tennis partners and friends,
Jenn, John, Jihoon, Zhengnan, Steven, Luke, Francesca, Wensi, Wayne, and Wei over the past six
years. Special thanks to Medha, who has accompanied me through the hardest times and is
always there supporting me, and her family, who offered tremendous help and encouragement
when I was on the job market. I feel fortunate to have these friends who have made my daily
grind so much better. I also want to thank people who have hurt me. They have given me very
different experiences which have made me grow and become the person I am today. Without
some of them, I would probably not have started this Ph.D. at all.
Finally, I would like to dedicate this dissertation to my family. I am truly grateful for my
parents, grandparents, my aunt and cousin Hovey. They have been selflessly supporting and
taking care of me. Without them, I would not have been able to survive through this program. I
hope they are happy to know that there will be no more schooling for me!
ii

Contents
List of Tables ..................................................................................................................... iv
List of Figures .....................................................................................................................v
1. Overview .......................................................................................................................1
2. Consumer Demand for Luxury Goods: The Prestige and Substitution Effects of
Price ...............................................................................................................................4
2.1 Introduction ................................................................................................................4
2.2 Literature Review .......................................................................................................9
2.2.1 Effect of Price on Consumer Demand ....................................................................... 9
2.2.2 Luxury Product Market ............................................................................................ 11
2.3 Proposed Model ........................................................................................................12
2.3.1 Choice of the Best Price Version within Each Brand .............................................. 16
2.3.2 Choice of the Best Brand Conditioned on Optimal Price Versions ......................... 17
2.4 Empirical Application ..............................................................................................19
2.4.1 Background Information .......................................................................................... 19
2.4.2 Data Description ...................................................................................................... 20
2.4.3 Assumption Validation ............................................................................................ 25
2.4.4 Model Estimation ..................................................................................................... 26
2.4.5 Estimation Results ................................................................................................... 27
2.4.6 Benchmark Analysis ................................................................................................ 31
2.5 Managerial Implications ...........................................................................................35
2.5.1 Price Elasticity Analysis .......................................................................................... 35
2.5.2 What-if Analysis ...................................................................................................... 38
2.6 Conclusion ................................................................................................................40
3. When Fashion Firms Choose Their Customers for Brand Image: A Two-sided
Matching Approach ...................................................................................................44
3.1 Introduction ............................................................................................................44
3.2 Related Literature...................................................................................................49
3.2.1 Fashion Choices and Branding ................................................................................ 50
3.2.2 Two-sided Matching ................................................................................................ 52
3.3 The Model ..............................................................................................................53
3.3.1 Second Stage: Two-sided Matching ........................................................................ 54
3.3.2 First Stage: Brand Price-line Strategies ................................................................... 58
3.3.3 Identification Strategy .............................................................................................. 60
3.4 Empirical Application ............................................................................................62
3.4.1 Background Information .......................................................................................... 62
iii

3.4.2 Data Description ...................................................................................................... 65
3.4.3 Model Estimation ..................................................................................................... 68
3.4.4 Estimation Results and Model Comparisons ........................................................... 71
3.4.5 Counterfactual Analyses .......................................................................................... 77
3.5 Conclusion .............................................................................................................81
4. Conclusion ..................................................................................................................85
Bibliography .....................................................................................................................89

iv

List of Tables
Table 1. Summary Statistics of the Six Brands in Watch Category .................................22
Table 2. Summary Statistics of Demographic Variables ..................................................23
Table 3. Attribute Probability Prediction Based on Price ................................................25
Table 4. Proposed Model Estimation Results ...................................................................28
Table 5. Benchmark Models (Continuous Price Approach) ..............................................29
Table 6. Benchmark Models: A Reduced-Form Model ....................................................32
Table 7. Benchmark Models: An Alternative Decision Process Model ...........................34
Table 8. Summary Statistics of Price Elasticities at the Optimal Prices ..........................36
Table 9. What-if Analysis Results - 10% Higher Baseline Prestige Effect ......................39
Table 10. What-if Analysis Results – Income Expansion by 2 levels ..............................40
Table 11. Summary Statistics of Consumer Characteristics .............................................66
Table 12. Summary Statistics of the 43 Watch Brands ....................................................67
Table 13a. Estimation Results – Firm Preference ............................................................72
Table 13b. Estimation Results – Consumer Preference ...................................................73
Table 14. Estimation Results – Benchmark Model ..........................................................77
Table 15. Counterfactual Results - Sales and Price Line Strategies .................................79
Table 16. Counterfactual Results – Number of Brands in Each Price Tier ......................81
Table 17. Counterfactual Results – Consumers Characteristics of Each Group ..............81

v

List of Figures
Figure 1. Price Elasticities at the Optimal Prices .............................................................37

1. Overview
Over the past decade, the luxury fashion market has grown tremendously. The value of
the global fashion and luxury market reach $2.4 trillion in 2016, accounting for 2% of the
world’s GDP. Beyond its economic importance, this market has several interesting features
worth attention, such as the prestige effect and selective selling. However, there are very few
papers in economics or marketing studying this marketing using empirical methods. My
dissertation fills this gap by empirically investigating the Chinese luxury fashion watch market.
My first essay focuses on the consumer demand for luxury goods. It develops an
empirical modeling framework that accommodates the positive “prestige” effect of price
controlling for quality, while accommodating the negative effect of price on utility through the
“substitution effect” because it reduces the money available for consumption of other goods. The
proposed model is built upon the utility-maximization framework with two novel extensions.
First, unlike the classic demand model where price does not enter the marginal utility, this essay
allows price to affect the marginal utility of a product to capture the prestige effect of price,
while controlling for product attributes and consumer quality perception. Second, since each
luxury brand has many versions associated with different price points, and some price versions
may not be observed from data, this essay jointly models the decisions of which brand and at
what price of an individual consumer. This model is applied to a unique survey-based dataset on
Chinese consumer luxury purchase, supplemented with attribute information from another
source. Several interesting findings emerge from this essay. First, it detects a strong prestige
effect and substitution effect of price on consumer luxury demand. It confirms the hypothesis
that the positive effect of price on luxury demand goes beyond the price-quality inference. A
direct implication from this finding is that price elasticity can be positive for a luxury product
2

when the positive marginal prestige effect is larger than the negative marginal substitution effect
of price in magnitude. Second, it finds that family income has a U-shape relationship with the
prestige effect, suggesting that lower-end and higher-end of the middle income plus consumers
tend to enjoy more prestige from price. Finally, what-if simulations show that luxury brands can
increase their market shares and revenues by enhancing the prestige effect of price to consumers.
Moreover, an increase in income benefits higher-priced luxury brands but has a complex effect
on lower-priced ones.
My second essay examines the fashion market. Many fashion companies strategically
target preferred consumers because such consumers not only generate revenue, they also
influence the companies’ brand image. It is important to jointly model the preferences of
consumers and firms in this scenario because observed brand choice is an outcome of mutual
selection from both sides. The second essay develops a two-sided matching framework to model
demand as realized from such a two-sided selection process. An entry model is embedded to
capture the endogenous price-line decisions. To cope with computation challenges in the model
estimation, this essay applies approximate Bayesian computation and parallel computing
techniques. Applying the proposed structural model to consumer demand for fashion brands, this
essay finds empirical support for mutual preferences between European brands and well-
educated, wealthy consumers, and a standard discrete choice model leads to biased parameter
estimates. It also detects some unreciprocated preferences between young consumers and
European brands, meaning that the consumers below age 40 like European brands, although such
preferential relationship is not reciprocal. European brands will generate more revenue if they
target young consumers who are below 40. Counterfactual analyses show that if fashion brands
prioritize short-term revenue compared to brand image, prestigious brands would extend their
3

price-lines downward. Although these brands would gain more revenue, they would lose some
preferred consumers. Less-prestigious brands, on the other hand, would not adjust their price-line
strategies regardless of market and revenue losses.

4

2. Consumer Demand for Luxury Goods:
The Prestige and Substitution Effects of Price
2.1 Introduction
The market for luxury goods continues to grow globally both in the number of consumers
and the volume of consumption. With the rapid growth in emerging markets, especially China, the
global market has expanded from 140 million to over 350 million luxury product consumers in
just the last two decades (Kim and Ko 2012). According to the report of “The Changing Dynamics
of Luxury Consumption” from the Boston Consulting Group, the worldwide total expenditure on
luxury goods reached 1.8 trillion dollars in 2014, with an expected annual growth rate of 7% in
the near term. According to the same report, China is now one of the three largest luxury markets
in the world. Despite its growing importance in the economy, there is very limited empirical work
in marketing science and economics about consumer choice of luxury goods.
A distinguishing characteristic of luxury goods is that there can be a positive correlation
between price and utility after controlling for consumer quality perception and product attributes.
This is because luxury products can confer prestige to buyers (Veblen 1899; Hans Nunes and Dreze
2010). This positive correlation is named as the “prestige effect”. The prestige effect can be driven
by both extrinsic and intrinsic motivations. The extrinsic motivation refers to the incentive of
consumers to use their luxury consumptions to signal wealth or social status to others. For a luxury
good to have a “status signaling” effect in equilibrium, it should have a higher price than a
“standard good” of comparable quality (Bagwell and Bernheim 1996), so that with its purchase,
the buyer can be seen to have more affluence than one who buys the standard good. A buyer of the
Lexus ES, which is in many respects functionally and structurally similar to the Toyota Camry,
pays a $10,000 price differential, not merely because of the additional quality, features and service,
5

but also because it helps to signal the driver’s affluence relative to those driving a Camry.
Effectively, price enhances the buyer’s utility directly by conferring prestige (Leibenstein 1950;
Ng 1987; Lichtenstein, Ridgway and Netemeyer 1993), beyond the quality adjusted utilitarian
value.
The prestige effect of price can be also driven by intrinsic motivations. For example, luxury
consumption may make the individual feel good about him/her self. In particular, industry experts
claim that luxury products can help instill personal confidence, which is an important intrinsic
motivation to induce luxury product consumption for some consumers. In this essay, we do not
distinguish between these two different underlying driving forces, and instead, we try to model the
overall prestige effect.
On the other hand, even for luxury goods, higher prices can drive down demand (Mas-
Colell, Whinston and Green 1995), because it depletes the consumer’s budget available for
consumption from other categories. This is the standard “substitution” effect of price as defined in
economics. The substitution effect of price is generally greater among lower income consumers.
However, it becomes more relevant for luxury goods marketing, as the luxury market expands
downstream, i.e. towards more middle class consumers.
The goal of this essay is to develop an empirical modeling framework that accommodates
the positive “prestige effect” of price controlling for the quality effect, while accommodating the
negative effect of price on utility through the “substitution effect” because it reduces the money
available for consumption of other goods. Modeling and disentangling the heterogeneous positive
effects of price through prestige from the negative substitution effects of price in a demand system
is potentially important in counterfactual analysis, depending on whether the price change is likely
6

to impact more the substitution or prestige effect for those customers who find the product to be
within their budget for the category.
Note that the need for prestige or status, however, is not confined only to the wealthy;
neither is it necessarily monotonically increasing in wealth. At every level of income, the need for
prestige exists and the desire to signal status relative to neighboring income classes exists. The rise
of so-called “masstige” brands or prestige brands for the masses in many categories reflects this
insight. For example, Kate Spade and Michael Kors have started to offer handbags for 300 dollars
or less. In fact, the expansion of the Chinese luxury goods market is not only driven by the super-
wealthy but also by even lower middle class consumers, who save several months of incomes in
order to afford expensive products. While price sensitivities due to substitution effects are clearly
likely to be much lower among the higher income classes, there is no clear theoretical prediction
about who is likely to be more prestige sensitive (Veblen 1899; Sharma and Alter 2012). We
therefore consider the relationship between income and prestige effect as an empirical question.
We extend a standard model of consumer choice based on utility maximization subject to
budget constraint (Allenby, Arora and Ginter 1998) to model luxury good choice. First, we
accommodate the prestige effect by allowing price to affect the direct utility from the inside good.
We allow this prestige-related utility to be affected differentially by income and other
demographics to infer the heterogeneity in prestige effect. This direct effect of price on consumer
marginal utility leads to additional complexity in deriving the optimal consumer choice decisions.
Second, since luxury brands usually have a large number of versions associated with
different price points, and many price versions may not be fully observed from data, we jointly
model which brand and at what price version are chosen by an individual consumer. We derive the
optimal solution by developing a “max-in-max” approach, that is, to embed the optimal
7

version/price choice into the brand choice decision. More specifically, the “max-in-max” approach
can be summarized in the following two-step procedure. In the first step, we model consumer
choice of optimal price version within each brand. Since price enters the marginal utility and
budget constraint, we numerically derive the optimal price version for each brand for a consumer.
In the second step, given the best price version of each brand, the consumer will pick the brand
that gives the highest utility among all the brands.
We estimate the model using a unique survey-based dataset of Chinese middle to upper
class consumer purchases of high-end brands of watches, collected by one of the leading marketing
research companies. Since repeated purchase of luxury products is not common, it is not feasible
to obtain panel data as is common in the analysis of choice for repeatedly purchased consumer-
packaged goods. As such, the cross-sectional survey data need to be augmented with more
information about the products and households in order to generate insights on consumer purchase
behavior in luxury categories. We gather product attribute data from a large online watch retailer.
Beyond standard observable demographics such as gender, education and income, we also collect
typically “unobservable to the researcher” metrics that drive choices. In particular, we collect
information such as the quality perception of brands to control for individual heterogeneity in
brand preferences. More importantly, we observe information about budget allocated to the
category (rather than entire income), which is the key to identify the prestige and substitution
effects. Given that panel data on luxury goods categories are typically unavailable due to the
relative infrequency of purchases in these categories, our approach of using cross-sectional survey
data augmented with typically unobservable information about quality perceptions and budget
allocation to aid identification in this manner is a practically useful approach to gain insight into
consumer demand for luxury goods.
8

Several interesting findings emerge from our analysis. First, we detect strong evidence of
the positive prestige effect of price, after controlling for the negative substitution effect of price.
Although we find a positive correlation between price and perceived quality, the prestige effect
continues to remain significant even after controlling for consumer quality perception and product
attributes. Thus, the prestige effect is more than due to consumer taste for quality. A direct
implication from this finding is that price elasticity can be positive for a luxury product when the
positive marginal prestige effect is larger than the negative marginal substitution effect of price in
magnitude.
Second, we find that prestige effect has a non-monotonic U-shaped relationship with
income among the middle income plus households (incomes >200K Yuan). Thus, the lower end
and the upper end of the middle plus classes enjoy more prestige from price. Anecdotal evidence
about how purchase of Louis Vuitton handbags by secretaries has caused shifts among the super-
wealthy to move away from these brands supports the notion of the U-shaped link between prestige
effect and income. The low end of the newly emerging middle class needs to differentiate
themselves from the poor and gain confidence through conspicuous consumption. The very
wealthy have the most resource to enjoy the prestige. The moderately wealthy have the least need
for prestige.
Finally, what-if simulations show that luxury brands can increase their market shares and
revenues by enhancing the prestige effect of price to consumers. Moreover, an increase in income
benefits higher-priced brands but has a complex effect on lower-priced ones. This is because the
lower-priced brands may not provide high-end products to meet consumers’ demand for prestige.
Therefore, it is crucial for luxury companies to understand the complex interplay of these two price
effects in driving consumer demand for luxury goods.
9

The rest of the essay is organized as follows. In the next section, we review previous
work on price effect and luxury product market in the marketing, economics and psychology
literature. We then propose the model to capture the prestige and substitution effects of price. The
model section is followed by an empirical application where we introduce the data, estimate the
model and report the estimation results. We then derive managerial implications of this study. We
conclude the essay by highlighting our key contributions and pointing out limitations with future
research directions.
2.2 Literature Review
2.2.1 Effect of Price on Consumer Demand. Understanding how price affects consumer
demand has been a central topic in both economics and marketing. The classic economic theory
assumes that consumers’ direct utility depends on quantity of the goods consumed but not on price
(e.g. Mas-Colell, Whinston, and Green 1995). Price affects the total utility only through budget
constraint. That is to say, higher price deprives consumers of the ability to buy the outside good.
This negative effect on the budget constraint is known as the “substitution effect”. Although this
assumption is widely accepted in the literature, it faces challenges. For example, Erickson and
Johansson (1985) found that price plays both positive and negative roles in helping consumers
form product evaluations. One positive role comes from the correlation between price and quality.
This is consistent with a stream of literature who argued that consumers differentiate products
based on prices because a high price can send a message of high quality (Scitovsky 1945, Milgrom
and Roberts 1986, and Qian 2014).
Apart from the quality effect, price can positively affect consumer demand through other
channels. Lichtenstein, Ridgway and Netemeyer (1993) found that prestige sensitivity induced by
a higher price plays an important role in driving higher demand. Unlike the inference of the
10

product’s higher quality consumers can make from a higher price, one way that prestige effect
works is that higher price signals to others about the consumers themselves. An example given in
their work is expensive wine consumption. A purchase of an expensive wine is not because of the
quality perception per se. Instead, it is because of beliefs that others will perceive the high price as
a reflection of the purchasers’ certain traits (social status, good tastes etc.). This is widely supported
in the marketing literature that people make inferences about others on the basis of their
possessions (Belk, Bahn, and Mayer 1982, Belk 1988 and Burroughs, Drews, and Hallman 1991).
Meanwhile, Plassmann et al. (2008) showed that the high price of luxury products can make
consumers feel good even without signaling to others. Plassmann et al. (2008) used a neural
science method to show that an increase in price leads to more neural representations of
experienced pleasantness. This can be because the high price gives consumers a sense of self-
actualization since they work hard to afford luxury products.
It is worth noting the key difference between the quality effect and the prestige effect. For
the quality effect, price provides consumers with only an inference of the quality. It is the quality,
rather than the price, that directly affects consumers’ utility. In other words, price has an indirect
effect on the marginal utility and consumer demand. Erdem, Keane and Sun (2008) used a learning
framework to study this quality effect. Since quality perception data are unavailable, they allow
consumers to receive quality signals from price levels. In this essay, we use consumer quality-
perception data to directly control for this quality effect of price.
In contrast, price has a direct effect on consumers’ marginal utility as reflected in the
prestige effect. Since price is an attribute that people can “consume”, it requires the price to be
incorporated into the marginal utility function. Leibenstein (1950) and Kalman (1968) also
suggested considering a marginal utility function that depends on both prices and quantities of
11

consumption goods. Pollak (1977), Ng (1987) and Mandel (2009) applied a price-dependent utility
structure to model demand for luxury goods and derived some theoretical propositions. However,
previous work is mostly theoretical. To the best of our knowledge, this essay is the first to
structurally model the prestige effect of price on demand and estimate the model parameters using
choice data. This essay introduces a random-utility maximization framework to model consumer
choices of luxury watch brands, where price directly affects the marginal utility.
2.2.2 Luxury Product Market. This essay also contributes to the literature on luxury
products. Grossman and Shapiro (1988) pointed out that a luxury good is traditionally defined as
one such that the mere use or display of a particular product brings the owner prestige apart from
any functional utility. As stated in his landmark work “The Theory of the Leisure Class”, Veblen
(1899) claimed that what confers wealth is not the accumulation of wealth itself, but the signal or
evidence of wealth. The reason for a rich family to use luxury products is not because of their
practical function, but because of their capacity to show that this family can afford them. Although
conventional wisdom suggests that higher income groups are more likely to purchase expensive
goods, Sharma and Alter (2012) pointed out that the inferiority and unpleasant affect associated
with financial deprivation motivates consumers to purchase scarce goods rather than comparable
abundant goods. Thus, lower income consumers could benefit more from the prestige effect. In
this essay, we will account for a possibly non-linear relationship between income and the prestige
effect.
Several papers have studied the overall relationship between luxury demand and price.
Kemp (1998) found that demand for luxury goods decreases as their prices increase. However,
Bilge (2015) showed that demand and price are positively correlated for some luxury products.
These mixed findings suggest the importance of modeling both the prestige effect and the
12

substitution effect of price on luxury product demand. If the prestige effect dominates, we should
obtain a positive correlation between price and demand. However, if the substitution effect
dominates, we should then expect an overall negative correlation.
This essay also complements prior research in marketing that has examined the luxury
good market in the spirit of conspicuous consumption. For example, Amaldoss and Jain (2005)
developed an analytical model to show how purchase decisions are affected by consumer desire
for exclusivity and conformity. Han, Nunes, and Drèze (2010) studied consumers’ heterogeneous
preference for brand prominence in consumption of luxury goods with experimental data. Ward
and Dahl (2014) investigated how consumers’ perception of luxury goods is elevated by social
rejection. Pozharliev et al. (2015) found that the presence of another person magnifies the
emotional effect of a luxury brand.
2.3 Proposed Model
We propose a random-utility maximization framework to model consumer demand for
different brands. Following Satomura, Kim and Allenby (2011) and Arora, Allenby and Ginter
(1998), we adopt a Cobb-Douglas utility function to capture the benefit derived from consumption
of the inside good and an outside good:
𝑈 𝑖 = 𝛼 0
+ 𝛼 1
𝑙𝑛 (𝑈 𝑖 𝐼 ) + 𝛼 2
𝑙𝑛 (𝑍 𝑖 + 1) (1)
𝑈 𝑖 , individual 𝑖 ’s utility, is decomposed into two components: utility from the purchase of
the inside good 𝑈 𝑖 𝐼 and utility from the outside good 𝑍 𝑖 . The outside good can be measured by the
money left from consumer 𝑖 ’s budget after purchasing the inside good. It is possible that consumer
𝑖 uses up the entire budget in purchasing inside goods and 𝑍 𝑖 will be zero in this case. We therefore
specify the log form of utility from the outside good as 𝑙𝑛 (𝑍 𝑖 + 1).
13

The reason that we apply a Cobb-Douglas utility function rather than a simple linear model
is that the latter will lead to corner solutions, that is, a consumer will spend all s/he has either on
the inside product, or on the outside good, but not on both. In our dataset, most consumers do not
use up their total budgets on the luxury watch. Therefore, the linear model does not capture this
feature of our data. Please refer to Kim, Allenby and Rossi (2002) for more details on this
discussion.
Utility from inside good 𝑈 𝑖 𝐼 is specified as:
𝑈 𝑖 𝐼 = ∑ 𝛹 𝑖𝑗
𝑞 𝑖𝑗
𝐽 𝑗 =1
(2)
where 𝛹 𝑖𝑗
stands for the marginal utility from consuming brand 𝑗 and 𝑞 𝑖𝑗
is the
corresponding quantity purchased for brand 𝑗 by consumer 𝑖 . In our case, each consumer only
purchases one product in each purchase occasion. Thus, 𝑞 𝑖𝑗
equals 1 if alternative 𝑗 is chosen and
0 otherwise. We further model the marginal utility 𝛹 𝑖𝑗
as a linear combination of covariates:
𝑙𝑛 (𝛹 𝑖𝑗
) = 𝛽 0𝑗 + 𝛽 𝑄 𝑄 𝑖𝑗
+ 𝛽 𝐴 ′
𝑝 (𝐴 𝑖𝑗
) + 𝛽 𝑖𝑗
𝑙𝑛 ( 𝑃 𝑖𝑗
) + 𝜀 𝑖𝑗
(3)
Note that the key difference between Equation (3) and a standard utility-based demand
model is that price directly affects the marginal utility. This is consistent with the notion of the
prestige effect (Kalman 1968, Ng 1987). 𝛽 𝑖𝑗
captures such prestige effect, so that a higher price
could increase a consumer’s marginal utility if 𝛽 𝑖𝑗
is positive. Equation (3) also assumes that
consumer quality perception (𝑄 𝑖𝑗
) directly affects the marginal utility, and 𝛽 𝑄 is expected to be
positive, which captures the quality effect of price on utility and demand. Since consumer quality
perception is controlled in our model, 𝛽 𝑖𝑗
can be interpreted as the prestige effect. Note that the
prestige coefficient 𝛽 𝑖𝑗
is both individual and brand specific. This is because consumers may have
different perceptions on different brands. Due to this perception variation, the same amount of
price change may bring different benefits to consumers from different brands.
14

𝐴 𝑖𝑗
is a vector of product attributes. Because different people may choose different product
versions within the same brand, the price and attributes are both brand and individual specific. We
can directly use 𝐴 𝑖𝑗
if we observe the product attribute information for the watch purchased by
respondent 𝑖 . However, we only observe products’ prices but not the attribute information in our
survey data. Thus, we use predicted probabilities 𝑝 (𝐴 𝑖𝑗
) to capture the within-brand differentiation.
We form expectations on 𝐴 𝑖𝑗
given price 𝑃 𝑖𝑗
using some external data source. The vector 𝑝 (𝐴 𝑖𝑗
)
stands for the predicted probabilities of the purchased watch taking on specific product attribute
levels. This prediction is based on the price from the survey purchased data and the coefficients
estimated from external data. We will discuss how 𝑝 (𝐴 𝑖𝑗
) is specified in the empirical application
section.
In the utility-maximization framework, consumer 𝑖 faces a budget constraint as
∑ 𝑃 𝑖𝑗
𝑞 𝑖𝑗
𝐽 𝑗 =1
+ 𝑍 𝑖 = 𝐵 𝑖 (4)
where 𝐵 𝑖 stands for the consumer 𝑖 ’s budget on both the inside and the outside goods. The
utility maximization with respect to Equation (1) subject to the budget constraint specified in
Equation (4) leads to either an interior solution (i.e. spend on both the inside and outside goods)
or a corner solution (i.e. only spend on the inside good). In both scenarios, for the inside good,
only one brand is chosen because the utility function is linear on different options of the inside
good. This specification follows Chiang (1991) and Arora, Allenby, and Ginter (1998), and is
empirically consistent with our data. Combining Equations (1) – (4), we then write consumer 𝑖 ’s
utility maximization problem as in Equation (5). Consumers will choose the brand that gives the
highest utility given the budget constraint.
Maximize 𝑈 𝑖 = 𝛼 0
+ 𝛼 1
(𝛽 0𝑗 + 𝛽 𝑄 𝑄 𝑖𝑗
+ 𝛽 𝐴 ′
𝑝 (𝐴 𝑖𝑗
) + 𝛽 𝑖𝑗
𝑙𝑛 (𝑃 𝑖𝑗
) + 𝜀 𝑖𝑗
) + 𝛼 2
𝑙𝑛 (𝑍 𝑖𝑗
+ 1)
Subject to 𝑃 𝑖𝑗
+ 𝑍 𝑖𝑗
= 𝐵 𝑖 (5)
15

Note that we change the notation of the outside good from 𝑍 𝑖 in Equation (4) to 𝑍 𝑖𝑗
in
Equation (5). This is because Equation (4) gives out a general framework and defines the outside
good 𝑍 𝑖 as the difference between the budget and the money allocated in the luxury watches.
Without further specification of the utility function of the inside goods, consumers could possibly
choose multiple brands. In that case, the amount of money left for the outside good is not solely
affected by any single brand 𝑗 , but affected by the summation of money paid for all the brands. It
would be confusing if we denote the outside good as 𝑍 𝑖𝑗
there. Given our specification on the
inside good (i.e. the watch category), we ensure that the consumer only purchases one brand, as is
observed from all our data. Thus, the outside good depends only on the price of the chosen brand
and consumer 𝑖 ’s budget. The outside good is measured by the difference between budget and the
price paid (𝐵 𝑖 − 𝑃 𝑖𝑗
) and should be individual and brand specific.
A distinguishing feature of the brand choice model as laid out above is that consumers are
choosing not only brands but also price versions. In our empirical context of luxury products, each
brand usually has many different versions available with different price points, and some of these
price versions may not be observed from data. Because of the large price variation within a brand,
it is inappropriate to treat all the different versions as the same alternative even though they all
carry the same brand name.
The price version choice is unlikely to be a random process, and consumers will consider
a tradeoff. A higher priced version may provide more prestige, but at the cost of leaving less to
spend on the outside good. A lower price version may not bring so much prestige benefit, but with
the gain of having more to spend on the outside good. This intuition suggests that a consumer
would pick a price point as the best option for each brand. Then the best option under each brand
will compete with each other based on the overall utility, and the winner will be the consumer’s
16

final choice. Our proposed two-step “max-in-max” decision process is built upon the concept of
consideration set. There is a long history in psychology and marketing to understand formation of
consideration set. For example, extensive research has theorized the two-step decision process as
filtering the available alternatives and making the final choice within this reduced set (e.g.,
Nedungadi 1990). Numerous past studies have empirically shown the validity of the consideration
set formation process in helping consumers simplify the decision task (e.g., Hauser and Wernerfelt
1990, Shocker et al. 1991). Our proposed two-step decision process is calibrated in a structural
fashion, so that a consumer has a common utility function that determines the consideration set
and the final choice (Gilbride and Allenby 2004). We model consumer choice of brand and price
version as follows.
2.3.1 Choice of the Best Price Version within Each Brand. As discussed before, different
versions of the same brand with different price points differ in their abilities in delivering the
prestige effects. For each brand, an individual consumer is going to maximize the utility subject to
budget constraint, as laid out in Equation (5), by choosing the “optimal” price level. We
numerically solve for the optimal price 𝑃 𝑖𝑗
∗
. We call this a “continuous price approach”, which
assumes a continuous price in the utility maximization framework. An underlying assumption here
is that there is always an alternative available for that brand at any price point within a market
range. This assumption makes sense in our empirical context of the luxury watch market where
we find a large number of available versions on the market and rather large price variations within
each brand. The empirical evidence will be provided in the next section.
An alternative way of finding the best version/price within each brand is called the
“discrete price approach”. This is more straightforward without the need for numerical derivation
for the optimal price, and can be operationalized as follows. Imagine for a given brand, we observe
17

20 different price points paid in our sample. We then assume that these represent all the 20 available
versions of the brand on the market. The consumer will compare these 20 price points or versions
of a brand and pick the one that provides the highest utility given his/her preference and budget
constraint. A potential limitation of the “discrete price approach” is that it may underestimate the
number of available versions from the same brand on the market, especially when the sample size
is not very large.
2.3.2 Choice of the Best Brand Conditional on Optimal Price Versions. Recall that now
for each brand, we have found a winner, i.e. the best price version. Among these brand-specific
optimal price versions, it is rational for the consumer to pick one that provides the highest utility.
As the result from the proposed model, the consumer chooses a brand at an optimal price that will
achieve the highest utility given his/her budget constraint. The following maximization routine
illustrates the optimization logic:
𝑀𝑎𝑥 𝑗 ,𝑃 𝑖𝑗
𝑈 (𝑃 𝑖𝑗
, 𝐵 𝑖 − 𝑃 𝑖𝑗
, 𝑝 (𝐴 𝑖𝑗
))
= 𝑀𝑎𝑥 𝑗 {𝑀𝑎𝑥 𝑃 𝑖𝑗
|𝑗 𝑈 (𝑃 𝑖𝑗
, 𝐵 𝑖 − 𝑃 𝑖𝑗
, 𝑝 (𝐴 𝑖𝑗
)) } (6)
= 𝑀𝑎𝑥 𝑗 {𝑈 (𝑃 𝑖𝑗
∗
, 𝐵 𝑖 − 𝑃 𝑖𝑗
∗
, 𝑝 (𝐴 𝑖𝑗
∗
))}
= 𝑀𝑎𝑥 𝑗 { 𝛼 0
+ 𝛼 1
(𝛽 0𝑗 + 𝛽 𝑄 𝑄 𝑖𝑗
+ 𝛽 𝐴 ′
𝑝 (𝐴 𝑖𝑗
∗
)) + 𝛽 𝑖𝑗
𝑙𝑛 (𝑃 𝑖𝑗
∗
)) + 𝛼 2
𝑙𝑛 (𝐵 𝑖 + 1 − 𝑃 𝑖𝑗
∗
) + 𝛼 1
𝜀 𝑖𝑗
}
Note that the probability of product attributes 𝑝 (𝐴 𝑖𝑗
) is predicted from price 𝑃 𝑖𝑗
. 𝑝 (𝐴 𝑖𝑗
∗
)
denotes the product attribute probability at the optimal price 𝑃 𝑖𝑗
∗
. Equation (6) decomposes the joint
maximization into two sequential optimal maximization problems. Assuming the error terms are
i.i.d and follow the type I extreme value distribution, that is, 𝜀 𝑗 ~𝐸𝑉 (0,1) , the brand choice
probability then becomes:
𝑃𝑟 (𝑗 , 𝑃 𝑖𝑗
∗
) =
𝑒 𝑥𝑝 {𝛽 0𝑗 +𝛽 𝑄 𝑄 𝑖𝑗
+𝛽 𝐴 ′
𝑝 (𝐴 𝑖𝑗
∗
)+𝛽 𝑖𝑗
𝑙𝑛 (𝑃 𝑖𝑗
∗
)+
𝛼 2
𝛼 1
⁄ 𝑙𝑛 (𝐵 𝑖 +1−𝑃 𝑖𝑗
∗
)}
∑ 𝑒𝑥𝑝 { 𝛽 0𝑗 +𝛽 𝑄 𝑄 𝑖𝑗
+𝛽 𝐴 ′
𝑝 (𝐴 𝑖𝑗
∗
)+𝛽 𝑖𝑗
𝑙𝑛 (𝑃 𝑖𝑗
∗
)+
𝛼 2
𝛼 1
⁄ 𝑙𝑛 (𝐵 𝑖 +1−𝑃 𝑖𝑗
∗
)}
(𝑗 ,𝑃 𝑗 ∗
∈𝑅 𝑖𝑗
)
(7)
18

where 𝑅 𝑖𝑗
is the set of individual 𝑖 ’s optimal prices of all the brands that are lower than the
budget Bi.
Since we adopt the Cobb-Douglas utility function, the coefficients 𝛼 1
and 𝛼 2
need to be
positive. For the identification purpose, we reparameterize 𝛼 2
/𝛼 1
= 𝑒𝑥𝑝 (𝛼 2
∗
). 𝛽 𝑖𝑗
captures the
prestige effect and 𝑒𝑥𝑝 (𝛼 2
∗
) captures the substitution effect. We also incorporate the interaction
effect in the prestige coefficient 𝛽 𝑖𝑗
as follows:
𝛽 𝑖𝑗
= 𝑟 0𝑗 + 𝑟 1
𝑀 𝑖 + 𝑟 2
𝑀 𝑖 2
+ 𝑟 3
𝐸 𝑖 + 𝑟 4
𝐺 𝑖 (8)
𝑀 𝑖 measures the family income level of consumer 𝑖 . 𝐸 𝑖 𝑎𝑛𝑑 𝐺 𝑖 are education level and
gender of consumer 𝑖 respectively. These terms also capture the observed heterogeneity of
consumer prestige effect. The brand specific term 𝑟 0𝑗 captures the baseline prestige effect induced
by different brands. The term (𝑟 0𝑗 + 𝑟 1
𝑀 𝑖 + 𝑟 2
𝑀 𝑖 2
+ 𝑟 3
𝐸 𝑖 + 𝑟 4
𝐺 𝑖 ) as a whole captures the total
prestige effect. Previous research showed that income is an important factor affecting consumers’
prestige effect. However, the findings on how family income affects the prestige effect are mixed.
To be flexible, we adopt a quadratic functional form to test the relationship between income and
the prestige effect.
We next discuss how we can separately identify the prestige effect and the substitution of
price. Recall that the prestige effect measures the positive effect of price on the marginal utility
from the focal or inside product category, and it is modeled as the coefficient in front of the log
price (P
*
) in the utility function. On the other hand, the substitution effect measures the negative
effect of price on the utility from the outside good, and it is modeled as the coefficient in front of
the log remaining budget (i.e. the difference between budget and price, B - P
*
) in the utility function.
The key identification strategy is to use the price data and the budget data.
19

Note that, a unique aspect of our survey is that each respondent provides us with
information on his/her budget on the watch category. Different combinations of price of the
purchased watch and budget amount help us separately identify the prestige effect and the
substitution effect. In particular, variation in brand choices with respect to variation in purchased
prices across consumers helps identify the prestige effect, and the variation in brand choices with
respect to variation in the remaining budget across consumers helps identify the substitution effect.
If the budget information is not available, we will not be able to tell whether a purchase is due to
a large positive prestige effect or a small negative substitution effect.
2.4 Empirical Application
This section presents an empirical application of the proposed model using a survey dataset
of Chinese consumer consumption of six major luxury watch brands collected by a leading market
research company in China. This dataset provides information about the consumers as well as their
purchases. We augment this dataset with a secondary data source with product attribute
information. We first provide some background information about the luxury product market in
China in general and some existing findings on the local consumer behavior, followed by details
on the data. We then empirically validate some key modeling assumptions and describe the
estimation procedure. We finally report the estimation results and their implications.
2.4.1 Background Information. With the fast growth of the Chinese economy in the past
two decades, luxury products have become affordable to more Chinese consumers. Having leapt
past the Japanese market, Chinese consumers’ spending on luxury products now is among the top
three in the world. The market expansion renders new opportunities to examine Chinese consumers’
purchasing habits on luxury products. For example, Gao et al. (2009) gathered survey data from
12 large cities in China and created segments of luxury product consumers. They identified prestige
20

effect as an important motivation for Chinese consumers. Jung and Shen (2011) empirically
studied the relationship between brand equity and cultural difference. They found that Chinese
consumers care less about the perceived quality, brand awareness and brand association compared
to their American counterparts. Zhang and Kim (2013) showed that brand consciousness and social
comparison significantly affect Chinese consumers’ purchase intention on luxury products. This
essay adds to this stream of literature by offering a structural modeling approach to identify the
prestige effect and the substitution effect of the price in driving the luxury product demand from
Chinese consumers.
2.4.2 Data Description. We obtain the survey data from a large marketing research firm.
The sampling frame consists of those of club members of the firm, who are from the three largest
cities in China: Beijing, Shanghai and Guangzhou, with annual income over 200,000 RMB, and
aged between 25 and 60. Such sampling frame is largely representative of Chinese luxury
consumers who are mostly from large cities, with higher income and more knowledgeable about
the luxury market. The research firm received 900 responses from a random sample from this
sampling frame, and informed us that the response rate is over 90%. The final sample includes 439
respondents with complete information. Particularly, consumers also reported how much money
they planned to spend on buying a luxury watch. We use this information as a measurement of
consumers’ budget for the luxury watch category. All the purchases were made within 12 months
before the survey was conducted.
The final dataset contains 439 purchase incidences of any one of the six large luxury watch
brands in the year of 2012. We cannot reveal the names of the brands due to the non-disclosure
agreement with the research firm. Table 1 provides summary statistics of the six watch brands.
Looking at the choice shares, we note that Brand 1 is the most popular brand and Brand 6 has the
21

smallest choice share. Brand 2 and Brand 3 have the highest average price, followed by Brand 1
and Brand 4. Brand 5 and 6 have the relatively low average prices and offer fewer high-end
watches. There are a large number of different price levels paid for the same brand. We do not
detect any systematic pattern between average prices and choice shares of the six brands at the
aggregate level, suggesting that price could have a non-linear relationship with choice probability,
driven by different effects of price on luxury product demand via the prestige and substitution
effects. The budget information is also reported in Table 1 for all 439 purchase incidences.
In particular, we have a quality perception measure from each respondent for each brand
based on whether a respondent regards this product with high quality and recommendable. Table
1 reports the average quality measure for the six brands respectively. We make two observations.
First, the quality perception average varies from 0.08 to 0.3 for the six watch brands. Considering
the relatively high average price of all the 6 brands, the quality perception is quite low, which
suggests that quality may not be the most important reason that justifies a purchase. This is
consistent with the finding of Jung and Shen (2011).
Second, brands with relatively higher prices tend to have a higher mean quality. The
positive correlation between the quality and price validates the quality effect. We include the
quality perception data as a variable in the marginal utility specification to capture the quality
effect. As a higher price may associate with a higher quality, and if quality is found to increase the
marginal utility, then we establish the quality effect, i.e. the indirect positive effect of price on
demand via quality.

22

Table 1. Summary Statistics of the Six Brands in Watch Category
Brand Brand 1 Brand 2 Brand 3 Brand 4 Brand 5 Brand 6
Price Mean 15.89 46.18 28.73 8.25 4.43 6.62
Price Min 1.20 1.00 2.30 0.50 0.30 1.00
Price Max 158.00 280.00 100.00 65.00 35.00 27.00
Price Levels 54 47 35 42 49 33
Budget Mean 61.30 105.00 83.20 55.50 52.50 55.30
Budget Min 2.10 10.00 3.40 5.00 1.00 1.20
Budget Max 280.00 454.20 218.80 200.00 200.00 200.00
Quality 0.24 0.30 0.24 0.16 0.13 0.08
Choice Share 25.28% 17.31% 15.03% 14.12% 17.08% 11.16%
*Price and Budget Unit: 1,000 Yuan (Chinese Currency)

Table 2 reports the summary statistics of the three demographic variables of consumers. As
for household income, the mode is the bracket between 300k and 400k Yuan (approximately 65k
USD) for watch buyers. These will be counted as middle to high-income consumers. The modal
education level is bachelor degree. As to the gender composition, we have more male than female
watch buyers.

23

Table 2. Summary Statistics of Demographic Variables
Category Watch
Total Number of Observations 439
Family Income (Yuan)
Number of
Observations
200,000-300,000 23
300,000-400,000 207
400,000-500,000 84
500,000-1,000,000 81
1,000,000-1,500,000 23
1,500,000-2,000,000 7
2,000,000-3,000,000 13
3,000,000-5,000,000
5,000,000 and above
1
0
Education
Number of
Observations
High School 21
Higher Vocational College 104
Bachelor 273
Master 36
Doctor and Above 5
Gender
Number of
Observations
Male 255
Female 184

In the survey data, we do not observe the product attribute information, which is needed to
control for within-brand variations. Since it is rather difficult to trace the survey respondents, we
have decided to use a secondary source to impute the attribute information from price for those
purchased watches from the survey respondents. We take three steps:
Step 1: Gather information on product attributes. We gather product attribute information
(e.g. whether the watch is mechanical or not) and prices for several thousands of watches sold on
24

the largest watch online retailer in China (www.wbiao.cn). We choose this source for several
reasons. First, Wbiao is the largest online luxury watch retailer in China, making it a credible
secondary data source. Second, they sell more than 2000 products from the 6 focal brands we
study. Third, there is detailed product description and price information provided for each of the
listed watches, which gives us basis to quantify the relationship between price and attribute level.
We have written computer codes and scraped the product attribute and price information
from all watch products sold on this website in 2012. Based on expert and consumer reviews, we
choose to focus on five more important attributes: “Movement” (non-mechanical vs. mechanical),
“Case” (by other materials vs. with precious metals), “Dial” (without diamond vs. with diamond),
“Glass” (other materials vs. sapphire), and “Bracelet” (by other materials vs. with precious metals).
Step 2: Estimate the probability of a watch to possess a certain attribute level given price.
We assume that attribute information of a product can be predicted by price. For example, an
expensive watch is more likely to a have a mechanical movement than a cheap watch. We estimate
𝛾 0
and 𝛾 1
for each attribute from a probit model as in Equation (9) using the attribute and price
data obtained from the first step.
𝑝 (𝐴 𝑖𝑗
) = Φ(𝛾 0
+ 𝛾 1
𝑙𝑛 (𝑃 𝑖𝑗
)) (9)
Estimation results in Table 3 show that more expensive watches are more likely to have
mechanical movements, cases with precious metal, sapphire glasses, dials with diamond, and
precious metal bracelets.

25

Table 3: Attribute Probability Prediction Based on Price
INTERCEPT LOG(PRICE)
MOVEMENT (MECHANICAL) 0.140** 0.419**

CASE (PRECIOUS METAL) -0.902** 0.660**

GLASS (SAPPHIRE) 1.787** 0.453**

DIAL (DIAMOND) -1.646** 0.513**

BRACELET (PRECIOUS METAL) -1.382** 0.338**
* p<0.05, ** p<0.01.

Step 3: Predict the attribute level probabilities associated with the reported prices in the
data. Now with any price observed in the purchase data, we can impute the probability that a
certain watch possesses a certain level (e.g. mechanical) on an attribute (e.g. movement) using
estimates 𝛾 0
and 𝛾 1
gained from Step 2 using a probit link. For ease of demonstration, let us
assume only one attribute with two levels, and it is the feature of “movement”. It equals to 1 if
the watch is mechanical, and equals to 0 if the watch is not mechanical. In this simple example,
𝑝 (𝐴 𝑖𝑗
) is the imputed probability of the purchased watch version with price 𝑃 𝑖𝑗
being a
mechanical watch, that is, “movement” = 1. We incorporate the predicted probability 𝑝 (𝐴 𝑖𝑗
) to
capture the within-brand differentiation.
2.4.3 Assumption Validation. As discussed earlier, we make one assumption in the
“continuous price approach” in deriving the optimal price version an individual consumer would
choose within a brand, that is, one will find a corresponding version of a watch of a given brand
at the optimal price. With external data from Wbiao, we can validate the number of available
versions or price points offered in the market. We have two main findings. First, we find that
different alternatives from the same brand often have different prices. Second, each brand has
several hundreds of price versions. For example, the website shows that a watch brand in our study
26

has more than 600 versions. Besides, there could be some other versions at different prices that are
not provided by this online retailer. After accounting for these factors, we believe it is reasonable
to assume that a consumer can find a particular version of a brand at any price level that would
deliver the highest utility for the individual.
2.4.4 Model Estimation. We need to emphasize the estimation procedure of price-brand
process because a key feature is that we assume consumers choose an optimal price or version for
each brand (i.e. by following the “continuous price approach”). This is to say that for each non-
chosen brand, a consumer has an evaluation process, and because of that, the optimal price version
of the non-chosen brand that gives the highest utility to the consumer is determined in the system
and affected by consumer preferences. In order to estimate the consumer optimal decision model
in Equation (6), we need to estimate Equations (5) and (7) simultaneously. Specifically, we need
initial values of coefficients to calculate optimal prices for all brands as illustrated in Equation (5).
With optimal prices, we then estimate coefficients of the choice model in Equation (7). With these
estimated coefficients, we can update the optimal prices. Then we use updated optimal prices to
update parameters.
Note that the probability of product attributes 𝑝 (𝐴 𝑖𝑗
) is a function of price 𝑃 𝑖𝑗
, since it is
projected using Equation (9). Beyond the prestige and substitution effects, 𝑃 𝑖𝑗
also affects the
utility through 𝑝 (𝐴 𝑖𝑗
). Thus, we do not have an analytical solution to the maximization problem
when we calculate the optimal prices in Equation (5). We can only numerically derive a set of
optimal prices given coefficients.
We apply the Nelder-Mead algorithm to update optimal prices and parameters back and
forth until convergence. If the derived optimal prices were larger (smaller) than the maximum
(minimum) value of the price range, in our data we adjust them to the maximum (minimum) value.
27

Another constraint comes from an individual consumer’s budget. If derived optimal price is larger
than the reported budget, we set the optimal price as the budget. We use a similar routine for
estimating the model based on the “discrete price approach”.
Since the optimal prices are solved in the “continuous price approach”, we can only
empirically identify 𝐽 − 1 price coefficients as shown in our simulation exercise. Therefore, we
need to fix one baseline price coefficient. However, we cannot randomly assign any one to be zero,
because we are interested in the magnitude of the prestige effect. To solve this problem, we use
the “discrete price approach” as described earlier to obtain the baseline. The “discrete price
approach” assumes that the price levels observed for a brand in our sample represents the market
reality. For example, Brand 1 of the watch category has 54 price levels, and these 54 versions were
all the versions available in the market that consumers could choose from. The assumption allows
us to estimate the model and obtain the brand-specific prestige effect. We then use the estimated
prestige effect of Brand 1 from the “discrete price approach” as the baseline when applying the
“continuous price approach”. In other words, when estimating the proposed model using the
“continuous price approach”, we do not estimate the prestige effect of Brand 1 and instead, this
parameter is fixed at the estimated value obtained from estimation based on the “discrete price
approach”.
2.4.5 Estimation Results. We estimate Model 1, our proposed model, using both “discrete
price approach” and “continuous price approach” respectively and show the estimation results in
Table 4. We find that “continuous price approach” fits the data better than the “discrete price
approach” in terms of the BIC. We also estimate our model under different specifications using the
“continuous price approach”. In order to interpret the overall prestige effect, we estimate Model 2
where prestige effect is not interacted with demographics. Model 3 does not include predicted
28

product attributes, and Model 4 does not include quality perception. Table 5 reports our estimation
results from Models 2-4.
Table 4. Proposed Model Estimation Results
MODEL 1 DISCRETE PRICE
APPROACH
CONTINUOUS PRICE
APPROACH
BIC
1222.697 1215.007
INTERCEPT (𝜷 𝟎𝒋
)
BRAND 1
Fixed Fixed
BRAND 2
-2.062** -2.023**
BRAND 3
-0.977** -1.025**
BRAND 4
-0.348 -0.341
BRAND 5
0.184 0.245
BRAND 6
0.008 0.006
QUALITY (𝜷 𝑸 ) 2.549** 2.530**
ATTRIBUTES (𝜷 𝑨 )
MOVEMENT (MECHANICAL)
1.798** 2.014**
CASE (PRECIOUS METAL)
-1.782** -1.787**
GLASS (SAPPHIRE)
-4.222** -4.142**
DIAL (DIAMOND)
0.794 0.596
BRACELET (PRECIOUS METAL)
3.421* 3.573**
PRESTIGE EFFECT (𝒓 𝟎𝒋
)
BRAND 1
1.456** 1.456**
BRAND 2
2.329** 2.311**
BRAND 3
1.706** 1.757**
BRAND 4
1.363** 1.376**
BRAND 5
1.147** 1.159**
BRAND 6
1.257** 1.246**
INCOME (𝒓 𝟏 )
-1.666** -1.646**
INCOME SQ (𝒓 𝟐 )
0.300** 0.290**
EDUCATION (𝒓 𝟑 )
0.213** 0.236**
GENDER (𝒓 𝟒 )
0.463** 0.473
OUTSIDE GOOD (𝜶 𝟐 /𝜶 𝟏 ) 1.824** 1.721**
* p<0.05, ** p<0.01.

29

Table 5. Benchmark Models (Continuous Price Approach)
MODEL 2 MODEL 3 MODEL 4
BIC
1250.718 1248.515 1613.813
INTERCEPT (𝜷 𝟎𝒋
)
BRAND 1
Fixed Fixed Fixed
BRAND 2
-0.927** -0.797** -1.665**
BRAND 3
-1.274** -1.220** -0.690**
BRAND 4
-0.274 -0.491 -0.390**
BRAND 5
0.344 0.645** -0.049
BRAND 6
-0.164 -0.579 -0.698
QUALITY (𝜷 𝑸 ) 2.517** 2.645**
ATTRIBUTES (𝜷 𝑨 )
MOVEMENT (MECHANICAL)
0.399 3.000**
CASE (PRECIOUS METAL)
-2.710 -2.041**
GLASS (SAPPHIRE)
-2.980 -3.134**
DIAL (DIAMOND)
0.291 1.510**
BRACELET (PRECIOUS METAL)
-0.122 2.746**
PRESTIGE EFFECT (𝒓 𝟎𝒋
)
BRAND 1
2.283** 1.713** 1.816**
BRAND 2
2.221** 1.937** 2.711**
BRAND 3
2.210** 2.344** 2.007**
BRAND 4
2.069** 2.302** 1.623**
BRAND 5
1.625** 1.811** 1.346**
BRAND 6
1.000** 2.656** 1.749**
INCOME (𝒓 𝟏 )
-2.524** -2.639**
INCOME SQ (𝒓 𝟐 )
0.449** 0.473**
EDUCATION (𝒓 𝟑 )
0.753** -0.053*
GENDER (𝒓 𝟒 )
2.090** 0.092*
OUTSIDE GOOD (𝜶 𝟐 /𝜶 𝟏 ) 1.177* 1.811** 1.814**
* p<0.05, ** p<0.01.

We highlight several key findings. First, the coefficient estimate for the outside good (i.e.
budget minus price) is significant and positive, suggesting the substitution effect, that is, the higher
the price, the less of outside good can be purchased and the lower the utility generated from it.
30

Second, we find a significant and positive prestige effect for all the watch brands, that is,
as price increases, consumers will obtain more utility after controlling for the substitution effect
and the quality effect from price. This is confirmed with Model 2 where we do not allow
demographics to affect the prestige effect (i.e. only estimating 𝛽 𝑖𝑗
to obtain the average prestige
effect).
Third, to understand drivers of the prestige effect, we further allow family income,
education and gender as moderators. We find a significantly negative coefficient of the linear term
and a significantly positive coefficient of the quadratic term of family income. This indicates that
income and prestige effect have a U-shape relationship, that is, the prestige effect is stronger for
the two ends of high-income and low-income consumers than their middle-income counterpart.
By definition, luxury goods are those highly desired and associated with wealthy or affluent people,
and higher-income consumers have more resources to enjoy prestige (Veblen 1899). However,
Sharma and Alter (2012) showed that lower-income consumers may have a stronger incentive to
signal status with luxury product consumption. Our finding reconciles two divergent predictions
in the literature on the prestige incentive or needs across income classes. Our finding is also
consistent with empirical findings on private label consumption and modern retail patronage. Low
and high-income consumers purchase higher shares of national brands which are generally more
expensive, whereas middle-income households are more prone to purchasing lower priced private
labels (Fitzell 1992, Sethuraman and Gielens 2014). Similarly, Narayanan, Rao and Sudhir (2015)
found a U-shaped relationship between socioeconomic class and modern retail patronage among
Indian consumers.
31

We find that education is positively correlated with the prestige effect, while gender does
not affect the prestige effect significantly. This result implies that well educated consumers are
more likely to enjoy the prestige effect of the high price.
Finally, the proposed model (Model 1) performs better than Model 3 and Model 4. It shows
the importance to control for product attributes and brand quality perceptions. We also find that
imputed product attributes affect consumer utility.
2.4.6 Benchmark Analysis. We test two benchmark models to see how our proposed
model compares to some reduced-form models as well as some other settings. The first benchmark
model does not consider the prestige effect or the substitution effect of price, and instead estimates
an overall effect of price as in a standard brand choice model. Consumer’s brand-specific utility is
specified as:
𝑈 𝑖𝑗
= 𝛽 0𝑗 + 𝛽 𝑄 𝑄 𝑖𝑗
+ 𝛽 𝐴 ′
𝑝 (𝐴 𝑖𝑗
) + 𝛽 𝑖𝑗
𝑙𝑛 (𝑃 𝑖𝑗
) + 𝜀 𝑖𝑗
(10)
The error terms are assumed to follow Type I extreme value distribution as before. The
price coefficient is modeled as a function of the four demographic variables as in Model 1. Since
we cannot implement the continuous price approach to numerically derive the optimal price
version for each brand as we did in our proposed model, we use the discrete price approach only.
We estimate the benchmark model, and find that our proposed model (Model 1 under the
continuous price approach) outperforms this benchmark model. Our proposed model is better not
only in providing more insights on how prices affect consumer demand but also in terms of fitting
the actual data, which highlights the importance of accounting for the prestige effect and the
substitution effect of price. Table 6 reports the estimation results from the first benchmark model.

32

Table 6. Benchmark Models: A Reduced-Form Model
MODEL 5
BIC
1219.975
INTERCEPT (𝜷 𝟎𝒋
)

BRAND 1
Fixed
BRAND 2
-2.254**
BRAND 3
-1.063**
BRAND 4
-0.277
BRAND 5
0.418
BRAND 6
0.233
QUALITY (𝜷 𝑸 )
2.492**
ATTRIBUTES (𝜷 𝑨 )

MOVEMENT (MECHANICAL)
4.315**
CASE (PRECIOUS METAL)
-2.281
GLASS (SAPPHIRE)
4.126
DIAL (DIAMOND)
4.624
BRACELET (PRECIOUS METAL)
8.353
PRICE (𝒓 𝟎𝒋
)

BRAND 1
0.081
BRAND 2
0.770
BRAND 3
0.354
BRAND 4
0.079
BRAND 5
-0.080
BRAND 6
-0.000
INCOME (𝒓 𝟏 )
-2.109**
INCOME SQ (𝒓 𝟐 )
0.289**
EDUCATION (𝒓 𝟑 )
0.120**
GENDER (𝒓 𝟒 )
0.097
* p<0.05, ** p<0.01.

The second benchmark analysis tests an alternative decision-making process. In our
proposed model, a consumer picks an optimal price version within each brand first. Then the
optimal price versions compete with each other and the winner becomes the final choice. To
33

validate our proposed price-brand decision process, we test a brand-price decision process. We
assume a consumer can pick one brand as the best option under each price range first. Then the
best brand option under each price range will compete with each other based on the overall utility,
and the winner will be the consumer’s final choice. We model this decision process as follows.
Based on the price distributions, we divide the price range into 6 sub-ranges. Now we have several
price ranges and brand combinations. In the first step, a consumer picks an optimal brand within
each price range to maximize his/her utility. For any combination that the consumer does not
actually purchase, we use the average of the brand’s price points within the price range as an
approximation. We then calculate each consumer’s utility and determine the brand, which gives
him/her the highest utility, as the optimal brand in each price range. In the second step, optimal
brands with different prices compete with each other and the winner in this step is the final choice
of a consumer. We adopt the same utility function and statistical assumption as in the price-brand
process approach. Our proposed model of our original decision process fits the data better than the
one that captures this alternative decision process. Results are reported in Table 7.
34

Table 7. Benchmark Models: An Alternative Decision Process Model
MODEL 6
BIC
1295.266
INTERCEPT (𝜷 𝟎𝒋
)

BRAND 1
Fixed
BRAND 2
-1.485**
BRAND 3
-0.599**
BRAND 4
-0.265**
BRAND 5
-0.242**
BRAND 6
-0.312**
QUALITY (𝜷 𝑸 )
1.177**
ATTRIBUTES (𝜷 𝑨 )

MOVEMENT (MECHANICAL)
1.221**
CASE (PRECIOUS METAL)
-2.106**
GLASS (SAPPHIRE)
-1.815**
DIAL (DIAMOND)
1.109**
BRACELET (PRECIOUS METAL)
0.932**
PRESTIGE EFFECT (𝒓 𝟎𝒋
)

BRAND 1
1.185**
BRAND 2
2.063**
BRAND 3
1.554**
BRAND 4
0.503**
BRAND 5
1.192**
BRAND 6
1.548**
INCOME (𝒓 𝟏 )
-1.839**
INCOME SQ (𝒓 𝟐 )
0.142**
EDUCATION (𝒓 𝟑 )
0.021**
GENDER (𝒓 𝟒 )
-0.102**
OUTSIDE GOOD (𝜶 𝟐 /𝜶 𝟏 )
1.453**
* p<0.05, ** p<0.01.

35

2.5 Managerial Implications
2.5.1 Price Elasticity Analysis. The prestige effect is one important feature of the luxury
products. The overall price effect is not clear since the prestige effect and the substitution effect
have the opposite directions. Analysis on the price elasticity can help practitioners better
understand the market and adjust their pricing strategies. This essay only on the own price elasticity
in our analysis, because the emphasis of our proposed model is on the prestige effect for individual
brands rather than the competition across brands.
In our model, each brand provides many price points. It is difficult to derive the price
elasticity directly from the whole price distribution change, since a change in the price distribution
affects each individual’s optimal price nonlinearly and creates discontinuity in the correspondent
choice probability. For the convenience of demonstrating the unique aspect of our proposed model
from a standard model, we derive the price elasticity 𝑒 𝑃 𝑖𝑗
∗
with respect to the optimal price 𝑃 𝑖𝑗
∗
(i.e.
the price point within each brand that maximizes the consumer overall utility from inside good and
outside good).
𝑒 𝑃 𝑖𝑗
∗
= (1 − 𝑝𝑟𝑜𝑏 𝑖𝑗
)𝑃 𝑖𝑗
∗
(
𝛽 𝑖𝑗
𝑃 𝑖𝑗
∗
−
𝛼 2
𝛼 1
⁄
𝐵 𝑖 −𝑃 𝑖𝑗
∗
+1
) (11)
where 𝑝𝑟𝑜𝑏 𝑖𝑗
is consumer 𝑖 ’s choice probability of brand 𝑗 at 𝑃 𝑖𝑗
∗
.
There are some notable features of the derived price elasticity. First, the own elasticity of
a luxury product can be positive. More specifically, the sign of the own elasticity is determined by
the sign of the term
𝛽 𝑖 𝑗 𝑃 𝑖𝑗
∗
−
𝛼 2
𝛼 1
⁄
𝐵 𝑖 −𝑃 𝑖𝑗
∗
+1
. We can see that
𝛽 𝑖𝑗
𝑃 𝑖𝑗
∗
−
𝛼 2
𝛼 1
⁄
𝐵 𝑖 −𝑃 𝑖𝑗
∗
+1
is a decreasing function of 𝑃 𝑖𝑗
∗
.
When 𝑃 𝑖𝑗
∗
<
𝛽 𝑖𝑗
(𝐵 𝑖 +1)
𝛼 2
𝛼 1
⁄ +𝛽 𝑖𝑗
, the own price elasticity of a brand is positive and vice versa. In a standard
discrete choice model, the price elasticity is usually negative.
36

Second,
𝛽 𝑖𝑗
𝑃 𝑖𝑗
∗
captures the marginal prestige effect, while
𝛼 2
𝛼 1
⁄
𝐵 𝑖 −𝑃 𝑖𝑗
∗
+1
captures the marginal
substitution effect. We can then interpret the term
𝛽 𝑖𝑗
𝑃 𝑖𝑗
∗
−
𝛼 2
𝛼 1
⁄
𝐵 𝑖 −𝑃 𝑖𝑗
∗
+1
as the difference between the
marginal prestige effect and the marginal substitution effect. A small 𝑃 𝑖𝑗
∗
does not provide enough
prestige effect. The marginal prestige effect can be larger than the marginal substitution effect
when 𝑃 𝑖𝑗
∗
is small. Increasing the price will provide a higher utility. This explains why the own
elasticity can be positive.
We have also calculated each consumer’s elasticity with respect to optimal price for each
of the six brands in our data. We present their summary statistics in Table 8 and histograms in
Figure 1. There are several findings. First, we find a rather substantial variation of price elasticities
within each brand. This is because each brand provides many different price points and consumers
have different elasticities at different optimal prices. Second, the elasticity distribution varies
substantially across brands, driven by the fact that the prestige coefficient is different across brands.
Last, the average elasticities of Brand 5 and 6 are positive and higher than other brands. This is
likely due to the relatively low price levels of these two brands, consistent with our theoretical
prediction that low prices do not provide sufficient prestige effect to consumers. It may be more
profitable for Brand 5 and 6 to increase price.
Table 8. Summary Statistics of Price Elasticities at the Optimal Prices
Brand Brand 1 Brand 2 Brand 3 Brand 4 Brand 5 Brand 6
Mean -0.088 0.013 -0.045 -0.023 0.103 0.234
Standard
Deviation
0.200 0.479 0.313 0.289 0.337 0.422
Min -0.417 -0.375 -0.321 -0.253 -0.162 -0.140
Max 1.196 2.347 1.744 1.958 2.089 2.252

37

Figure 1. Price Elasticities at the Optimal Prices

38

2.5.2 What-if Analysis. Given estimates of our proposed model, we run two sets of what-
if simulations to derive managerial implications. One important reason for consumer luxury
consumption is the prestige benefit. If luxury firms invest more in their images, they can have
stronger prestige effects. In the first set of analyses, we investigate the impact from increased
prestige effect. Table 9 shows how the market share, average optimal price and revenue would
change when each brand’s baseline prestige effect increases by 10%. Each column represents a
situation when one specific brand increases its baseline prestige effect. For example, in the column
of “Brand 1”, we report the simulated share, average price and revenue of Brand 1 before and after
Brand 1’s baseline prestige effect changes, holding the prestige effects of other brands unchanged.
The magnitude of the change measured in percentage is also reported.
We find that the market share of the focal brand would increase when the brand’s prestige
effect is stronger. Such increase is larger for more prestigious brands. This result is not surprising.
When a brand’s prestige effect is stronger, it provides more prestige at the same price and is more
attractive to consumers. Furthermore, with an increase on a brand’s prestige effect, consumers tend
to choose higher-priced items within the brand. This is consistent with the theoretical prediction
that the optimal price would shift upward with a more positive prestige coefficient. Since revenue
is determined by choice probability and purchased price, larger prestige effect leads to increased
revenue for the focal brand. An important takeaway from this analysis is that luxury brands should
promote their brands, which will help provide more prestige to consumers and increase their
market shares and revenues.

39

Table 9. What-if Analysis Results - 10% Higher Baseline Prestige Effect
Brand Brand 1 Brand 2 Brand 3 Brand 4 Brand 5 Brand 6
Market Share
Original 24.73% 17.30% 14.88% 14.36% 17.43% 11.29%
Higher
Prestige
26.55% 20.67% 17.03% 15.44% 17.92% 11.81%
Change 7.33% 19.43% 14.50% 7.57% 2.79% 4.54%
Average
Optimal Price
Original 25.54 32.19 28.87 23.40 16.96 16.80
Higher
Prestige
27.21 33.34 30.22 24.99 18.69 17.81
Change 6.54% 3.58% 4.67% 6.77% 10.18% 6.05%
Revenue
Original 3451.55 5108.04 2960.46 1845.55 1421.23 908.59
Higher
Prestige
4132.92 6381.71 3674.11 2182.43 1608.55 1010.49
Change 19.74% 24.93% 24.11% 18.25% 13.18% 11.22%
Revenue and Price Unit: 1,000 Yuan

According to a report from McKinsey, Chinese are getting richer fast, and the per-
household disposable income of urban consumers will double between 2010 and 2020. It is
managerially relevant to see which brands will benefit more from the income expansion of Chinese
consumers. In the second what-if analysis, we consider the scenario that the family income level
of every consumer increases by 2. Table 10 reports the predicted choice shares, average optimal
prices and revenues for all watch brands before and after all consumers’ family income levels
expand. As we expected, most richer consumers prefer higher end versions for the prestige effect.
Thus, an income increase leads to higher average optimal prices for all the brands. Since some
lower tier brands do not provide enough high-end product versions, they cannot satisfy some
consumers’ needs for prestige after these consumers become richer. These consumers then would
switch to other brands. This is why we observe that an income increase leads to higher choice
40

shares for the first four brands, but lower choice shares for Brand 5 and 6, which are relatively
lower-tier. Furthermore, in terms of revenue, income expansion benefits every brand except Brand
6. Brand 5, which also experiences a drop in the share as Brand 6, is able to gain more revenue as
income increases. This is because Brand 5 offers more higher-priced versions than Brand 6. The
increase of the average optimal price is big enough to offset the market share loss for Brand 5.
Table 10. What-if Analysis Results – Income Expansion by 2 levels
Brand Brand 1 Brand 2 Brand 3 Brand 4 Brand 5 Brand 6
Market Share
Original 24.73% 17.30% 14.88% 14.36% 17.43% 11.29%
Higher
Prestige
25.03% 18.12% 15.34% 14.38% 16.45% 10.69%
Change 1.20% 4.71% 3.08% 0.16% -5.63% -5.38%
Average
Optimal Price
Original 25.54 32.19 28.87 23.40 16.96 16.80
Higher
Prestige
27.96 33.37 30.59 25.73 19.96 18.31
Change 9.49% 3.66% 5.98% 9.94% 17.66% 9.01%
Revenue
Original 3451.55 5108.04 2960.46 1845.55 1421.23 908.59
Higher
Prestige
3843.99 5520.69 3230.32 1991.45 1466.29 889.42
Change 11.37% 8.08% 9.12% 7.91% 3.17% -2.11%
Revenue Unit: 1,000 Yuan

2.6 Conclusion
Price plays an essential role in shaping consumer demand for luxury goods. One
distinguishing feature of luxury products is that they are often bought with a high price to support
self-worth and status, going beyond the utilitarian value derived from quality. On the other hand,
a high price could reduce consumer demand for luxury goods due to the negative substitution effect.
While most previous studies have focused on the overall relationship between price and demand,
41

we examine the two underlying mechanisms that explain the general price effect, namely, the
prestige effect and the substitution effect. No prior research has empirically examined these two
important price effects related to consumer luxury demand.
We develop a model based on the utility-maximization framework that accommodates the
two price effects on consumer demand for luxury products. Unlike the standard setup, we allow
price to affect marginal utility to capture the prestige effect. Negative effect of price from the
outside good captures the substitution effect. We also develop a “max-in-max” procedure to derive
the optimal choice solution to account for unobserved price versions within each brand. This
procedure allows us to derive the choice probability and estimate the model parameters.
We apply our model to a survey dataset collected from middle-to-high income Chinese
consumers on their purchases of six luxury watch, supplemented with attribute information from
another source. While controlling for product attributes and consumer product-quality perception,
we find a significant prestige effect as well as a substitution effect of price on demand. More
interestingly, we find that a U-shape relationship between income and prestige effect, such that the
lower end and the upper end of the middle plus classes have the greatest prestige effect. We also
show that the price elasticity can be positive when the price is low enough that the marginal
prestige effect is larger than the substitution effect. In some cases, it is more profitable to increase
the price of luxury products because the low price does not provide enough prestige effect. Our
what-if simulations show that luxury brands can gain higher market shares and revenues when
they can promote their brand to provide more prestige to consumers from price. While higher-price
brands benefit from consumer income expansion with increased shares and revenues, income
expansion has a more complex effect on lower-priced brands.
42

This essay makes two important contributions. First, to our best knowledge, this essay is
the first that offers a new modeling framework to examine the effect of price on consumer demand
for luxury goods by incorporating both the prestige effect and the substitution effect of price. While
previous papers examined the prestige effect through qualitative, analytical or experimental
methodologies, none of them used secondary data to explicitly identify and test the prestige effect.
Second, this essay contributes to the modeling literature by quantifying the prestige effect
of price and developing a “max-in-max” method to account for unobserved versions/prices of a
brand available in the market and solve the utility maximization problem. In a standard economic
modeling framework based on utility maximization subject to budget constraint, price is assumed
to affect demand only via affecting the budget constraint (i.e. the “substitution effect”). In other
words, utility from a product is only affected by the intrinsic properties of the product (such as
color, texture, speed, etc) and by the state of the consumer, but not price. We extend the classical
demand framework by incorporating price into the marginal utility. Such extension leads to
additional complexity in model derivation and estimation. Third, our price elasticity analysis and
what-if simulations help generate useful managerial insights.
Like any other research, this essay has limitations, which offer several future directions.
First, we only have data on one category from different consumers, which is not enough to capture
potential behavioral synergies across categories. With richer data on each individual consumer’s
consumption on different product categories, one can study consumer cross-category demand
patterns, and examine whether the prestige effect is stronger in some categories and why.
Furthermore, it will be interesting to investigate whether luxury products in different categories
are perceived to be substitute or complementary to each other for the same individual. Some
consumers may choose higher-priced items from fewer luxury categories due to the prestige effect,
43

whereas others may choose lower-priced items in all categories to maintain an overall image.
Uncovering these behavioral patterns enables luxury companies to more effectively market their
products and target the right individuals for cross-selling opportunities.
Second, our data are cross-sectional in nature. Since we only have one observation for each
consumer, we are unable to infer if this one observation represents the individual’s general
preference or a random shock, and thus are unable to estimate the mean prestige effect and
substitution effect for this individual consumer. Instead of estimating individual specific
preference, we utilize the observed characteristics of consumers, and infer the prestige effect for
different types of consumers by incorporating observed consumer heterogeneity. Only with
repeated observations from the same individual (i.e. panel data), we can infer the individual’s mean
preference. Without panel data, we cannot explore potentially interesting dynamic patterns. With
panel data, one can examine how the prestige effect and the substitution effect change over time,
and whether the two effects influence each other. Uncovering these dynamic effects can help firms
develop the optimal sequence of “product versions” to offer and cultivate customer brand loyalty.
Lastly, we focus on the overall prestige effect, but do not differentiation alternative
underlying driving forces for such effect. It can be driven by an extrinsic motivation that the
consumers can use the luxury purchase to signal their social status to important others, as well as
an intrinsic motivation that the consumers purchase luxury products so they feel good about
themselves. It would be interesting to distinguish these two forces and see which force is
dominant in driving up the prestige effect. Notwithstanding these limitations, hope this essay will
generate further interest in exploring the important area of luxury product marketing.

44

3. When Fashion Firms Choose Their Customers for Brand Image:
A Two-sided Matching Approach
3.1 Introduction
Over the past decade, the fashion industry has become an economic success story,
maintaining an annual growth rate of 5.5%. The value of the global fashion industry reached $2.4
trillion in 2016, accounting for approximately 2% of the world’s GDP. The industry would be the
world’s seventh-largest economy if ranked alongside the GDP of individual countries. In addition
to its importance in the global economy, the fashion industry has some interesting features. One is
that many fashion companies are extremely selective. In fact, many have made the decision not to
sell products to certain consumers who could in fact generate more revenue. For example, some
fashion companies, such as Marc Jacobs and Tom Ford, publicly announced that they would not
dress Melania Trump, the First Lady and a public figure to whom fashion brands are usually eager
to serve. This type of selection goes beyond just the exclusion of celebrity consumers. Hermes
sells its signature handbags mostly to customers on its “A-list,” which excludes many potential
buyers without high social status or long-term relationships with the brand. Chanel selects
consumers through regular exclusive invitation-only sales events.
All of these fashion brands select a small group of consumers even though it would be
more profitable to target a broader spectrum. This strategy seems to be irrational, but it is well
explained by the branding literature, which asserts that companies should select their customers to
maintain a good brand image. Researchers show that product users represent a powerful signaling
source and play an important role in creating and improving a brand’s image (Da Silveira, Lages,
and Simoes, 2013). Customers simultaneously seek out and contribute to a brand image (Arnould
& Thompson, 2005). The image associated with a brand name can be affected by the traits of the
45

brand’s regular customers. Fashion consumers usually favor a brand not only because of the quality
of its products, but also because the brand is more popular among a certain group of people with
whom consumers desire to be associated. Because of such consumption externality, fashion brands
are incentivized to select the “right” consumers in order to obtain a good brand image and steady
growth (Kapferer, 1998; Ferraro, Kirmani, and Matherly, 2013). Although previous studies in
branding show the type of consumer who helps to improve brand image and who should be targeted
by fashion brands they fail to predict whether firms can actually acquire these consumers as they
have not considered consumer preference and brand choice. For the same reason, the branding
literature has also ignored how such selection of consumers affects revenue and thus cannot guide
companies with an effective targeting strategy.
Another large stream of work in the marketing and economics literature has examined
consumer preference. Originated by Kamakura and Russel (1989), discrete choice models have
been extensively applied to capture consumer choice. Berry, Levinsohn, and Pakes (1995) and
Sudhir (2001) extend this framework to consider both the demand and supply side of the market.
However, they assume firms aim to only maximize their profits and do not actively select
consumers to maintain a good brand image. It is problematic to ignore strategic consumer selection
by firms if we investigate some markets in which brand image plays a vital role and consumer
selections are widely witnessed. By observing a certain type of consumer who does not purchase
a brand, researchers cannot conclude that such consumers do not like the brand; the reason could
be that the firm does not target these consumers. A discrete choice model fails to consider this
possibility and induces biased inferences.
Missing from both the branding and consumer choice literature is how to simultaneously
model both consumer and firm preferences. This is important because observed consumer purchase
46

behavior is indeed the outcome of mutual selection between consumers and firms when firms
select consumers for brand image. However, both branding literature and consumer choice
literature have focused on preference from only one side and have thus overlooked the role of such
mutual selection. This essay fills the gap by modeling the consumer and firm mutual-selection
process.
Specifically, this essay develops a structural two-sided matching framework. There are two
stages in the model. In the first stage, brands make decisions to provide products at certain price
tier(s) based on both the matching outcome expectations in the second stage and the production
cost. Firms also consider how different product combinations affect consumer perceptions of the
brand. Not only is the optimal price-tier entry decision profitable, it also helps the brand attract its
desired customers to improve brand image. After firms make entry decisions, consumers and firms
try to find their best matches in the second stage. A transaction can only be made when a consumer
prefers the brand and the brand also wants to sell to her. In other words, observed purchase
behavior is the realization of the mutual preference between consumers and firms. Note that the
available products and prices in the second matching stage are endogenously determined by firms’
entry decisions in the first stage. Our framework is the first to use an entry model to deal with this
kind of endogeneity in the matching literature.
To estimate the structural model, we seek two unique data sets from the fashion watch
market in China. The Chinese market is one of the main driving forces behind the rapid growth of
the global fashion industry. Total sales in the Chinese fashion market are expected to reach $200
billion in 2020, which is three times higher than in 2010 ($60 billion). Many fashion brands have
entered or have planned to enter the Chinese market. Investigating this market provides useful
insights for existing and future firms in China as well as in other emerging markets.
47

Our first data set derives from a survey conducted by one of the leading marketing research
companies. More than 1,000 respondents indicated whether they had purchased a watch from 43
major fashion watch brands and provided purchase information. This data set shows the realized
match between consumers and fashion watches. Beyond standard observable consumer
demographic variables including gender, age, family income, and education, this data set also
collects some useful psychographic variables such as whether consumers prefer exclusivity or
conformity. Although the data set provides detailed information that helps us identify mutual
preferences in the matching game, it does not provide the big picture of each brand’s price-line
strategy because it shows only the products consumers actually purchased, not all of the products
provided. We thus collected a second data set from a large watch retailer. This data set clearly
shows the exact products provided by all 43 watch brands and the price-line strategy that each
brand adopts. The augmentation of these two data sets helps us estimate the structural two-sided
matching model by considering the endogenous price-line decisions. To ensure that the two data
sets are compatible, we collect the information from both for the same time period.
The model is estimated using a new algorithm, the approximate Bayesian computation
(ABC), which originates from biostatistics research. We choose this estimation method because
the presented model is very complicated and a likelihood-based estimation algorithm involves
solving more than 1,000 matching games for each iteration. The ABC, which bypasses calculating
the likelihood of complicated models and allows for parallel computing, helps to boost the
estimation speed significantly. It is approximately 44 times faster than the MLE when estimating
our model.
Several key findings emerge from the analyses. First, fashion brands overall prefer well-
educated, wealthy, and exclusivity-oriented consumers. Consumers generally prefer watches with
48

mechanical movements and precious materials from well-known European brands. Consumers
that prefer exclusivity and those preferring conformity have very different tastes. The former prefer
well known, but not necessarily very prestigious brands that cover a wide range of price tiers,
while the latter prefer brands with the exact opposite features. This finding implies that a fashion
brand should concentrate its products at fewer price tiers if it wants to attract more exclusivity-
oriented consumers.
Second, we detect some mutual preferences between certain consumer groups and
fashion brands. For example, well-educated consumers like European brands, while European
brands also prefer these consumers. Such mutual preferences lead to more matches between
these two parties. Similar mutual preferences are also detected between well-recognized
European brands and wealthy consumers. More importantly, we find some unreciprocated
preferences between fashion brands and consumers. For example, young consumers under 40 are
interested in European brands, but European brands do not like young consumers. Such an
unreciprocated preference indicates that European brands will generate more revenue if they
target young consumers. This finding can be obtained only from the two-sided matching
framework rather than a discrete choice modeling framework because the latter cannot separately
identify consumer and firm preferences. For the same reason, a discrete choice model leads to a
biased inference of consumer preference. In addition, our model comparison shows that the
discrete choice model underperforms the two-sided matching model. Our proposed model is
better not only in providing more insights into consumer and firm preferences, but also in terms
of fitting the actual data, which highlights the importance of considering that firms select
consumers in the fashion market.
49

The counterfactual analyses show how brands would adjust their price-line strategies when
they value the brand image less than they do the short-term revenue. Prestigious brands tend to
extend their price-lines downward to help them obtain higher market shares and revenue. It is
noteworthy that prestigious brands would also lose some previously desirable consumers, which
is why such brands do not include many price tiers if they care more about brand image. In addition,
we do not find major changes in the price-line strategies of less prestigious brands, although they
would experience both revenue and market share losses that would come from more fierce
competition. The reason may be because these brands have already concentrated their products in
low price tiers, so they cannot go even lower.
This essay makes several contributions. Theoretically, we simultaneously study the mutual
selection between consumers and firms. This is an extension of both the branding literature, which
has ignored consumer choice, and the consumer choice literature, which has overlooked the fact
that firms also prefer and select certain consumers. Managerially, the model helps practitioners
make better decisions by revealing preferences from both sides. If a firm tries to expand its market
and target new consumers, our model offers guidance to firms in terms of price-line strategies and
helps them determine which consumers are easier to acquire.
The rest of this essay is organized as follows. In the next section, we review previous work
on the fashion market and two-sided matching in the marketing and economics literature. We then
propose the model to capture the joint preferences between firms and consumers. The model
section is followed by an empirical application in which we introduce the industry background,
our data sets, model estimation results, and the counterfactual analyses. This essay is concluded
by highlighting the key contributions and pointing out limitations with future research directions.
3.2 Related Literature
50

This essay primarily draws on two main research areas: fashion choices and branding
literature and the two-sided matching literature. In this section, we summarize existing research in
these areas and how it relates to this essay.
3.2.1 Fashion Choices and Branding. Fashion literature dates back to the essay by Veblen
(1899) that emphasizes the role of fashion as a signaling tool among consumers. A consumer
purchases a fashion product not only for its practical function, but also for what that product
represents in terms of the consumer’s knowledge of taste or behavior of people in a certain social
class. Built on this work, many studies have investigated consumer preference for fashion products.
Phau and Prendergast (2000) find that consumers generally prefer fashion brands that provide a
sense of exclusivity, have a well-known brand image, a better brand awareness, and perceived
quality. Simmel (1904) states that fashion consumption satisfies two social needs of consumers:
the need for exclusivity and the need for conformity. Amaldoss and Jain (2005a) develop an
analytical model to show how such needs affect purchase decisions. Robinson (1961) introduces
a trickle-down theory of fashion, which suggests that higher-status consumers and imitation by
lower-status consumers usually initiates consumption of a fashion product.
Recently, more research papers have focused on the consumption externality in the fashion
market and find that consumers’ perceptions of a fashion brand depend on who else is purchasing
the same brand. Karni and Schmeidler (1990) investigate the demand for fashion products with
two consumer segments. The first segment prefers products adopted by more consumers from the
same segment with fewer consumers from the second segment, while the second segment prefers
products purchased by more consumers from both segments. They reveal a fashion cycle in this
analytical framework. Berger and Heath (2008) also show that people tend to abandon products
that are used by undesired social groups, because those would signal undesired identities.
51

Because of such consumption externality in the fashion market, a stream of branding
literature studies how consumers affect brand image. Brand image is the impression a consumer
holds of a brand’s “personality.” Consumers are not only brand image seekers, but also brand
image contributors (Arnould and Thompson, 2005; Brown, Koznets, and Sherry, 2003; Payne,
Storbacka, Frow, and Know, 2009). This is because a brand image is associated with traits of
typical brand users. A brand is considered high-end if high-status consumers use it often (Solomon,
1983; Kapferer, 1998; Vigneron and Johnson, 2004). Bagwell and Bernheim (1996) document that
fashion retailers can damage a glamorous brand’s image by selling their products too cheaply and
thus attract low-status consumers. Ferraro, Kirmani, and Matherly (2013) also find a similar brand-
image dilution effect from consumers. Since consumers have a great impact on a brand image,
fashion brands thus need to carefully select their consumers not only to generate higher revenue,
but also to maintain a good image, which has a longer-term impact on the brand (Wilson, 2009;
Ward and Dahl, 2014; Peterson, Francine Espinoza; 2014).
While most previous research has investigated how consumers affect brand image and what
kind of consumers firms should target, less work has been done to examine how consumers react
to such targeting strategy and whether these consumers will actually make a purchase. Pesendorfer
(1995) considers the optimal pricing strategy of a monopoly firm when consumers prefer to
associate with the desired type of consumers through fashion purchases. Amaldoss and Jain
(2005b) investigate pricing strategies when consumers prefer exclusivity or conformity. However,
none of these papers have explicitly studied fashion product choice when a brand strategically
selects preferred consumers. This essay fills this gap by modeling a fashion product choice as the
outcome of a mutual selection to reveal the preferences of consumers and brands.
52

3.2.2 Two-sided Matching. The empirical approach employs a two-sided matching model
that originates from social science and economics literature and was first used to study the college
admissions problem (Gale and Shapley 1962). Becker (1973) uses an assortative matching model
to investigate the marriage market. Most matching papers had used analytical tools before the
seminal work by Choo and Siow (2006), who apply an empirical aggregate matching model to
study the marriage market. Fox (2010) also develops an empirical approach to study the supplier-
manufacturer relationship.
The two-sided matching framework has not been applied as extensively in the marketing
literature compared to the economics literature. However, increasingly more researchers have used
this tool to explain marketing phenomena, including matching between sports teams and athletes
(Yang, Shi and Goldfarb 2009), advertisers and publishers in online advertising (Wu 2015),
marketing departments and job market candidates (Zamudio, Wang and Haruvy 2013), and English
football teams and sponsors (Yang and Goldfard 2015). All of these studies use the matching model
to investigate questions in the B2B market. Bonnet, Galichon, and Shum (2017) state that the
matching framework can also be applied to study consumer choice. They prove that observed
consumption choices may come from a two-sided matching process. The reason that few
researchers have applied a two-sided matching model to study the product choice problem is that
it is not intuitive to assume products have preferences and actively select consumers. However,
this is not a problem in our context in which fashion brands have strong economic incentives to
choose their consumers to improve brand image. Thus, a two-sided matching model is appropriate
to investigate the fashion market and this essay is the first to empirically apply this framework to
capture demand. Compared to a discrete choice model, this approach better reveals the market
preferences of both sides by allowing for interaction between choices made by different agents.
53

3.3 The Model
In this section, we propose an empirical two-sided matching framework that evolves in two
stages. In the first stage, companies choose their price-line strategies. More specifically, they need
to decide the price tiers through which to enter and provide products. These decisions determine
the products and their market prices. In the second stage, consumers try to find products they prefer
and firms try to sell their products to desirable consumers. Here, we assume that firms can choose
consumers, because firms prefer consumers who not only generate more profit, but also help to
improve the brand image. Companies can strategically target these consumers and exclude those
they dislike. We provide more detail on the implementation of consumer selection in the empirical
application section. Because consumers choose brands while firms also choose consumers, a two-
sided matching framework is appropriate to study such mutual selection.
The proposed model has two main advantages compared to a discrete choice model. First,
a two-sided matching model facilitates understanding of not only consumer, but also firm
preferences. Previous consumer choice models have either ignored the supply side completely or
have assumed that firms only care about monetary revenue. As discussed earlier, “good”
consumers can help brands improve the brand image and thus bring some extra benefit to the firm.
The traditional profit-maximization framework fails to examine this effect, as it assumes that
selling the same products to different consumers brings the firm exactly the same benefit. Second,
a two-sided matching framework is flexible enough not to rely on the assumption of mutual
selection. On one hand, when firms can select consumers and observed purchases are the outcome
of mutual selection between consumers and firms, the two-sided framework is superior to discrete
choice models, because it allows for the interaction between choices from both sides of the market.
On the other hand, even when firms are not actively selecting consumers and the purchase outcome
54

is only affected by consumer preference, a matching model still provides robust estimation results.
Bonnet, Galichon, and Shum (2017) mathematically and empirically prove these results. The
model in this essay is flexible enough to study consumer purchase behavior regardless of whether
brands have preferences and choose consumers.
Note that what products and prices are available on the market in the second stage is an
endogenous decision by firms. Such a decision determines product assortment, which not only
affects the structure of the matching market, but also influences consumer perception of the brands.
Firms thus need to strategically design their price lines in order to match desired consumers to
achieve both profit and brand image. This endogeneity is captured through the price-tier entry
model in the first stage. Forward-looking companies form expectations of the payoffs in the second
stage when they choose their price-line strategies in the first stage. Thus, the model needs to be
solved in a backward manner. In the remaining part of this section, we first model the second stage,
which is the matching between consumers and products, in Section 3.3.1, before investigating
firms’ entry decisions in the first stage in Section 3.3.2. The identification strategy is introduced in
Section 3.3.3.
3.3.1 Second Stage: Two-sided Matching. In this essay, we study a bipartite matching
system and assume, for simplicity, that no asymmetric information exists among potential partners.
In this section, we introduce the notations of agents and matches in 3.3.1.1, formalize the
preferences of both sides in 3.3.1.2, and discuss the matching equilibrium in 3.3.1.3.
3.3.1.1 Agents and Matching Notations. We use finite sets 𝐼 and 𝐽 to denote consumers
and brands, respectively. A brand 𝑗 may provide multiple product versions at price tier 𝑚 . We use
𝑘 to denote a product version and 𝑘 𝑗𝑚
or 𝑘 ∈ 𝐾 𝑗𝑚
to denote a product version provided by brand 𝑗
at price tier 𝑚 . 𝐾 𝑗𝑚
is the set of products provided by brand 𝑗 at price tier 𝑚 , and 𝐾 is the set
55

including all products in the market. In this essay, “product” and “product version” are used
interchangeably, and we use “product unit” to refer to one unit of sellable item of product version.
As such, only one consumer can purchase each product unit, while a product version 𝑘 can match
more than 1, but no more than 𝑛 𝑘 consumers where 𝑛 𝑘 is the number of product units of version
𝑘 . Without loss of generality, we assume that a consumer can purchase at most one unit of product,
which is consistent with our observation from the data. This assumption induces a one-to-many
matching model, and facilitates our computation. It is very straightforward to release this
assumption and generalize our model to a many-to-many matching model.
A matching 𝝁 = (𝜇 𝑖𝑘
) is a matrix such that 𝜇 𝑖𝑘
= 1 if consumer 𝑖 and product 𝑘 are
matched, 𝜇 𝑖𝑘
= 0 otherwise. We use 𝜇 𝑖 0
= 1 to capture that consumer 𝑖 does not match with any
product, or “stays single” in matching jargon. Similarly, 𝜇 0𝑘 = 1 means that product 𝑘 does not
sell to any consumers, or stays single.
3.3.1.2 Preferences. In a two-sided matching framework, the matching outcome is
generated from both parties’ preferences. We first assume that consumer 𝑖 ’s utility from matching
with product 𝑘 is
𝑢 𝑖𝑘
= 𝑢 𝑖𝑘
′
+ 𝜀 1𝑖𝑘
= 𝛼 1
𝑋 𝑘 + 𝛽 1
𝑌 𝑖 𝑋 𝑘 + 𝛾 1
𝑃 𝑖𝑘
+ 𝜀 1𝑖𝑘
. (1)
Consumer 𝑖 prefers product 𝑘 to 𝑘 ′
if 𝑢 𝑖𝑘
> 𝑢 𝑖 𝑘 ′ . 𝑢 𝑖𝑘
′
in Eq. (1) captures the systematic
utility, while 𝜀 1𝑖𝑘
is a standard Type I Extreme Value error term. We further specify 𝑢 𝑖𝑘
′
= 𝛼 1
𝑋 𝑘 +
𝛽 1
𝑌 𝑖 𝑋 𝑘 + 𝛾 1
𝑃 𝑖𝑘
, where 𝑋 𝑘 is a vector of product 𝑘 ’s features and 𝑌 𝑖 is a vector of consumer 𝑖 ’s
characteristics. 𝛼 1
𝑋 𝑘 captures the consumer’s baseline preference for product 𝑘 and 𝛽 1
𝑌 𝑖 𝑋 𝑘
captures the observed preference heterogeneity. 𝑃 𝑖𝑘
is the price of product 𝑘 paid by consumer 𝑖 .
𝛾 1
𝑃 𝑖𝑘
is characterized as utility from the money paid by consumer 𝑖 , which is defined as “transfer”
56

in the matching literature. 𝑢 𝑖𝑘
′
− 𝛾 1
𝑃 𝑖𝑘
= 𝛼 1
𝑋 𝑘 + 𝛽 1
𝑌 𝑖 𝑋 𝑘 is known as pre-transfer utility. If
consumer 𝑖 stays single and does not match any product, 𝑢 𝑖 0
′
is normalized to 0.
We assume brand 𝑗 ’s utility is generated by all its products. Product 𝑘 ’s utility from
matching with consumer 𝑖 is characterized as:
𝑣 𝑖𝑘
= 𝑣 𝑖𝑘
′
+ 𝜀 2𝑖𝑘
= 𝛼 2
𝑌 𝑖 + 𝛽 2
𝑋 𝑘 𝑌 𝑖 + 𝛾 2
𝑃 𝑖𝑘
+ 𝜀 2𝑖𝑘
. (2)
Product 𝑘 prefers consumer 𝑖 to 𝑖 ′
if 𝑣 𝑖𝑘
> 𝑣 𝑖 ′
𝑘 . Similarly, 𝑣 𝑖𝑘
′
captures the systematic
utility and 𝜀 2𝑖𝑘
is an error term following the Type I Extreme Value Distribution. We further
specify 𝑣 𝑖𝑘
′
= 𝛼 2
𝑌 𝑖 + 𝛽 2
𝑋 𝑘 𝑌 𝑖 + 𝛾 2
𝑃 𝑖𝑘
. Variables 𝑌 𝑖 , 𝑋 𝑘 and 𝑃 𝑖𝑘
are the same as previously
defined. 𝛾 2
𝑃 𝑖𝑘
is the part of utility from the transfer, which captures the utility gained from sales
revenue. We follow the standard assumption in the transferable utility matching framework to
restrict 𝛾 2
= −𝛾 1
. The “pre-transfer” utility 𝑣 𝑖𝑘
′
− 𝛾 2
𝑃 𝑖𝑘
= 𝛼 2
𝑌 𝑖 + 𝛽 2
𝑋 𝑘 𝑌 𝑖 captures the non-
monetary influence from consumer to brand image. Such an effect is non-negligible in many
industries, such as the fashion and luxury market, in which firms care more about brand image
because a good brand image attracts more consumers. 𝑣 0𝑘 ′
is normalized to 0 for product 𝑘 ,
which stays single.
Brand 𝑗 ’s utility is the summation of the utility generated by every product of the brand
and depends on both the price-line strategy adopted by the brand and the matching outcome. This
will be specified in Section 3.2. Note that, if firms do not have preferences towards consumers,
the utility of product 𝑘 matching with consumer 𝑖 depends only on price 𝑃 𝑖𝑘
. The two-sided
matching framework is equivalent to a choice model with firms maximizing revenue on the
supply side.
3.3.1.3 Matching Equilibrium. Consumers prefer to purchase a product that generates
the highest utility, while firms try to sell their products to ideal consumers who generate higher
57

revenue and help to maintain good brand image. A matching can only happen when both sides
prefer each other. Thus, the observed purchases are indeed realized from both sides’ preferences
and are the equilibrium outcome of the matching market. We now discuss how to solve the
matching model to generate the equilibrium outcome from consumer and firm preferences.
Our model is similar to the college admissions setting described by Gale and Shapley
(1962) who also propose a one-to-many matching model and prove that an equilibrium matching
always exists in this type of model. A matching outcome can only be an equilibrium if it is
feasible and stable. In our case, a matching is feasible if for every 𝑖 and 𝑘 , ∑ 𝜇 𝑖𝑘
= 𝑛 𝑘 𝑖 ∈𝐼 0
and
∑ 𝜇 𝑖𝑘
= 1
𝑘 ∈𝐾 0
, where 𝐼 0
= 𝐼 ∪ {0}, 𝐾 0
= 𝐾 ∪ {0} and 0 ≤ 𝜇 𝑖𝑘
≤ 1. The first equation simply
means that the sum of product units sold to all consumers, plus the number of product units
unsold, equals the total number of product units provided by the firm. The second equation
means that each consumer either matches one unit of product or stays single. Gale and Shapley
(1962) define a feasible matching as stable if it is impossible for any agents 𝑖 and 𝑘 to deviate
from their current matches and form a new match that makes both agents better off. This is
documented as the “pair-wise stability” or “no-blocking pair” condition and is widely used in the
matching literature. To solve the matching game using this equilibrium definition, researchers
need to simulate and compare the matching payoff of every possible pair. It is very
computationally burdensome when there are as many players as in the current study.
Shapley and Shubik (1972) prove that previously defined stable matchings coincide with
the set of competitive equilibria. In other words, a stable matching maximizes the social surplus
over the set of feasible matchings 𝝁 = (𝜇 𝑖𝑘
). Solving a matching game using the pair-wise
stability condition is equivalent to solving a constrained linear maximization problem, which is
formalized as follows:
58

𝑚𝑎𝑥 𝜇 𝑖𝑘
∑ ∑ 𝜇 𝑖𝑘
(𝑢 𝑖𝑘
+ 𝑣 𝑖𝑘
)
𝑘 𝑖
s.t. ∑ 𝜇 𝑖𝑘
= 1
𝑘 ∈𝐾 0
, ∀ 𝑖
∑ 𝜇 𝑖𝑘
= 𝑛 𝑘 𝑖 ∈𝐼 0
, ∀ 𝑘
0 ≤ 𝜇 𝑖𝑘
≤ 1, ∀ (𝑖 , 𝑘 )
(3)
This approach bypasses simulations and pair-wise comparison and only requires a linear
programming technique, which significantly improves the speed of the estimation. We use this
approach to solve our matching games to obtain the matching matrix.
3.3.2 First Stage: Brand Price-line Strategies. In the first stage, firms decide whether to
enter and provide products at each price tier 𝑚 ∈ {1, 2, … , 𝑀 }. A combination of different entry
decisions forms the price-line strategy 𝑠 . More formally, a price-line strategy is characterized as
𝑠 = (𝑑 1
𝑠 , … , 𝑑 𝑚 𝑠 , … 𝑑 𝑀 𝑠 ), where 𝑑 𝑚 𝑠 = 1 if brand 𝑗 decides to enter price tier 𝑚 and 0 otherwise.
We use 𝑊 𝑗 𝑠 to denote brand 𝑗 ’s overall utility from strategy 𝑠 and formalize it as:

𝑊 𝑗 𝑠 = ∑ 𝑉 𝑗 𝑑 𝑚 𝑠 𝑀 𝑚 =1
+ 𝜀 𝑗𝑠
.
(4)
The first term on the right-hand side, ∑ 𝑉 𝑗 𝑑 𝑚 𝑠 𝑀 𝑚 =1
, captures the deterministic part of brand
𝑗 ’s utility, which is the sum of expected utilities over price tiers. 𝑉 𝑗 𝑑 𝑚 𝑠 , the expected utility from
price tier 𝑚 under strategy 𝑠 , can be further modeled as:

𝑉 𝑗 𝑑 𝑚 𝑠 = {
∑ ∑ 𝑣 𝑖𝑘
′
𝜇 𝑖𝑘
𝑖 𝑘 ∈𝐾 𝑗𝑚
+ ∑ 𝜌 𝑍 𝑘 𝑛 𝑘 𝑘 𝑑 𝑚 𝑠 = 1
0 𝑑 𝑚 𝑠 = 0

. (5)
If the brand enters price tier 𝑚 (𝑑 𝑚 𝑠 = 1), the expected utility is ∑ ∑ 𝑣 𝑖𝑘
′
𝜇 𝑖𝑘 𝑖 𝑘 ∈𝐾 𝑗𝑚
+
∑𝜌 𝑍 𝑘 𝑛 𝑘 𝑘 . 𝑣 𝑖𝑘
′
is the expected utility generated by product 𝑘 if it matches with consumer 𝑖 , while
59

𝜇 𝑖𝑘
is the matching indicator. ∑ 𝑣 𝑖𝑘
′
𝜇 𝑖𝑘 𝑖 captures the expected utility gained by the product 𝑘 .
Summing the utility from all the products gives the expected utility gained from sales if the
brand enters price tier 𝑚 .
Brands should also consider the production cost when choosing price-line strategies,
which is captured in the second term, ∑𝜌 𝑍 𝑘 𝑛 𝑘 𝑘 , in Eq. (5). 𝑍 𝑘 is a vector of product attributes
and 𝑛 𝑘 is the number of product units provided. 𝜌 is a vector of coefficients and is expected to be
negative. If the utility loss from the cost exceeds the expected utility gained from sales, brand 𝑗
has the option not to enter the price tier 𝑚 (𝑑 𝑚 𝑠 = 0). The expected utility from this market is
normalized to 0.
We acknowledge that when a brand chooses its price-line strategy, it needs to consider all
other brands’ strategies, which influence the matching outcome 𝜇 𝑖𝑘
of the focal brand. Thus, we
should solve a game in which each brand’s price-line strategy is a function of other brands’
strategies. This game is very complicated to solve, especially considering that we have 43
brands, and each brand has 32 price-line strategies from which to choose. To facilitate model
solving and estimation, we assume complete information, and when fashion brands make entry
decisions, they can correctly predict other brand’s price-line strategies.
Rational brands choose the optimal strategies that generate the highest expected utility. The
Type I Extreme Value error term 𝜀 𝑗𝑠
in Eq. (4) induces a closed-form probability that firm 𝑗 adopts
strategy 𝑠 :

𝑝 𝑆 𝑗 =
𝑒𝑥𝑝 (𝑊 𝑗 𝑠 )
∑ 𝑒𝑥𝑝 (𝑊 𝑗 𝑠 ′
)
𝑠 ′
=
𝑒𝑥𝑝 (∑ 𝑉 𝑗 𝑑 𝑚 𝑠 𝑀 𝑚 =1
)
∑ 𝑒𝑥𝑝 (∑ 𝑉 𝑗 𝑑 𝑚 𝑠 ′
𝑀 𝑚 =1
)
𝑠 ′
.
(6)
Note that we need to obtain brand 𝑗 ’s expected utility of every possible price-line strategy
to calculate the choice probability in Eq. (6). Each price-line strategy induces a different
60

matching game to solve. 𝑀 price tiers lead to 2
𝑀 different entry strategies for a brand to choose
from and thus 2
𝑀 − 1 different matching games for researchers to solve for each brand.
An alternative approach is to assume that each brand makes entry decisions independently
across price tiers. This approach requires the solving of 𝑀 rather than 2
𝑀 − 1 matching games for
each brand, which would reduce the computational load. However, it assumes that a brand’s entry
decision at one price tier does not affect the entry outcome from other price tiers. Considering that
entering a new price tier may cannibalize the revenue from another price tier, the interdependence
between entry decisions in different price tiers is not negligible. This alternative approach cannot
capture this effect, which is why, although it is simpler, we do not apply this approach.
3.3.3 Identification Strategy. In this section, we discuss how a two-sided matching model
can separately identify the preference from each side. Our identification strategy is built upon
Choo and Siow (2006), Galichon and Salanie (2015), and Agarwal (2015).
There are two identification resources. The first resource is from the price information.
Choo and Siow (2006) develop a similar two-sided matching transferrable utility framework to
study the Canadian marriage market. They show that a two-sided matching model combines two
discrete choice models through the equilibrium transfer. In other words, the transfer is
endogenously determined to clear the demand and supply side of the market. If the transfer is
observed, the utility from both sides can then be separately identified. In our case, the observed
price serves as the transfer in the matching game, and this piece of information is one important
identification resource.
The second identification resource is the observed matching pattern. Agarwal (2015) uses
matching between resident physicians and hospitals as an example of how the matching patterns
help with the identification. He states that, if a hospital has a strong preference for one type of
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residents, researchers are more likely to observe that the hospital program matches many
residents with similar characteristics. Thus, the preference of hospitals can be identified through
the variation in the characteristics of residents hospitals match, and the preference of residents
can be identified following the same logic. In our case, if we observe many matches between a
brand and many consumers of the same type, we can conclude that the brand prefers this
consumer type and/or the consumer type prefers this brand. If we also observe that the focal
brand matches only this type of consumer, we can then infer that the observed matches mostly
come from the brand’s strong preference. The reason is understandable: if the preference of the
brand were not strong, we would see the brand also match with some other types of consumers.
This is how brand preference is identified and consumer preference can be similarly identified.
Similarly, Galichon and Salanie (2015) report that the equilibrium utilities of all participants can
be identified from a two-sided matching framework given the matching pattern. They
mathematically prove that the expected utility of each side can be obtained from derivatives of
the terms that constitute generalized entropy, which is a function of the observed matching
matrix.
In our case, we have four sets of parameters: consumer preference parameters (𝛼 1
and
𝛽 1
), firm preference parameters (𝛼 2
and 𝛽 2
), transfer parameters (𝛾 1
and 𝛾 2
), and firm cost
parameters (𝜌 ). The observed matching pattern, as well as the transfer information, allows us to
separately identify the systematic utilities 𝑢 𝑖𝑘
′
= 𝛼 1
𝑋 𝑘 + 𝛽 1
𝑌 𝑖 𝑋 𝑘 + 𝛾 1
𝑃 𝑖𝑘
and 𝑣 𝑖𝑘
′
= 𝛼 2
𝑌 𝑖 +
𝛽 2
𝑋 𝑘 𝑌 𝑖 + 𝛾 2
𝑃 𝑖𝑘
. Variation in product and consumer characteristics identifies consumer
preference parameters 𝛼 1
and 𝛽 1
and firm preference parameters 𝛼 2
and 𝛽 2
. Variation in the price
and price-tier entry strategies identify the transfer parameters 𝛾 1
and 𝛾 2
, as well as the cost
parameter 𝜌 .
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3.4 Empirical Application
This section presents an empirical application of the proposed model in the context of the
Chinese fashion watch market. It opens with some background information about the fashion
market in Section 3.4.1. Two data sets in the Chinese fashion market are presented in Section 3.4.2.
Section 3.4.3 introduces the approximate Bayesian computation as the estimation algorithm and
explains how it allows parallel computing and facilitates our model estimation. The section ends
with estimation results and implications in Section 3.4.4, as well as counterfactual analyses in 3.4.5.
3.4.1 Background Information. Over the past decade, the fashion industry has been an
economic success story. After 10 years of steady growth at an annual rate of 5.5%, the value of the
global fashion industry reached $2.4 trillion in 2016, accounting for approximately 2% of the
world’s GDP. It would be the world’s seventh-largest economy if ranked alongside the GDP of
individual countries.
In addition to the importance of the fashion industry in the global economy, fashion product
consumption has some interesting features that may attract the attention of researchers. First, some
researchers have studied consumption externality in the fashion market and have found that fashion
products are consumed for more than just functional use. Such products also fulfill consumers’
social needs by helping them represent themselves as who they are and who they want to be
(Yoganarasimhan, 2012). Consumers purchase fashion brands to fit into a particular subculture or
peer group, and thus they are more attracted to brands adopted by their preferred social groups. If
a brand is abandoned, it is not due to product dysfunction but rather because outsiders or social
groups with whom they do not wish to be associated adopted the brand (Berger and Heath, 2008).
Consumer traits of the fashion brand can directly affect the brand image and, as such, eventually
affect others who may purchase the product.
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Because of the consumption externality, fashion firms do not target certain consumers even
if the latter could generate more revenue for the firm. Instead, firms try to deliver their products to
carefully selected consumers who not only generate revenue, but also help the firm improve the
brand image. Many fashion brands tend to market their products to “elite” social groups in order
to convey a desirable image. Brand image has a long-term effect on a company. A fashion
marketing manager states that fashion brands have to carefully select consumers to maintain the
image or they “would double sales for six months and then would sell nothing.”
Consumer selection is widely practiced in the fashion industry and is implemented in
several ways. The most direct and “brutal” way is through salespeople who are trained to reject
some consumers. This is shown in a quote from a customer discussion at
http://www.fashionspot.com cited by Ward and Dahl (2014): “When I went to Louis Vuitton… It
was like walking into a freezer, they were so cold toward me.” A former employee of the Yves
Saint Laurent shop also confirms such consumer rejection (Wilson 2009). Occasionally, sales
assistants will serve undesired consumers, but they will not display all of the available products. It
has been documented that some fashion stores do not display all products on the floor and
intentionally leave some products in the back for targeted customers.
Another direct approach to select consumers is through “invitation only” sales events. For
example, Chanel regularly invites preferred consumers to its sales events, where some limited
editions are sold. Only consumers with invitation letters or emails can enter and purchase these
products. This strategy is more widely applied by fashion brands and has been proven effective
according to the director of a high-end fashion and sterling silverware brand. Such client selection
not only enhances the brand image, but also generates more profit, as it incentivizes regular
clientele. Some other brands select consumers through product assortment. Many potential
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customers are excluded by Versace simply because the designer does not provide clothes in larger
sizes (Peterson, Francine, Espinoza, 2014).
Firms also select consumers in indirect ways, such as targeted advertising. Ferrari invests
little in mass market advertising, especially compared to its investment in Formula 1 events, which
is restricted to a small, selected group of consumers (Peterson, Francine Espinoza, 2014). Some
famous fashion watch brands do not even try to impress many potential consumers. The Wall Street
Journal introduced several prestigious watch brands that most consumers never hear of. These
brands only advertise to a very small group of consumers who match the image of these brands,
and those who do not are excluded, even though they may be wealthy. Firms exclude such
consumers by not advertising to them and, as such, consumers remain unaware of the value of
these brands or even of their existence.
Since a purchase can be made only if both the consumer and the brand want to buy and sell,
the observed fashion purchase is indeed a mutual selection process. Thus, our proposed two-sided
matching model is more appropriate for the study of the fashion market. In this study, we are
especially interested in the Chinese fashion market for two reasons. First, with the rapid increase
in urbanization, Chinese customers have more spending power and allocate more money to fashion
goods. The fashion industry has expanded at an exponential rate. According to a report from Daxue
Consulting Group, total fashion sales in 2020 are expected to reach $200 billion, 3 times of that in
2010 ($60 billion). China is too big of a market to ignore. Many fashion brands have already
entered or plan to enter the market. As such, investigating this market provides useful insights for
existing and future fashion firms in China as well as in other emerging markets. Second, Chinese
fashion consumers have their own tastes. They are found to care more about brand awareness and
brand associations rather than perceived quality, compared to U.S. consumers (Jung and Shen
65

2011). This insight is consistent with Zhang and Kim (2013), who show that brand consciousness
and social comparison significantly affect Chinese consumers’ intentions to purchase. These
findings imply that, in China, fashion brands select consumers more carefully to improve their
brand image in order to succeed. Thus, it is important to consider how fashion brands select
Chinese consumers for brand image as well as consumer choice under such selection.
3.4.2 Data Description. We obtain two unique data sets on the Chinese fashion market.
The first data set is from a survey obtained by a large marketing research firm. The firm carefully
selected respondents from three big cities: Beijing, Shanghai, and Guangzhou. Considering that
most big fashion brands choose these three cities to expand into the Chinese market, residents are
more knowledgeable about fashion. The screening process excludes consumers with insufficient
buying power and includes only respondents experienced in purchasing fashion products. This
leaves a total of 1,059 respondents in our data.
The firm records a great deal of demographics about respondents including age, gender,
education, and family income. Table 11 provides summary statistics about the respondents. There
are 554 male and 505 female respondents between 25 and 59 years of age, with annual incomes
exceeding 200,000 RMB (approximately $30,000). Most of the respondents are below age 40, with
an annual income between 200,000 and 1,000,000 RMB (approximately $30,000~$160,000).
These respondents comprise the major groups of consumers of fashion watch brands. Although the
education level in the sample ranges from high school to doctor, most of the respondents have a
degree from a four-year college or a junior college (similar to community colleges).
Beyond demographics, respondents also provide some psychographic information
including whether they prefer conformity or exclusivity. This piece of information is important in
studying fashion consumption, since many purchases are not only for functional use of the product,
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but also for self-representation and signaling. In our data, 392 respondents like exclusivity and
uniqueness, while 276 respondents prefer conformity.
Table 11. Summary Statistics of Consumer Characteristics
Income Obs. Education Obs.
200 - 300k 74 High School 73
300 - 400k 479 Junior College 256
400 - 500k 220 Bachelor 601
500k - 1m 166 Master 110
1 - 1.5m 62 Doctor 19
1.5 - 2m 16 Age Obs.
2 - 3m 26 Young (25-39) 729
3 - 5m 9
Middle Age
(40-59)
330
5m and above 7 Exclusivity Obs.
Gender Obs. Yes 392
Male 554 No 667
Female 505 Conformity Obs.
Total 1059 Yes 276
No 783

Although all 1,059 respondents consider purchasing a watch, only 702 actually purchase a
watch from one of the 43 major fashion watch brands, and none is observed to purchase more than
one watch. Respondents also provide information about which watch they purchase and at what
price. Since all purchases were made within 12 months before the survey, respondents can recall
information about their purchases. Although we observe the brand names from the data, we cannot
reveal them because of non-disclosure agreements. Table 12 shows some summary statistics of
brand information. Most of the brands are from Europe. The market shares of the 43 brands vary
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significantly. The largest company takes 15.46% of the total market shares while the smallest takes
only 0.29% of the market share. The third row in Table 12 shows the average price paid for each
brand. The average price of the most luxurious brand is 707,400 RMB (approximately $110,000)
while that of the cheapest brand is 2,640 RMB (approximately $400). Table 12 also gives the
summary statistics of brand awareness in the fourth row. It is calculated by the research firm, which
asked another set of respondents whether they had heard of each of the 43 brands. The most popular
brand is recognized by 87.78%, while the niche brand is recognized by only 5.33% of the
respondents.
Table 12. Summary Statistics of the 43 Watch Brands

Mean Median Min Max
Brand Origin
(European=1)
0.88 1.00 0.00 1.00
Market Share (%) 2.33 1.57 0.29 15.81
Average Price (1,000 RMB) 94.73 21.94 2.64 707.40
Brand Awareness (%) 30.63 22.56 5.33 87.78
% of Watches with
Mechanical Movements
64.13 69.23 0.00 100.00
% of Watches with
Precious Metals
38.66 32.84 0.00 100.00
Number of Products 147.7 100 5 642
Price Tiers Covered 2.767 3 1 5

The first data set gives rich information of matchings between consumers and fashion
products. However, we can only observe the products that were matched with consumers, not the
provided but unmatched products. Without this piece of information, we do not have the whole
picture of the matching market or brands’ price-line decisions. We thus seek a second data set from
a fashion watch retailer in China (www.wbiao.cn). This is the largest watch retailer in China and
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is a credible data source to augment our first data set. It provides detailed information on available
product versions for each brand, how many product units are available for each version, and
product attributes. With this extra information, we can better investigate the matching market with
consideration of firms’ price-line strategies.
The fifth row in Table 12 reveals the percentage of watches from each firm with mechanical
movements, and the sixth row shows the percentage of the watches that are made with gems or
precious metals. We can see that some companies produce only high-end fashion watches with
mechanical movements and precious metals, while others provide only low-end products with
quartz movements and cheaper materials such as steel or aluminum. The seventh row in Table 12
shows the summary statistics of the number of product units provided. Some companies provide
only a very limited number of product units in order to target a niche market, while others offer
more to target a broader range of consumers. This indicates that firms may adopt different price-
line strategies. To see this more clearly, we further divide the Chinese fashion watch market into
five price tiers. Industry wisdom indicates that entry- level fashion watches are usually priced
between 1,000 and 3,000 RMB, while basic-level watches are priced between 3,000 and 10,000
RMB. Watches above 10,000 RMB are luxury fashion watches, but only those with prices higher
than 28,000 and 65,000 RMB can be considered high-end luxury and ultra-luxury watches. The
last row in Table 12 presents information on the number of price tiers covered by each brand. Some
brands provide products in all five tiers to attract more consumers, while others only offer one
price tier to target a homogenous market.
3.4.3 Model Estimation. As previously discussed in the model section, our structural
model requires that we solve multiple matching games to obtain the choice probability of price-
line strategies. More specifically, we have 5 price tiers and 43 brands, which yield 1,333
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matching games to solve. We apply social surplus maximization matching equilibrium that
requires constrained linear programming rather than simulation, and follow Galichon and Salanie
(2015) to adapt the iterative projection fitting procedure to facilitate model solving. Traditional
likelihood-based methods, such as the MLE, are not feasible for estimation in our model, as each
iteration leads to a new set of matching games and the MLE requires the solving of each set of
matching games sequentially until convergence.
To deal with this problem, we apply an approximate Bayesian computation (ABC)
algorithm for estimation. The ABC is a likelihood-free computation to perform Bayesian
inference. In Bayesian inference, the posterior distribution is given by 𝜋 (𝜃 |𝑦 ) ∝ 𝜋 (𝑦 |𝜃 ) 𝜋 (𝜃 ).
Traditional Bayesian inference requires the calculation of the likelihood 𝜋 (𝑦 |𝜃 ) to form the
posterior distribution. This inference would be very time consuming if the model were complex
enough that the likelihood function 𝜋 (𝑦 |𝜃 ) was difficult to evaluate. In such cases, the ABC is
introduced. The ABC applies simulation-based approximation, which does not require the
explicit evaluation of likelihood. In addition, it is amenable to parallelization techniques, as it
separates data simulation and parameter estimation into two independent processes. Thus, the
ABC is a better algorithm to help us significantly speed up the estimation.
The ABC is widely used in biostatistics to estimate complex models (Beaumont et al.
2002, Blum and Francois 2010). Economists such as Creel, Gao, Hong, and Kristensen (2015)
recently applied it to prove the robustness of the method compared to GMM. Considering that
this algorithm has not been used in marketing, we briefly introduce the philosophy of ABC first
and then provide more implementation details.
Similar to the traditional MCMC, the ABC starts from an uninformative distribution of
parameters. For a candidate parameter vector 𝜃 , researchers need to generate a data set 𝑥 from the
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model 𝑥 ~𝜋 (𝜃 ). If the simulated data set 𝑥 and the observed dataset 𝑦 are similar enough, 𝜃 is then
a good candidate to have generated the observed data from the given model and should be accepted.
If the simulated and the observed data sets are not similar, 𝜃 is then less likely to generate the
observed data and should be discarded. The retained parameter vectors form the parameter base
for the posterior distribution 𝜋 (𝑦 |𝜃 ). The ABC can take several forms in terms of how to specify
the posterior distribution from the parameter base, including rejection-based approximate
Bayesian inference, regression adjusting and weighting, local-linear regression and neuro network
Bayesian inference. These forms are summarized in Beaumont, Zhang, and Balding (2002) and
Blum and Francois (2010). We estimate our model using all of these specifications and obtain
similar results. The estimation results reported in this essay are from the neuro-network ABC.
In our case, we simulate 250,000 sets of candidate parameters 𝜃 from a uniform
distribution 𝜃 ~𝑈 (−5,5) and generate two sets of data from the proposed model: price tier entry
data and the matching data. To measure the similarity between the simulated and observed data
sets, we calculate the number of price tiers each brand enters and the number of brands in each
price tier from the price tier entry data, and the market shares from the matching data, for a total
of 91 moments. We then calculate the distance between the moments from the simulated and the
observed data sets, and keep the top 1% parameters that generate the closest simulated data
compared to the real data and form the posterior distribution.
Note that the ABC completely separates the model solving and parameter search
processes. The candidate parameters 𝜃 are generated together in the first step. We can
simultaneously solve the model and calculate the value of the required moments based on the
pre-generated parameters and thus implement parallel computing in this step. We select
candidate parameters to form the posterior distribution only after we finish the model-solving
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step. If we had used the MLE, we would have first needed to solve the model given an initial set
of parameters to generate likelihood and obtain the gradient and Hessian matrix. We would then
use the newly generated gradient and Hessian matrix to obtain the next set of parameters. We
would also have to sequentially repeat such steps until convergence.
The importance of running the ABC and parallel computing is obvious considering that
we need to solve 1,333 matching games for one single set of candidate parameters. It takes
approximately 350 seconds to solve the model and calculate the likelihood in one iteration. It
would take 1,012 days to finish 250,000 iterations. We use snowfall to parallel solve the
proposed model using 80 nodes. The ABC takes 31.4 days to solve the model and achieve the
moments from our parameter candidates, which is 44 times faster.
3.4.4 Estimation Results and Model Comparisons. We specify a full model to consider
all possible baseline and interaction effects of consumer and brand preferences and present only
significant coefficients in Table 13a and 13b. Table 13a shows the posterior means and 95%
posterior density intervals of a firm’s utility primitives. Firms generally prefer older, exclusivity-
oriented consumers with higher educations and family incomes. European brands show an even
stronger preference towards older, wealthier, and better-educated consumers. While well-known
brands prefer such consumers, these brands are also interested in acquiring consumers who
prefer exclusivity. In terms of other parameters capturing profit, the price coefficient is, as
expected, positive for fashion brands, since higher price generates more revenue. The negative
coefficients of mechanical movements and precious metals show that it is costly to produce a
watch with these features.

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Table 13a. Estimation Results – Firm Preference

Estimates Confidence Interval
Young -0.628 (-0.902, -0.354)
Education 0.877 (0.637, 1.109)
Income 1.262 (0.748, 1.774)
Exclusivity 0.968 (0.374, 1.563)
Young * European Brand -2.165 (-2.422, -1.766)
Education * European Brand 0.511 (0.361, 0.660)
Income * European Brand 0.812 (0.548, 1.075)
Conformity * European Brand -0.564 (-0.707, -0.421)
Education * Brand Awareness 1.292 (1.177, 1.418)
Income * Brand Awareness 0.722 (0.275, 1.170)
Exclusivity * Brand Awareness 0.407 (0.097, 0.716)
Price 2.035 (1.183, 3.527)
Mechanical Movement (cost) -1.255 (-1.328, -1.144)
Precious Metal (cost) -2.329 (-3.289, -0.727)

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Table 13b. Estimation Results – Consumer Preference

Estimates Confidence Interval
European Brand 0.773 (0.462, 1.080)
Brand Awareness 1.024 (0.649, 1.491)
Mechanical Movement 1.355 (0.998, 1.874)
Precious Metal 1.781 (1.156, 2.456)
Price -2.035 (-3.527, -1.183)
Young * European Brand 1.569 (1.052, 2.083)
Young * Precious Metal -1.591 (-2.006, -1.174)
Male * Brand Awareness -1.478 (-1.759, -1.197)
Male * Mechanical Movement 2.390 (1.942, 2.833)
Male * Price 1.433 (1.059, 1.807)
Education * European Brand 1.561 (1.012, 2.109)
Education * Average Price 2.658 (2.016, 3.300)
Education * Brand Awareness -1.835 (-2.389, -1.280)
Income * European Brand 1.064 (0.648, 1.481)
Income * Average Price 1.276 (0.977, 1.513)
Income * Brand Awareness 1.377 (0.425, 2.316)
Income * Precious Metal 1.887 (1.544 2.230)
Income* Price 2.052 (1.342, 2.767)
Conformity * European Brand -0.785 (-1.409, -0.159)
Conformity * Average Price -1.144 (-1.738, -0.551)
Conformity * Brand Awareness 1.082 (0.600, 1.562)
Conformity * Price Tier Coverage 2.736 (2.450, 3.023)
Exclusivity * Average Price 0.808 (0.368, 1.246)
Exclusivity * Brand Awareness -1.813 (-2.157, -1.468)
Exclusivity * Price Tier Coverage -1.202 (-1.491, -0.915)
Exclusivity * Precious Metal 1.605 (1.220, 1.992)
Exclusivity * Price 2.086 (1.610, 2.560)

Table 13b shows consumer preference for fashion watches. Consumers generally prefer
fashion watches with mechanical movements and precious metals from well-known European
brands. Heterogeneous consumer preferences are also detected by the interaction terms.
Although younger consumers like European brands, they do not care as much whether a watch is
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made of precious materials. Male consumers appreciate fashion watches with mechanical
movements from niche brands. Interestingly, male consumers are less price sensitive than female
consumers are. This finding is not surprising considering that the study is in the fashion watch
market, one of the very few markets within which men have great interest. Well-educated
consumers and wealthy consumers both show a stronger preference towards more prestigious
European brands, but have different tastes in terms of brand awareness. Highly educated people
like niche brands, while wealthy customers admire well-known brands. Wealthy consumers also
tend to purchase more expensive watches with precious materials.
Psychographic information is also useful in predicting consumer preference. Conformity-
oriented consumers and exclusivity-oriented consumers like different brands. The former
generally prefer well known, but not necessarily highly prestigious Asian brands, while the latter
prefer brands with the exact opposite features and are particularly interested in more expensive
watches with precious materials. Another interesting finding is that conformity-oriented
consumers appreciate brands that include more price tiers, while exclusivity-oriented consumers
like brands that include fewer price tiers. This result is consistent with Petroshius and Monroe’s
(1987) finding that overall product line and product assortment affect a consumer’s brand
evaluation.
More findings arise when we compare consumer and firm preferences. First, some mutual
preferences emerge between certain consumer groups and watch brands. For example, we find
that wealthy consumers like European brands and vice versa. Such mutual preferences also occur
between well-educated consumers and European brands as well as wealthy consumers and well-
recognized brands. These mutual preferences explain more matchings between these two parties.
Second, we detect some unreciprocated preferences. More specifically, young consumers are
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more interested in European brands, but European brands do not reciprocate with a preference
for the young generation. Such unreciprocated preferences can only be identified under our
framework, and as we will show, a discrete choice model will biasedly infer that young
consumers dislike European brands. Such unreciprocated preferences also show up between
well-educated, exclusivity-oriented consumers and well-known brands.
Our empirical findings have strong managerial relevance. First, they help fashion brands
target the right consumers with a better understanding of consumer preference. A fashion
company occasionally needs to reposition its brand and target new consumers to expand its
market. Understanding consumer preference helps firms understand what kind of new consumers
are easier to acquire and are profitable to target. For example, although we would not see young
consumers purchase many European watches, our results indicate that this is because European
brands do not target young consumers who are under 40. It will be profitable for European
brands to target young consumers to expand their market in China, because such consumers are
easier to acquire. Second, our results show how firms should adjust their price-line strategies to
attract certain consumers. Since well-known brands hope to attract more consumers who prefer
exclusivity, they should shrink their price lines to provide products mostly in high-price tiers, as
their targeted consumers prefer brands that are unique and cover fewer price tiers.
To explicitly show the importance of the two-sided matching model, we ran a simple
logit model as a benchmark. Estimation results of the logit model are shown in Table 14. We can
see that the coefficient of the younger generation and European brand interaction term is
negative. Recall that we detect in the matching model that European brands prefer older
consumers, while younger consumers actually show more interest in European brands. This
unreciprocated preference between two parties cannot be revealed in the discrete choice model.
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Similarly, other coefficients of consumer preferences are biased, because coefficients in the
discrete choice model include much noise from the firm preference. Moreover, the BIC of the
logit model is 8296.52, while that of our proposed model is 7705.21. The two-sided matching
model better describes the fashion watch market compared to a discrete choice model.

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Table 14. Estimation Results – Benchmark Model

Estimates Confidence Interval
European Brand 0.448 (0.168, 0.729)
Brand Awareness 0.805 (0.057, 1.553)
Mechanical Movement 1.997 (1.135, 2.860)
Precious Metal 1.526 (0.994, 2.058)
Price -1.905 (-2.336, -1.474)
Young * Europe -0.506 (-0.748, -0.263)
Young * Brand Awareness -0.429 (-0.636, -0.221)
Young * Precious Metal -0.944 (-1.692, -0.196)
Male * Brand Awareness -0.378 (-0.496, -0.260)
Male * Mechanical Movement 1.838 (1.460, 2.215)
Male * Price 2.327 (1.722, 2.933)
Education * European Brand 1.275 (0.170, 2.381)
Education * Average Price 2.671 (0.959, 4.382)
Education * Awareness 0.647 (0.464, 0.830)
Income * European Brand 2.399 (0.487, 4.310)
Income * Average Price 2.132 (1.417, 2.846)
Income * Brand Awareness 0.642 (0.103, 1.180)
Income * Precious Metal 2.736 (0.618 4..854)
Income * Price 0.799 (0.058 1.540)
Conformity * European Brand -2.742 (-3.635, -1.849)
Conformity * Average Price -0.921 (-1.462, -0.380)
Conformity * Brand Awareness 1.310 (0.928, 1.692)
Conformity * Price Tier Coverage 1.449 (0.396, 2.501)
Exclusivity * European Brand 0.825 (0.260, 1.390)
Exclusivity * Average Price 0.839 (0.216, 1.462)
Exclusivity * Brand Awareness -0.178 (-0.341, -0.016)
Exclusivity * Price Tier Coverage -0.520 (-0.994, -0.046)
Exclusivity * Precious Metal 0.395 (0.171, 0.618)
Exclusivity * Price 0.683 (0.457, 0.908)

3.4.5 Counterfactual Analyses. Firms usually need to make a trade-off between
generating more short-term revenue and maintaining a brand image. Although fashion brands
care significantly about brand image, they might occasionally need to adjust their objectives due
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to a changing environment. One example is the way in which fashion brands had to prioritize
short-term revenue during the 2008 recession. What strategies should fashion watch companies
take to boost their sales to survive through the recession? Given estimates of our proposed
model, this question is answered with our counterfactual analyses.
To better interpret the counterfactual results, we divide the 43 brands into 2 groups: a
prestigious group and a less-prestigious group. The prestigious group includes 22 brands, which
only enter one or more of the luxurious price tiers (ultra-luxury, high-end luxury and luxury-
fashion price tiers), but does not provide products at any of the lower-price tiers (basic fashion
and entry fashion tiers). The less-prestigious group includes 21 brands, which provide most, if
not all, of their products to lower-price tiers. The third row in Table 15 shows a significant
difference between the average prices of the prestigious brands (192,960 RMB) and the less-
prestigious brands (10,690 RMB).

79

Table 15. Counterfactual Results - Sales and Price Line Strategies
Brand Groups Prestigious Group Less-Prestigious Group
Number of Brands 22 21
Average Price 192.96 10.69
Average
Number of
Price Tiers
Original 2.18 3.38
Predicted 3.09 3.22
Change 0.97 -0.16
Sum of
Market Share
Original 39.60% 60.40%
Predicted 52.06% 47.94%
Change 12.46% -12.46%
Sum of
Revenue
Original 20,872.40 4,136.088
Predicted 22,738.42 3,565.619
Change 8.94% -13.80%

The rest of Table 15 shows how brands in each group would adjust their price-line
strategies and changes in the market shares and revenue if the preferences of fashion brands
toward consumer characteristics become 20% weaker. The third and fourth columns display the
average number of price tiers that each group enters as well as the sum of the market shares and
revenues of each group. The magnitude of the change measured in percentage is also reported.
We find that the prestigious brands tend to extend their price lines. The average price tiers
entered by prestigious brands would increase from 2.18 to 3.09. This change would help them to
generate higher market shares (12.46%) and more revenue (8.94%). Because of the aggressive
pricing strategies from prestigious brands, the less-prestigious brands would also face more
competition. Although losses in both market shares (-12.46%) and revenue (-13.80%) would
occur, less-prestigious brands would still provide products in almost the same number of price
tiers (from 3.38 to 3.22).
80

To better understand different strategies adopted by the two groups, we show how many
brands would have entered each price tier after the preference change in Table 16. We observe
that prestigious brands and less prestigious brands have different price line strategies. For the
prestigious group, significantly more brands would appear in the basic fashion and entry fashion
tiers, while some prestigious brands would leave the ultra-luxury market and high-end luxury
markets. On the other hand, less prestigious brands do not adjust their price lines very
significantly.
To understand the reason for the change in the price line strategies, we summarize the
characteristics of consumers for each group and present the result in Table 17. Note that
prestigious brands used to attract wealthier, better educated, and more exclusivity-oriented
consumers. Our result shows that when prestigious brands place less value on the brand image,
they acquire fewer such consumers after price-line strategy changes. This explains why
prestigious brands previously chose not to enter lower price tiers although these tiers are
profitable. For the same reason, prestigious brands leave the higher-price tiers, which previously
helped them attract some “elite” consumers these brands preferred. Now firms value less of the
brand image, the benefit of acquiring these “elite” consumers does not offset the cost of this
expensive price tier. Because less-prestigious brands originally entered mostly the lower market
tiers, they cannot extend their price-lines even lower now. Their price-line strategies and
consumer characteristics would not change significantly.

81

Table 16. Counterfactual Results – Number of Brands in Each Price Tier
Price Tier Prestigious Brands Less-Prestigious Brands
Ultra-Luxury
Original 19 0
Predicted 13 0
High-end Luxury
Original 18 9
Predicted 14 7
Luxury-Fashion
Original 11 14
Predicted 16 13
Basic Fashion
Original 0 21
Predicted 13 19
Entry Fashion
Original 0 16
Predicted 12 19

Table 17. Counterfactual Results – Consumers Characteristics of Each Group

Prestigious Brands Less-Prestigious Brands
Original Predicted Original Predicted
Young 0.38 0.43 0.42 0.45
Male 0.57 0.54 0.52 0.51
Education* 3.54 3.12 2.93 2.90
Income** 4.19 3.49 3.21 3.08
Conformity 0.20 0.42 0.39 0.40
Exclusivity 0.60 0.37 0.46 0.39

3.5 Conclusion
Because consumers not only generate revenue, but also influence fashion companies’ brand
image, many firms strategically select consumers to maintain a good image. Such selection of
consumers makes the observed purchases the outcome of mutual preferences from both consumers
and firms. This phenomenon has been overlooked in the literature. Branding literature has focused
mainly on the firm’s perspective and how consumers affect the brand image, but has ignored
consumer preference. Consumer choice literature, on the other hand, has mostly studied consumer
82

preference without considering that firms that select consumers also affect consumer choice. To
fill this gap, we develop a structural model based on the two-sided matching framework to capture
demand as realized from a two-sided matching process. An entry model is embedded to capture
the endogenous price-line decisions. To cope with computational challenges, we apply an
approximate Bayesian computation (ABC) estimation algorithm as well as parallel computing
techniques.
Applying our model to two unique data sets from the Chinese fashion watch market, we
find that firms generally prefer older, exclusivity-oriented consumers with higher levels of
education and family income, while consumers generally prefer fashion watches with mechanical
movements and precious metals from well-known European brands. Some mutual preferences
emerge between European brands and well-educated, wealthy consumers. Interestingly, we find
that young consumers show great interest in European watches even though they are not targeted
by these brands. Our model performs better than a discrete choice model, which cannot
separately identify the consumer preference and brand preference and gives biased estimates of
consumer preference.
Findings in this essay have high managerial relevance. The reciprocated preference
between the younger generation and European brands implies that it is profitable for European
watch brands to reach out to young consumers. In addition, well-known brands should shrink
their price lines to provide products mostly in high-price tiers because their targeted consumers
prefer brands that are unique and offer fewer price tiers. Our counterfactual analyses show that, if
fashion brands hope to generate higher current revenue and place less value on brand image,
prestigious brands would extend their price-lines downward to attract more consumers at the cost
of losing some consumers they prefer. Less-prestigious brands, on the other hand, do not adjust
83

their price-lines significantly, although they will face losses in terms of both market share and
revenue due to more fierce competition from prestigious brands.
This essay makes several contributions. Theoretically, it contributes to the branding
literature and consumer choice literature, both of which focus on only one side of the market. This
essay is the first to model consumer demand as the outcome of mutual selections from both sides.
Our empirical application proves its importance, since the discrete choice model leads to biased
estimation results. Methodologically, we embed an entry model to a two-sided matching
framework in order to control for the endogenous price-line decisions, which has not been
conducted in the two-sided matching literature. Moreover, we introduce a new estimation
algorithm to the marketing field, the approximate Bayesian computation, which is capable of
estimating very complicated models. It bypasses the likelihood calculation procedure and allows
for parallel computing by separating model solving and parameter search processes.
This essay also has some limitations, which offer opportunities for further research. First,
this study does not explicitly model the social effects of fashion consumption, although it is a
reason that firms strategically select consumers. Our data shows whether consumers prefer
exclusivity or conformity, but does not directly reveal how many other consumers have
purchased the brand and how this number affects each consumer’s purchase decision. With richer
data, researchers would be able to quantify the social effect and its effect on firms’ selection of
consumers. Second, our data is cross-sectional in nature and cannot be used to estimate
unobserved preference heterogeneity or to consider incorporate dynamic matching patterns in
our model. Last, the computational difficulty of the estimation requires some compromises in
model specifications. Several assumptions are proposed here to facilitate the computation. For
example, we consider only whether a brand enters the market or not, rather than how many
84

products to provide in each market. We also assume that when a fashion brand decides on entry
strategies, the firm is able to correctly form other firms’ entry strategy expectations. These
assumptions could be waived with alternative data and stronger computational power.

85

4. Conclusion
The luxury fashion market is an important sector of the general economy and has many
interesting features. However, not enough empirical research has been done in this field. This
dissertation fills the gap in the literature by studying two important features using data from the
Chinese luxury fashion market.
The first essay focuses on the price effect of luxury goods. One distinguishing feature of
luxury goods is the prestige effect associated with their price. The prestige effect is defined as
the extra utility generated by the high price of luxury products. However, the existence of the
prestige effect does not mean that luxury companies should price their products as high as
possible because of the substitution effect. The substitution effect applies to all products, since
the higher price paid for the focal product reduces the resource that can be allocated to other
goods. It is managerially important to disentangle these two effects of price in the luxury market,
but this type of disentanglement has not been successfully accomplished in the literature. My
first essay fills this gap by empirically modeling both the prestige and substitution effects using a
survey dataset from the luxury watch market in China.
Several interesting findings emerge from this essay. While controlling for product
attributes and consumer product-quality perception, we find a significant prestige effect as well
as a substitution effect of price on demand. More interestingly, we find a U-shaped relationship
between income and prestige effect, such that the lower end and the upper end of the middle plus
classes have the greatest prestige effect. We also show that the price elasticity can be positive
when the price is low enough that the marginal prestige effect is larger than the substitution
effect. In some cases, it is more profitable to increase the price of luxury products because the
low price does not provide enough prestige effect. Our what-if simulations show that luxury
86

brands can gain higher market shares and revenues when they can promote their brand to provide
more prestige to consumers from price. While higher-price brands benefit from consumer
income expansion with increased shares and revenues, income expansion has a more complex
effect on lower-priced brands.
My second essay starts from the phenomenon that some companies prefer to sell their
products to certain types of consumers while trying to stop non-targeted consumers from buying.
The reason behind this strategy is that the “good” consumers not only generate revenue, but also
influence the companies’ brand image. If a company’s preference is strong enough, it would
influence the consumer purchasing decisions. Although this effect is more prominent in the fashion
industry, it applies to many companies in other industries that care about their corporate image.
However, a classic discrete choice modeling framework cannot consider the company’s preference
and might flip the predicted consumer preference. The goal of my second essay is to develop a
two-sided matching framework to correctly reveal both consumers’ and companies’ preferences.
Using cross-sectional data from the fashion watch market in China, we find that our
model outperforms a discrete choice model. It illustrates that the fashion firms indeed conduct
selective selling in China. Our empirical results show the mutual preferences between European
brands and well-educated, wealthy consumers. More importantly, our results find some
unreciprocated preferences between young consumers and European brands. This cannot be
detected using a standard discrete choice model. As a matter of fact, a discrete choice model
leads to biased parameter estimates of the consumer preference. This finding suggests that
European brands would generate more revenue if they targeted young consumers under 40.
This essay makes two major contributions. First, it shows the importance of using a two-
sided matching framework, instead of a standard discrete choice modeling framework, to study
87

consumer preference when companies conduct selective selling. Second, it embeds an entry
model to capture the endogenous price-line decisions. We are the first to control for the
endogeneity of the formation of the matching market in the two-sided matching literature.
Like any other research, my dissertation has limitations, which open up several future
directions for further study. First, both our datasets are cross-sectional in nature. Since we have
only one observation for each consumer, we are unable to infer if this one observation represents
the individual’s general preference or a random shock, and thus are unable to estimate the
individual specific consumer preference and the prestige effect. We could only use demographic
variables to capture observed heterogeneity. With new datasets and repeated purchases,
unobserved heterogeneity can be considered under our current modeling framework.
Second, we have data on only one category from different consumers. We thus cannot
detect whether the prestige effect and mutual selection exist in other categories. What is more, with
proper data, it would be very interesting to model how consumers allocate their budget to different
luxury fashion categories with proper data. For example, some consumers tend to spread their
budgets more broadly, spending in more categories but less within each category, while others may
purchase products from fewer categories but spend more within each category. Some consumers
might prefer to allocate their money evenly in different categories to create a consistent image,
while others might prefer a high-low allocation for “mix-and-match.” Uncovering these cross-
category patterns enables luxury companies to more effectively market their products and target
the right individuals for cross-selling opportunities.
Last but not least, more research can be done to consider the social effect in the luxury
fashion market. The social effect can be a very important driving force behind both the prestige
effect and firms’ selective selling. In this dissertation, we cannot directly model the social effect
88

because we do not know whether consumers in our data have many friends carrying the same
products or not. With richer data, researchers would be able to quantify whether the social effect
drives the prestige effect up or down, and its effect on firms’ selection of consumers.

89

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Abstract (if available)

Abstract Over the past decade, the luxury fashion market has grown tremendously. The value of the global fashion and luxury market reach $2.4 trillion in 2016, accounting for 2% of the world’s GDP. Beyond its economic importance, this market has several interesting features worth attention, such as the prestige effect and selective selling. However, there are very few papers in economics or marketing studying this marketing using empirical methods. My dissertation fills this gap by empirically investigating the Chinese luxury fashion watch market. ❧ My first essay focuses on the consumer demand for luxury goods. It develops an empirical modeling framework that accommodates the positive “prestige” effect of price controlling for quality, while accommodating the negative effect of price on utility through the “substitution effect” because it reduces the money available for consumption of other goods. The proposed model is built upon the utility-maximization framework with two novel extensions. First, unlike the classic demand model where price does not enter the marginal utility, this essay allows price to affect the marginal utility of a product to capture the prestige effect of price, while controlling for product attributes and consumer quality perception. Second, since each luxury brand has many versions associated with different price points, and some price versions may not be observed from data, this essay jointly models the decisions of which brand and at what price of an individual consumer. This model is applied to a unique survey-based dataset on Chinese consumer luxury purchase, supplemented with attribute information from another source. Several interesting findings emerge from this essay. First, it detects a strong prestige effect and substitution effect of price on consumer luxury demand. It confirms the hypothesis that the positive effect of price on luxury demand goes beyond the price-quality inference. A direct implication from this finding is that price elasticity can be positive for a luxury product when the positive marginal prestige effect is larger than the negative marginal substitution effect of price in magnitude. Second, it finds that family income has a U-shape relationship with the prestige effect, suggesting that lower-end and higher-end of the middle income plus consumers tend to enjoy more prestige from price. Finally, what-if simulations show that luxury brands can increase their market shares and revenues by enhancing the prestige effect of price to consumers. Moreover, an increase in income benefits higher-priced luxury brands but has a complex effect on lower-priced ones. ❧ My second essay examines the fashion market. Many fashion companies strategically target preferred consumers because such consumers not only generate revenue, they also influence the companies’ brand image. It is important to jointly model the preferences of consumers and firms in this scenario because observed brand choice is an outcome of mutual selection from both sides. The second essay develops a two-sided matching framework to model demand as realized from such a two-sided selection process. An entry model is embedded to capture the endogenous price-line decisions. To cope with computation challenges in the model estimation, this essay applies approximate Bayesian computation and parallel computing techniques. Applying the proposed structural model to consumer demand for fashion brands, this essay finds empirical support for mutual preferences between European brands and well-educated, wealthy consumers, and a standard discrete choice model leads to biased parameter estimates. It also detects some unreciprocated preferences between young consumers and European brands, meaning that the consumers below age 40 like European brands, although such preferential relationship is not reciprocal. European brands will generate more revenue if they target young consumers who are below 40. Counterfactual analyses show that if fashion brands prioritize short-term revenue compared to brand image, prestigious brands would extend their price-lines downward. Although these brands would gain more revenue, they would lose some preferred consumers. Less-prestigious brands, on the other hand, would not adjust their price-line strategies regardless of market and revenue losses.

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Creator Yao, Yao (Alex) (author)

Core Title Essays on the luxury fashion market

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Publication Date 04/13/2021

Defense Date 03/08/2019

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag fashion marketing,luxury products,OAI-PMH Harvest,prestige effect,two-sided matching

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Yang, Sha (committee chair), Hsieh, Yu-Wei (committee member), Luo, Lan (committee member), Siddarth, Sivaramakrishnan (committee member)

Creator Email yao.yao.2018@marshall.usc.edu,yaoyao.chn@gmail.com

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