Aspiration-adaptation, Price Setting,
and the Used Car Market
FLORIAN ARTINGER a ,* , GERD GIGERENZER a
a
Max Planck Institute for Human Development
Simon (1955) made reference to pricing when putting forth the idea of
aspiration levels. In this paper we investigate what type of pricing strategies
used car dealers employ which operate in a highly transparent market. An
analysis of on-line pricing data shows that the majority of 748 car dealers
follow the principles of aspiration-adaptation, rather than competitive, statedependent pricing. Interviews with dealers in high-competitive markets
eliminate alternative explanations by seven theories listed in Blinder et al.
(1998). We show that a pricing strategy with an initially high aspiration level
and a 30-day time interval leads to higher profit than the alternative strategies
used in the market. (JEL D22, D83, L81)
Keywords: Pricing, Search, Uncertainty, Bounded Rationality, Online Market
* Corresponding author: Florian Artinger, Max Planck Institute for Human Development,
Center for Adaptive Behavior and Cognition, Lentzeallee 94, 14195 Berlin, Germany, Phone:
+49 30 82406 699, [email protected].
1
“Price setting involves an enormous burden of information gathering and
computation that precludes the use of any but simple rules of thumb as guiding
principles.” (Simon 1962, p. 10)
Introduction
At the largest BMW dealership in Germany: after some time searching, one
of the authors discovers a used car that seems just like another car the
dealership sells, however, at a much lower price. The dealer is quick to explain
that this is not an error but rather that one of the two cars has been simply on
the lot longer, resulting in different prices for the two cars. This suggests a
violation of the law of one price, whereby identical goods must sell for the
same price. Such a violation, which results in price dispersion, has been
observed even in the case of homogenous goods sold on online markets where
search costs are minimal (e.g., Brynjolfsson and Smith 2000; see for a review
Baye, Morgan, and Scholten 2006). Yet, it seems quite bewildering that even
within a dealership pricing runs counter to conceived economic wisdom.
Could it be that pricing strategies systematically violate the law of one price?
To date, firms are largely modeled as fully rational profit maximizers, yet, a
dearth of field data on firm behavior has hampered testing this hypothesis
(Ellison 2006). The basic model rests on the rational expectations laid out by
Muth (1961), where the agent optimizes using all available information. In an
effort to better understand firm behavior and particularly price setting,
following Blinder et al. (1998), a number of studies have used interviews with
a joint sample of several thousand managers across the U.S., Canada, Europe,
and spanning a number of industries (Fabiani et al. 2007; Apel, Friberg, and
Hallsten 2005; Hall, Walsh, and Yates 2000). The particular focus in these
studies is price stickiness, i.e., the stylized fact that prices do not adjust
instantaneously to changes in the market fundamentals.
2
Accounting for mainstream theories of price stickiness, the studies suggest
that price setting might not correspond to the rational expectation hypothesis.
Companies either employ a purely time-dependent pricing rule, or timedependence is complemented by some degree of state-dependence. Timedependence implies that firms undertake price reviews only in fixed time
intervals. This is considered sub-optimal since changes in the market or cost
structure of firms are only taken into account with delay. In line with these
findings, models on monetary policy where firms are assumed to set prices
according to heuristics provide a better representation of observed price
development than models that assume that firms operate according to rational
expectations (GalıH, Gertler, and López-Salido 2001; GalıH and Gertler 1999).
Research on price dispersion and research on price stickiness has largely
developed separately. However, if firms use a time-dependent pricing rule and
if they are not perfectly synchronized, prices stickiness necessarily leads to a
violation of the law of one price as observed by one of the authors in the used
car market.
The use of time-dependent rules in pricing stands in contrast to pricing
models developed in economics and management of which the vast majority is
state-dependent (see for a review Aviv and Vulcano forthcoming; Fabiani
et al. 2007). Here, the fully rational agent continuously undertakes a cost and
benefit analysis as whether to change prices. A reason why time-dependent
pricing might be used is the inherent uncertainty that many firms operate in.
There are three main elements from which uncertainty can arise:
i. Demand: The seller has only imperfect knowledge about the frequency
distribution and numbers of customers with a given willingness to pay
(WTP). The WTP might depend on the amount of information customers
gather which is limited even in online markets (Johnson et al. 2004) and
the strategic purchasing behavior, i.e., whether customers would risk not
3
buying today but in the next period at a potentially reduced price (Coase
1972).
ii. Competitors: The seller needs to take into consideration how competitors
might respond to a posted price.
iii. Market: A change in market fundamentals such as prices of substitutes,
complements, shocks to national income, interest rates, etc. can shift
demand and supply. Once a product has been successfully sold, this does
not imply that at a later point in time the very same price would yield the
highest profit.
The challenge of modeling these complex dynamics with closed-form
algebraic representations has been commented on for instance by
Aviv and Pazgal (2005) and particularly by Lovejoy (1991). The complexity
originates from the high dimensionality of the decision problem in
combination with strategic interaction between the different agents. This has
posed a challenge for pricing practitioners and theoreticians alike.
An alternative to assuming full rationality in modeling firms has been
proposed by Simon (1955) with the concept of bounded rationality. An
important element is the idea that individuals and organizations use aspiration
levels. Simon refers to the setting of an aspiration level as satisficing, where,
in its simplest form, search continues until a satisfactory alternative is found.
However, aspiration levels might not necessarily be constant over time but
rather dynamically adjust, reflecting a learning process (Selten 1998; Selten
2001; Sauermann and Selten 1962; Cyert and March 1963). The relevance of
aspiration levels for managerial decision making has been highlighted in
research in organizational behavior (March and Simon 1958; Cyert and March
1963). In one of the few studies with field data of firm behavior,
Mezias, Chen, and Murphy (2002) show that sales targets in a U.S. financial
services organization reflect the use of aspiration levels. Echoing this finding
with laboratory data and interviews, a direct comparison of an adaptive
4
learning mechanism with the rational expectation hypothesis reveals that
managers rather follow an aspiration level approach (T. Lant and Shapira
2008; T. K. Lant 1992).
In his foundational article on bounded rationality, Simon (1955) used price
setting in the housing market in order to illustrate the concept of aspiration
levels. Yet, to date no study has been undertaken whether price setting, and
hence price rigidity and dispersion, is best captured by rational expectations or
rather aspiration levels. We address this question using data from an online
used car market and interviews with used car dealers, with the latter following
Blinder et al. (1998). The used car market provides a rich data on the
employed pricing strategies: each price of a car that a dealer posts online
serves as an observation from which we construct the strategy a dealer
follows. Due to 90% of used cars being listed online, prices are
instantaneously and at minimal cost observed (Dudenhöffer and Schadowski
2011). Used cars are an important source of revenues for car dealers: in 2008,
6.1 million used cars were sold compared to 3.1 million new cars in Germany
(Michel 2009). There is considerable competitive pressure in the used car
market due to a large number of market participants and a push for M&A
activities, resulting in slim margins (Dudenhöffer et al. 2005). Classically, the
used car market is associated with asymmetric information where dealers are
better informed than consumers leading to a market for lemons where only
cars with the worst quality are offered (Akerlof 1970). In response to these
concerns, the German government issued a mandatory warranty of 1 year for
each used car, aiming to eliminate concerns for asymmetric information.
In order to test whether pricing adheres rather to the principles of bounded
rationality or the rational expectation hypothesis, a central element is the use
of information. The principles of pricing based on the rational expectation
hypothesis are for instance manifested in Lazear (1986) who was the first to
model a firm with price setting power in the face of an uncertain but uniform
5
demand where, due to a learning process, prices continuously update making
use of all available information instantaneously. Analogously, in the used car
market there is ample information available from the online market as well as
individual learning on customers’ WTP by each dealer. Accounting for
possible direct and indirect costs of price adjustment as reflected in the
classical
theories
of
price
stickiness
investigated
for
instance
by
Blinder et al. (1998), a process of continuous adjustments of prices should be
observed indicating state-dependent pricing.
This stands in sharp contrast to the predictions of pricing based on aspiration
levels. Following Berninghaus et al. (2011), we distinguish between two
conceptions of boundedly rational strategies: “aspiration-based satisficing” is
in line with the simplest original conception of satisficing. The decision maker
keeps exploring until an alternative is found that is equal to or above the
aspiration level (Karandikar et al. 1998). We will refer to this strategy simply
as satisficing. In our context this implies that a dealer posts a price and
maintains it until the car sells. Information from the online market or from
individual learning is only used to set the initial price. The second category of
a boundedly rational strategy is labeled
“aspiration-adaptation” where the
aspiration level adjusts due to a learning process. Lounamaa and March (1987)
formally show for a coordination problem set in a noisy environment, that
frequent and small changes in aspiration level lead to a decrease in
performance. Instead they suggest a slow rate of adaptation where information
is initially accumulated before the decision maker responds. Prices would be
kept constant testing whether there are any customers with a WTP that is equal
or higher than the price. If no such customer is found after a certain time, the
price is lowered. Prices are actively only attended to each time they are
adapted, thereby neglecting potential information in the meantime. Note, that
such an approach closely resembles time-dependence. The classical theories
on price stickiness as investigated by Blinder et al. (1998) should not apply.
6
Due to the competitive pressure in the used car market, only the pricing
strategy should be practiced that is well adapted to the given environment.
Traditional theory postulates that such a strategy reflects concurrent price
competition using all available information from which an optimal solution is
derived. However, previous interview studies suggest that there might be
substantial degree time-dependent pricing which likely is sub-optimal (Fabiani
et al. 2007; Apel, Friberg, and Hallsten 2005; Hall, Walsh, and Yates 2000;
Blinder et al. 1998). With the used cars dataset we can not only test which
type of pricing strategy is predominately used but also how well such a pricing
strategy performs.
Savage (1954), who is the founding father of Bayesian decision theory
highlights that optimization only functions in ‘small worlds’ where all
alternatives and probabilities are known. In a ‘large world’, where the decision
maker lacks complete knowledge and is faced with uncertainty, optimization
is out of bounds (Binmore 2007). Research on organizational behavior point to
that firms tend to use simple rules, for instance as captured by the use of
aspiration
levels
(Cyert
and
March
1963).
Gigerenzer, Todd, and the ABC Research Group (1999) show that simple
rules, referred to as fast and frugal heuristics, can perform well if there is
substantial uncertainty. In contrast, optimization models are performing best if
there is a low degree of uncertainty and a large sample such that parameters of
a model can be estimated with small error (Gigerenzer and Brighton 2009).
Such simple decision rules emerge from an adaptive process in an uncertain
environment which weeds out decision strategies with weak performance. This
suggests that pricing based on aspiration levels might in fact perform very
well.
7
Price stickiness
Classical models on price stickiness that due to costs, prices only adjust to
changes in the market or cost structure of the firm if they get sufficiently ‘out
of line’. However, conventional econometric testing of competing models is
out of bounds (see for a review Blinder et al. 1998). It has been difficult to
find a metric to measure the speed at which the market clearing price adjusts
which could serve as a benchmark for price stickiness. A second aspect why
empirical testing has been difficult is that many of the most prominent theories
rely on unobservable variables (Blinder et al. 1998). As a solution to this
conundrum, interviews with managers that set prices have been conducted in
order to evaluate which theory describes actual pricing decisions well (Apel,
Friberg, and Hallsten 2005; Amirault et al. 2006; Blinder et al. 1998; Fabiani
et al. 2007; Hall, Walsh, and Yates 2000). To evaluate the relevance of
theories on price stickiness for the used car market, we selected eight out of
twelve theories that Blinder et al. (1998) investigate.1 Seven classical theories
1
Four theories are dropped as previous studies show that they are not relevant to price
setting and they also do not relate to the used car market. In the following, the theories are
listed, the question that Blinder et al. (1998) employ is stated, and for each theory an
explanation is given why they were not used here: 1. Procyclical elasticity of demand. “It has
been suggested that when business turns down, a company loses its least loyal customer first
and retains its most loyal ones. Since the remaining customers are not very sensitive to price,
reducing markups will not stimulate sales very much” (Blinder et al., 1998, p.326). In the
used cars business, we expect that a relatively small share of business is made with the same
customers. Hence, there is a small base for loyal customers to emerge. 2. Constant costs. “It
has been suggested that many firms base prices on costs. Hence firms with constant variable
costs per unit have no reason to change prices when production changes” (Blinder et al.,
1998, p.329). This theory received very low scores in Blinder et al. (1998) and apparently
interviewees had difficulties understanding the question. 3. Hierarchies. “Some people think
that price changes are slowed down by the difficulty of getting a large, hierarchical
organization to take action” (Blinder et al., 1998, p.332). Car dealers are frequently rather
small in size, hence this theory is not relevant for the average dealer. 4. Inventories
“According to this idea, a firms’ initial response to fluctuations in demand is to let inventory
stocks, rather than prices vary. That is, when demand rises, they first let inventories fall
rather than raise prices. And when demand falls, they first let inventories build up rather
than reduce prices” (Blinder et al., 1998, p.333). Generally, car dealers do not have storage
facilities which they can use to build up an inventory.
8
of price stickiness that focus on are direct or indirect costs associated with
price changes complemented by a more recent observation on price setting
behavior that likely induces sticky prices:
1.
Cost based pricing. The cost of material and labor are essential for
price calculations. The assumption here is that even in the face of a changing
market if costs stay constant, prices do not change instantly (e.g., Bils 1987).
2.
Explicit contracts. Firms have contractual agreements with customers
which determine prices in advance of a transaction (e.g., Fischer (1977) who
first introduced this idea for the case of wages). Breaking such contracts in
order to adjust prices can be costly.
3.
Implicit contracts. Firms build long term relationships with customers.
One tool in doing so is to change prices as little as possible. Even if there are
changes in the market or cost structure, firms might not instantaneously
respond with a price change. This is modeled by Okun (1981).
4.
Co-ordination failure. If a firm would raise the price, customers buy at
competitors that maintain the cheaper price; likewise if a firm reduces its
price, competing firms need to reduce prices to attract customers. If there is no
coordinating mechanism which allows all firms to move together in case of
changes
in
costs
or
the
market,
prices
remain
constant
(e.g., Cooper and John 1988).
5.
Non-price competition. Prices are not necessarily the only element that
facilitates market clearance. Instead of adjusting the price, firms can for
instance
adjust
service
keeping
the
price
constant
(e.g., Carlton 1986; Maccini 1973).
6.
Judging quality by price. Firms do not reduce a price in a slack market
out of fear that this is interpreted as a reduction in product quality
(e.g., Allen 1988).
7.
Menu costs. Changing prices in itself is costly, due to costs of
advertising these anew, printing new price tags etc. Therefore, prices do not
9
adjust perfectly to changes in market conditions (e.g., Akerlof and Yellen
1985; Mankiw 1985).
A further theory that Blinder et al. (1998) test, does not take into account
any direct or indirect costs of changing prices but rather focuses on
consumers’ perception of prices:
8.
Price points. Levy, Lee, Chen, Kauffman, and Bergen (2011) show that
‘9’ is the most frequent price ending for a number of retail products in a
brick-and-mortar store and on the internet. The most frequent price change is
one where the terminal digit is ‘9’. If prices have to ‘jump’ to the next
psychologically attractive digit, they might be less sensitive to changes in
costs or the market.
In order to differentiate between the two bounded rational strategies,
aspiration-adaptation and satisficing, the online data provides sufficient
insights. However, to clearly and explicitly differentiate between the rational
expectation hypothesis and aspiration-adaptation, an additional question is
used. The previous questions one to seven explicitly evaluate whether any one
of the relevant, classical theories that are all based on rational expectations
drive price stickiness. The last question therefore explicitly addresses the
validity of aspiration-adaptation as driving price stickiness:
9.
Aspiration-adaptation. Dealers are explicitly asked whether changing
prices in regular time intervals is due to a learning process.
We evaluate the relevance of these theories for pricing in the used car
market in interviews with dealers following in the footsteps of earlier studies
on price stickiness. Interestingly, none of these models targets learning in the
face of an uncertain demand as a potential source of price stickiness.
10
Methods
We use data from an online used car market to investigate the pricing
strategies used car dealers employ and their performance. To test the reasons
for price stickiness we further conducted interviews with used car dealers.
This also provides insights on the information use of used car dealers in
pricing.
Online data
We collected data from the online use car market Autoscout.de which
covers 78% of the used car market in Germany (Dudenhöffer and Schadowski
2011). We focus on two types of cars, 320 and 730 from BMW. BMW is one
of the largest car manufacturers with about 3 million cars in use in Germany in
2010 (BMW Group 2011). The online data was collected for nine months
starting 8th of December 2010. At the beginning of the online data collection,
the car type 320 was the most widely traded BMW on Autoscout.de. The 730
BMW is more expensive than the 320 and serves to investigate whether
dealers that offer a larger number of highly priced cars tend to employ
different pricing strategies. Of the collected data, the 320 BMW sells in the
mean for 25,670€ (SD = 9,434), 730 BMW sells in the mean for 53,133€ (SD
= 18,819). Comparing the online data on pricing for 320 BMW and 730 BMW
one finds that the median time span until a price adjusts is about 40 days for
both cars. The median price dispersion for 320 BMW is 8.3%, that of 730
BMW is 7.1%. These data suggest that both cars are priced in a similar
manner suggesting that dealers do not employ different pricing strategies
depending on the type of car. This is also confirmed by the interviews; the
data will be therefore pooled for each dealer across the two cars.
The data was collected by searching Autoscout.de bi-weekly for all 320 and
730 BMW. The results pages were downloaded and the data for each car
extracted. The result pages contain 11 attributes for each car: type of car,
11
price, mileage (in km), the date when the car was first put into service, horse
power, type of petrol, type of gears, car body, extra warranty that the car is
sold with, ZIP code and city where the dealership is located. A caveat applies
to the number of dealerships for which pricing strategies can be observed: the
results page of Autoscout.de does not contain the name of the dealership but
only the ZIP code and city where the car is sold. Some dealerships have the
same ZIP code and city, which implies that a unique attribution of the
observed prices to a specific dealer is possible for 748 out of 871 dealers with
24,482 cars from originally 33,752 observed cars.2 The mean dealer has 32.7
(SD = 65.5) cars during the entire period of data collection, the median is 13.0.
At the mean dealership, 93.7% (SD = 14.3%) of the observed cars are 320, the
rest 730 BMW. In the mean it takes 47.7 (SD = 31.5) days until a car sells.
There is considerable fluctuation in the number of cars on offer over time.
For the 320 BMW, the minimum number of cars on offer is 3,949, the
maximum number is 5,053. For the 730 BMW the minimum number is 420,
the maximum is 546 cars. The peak in the number of cars on offer for 320
BMW occurs in September, whereas for the 720 BMW the peak occurs in
February. This indicates that there is a considerable degree of uncertainty
induced by fluctuations in the supply as an important source of market
uncertainty.
Interviews
The interview contains three parts (see appendix for the complete interview
manuscript). The first part consists of questions regarding the specific
characteristics of a dealership and the background of the interviewee. In the
second part, pricing strategies are investigated. In the third part, we inquire
about the relevance of nine theories of price stickiness and how these relate to
2
Autoscout.de listed 902 used car dealers selling BMWs from which interviewees were
selected. Of these 871 were active during the data collection period.
12
the practice of the dealers. In this last part of the interview, the order of
questions, i.e., theories, is randomized to prevent order effects.
The interviewees were recruited from a list of 902 used car dealers listed on
Autoscout.de and selling used BMWs in Germany in December 2010. In order
to minimize noise in the data we focused on dealerships that operate in a more
competitive environment. To measure competitiveness, we used the city and
ZIP code of dealerships to calculate the total number of used car dealers in a
given combination of city and ZIP code. We ranked this data from highest to
lowest density of the number of dealerships. All dealerships up to rank 450
were sent an invitation by mail to participate in the interview. Overall, 55
dealerships agreed to be interviewed. 30 interviews were conducted in person
and a further 25 via telephone. Interviewees were randomly allocated to one of
the two ways of conducting the interview. The responses were not different
depending on the method used to gather the data (testing the pricing strategies
that dealers employ, these are not statistically different whether interviews in
2
person or by phone, χ ( 6 ) = 7 . 95 , p = . 21 , the same holds for the evaluation of
theories
χ 2 (9 ) = 2 . 38 , p = .98 ).
The
dealerships
were
geographically
dispersed across Germany, resulting in a distance travelled for the interviews
that were conducted in person of close to 3.000 km.
The interviews lasted about 20 minutes and were recorded on audio tape and
later transcribed. These were given to two independent raters to categorize
answers. The inter-reliability of raters is 96%; where differences existed, raters
discussed these and agreed on a common rating.
13
Results
Pricing strategies in the online data
There are three principle components of a pricing strategy for used cars that
can be observed in the online data: i) initial price; ii) size of a price change; iii)
time span a price is maintained. In a first step, these are analyzed separately.
Components of a pricing strategy
In order to evaluate the level of the initial price and the extent of price
changes a reference class is needed. For this we match for each day those cars
that have identical values on following attributes: type of car, year put into
service, horse power, type of petrol, type of gears, car body, extra warranty
that car is sold with, and mileage differing by a maximum of 10.000 km. This
generates for each car on any given day a reference class we use to evaluate
the initial price and price changes of a car. This procedure also allows
determining the minimum price on any given day in a reference class. In total,
for 81.2% of the recorded prices a match can be found. In the mean the
number of cars that match results is 9.0 (SD = 10.4) cars being grouped
together in a reference class, in the median a group contains 5 cars. The
reference class can also be used to investigate how often the initially observed
paradox occurs that a dealer sells two or more identical cars at the same time:
for 12.0% of all cars there is at least one other car on that day by the very
same dealership for a different price.
The histogram in figure 1A shows the initial price dispersion in the used car
market. The initial price dispersion is computed using the initial price of a car
minus the minimum price of the cheapest, matching car on the day the car was
posted online. The difference is standardized using the minimum price as a
denominator. For each dealer the mean is computed across all cars of the
14
dealer. 3 The bin size is 1% deviation of the initial price from the minimum
price. A first inspection of figure 1A indicates that there is a considerable
number of dealers who post an initial price of a car that is very competitive. In
total, 19.5% of dealers are contained in the first bin. Of these, 16.0% of
dealers start in the mean with a price such that they are the cheapest in the
market. However, 9.6% of dealers do not have a single car that matches
another car resulting in that these dealers cannot have an initial price
dispersion larger than 0%. This leaves 6.4% of dealers who start out in the
mean with a price that is the lowest in a group of matching cars. Overall, the
mean dealer posts an initial price of 7.7% (SD = 6.6) above the minimum
price.4
FIGURE 1. PRICING COMPONENTS HISTOGRAMS.
MEAN VALUE PER DEALER USED FOR: 1A.
MINIMUM PRICE
MEAN RELATIVE DIFFERENCE OF INITIAL PRICE FROM
(N=748). 1B. MEAN RELATIVE PRICE REDUCTION (N=637). 1C. MEAN
3
This measure also has been employed for instance by Brynjolfsson and Smith (2000) and
Pratt, Wise, and Zeckhauser (1979), for a discussion of different measures of price
dispersions see Baye, Morgan, and Scholten (2006).
4
If one excludes dealers who do not have any car for which another matching car can be
found the mean dealer’s initial price is 8.1% (SD = 5.00) above the minimum price, the
median dealer is 7.5% above the minimum price.
15
DURATION BEFORE A PRICE IS CHANGED IN DAYS EXCLUDING THE LAST PERIOD WHEN CAR IS
SOLD (N=637).
Research shows that thin markets with few buyers and sellers display a
substantial price dispersion, which is reduced the thicker a market gets
(e.g., Tauchen and Pitts 1983; Telser and Higinbotham 1977). Does the initial
price dispersion decrease the greater the number of cars that match each other,
i.e., the thicker the market and the greater the competitive pressure? If this
holds, one would observe a negative correlation between the number of cars
that match each other and the difference of the initial price from the minimum
price. Analyzing the proposition both at the level of the dealer as well as at the
level of the cars indicates that there is a positive correlation (dealers: r = .49 (p
= .001); cars: r = .40 (p = .001)). The result is depicted in figure 2; it shows the
mean number of matching cars for each dealer mapped onto the mean initial
price dispersion that a dealer sets. This suggests that the higher the degree of
competitiveness and the larger the number of cars that match each other the
greater the initial price dispersion. A likely mechanism that yields this result is
that a new car compared to a group of matching cars tends to be priced higher
than those already in the market.
FIGURE 2. MARKET THICKNESS AND PRICE DISPERSION – SCATTERPLOT.
16
MEAN NUMBER OF MATCHING CARS AND INITIAL PRICE DISPERSION PER DEALER WITH A FITTED
LOESS CURVE AND GAUSSIAN NOISE ADDED (N = 748).
The second component of a pricing strategy observed in the online market is
the size of a price change. Figure 1B shows a histogram with the mean price
reduction per dealer for those dealers that undertake price changes (N = 637).
A price change that a dealer undertakes is standardized by taking the
difference between the old and the new price dividing this by the old price.
Each time the dealer reduces the price the mean dealer does so by 3.9% (SD =
4.3).
The third component of pricing strategies is the length of the time interval
until a price changes. To make an inference about the pricing strategy of a
dealer, one needs to consider the time span until a dealer changes the price of
an unsold car. We observe this for 637 of 748 dealers. Figure 1C displays the
histogram of the mean days before a price is changed excluding the final
period in which the car is sold. Since the data was collected bi-weekly as a
conservative measure the data is binned in time spans of 7 days. Only 3.0% of
dealers fall into the first bin of changing a price at least once every 7 days. In
the mean, a dealer changes the price of a car after 36.2 (SD= 24.0) days.
The above analysis shows that there is a considerable time lag for most
dealers before they adjust prices. However, there is also a considerable spread
contained in each of the three pricing components. In the following, we
addresses to what extent this spread can be attributed to a number of
homogenous subgroups of pricing strategies.
Differences between dealers
The set-up we chose suggests three different pricing categories: rational
expectation, satisficing, and aspiration-adaptation. Satisficing is readily
deduced from the online data as it implies that dealers do not change prices
once a car has been put online for the first time. However, a differentiation
17
with regards to the other two strategies is not straight forward if one considers
the main focus here, the time until price change as an indication for how much
information from the online market is used. This becomes evident in figure 1C
which displays the duration the price is constant and shows a fairly smooth
distribution.
In order to make an informed comparison between the three strategies, we
used a cluster analysis based on the three pricing components of each dealer. It
employs the Ward method with the squared Euclidian distance as a measure
for proximity. The goal of the Ward method is to minimize the variance within
a cluster. The cluster analysis treats 111 dealers that use satisficing as a
separate cluster. The remaining 637 dealers are grouped into four clusters
shown in table 1. The first row in table 1 displays the number of dealers, the
second displays the number of observed cars. An F-value for a component of a
pricing strategy below one indicates a lower variance and hence larger degree
of homogeneity for that cluster than in the complete data set.
18
TABLE 1. PRICING STRATEGIES
Complete
data
Competitive
Aspirationadaptation High
Aspirationadaptation Medium
Other
Satisficing
Number of
dealers
(share)
748
(100%)
212
(28%)
185
(25%)
201
(27%)
39
(5%)
111
(15%)
Number of
observed cars
(share)
24,482
(100%)
4,732
(19%)
12,674
(52%)
5,903
(24%)
843
(3%)
357
(2%)
FMean
value
SD
Initial price
from min price
7,7%
6,6%
4,1%
3,2%
0,2
14,2%
5,7%
0,7
6,3%
3,5%
0,2
10,8%
9,0%
1,9
Price change
3,9%
4,3%
3,2%
6,2%
2,1
3,7%
1,7%
0,2
4,5%
3,1%
0,5
6,2%
3,9%
0,9
Days until
price change
without last
period*
36
24
20
8
0,1
29
9
0,2
47
14
0,3
102
31
1,7
Duration 1
(days)
Duration 2
(days)
Duration 3
(days)
Mean
SD
NMean
dealer
SD
NMean
dealer
SD
NMean
dealer
SD
FMean
value
Mean
SD
SD
FMean
value
SD
Mean
SD
FMean
value
Mean
SD
5,1%
NMean
dealer
37
27
20
10
212
30
15
185
49
18
201
106
38
39
33
21
23
14
163
31
13
168
41
23
166
57
45
20
27
19
20
11
120
27
14
141
33
24
114
54
27
11
* ‘Days until price change without last period’ for the complete data refers to N = 637 dealers.
Dealers contained in the cluster ‘Competitive’ change prices after the
shortest time interval with 20 days, and start with an initial price that is the
lowest above the minimum price of a matching car. This cluster serves as a
benchmark to compare with the other clusters and is regarded to be closest to
what the rational-expectation hypothesis would prescribe since it takes the
least time before a price is adjusted. Also note that the F-value for days until
price change, the main variable of interest here, is very small. Dealers
contained in the cluster ‘Aspiration-adaptation High’ start with a much higher
19
SD
8,0%
SD
Fvalue
1,4
Ndealer
initial price and also take considerably longer for their price adjustment than
Competitive dealer with 29 days in the mean. There is a further cluster which
uses an extensive time lag before adjusting prices, labeled ‘Aspirationadaptation Medium’. The aspiration-adaptation clusters are the most
homogenous with all of the pricing components receiving F-values well below
1.
Aspiration-adaptation High and Medium account together for 52% of all
dealers (76% of all cars). Satisficing is practiced by 15%, and the competitive
strategy by 28%. The heterogeneity in the data set is captured in the cluster
‘Other’ that contains 5% of dealers.
At the bottom of table 1 is the mean duration until a price changes, listed
separately for the first, second, and third time span, each separated by a price
change. Dealers in the Competitive and Aspiration-adaptation High clusters
employ fairly constant time intervals.
Dealers in the cluster Aspiration-
adaptation Medium shorten the time interval the more often they have to
change the price.
In summary, aspiration-adaptation is by far the most common strategy,
however, there is also a considerable number of competitive dealers that
relatively quickly change prices. Particularly the interviews will show whether
the reason for not adjusting prices frequently adheres to any of the classical
theories of price stickiness or whether this is rather due to a learning process
reflecting aspiration-adaptation.
Interviews
Pricing strategies
As can be seen in figure 3, similar to the online data, 73% of interviewees
indicate that they set the initial price higher than the price of a comparable car
20
of a competitor that is currently in the market; 11% underbid and 16% match
the price.
The total percent of those who regularly change prices account for 95% of
all interviewees. Of those 95%, a fixed time interval is employed by 87%; the
remaining 8% change prices if they observe shifts in the market or the cost
structure. 54% of interviewees consider a price change for a used car every 30
days. Further 33% either have a fixed time interval of more than 30 days
before they consider a price change, or initially wait for 30 days followed by
shorter periods at which they consider to change the price of a car.
FIGURE 3.USE OF PRICING STRATEGY COMPONENTS (N = 55).
21
If the time for a price change is due after the time interval expired, 71%
consult the online market or market surveys. However, 24% already determine
with the initial price by how much a price will be reduced if the car does not
sell. They do not consult any further information when prices are changed.5
Do dealers employ multiple pricing strategies? 71% of interviewees’ state
that they only employ one pricing strategy, 29% use some variations but these
do not apply to the standard used car sold to consumers but are employed if
cars are sold to other dealerships or for special used cars such as old timers.
All interviewees indicate that they advertize cars immediately online once a
car is on the lot. This implies that the online market does provide a very good
source with regards to the current market except for those 10 percent of cars
that are not listed. Do interviewees at any one time aim to offer the cheapest
car within a set of comparable cars? 58% of interviewees state, that if a car is
not sold within at most 180 days they will set the price of a car such that it is
the cheapest in the market. However, for 27% of interviewees this is not a
good strategy as in their opinion the cheapest car likely constitutes a
fraudulent offer. The remaining 9% of interviewees that do implement price
changes opted not to respond to the question. In the mean interviewees
consider about 40% (SD = 32) of customers to be price sensitive.
5
Considering the pricing strategies that are most frequently applied, 45% start with an
initially high price and undertake price changes at fixed time intervals. Information from the
online markets or market surveys inform these changes. The second most prominent pricing
strategy used by 24% of interviewees also entails starting with a high price, reducing the
price at fixed intervals but, different to the first strategy, by an amount determined as soon
as the car enters the lot. Both strategies together reflect the use of aspiration-adaptation,
whereby the price is sequentially lowered if no sale occurs after a fixed time period. Thus,
aspiration-adaptation accounts in total for 69% of the pricing strategies in the interviews. A
further 11% of interviewees start with a price that is similar to that of competitors with price
changes at fixed intervals where new information from the market or surveys is used. There
are a number of further strategies employed that each individually accounts for less than 5%
of all strategies and in sum for 20%.
22
Pricing theories
Interviewees responded to nine statements that each reflect a particular
pricing theory. Each interviewee rated each theory according to following
scale:
1 = totally unimportant
2 = of minor importance
3 = moderately important
4 = very important
FIGURE 4. MEAN RATINGS OF RELEVANCE OF PRICING THEORIES FOR PRICING OF USED CARS FOR
EIGHT THEORIES PREVIOUSLY INVESTIGATED AND SEARCH IN THE FACE OF AN UNCERTAIN
DEMAND.
As can be seen in figure 4, only two theories receive in the mean more than
2 points. Blinder et al. (1998) regards this as a critical mark below which a
theory bears relatively little relevance for actual pricing: Aspiration-adaptation
receives a mean rating of 2.9 (SD = .9). The highest ranking statement refers
to price points as an important element when setting prices with a mean rating
of 3.0 (SD = 1.2). It suggests that prices rather ‘jump’ to psychotically
attractive numbers. This is also reflected in the online data (see table A2 in
appendix): particularly the third digit from the right of a price stands out with
41% of all recorded prices being a ‘9’; similar results are obtained if one
23
considers prices after they have been changed. Dealers classified as
Competitive are not as likely to quote a price with a ‘9’ on the third place as
dealers in the other clusters. In fact, the distributions of digits in the
Competitive and Aspiration-adaptation Medium (which is the closest in its
distribution to Competitive) clusters differ significantly (K-S = 7.37, p = .001).
In summary, the interviews indicate that dealers do not adjust prices due to
changes in the market but rather due to a fixed time interval. About one
quarter of dealers even only considers market information when setting the
initial price; the size of subsequent price changes is predetermined at the time
when the car is put online. With regards to why such a fixed time interval is
used, the interviews indicate that it is due a learning process reflecting
aspiration-adaptation and due to the importance of price-points. Classical
theories of price-stickiness are not considered as important by the
interviewees.
Success of pricing strategies
Previous studies find that time-dependent pricing is widespread, however,
they
suggest
that
this
might
be
suboptimal
(e.g., Fabiani et al. 2007; Blinder et al. 1998). In the following we address this
by analyzing how a proxy for profit develops with time and how the different
identified strategies perform.
In order to compute a proxy for profit we use the last price that a dealer
advertizes online for a car as an indication for how much the car
approximately sells for. From this, the minimum price of the group of
matching cars is subtracted which yields the dispersion of the last price. The
difference is standardized using the minimum price as a denominator. For each
day the car is on the lot; these costs reduce the profit by about .01% per day
that a car is on the lot (Löhe 2010). Multiplying the days until a car sells with
.01% yields the costs per car which are subtracted from the standardized
24
dispersion of the lat price. The result is the proxy for profit per car. We also
take into account the difference in time the dealers need
need to sell a car which
allows those that are quicker to sell more cars. This is done by taking the total
number of days in a year divided by the mean number of days a dealer needs
to sell a car. This is then multiplied with the proxy for profit per car. From
Fro
this, a mean is computed for each dealer.
The proposition that dealers should be concurrently updating prices in order
to best respond would suggest that there is a negative correlation between the
duration and the proxy for profit. However, as figure 5A suggests, this is not
the case. The fitted LOESS curve does not start high and fall with increasing
duration. Rather, it starts low and peaks around 30 days suggesting that more
frequent price adjustment does not yield increased performance.
FIGURE 5. PROFIT.
5A: MEAN DURATION A PRICE IS CONSTANT AGGREGATED FOR EACH DEALER. DURATION
EXCLUDES LAST PERIOD WHEN CAR IS SOLD.
SCATTER PLOT CONTAINS A FITTED LOESS
LO
CURVE
AND GAUSSIAN NOISE ADDED. (N=637). 5B: PROFIT PER STRATEGY.
Considering the main pricing strategies in figure 5B, it becomes clear that
dealers who employ Aspiration-adaptation
Aspiration
and start out with a high price
25
make the most profit. Competitive dealers and those employing Aspirationadaptation Medium, i.e., starting with an intermediate initial price but
maintaining the price also for a considerable time, make about equal profits.
The worst strategy with respect to profits made is Satisficing.
Are these results robust with regards to individual characteristics of a
dealership, for instance the mean mileage of cars that a dealership sells or
whether the dealership is an official partner of BMW, both potential indicators
of the quality of a used car? Using a multinomial logistic regression this is
investigated with regards to seven characteristics of a dealership that can be
inferred from the online data (see appendix). Overall, the picture remains the
same. Most interestingly, the data suggest that the competitiveness of the
environment that a dealer is operating in does not affect the choice of pricing
strategy. Also, the choice of pricing strategy does not differ depending on the
share of 320 BMW sold compared to 730 BMW.
In summary, the data suggest that it is best to keep the price constant for
about 30 days. A quicker turnover as practiced by dealers employing
Competitive pricing seems to be detrimental to profits. Starting with a high
price is also conducive to high profits.
Price stickiness and dispersion
The literature on sticky prices highlights that it is difficult to identify at
which speed a market clearing price would move and therefore to evaluate to
what extent prices might indeed be sticky (Blinder et al. 1998). The data on
the used car market provides a workaround. Dealers that are part of the
Competitive cluster compete on price aiming to be the cheapest in a group of
matching cars. In order to evaluate the degree of price stickiness the time
interval that competitive dealers need to adjust a price is used as
approximating the speed at which the market clearing price moves. In the
mean, prices of dealers of the Competitive cluster change after 20 days, with a
26
median of 21 days. In comparison, prices change in the mean at all other
dealerships after 42 days with a median of 35 days. Using the median values
as a more robust measure, this implies a price stickiness of 66.7% of the prices
of dealerships that are not part of the Competitive cluster.
The mean price dispersion of a dealer is calculated using the mean relative
difference of the initial price minus the minimum price of the cheapest,
matching car. The difference is standardized using the minimum price as a
denominator and a mean is computed for each dealer across all prices posted.6
The mean price dispersion is 7.3% (SD = 6.2), the median is 7.0%.
Discussion
Previous studies have found that across a number of countries and
industries, time- dependent pricing is widely used (Apel, Friberg, and Hallsten
2005; Blinder et al. 1998; Fabiani et al. 2007; Hall, Walsh, and Yates 2000).
Unless this is caused by costs associated with price changes, such a practice is
considered suboptimal as it implies ignoring information to which firms could
best respond. Simon (1955) had pointed to that aspiration levels might also be
used when setting prices, which would in principle reflect time-dependent
pricing. Using the online used car market as a case study, we find that despite
the proliferation of information due to the high transparency of the supply side
of the market, most dealers employ a strategy in accordance with aspirationadaptation. The use of such a strategy is not driven by direct or indirect costs
of price adjustment as reflected in any of seven classical theories on price
stickiness. Rather, the interview data reveal that dealers regard their pricing
strategy as a mechanism to learn about an uncertain demand. The centrality of
6
This procedure deviates from literature that frequently computes the range between the
two most extreme price points and neglects other data points (e.g., Brynjolfsson & Smith,
2000), however this would be prone to outliers which are very likely to occur in the used car
data set.
27
assessing what consumers are willing to pay is further stressed by dealers
pointing to the importance of psychologically attractive prices.
A basic notion that the results point to is that dealers use the available
information of the online market frugally. Classical economics posits that in
perfect competition in equilibrium, prices are sufficient for coordination
giving rise to the law of one price. However, price dispersion is widely
observed even in homogenous, highly competitive online markets. In such a
context, simply observing prices is not sufficient but firms might also profit
from individual learning (Balvers and Cosimano 1990). This hints at that
dealers in fact need to attend to two different sources to make an inference
which price to set: supply is capture by the online market which provides
readily information on prices of competitors, demand and particularly
consumers’ WTP can be inferred from individual learning. Pricing models in
that target an uncertain demand continuously update, however, this is clearly
not the case here.
A second element of a successful pricing strategy in an uncertain
environment is to start with a high price and to sequentially lower it in the
search for the best price. Moreover, we find that price dispersion increases
with the number of matching cars, which suggest that dealers on aggregate
start out with an initial price that is higher than that of competitors, testing the
market for consumers that are willing to pay such a price. Starting with a high
price and successively lowering it effectively price discriminates in an
environment with heterogeneous consumers that differ for instance with
regards to information search or the extent to which they act strategically.
The use of aspiration-adaptation leads to the emergence of price stickiness
due to time-dependence. As price changes are not perfectly synchronized and
as dealers rather initially overbid each other, price dispersion occurs. Both
stylized facts are emergent phenomena of the underlying pricing strategies..
28
Further research needs to validate in how far the emergence of price stickiness
and dispersion in other markets is due to such pricing mechanism as
encountered here. Similar environments can be found for instance in the
housing market (e.g., Levitt & Syverson, 2008), or with ‘one-of-a-kind’
products such as designer gowns (Lazear 1986). Demand uncertainty can even
be an issue with homogenous products, particularly at their introduction. This
has been shown with the case of pharmaceuticals. Many drugs differ in their
idiosyncratic side effects that might show up only when used in a wider
population. Even after extensive research the firm does not know the value of
its product exactly and needs to search for the best price (Crawford and Shum
2005).
An alternative explanation of the above results is that tacit collusion takes
place which allows market participants to reap benefits above market clearing
price. Yet, the degree of collusion and hence the choice of pricing strategy
should be affected by the competitiveness of the environment that dealers
operate in. A regression analysis shows that the degree of competitiveness
does not affect the choice of pricing strategy. Moreover, collusion becomes
less likely if the outcome of such action is not deterministic but stochastic
(Artinger et al. 2012). The issue of whether dealers interact in a collusive or
competitive manner also highlights that to date theoretical research on pricing
in the face of an uncertain environment has only addressed uncertainty about
demand and market fundamentals. What has been absent is to investigate how
competition evolves in such an environment.
Recent dynamic pricing models investigate the effect if certain elements of
the environment are disregarded such as the interdependence of market
fundamentals with uncertain demand (Aviv and Pazgal 2005) or strategically
acting customers (Mersereau and Zhang 2012). These models perform
surprisingly well. The above analysis suggests that a certain degree of timedependence is a further element that leads to good performance of a pricing
29
strategy. All these elements considerably simplify the decision problem from
one that is at the outset computationally intractable (Lovejoy 1991). Beyond
this, the current study hints at a more fundamental issue: optimization, as the
standard technique and at the heart of state-dependent models might not
necessarily achieve the best outcomes in the context of an uncertain
environment such as the one investigated here. To further explore this
suggestion, competitive model testing can yield further insights pitching
optimization models against satisficing models. Using such an approach for
instance Gigerenzer & Goldstein (1996) and Brighton (2006) show that fast
and frugal heuristics can indeed outperform models are computationally more
intensive.
30
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For online publication.
Appendix
Interview with car dealers
•
Text in italics and underlined is only meant for the interviewer
•
The interview is recorded on audio tape and transcribed
•
The interview lasts about 20 minutes
•
Each interview is given an ID. This ID is identical to the ID from the
online data set in order to compare statements made in the interview to the
actual pricing behavior.
•
UC = used car
The xxx is interviewing used car dealers for the Germany-wide study “Pricing
behavior of used car dealers”. You will be asked to respond to questions
regarding how you set prices for UCs in order to contribute to the success of
your enterprise. The aim of the study is to document how UC dealers price.
Anything you say is anonymized and analyzed only on an aggregate level. For
this the audio recordings will be transcribed and destroyed thereafter. The final
analysis is based on the interviews and data from the online market
Autoscout.de
I. General Questions
1. What is your function in the dealership: _____________________
2. a) How many cars, old and new, are currently on offer in this dealership:
_____
b) How many of these are UCs: _____
c) How many UCs are BMWs: ______
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3. How large is the degree of returning customers, i.e., those that have
bought at least their last car at the dealership: ________
4. a) Is the dealership part of a larger organization and if so, how many
branches does this have: _______
b) if a. > 1: Are the prices for UCs
centrally done
individually done at each dealership
5. Since when do you price UCs: ________
II. Prices – specific questions
6. Initial price: a) What do you do if you have to price a UC the first time:
____________________________________________________________
____________________________________________________________
b) Which information is important to determine the initial price:
____________________________________________________________
____________________________________________________________
7. You are faced with the situation where your competitors offer a similar
UC. The initial price of your UC is
i) lower than the price of the competitor
ii) the same as the competitor
iii) higher than the competitor
8. What is the geographical size of the market you are selling your product
(km in diameter) __________________
9. a) Do you commonly change prices: yes or no
b) if a = yes: How do you proceed if you have to change a price?
____________________________________________________________
____________________________________________________________
c)
When
do
you
change
a
price:
(time
interval,
date,
event):_______________
d) By how much do you change the price: (in % or €):___________
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e) If you change the price of a UC, do you collect information on the
current price of a similar car of a competitor each time you do this:
____________________________________________________________
f) Is there a point of time when you offer the UC cheaper than similar cars
of your competitors, hence your car is ranked first in the online market:
____________________________________________________________
g) if f = no: Why not:
____________________________________________________________
10. a) Are you using the same pricing strategy for all (most) of your UCs:
yes or no
b1) if a = no: Which criterion do you apply to differentiate between UCs,
which pricing strategy do you apply and how often do you apply them?
____________________________________________________________
11. a) Are all UCs on the lot also advertized on the internet market? yes or no
b) if b = no: Why not: ________________________________
12. How large is the share of customers that only focus on price for their
buying decision:________
III. Economic Theories
How important is any of the following theories with regards to the pricing
of second hand cars in your daily business.
I.
1 = totally unimportant
2 = of minor importance
3 = moderately important
4 = very important
(cost based pricing) A different idea holds that prices depend mainly on
the costs of labor and of materials and supplies that companies buy from
other companies. Firms are thought to delay price increases until their
costs rise, which may take a while. But then they raise selling prices
promptly (as in Blinder et al. (1998) question B6).
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II.
(explicit contracts) One idea is that many goods are sold under explicit
contractual agreements that set prices in advance, so firms are not free to
raise prices while contrasts remain in force (as in Blinder et al. (1998)
question B1).
III.
(implicit contracts) Another idea has been suggested for cases in which
price increases are not prohibited by explicit contracts. The idea is that
firms have implicit understandings with their customers – who expect
the firms not to take advantage of the situation by raising prices when
the market is tight (as in Blinder et al. (1998) question B2).
IV.
(co-ordination failure) The next idea is that firms would often like to
change their prices, but are afraid to get out of line with what they
expect competitors to charge. They do not want to be the first ones to
raise prices. But, when competing goods rise in price, firms raise their
own prices promptly (as in Blinder et al. (1998) question B10).
V.
(non-price competition) The idea here is that firms don’t cut prices much
when demand falls because price is just one of several elements that
matter to buyers. More frequently, they shorten delivery lags, make
greater selling efforts, improve service, or improve product quality (as in
Blinder et al. (1998) question B12).
VI.
(judging quality by price) One idea is that firms hesitate to reduce their
prices because they fear that customers will interpret a price cut as a
signal that the quality of the product has been reduced (as in Blinder et
al. (1998) question B3).
VII. (menu costs) Another idea is that the act of changing prices entails
special costs in itself, so firms hesitate to change prices too frequently or
buy too much. The costs we have in mind are not production costs but
costs like printing a new catalogue, price lists, etc. or hidden costs like
loss of future sales by antagonizing customers, decision making time of
executives, problems with sales person and so on (as in Blinder et al.
(1998) question B8).
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VIII. (price points) Another idea is that particular threshold prices are more
attractive to customers than other prices. For instance, prices rather
change from 10.500€ to 9.999€ than to 10.050€.
IX.
(aspiration-adaptation) A theory says that firms know approximately
the price range that customers are willing to pay. In order to achieve the
best possible price, firms adapt the price in regular time intervals until a
customer is willing to pay the advertised price.
Further statistics
Regression analysis
Besides prices, the online market also provides data that allow the
computation of seven characteristics that mark each dealership. These include
the (1) number of cars of 320 and 730 BMWs per dealer, (2) the share of 320
BMWs, the (3) mean mileage of the cars at a dealership as proxy for quality of
the cars on offer, and the (4) proportion of cars at a dealership that are offered
with an extra warranty. Furthermore, the (5) competitiveness of the
environment in which the dealership operates is assessed by using the first two
digits of the five-digit German ZIP code which marks an area of 76 km in
diameter. Those dealerships that share the first two digits are assumed to share
a competitive environment. The total number of cars that a dealership
advertized is then used as a proxy to evaluate how many cars in total are
offered in such a competitive environment. Further characteristics are (6)
whether the dealership is part of a network of car dealers, and the (7)
proportion of dealers that are official BMW partners.
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In order to investigate the influence of these independent variables on the
choice of a strategy of a dealer we use a multinomial logistic regression. The
dependent variable is the log of the probability with which the dealer belongs
to one of two pricing clusters as depicted in equation 1. The reference cluster
constitutes the dealers classified as ‘Competitive’.
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log[P (clusterX ) / P(competitiv e )] = b + ∑ wi bi
(1)
i =1
This results in four regression models as shown in table A1, the numerator
being either cluster Aspiration-adaptation High, Aspiration-adaptation
Medium, Satisficing or Other. The most distinctive characteristic is whether a
dealership is an official partner of BMW or not. This is significant for the
regression models comparing the dealers in the Competitive cluster with those
in the Satisficing, Aspiration-adaptation High, and Aspiration-adaptation
Medium price strategy clusters. The coefficient is large and positive,
indicating the dealerships that are official partner of BMW are more likely not
to use the pricing strategy Competitive. A further characteristic that
distinguishes the probability that a dealer is part of the Competitive cluster
from the clusters Satisficing and Aspiration-adaptation High is the number of
cars per dealer. However, the coefficients are relatively small. Interestingly,
the competitiveness of the environment does not influence the probability of
whether dealers employ Competitive or any of the other pricing strategies.
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TABLE A1. MULTINOMIAL LOGISTIC REGRESSION WITH COMPETITIVE AS REFERENCE
CATEGORY.
Reference category: Competitive
Coef.
p
Std.
Err.
1. Aspiration-adaptation High (N = 185)
Observed cars of 320 and 730
Proportion 320
Mileage
Proportion of cars with extra warranty
Competitive setting - number of cars
Part of network
Official partner of BMW
Constant
0,01
0,31
0,00
-0,29
0,00
0,50
0,78
-0,13
0,00
0,75
0,00
0,40
0,75
0,08
0,00
0,89
0,00
0,95
0,00
0,34
0,00
0,28
0,24
0,95
2. Aspiration-adaptation Medium (N =
201)
Observed cars of 320 and 730
Proportion 320
Mileage
Proportion of cars with extra warranty
Competitive setting - number of cars
Part of network
Official partner of BMW
Constant
0,00
0,46
0,00
0,28
0,00
0,18
0,68
-1,21
0,25
0,60
0,39
0,39
0,80
0,53
0,00
0,17
0,00
0,86
0,00
0,32
0,00
0,29
0,23
0,88
3. Satisficing (N = 111)
Observed cars of 320 and 730
Proportion 320
Mileage
Proportion of cars with extra warranty
Competitive setting - number of cars
Part of network
Official partner of BMW
Constant
-0,25
-0,62
0,00
0,05
0,00
-0,02
0,84
1,40
0,00
0,39
1,00
0,91
0,73
0,97
0,01
0,08
0,04
0,73
0,00
0,45
0,00
0,49
0,33
0,80
4. Other (N = 39)
Observed prices of 320 and 730
Proportion 320
Mileage
Proportion of cars with extra warranty
Competitive setting - number of cars
Part of network
Official partner of BMW
Constant
0,00
-0,79
0,00
-0,30
0,00
0,35
0,37
-1,56
0,96
0,46
0,26
0,64
0,82
0,49
0,37
0,18
0,01
1,08
0,00
0,63
0,00
0,50
0,41
1,17
N total = 748, Pseudo R² = .15, Log likelihood = -948.59
This analysis begs the question whether the characteristic that dealers are an
official partner of BMW affects which pricing strategy they should choose in
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order to incur the highest profits. Figure A1 shows the results of the proxy for
profit for the five pricing strategies. The figure suggests that the strategy
Aspiration-adaptation
adaptation High performs best regardless whether a dealer is an
official partner of BMW
W or not.
FIGURE A1. MEDIAN PROXY FOR PROFIT
PROF FOR THE 5 CLUSTERS SEPARATE FOR
R WHETHER
DEALERS ARE AN OFFICIAL
IAL PARTNER OF BMW (=1) AND WHETHER THEY ARE NOT (=0)
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Price digits
TABLE A2. FREQUENCY OF PRICE DIGITS.
position
/ digit
Occurrence - complete data
5th
4th
3rd
2nd
digit
digit
digit
digit
form
form
form
form
right
right
right
right
0
0%
1
2
Occurrence - 3rd digit from left per cluster
1st
digit
form
right
Cluster
/ digit
Satisficing
Competitive
Aspirationadaptation
Medium
Aspirationadaptation
High
Other
8%
1%
26%
79%
0
2%
1%
1%
1%
2%
25%
9%
1%
3%
2%
1
1%
1%
1%
1%
1%
34%
10%
3%
1%
2%
2
3%
5%
3%
3%
3%
3
26%
9%
4%
4%
1%
3
2%
5%
4%
4%
1%
4
7%
10%
13%
3%
1%
4
13%
18%
13%
12%
16%
5
3%
9%
8%
13%
5%
5
8%
6%
7%
8%
10%
6
2%
10%
4%
3%
1%
6
4%
5%
5%
4%
3%
7
1%
11%
7%
4%
2%
7
7%
8%
6%
6%
7%
8
1%
11%
16%
12%
2%
8
14%
16%
19%
16%
12%
9
1%
13%
41%
33%
5%
9
45%
34%
41%
44%
45%
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