Price Points and Price Rigidity
Daniel Levy*
Bar-Ilan University
Emory University
Rimini Center for Economic Analysis
Levyda@mail.biu.ac.il
Dongwon Lee
Korea University
mislee@korea.ac.kr
Haipeng (Allan) Chen
Texas A&M University
hchen@mays.tamu.edu
Robert J. Kauffman
Arizona State University
rkauffman@asu.edu
Mark Bergen
University of Minnesota
mbergen@csom.umn.edu
Last revision: April 29, 2010
JEL Codes: E31, L16, D80, M21, M30
Key Words: Price Point, 9-Ending Price, Price Rigidity
Forthcoming: Review of Economics and Statistics
* We thank two anonymous referees and the editor Mark Watson for constructive comments and suggestions. We thank Jurek
Konieczny, the discussant at the CEU Conference on “Microeconomic Pricing and the Macroeconomy” for comments, and the
conference participants: Marco Bonomo, Alan Kackmeister, Attila Ratfai, Julio Rotemberg, Harald Stahl, Jonathan Willis and
Alex Wolman for suggestions. Gershon Alperovich, Bob Barsky, Alan Blinder, Leif Danziger, Mark Gertler, Carlos Marques and
Jacob Paroush provided helpful comments. We thank the seminar participants at Bar-Ilan University, Deutsche Bundesbank,
Emory University, European Central Bank, Hebrew University, Federal Reserve Bank of Kansas City, Magyar Nemzeti Bank,
Texas A&M University, University of Minnesota, University of Piraeus, and Tel-Aviv University for comments. We thank Péter
Benczúr, Michael Ehrmann, David Genesove, Peter Gabriel, Zvi Hercowitz, Heinz Herrmann, Johannes Hoffmann, Péter Karádi,
Ed Knotek, Saul Lach, Benoît Mojon, Ádám Reiff, and Frank Smets for comments, Manish Aggrawal, Ning Liu, and Avichai
Snir for research assistance. Portions of this work have been also presented at the 2004 INFORMS Conference on Information
Systems and Technology, the 2004 International Conference on Systems Science, the 2005 IS Research Symposium, the 2006
Minnesota Symposium on Statistical Challenges in E-Commerce, the 2005 AMCIS Doctoral Consortium, and at the 2005
INFORMS Marketing Science Conference. We thank Chris Forman, Hemant Bhargava, D.J. Wu, Barrie Nault, Fred Riggins, Sri
Narasimhan, Rahul Telang, Sunil Milthas, and other conference participants for helpful suggestions. Some parts of this
manuscript were completed at the Monetary Policy and Research Division, at the Research Department of the European Central
Bank, where Daniel Levy was a visiting scholar. He is grateful to the Bank's Research Department for the hospitality. Daniel
Levy gratefully acknowledges also the financial support from the Adar Foundation of the Economics Department at Bar-Ilan
University. Dongwon Lee’s research is supported by an eBRC Doctoral Support Award from Pennsylvania State University and a
Research Grant from Korea University. Rob Kauffman acknowledges partial support from the MIS Research Center, and the
W.P. Carey Chair in Information Systems, Arizona State University. All authors contributed equally: we rotate co-authorship.
The usual disclaimer applies.
* Corresponding author: Daniel Levy, Department of Economics, Bar-Ilan University, Ramat-Gan 52900, ISRAEL.
Tel: + 972-3-531-8331, Fax: + 972-3-738-4034, Email: Levyda@mail.biu.ac.il.
Price Points and Price Rigidity
Abstract
We study the link between price points and price rigidity, using two datasets: weekly scanner
data, and Internet data. We find that (i) “9” is the most frequently used price-ending for the
penny, dime, dollar and ten-dollar digits, (ii) the most common price changes are those that keep
the price endings at these “9” digits, (iii) the 9-ending prices are less likely to change in
comparison to non-9-ending prices, and (iv) the average size of the price change is larger for the
9-ending prices in comparison to non-9-ending prices. Overall, we find that these 9-ending
prices form a substantial barrier to price changes - at all digits from pennies to dollars, across a
wide range of product categories, retail formats and retailers.
1
Nor does anyone know how important … [price points] are in practice.
Alan Blinder et al. (1998, p. 26)
I. Introduction
With the increased popularity of new Keynesian models, understanding the sources of
nominal price rigidity has become even more important.1 One of the recent theories of price
rigidity is price point theory, which Blinder et al. (1998) list among the twelve leading theories
of price rigidity. According to the authors (p. 26), practitioners’ “… belief in pricing points is
part of the folklore of pricing …” Consistent with this observation, they offer evidence from
interviews on the importance of price points. In their study of 200 U.S. firms, they found that 88
percent of retailers assigned substantial importance to price points in their pricing decisions.
Kashyap (1995), the first to explore the link between price points and price rigidity, found that
catalog prices tended to be “stuck” at certain ending prices. After concluding that the observation
cannot be explained by existing theories, he offered price point theory as a possible explanation.
As Blinder et al. (1998) note in the opening quote above, however, a major difficulty with
price point theory is that not much is known about the actual importance of price points or about
their relationship to price rigidity. Price points will be particularly important for macroeconomics
if they can be shown to contribute to price rigidity across a wide range of products and retailers.
The literature offers growing evidence on the use of price points, but still there is a lack of direct
evidence linking price points and price rigidity. The literature documenting a link between price
points and price rigidity using U.S. data is limited to Kashyap (1995) and Blinder et al. (1998).
Kashyap has emphasized the need for more direct evidence, stating that a “study focusing on
more goods … would have much more power to determine the significance of price points.”
Our goal is to fill this gap in the literature by offering new evidence on the link between
price points and price rigidity using two particularly appropriate but different datasets. One is a
large weekly scanner price dataset from a major Midwestern U.S. retailer, covering 29 product
categories over an eight-year period. The second comes from the Internet and includes daily
prices over a two-year period for 474 consumer electronic goods, such as music CDs, digital
1
See, for example, Carlton (1986), Cecchetti (1986), Warner and Barsky (1995), Dutta, et al. (2002), Levy, et al.
(2002), Ball and Romer (2003), Rotemberg (1987, 2005, 2009), Nakamura and Steinsson (2008, 2009), Kehoe and
Midrigan (2008), Klenow and Kryvstov (2008), Eichenbaum, et al. (2009), Alvarez, et al. (2010), and Midrigan
(2010). For recent surveys, see Willis (2003), Wolman (2007), and Klenow and Malin (2010).
2
cameras, notebook PCs, etc., from 293 different e-retailers, with a wide range of prices. Taken
together, the two datasets cover a diverse set of products, a wide range of prices, different retail
formats, and multiple retailers and time periods.
The following summarizes our findings. “9” is the most popular price point for the penny,
dime, dollar and the ten-dollar digits across the two datasets. The most common price changes
are those that keep the terminal digits at these “9”endings. When we estimated the probability of
a price change, we found that the 9-ending prices are less likely to change in comparison to non
9-ending prices. For the Dominick’s data 9-ending prices are at least 43–66 percent less likely to
change than non-9-ending prices. For the Internet data, these probabilities are in the range of 25–
64 percent. The average size of the 9-ending price changes are larger in comparison to non-9ending prices, which further underscore the extent of the 9-ending price rigidity.
The paper is organized as follows. We describe the data in section II. In section III, we
study the distribution of price-endings. In section IV, we assess the distribution of price changes.
In section V, we estimate the effect of 9-endings and 99-endings on price rigidity. In section VI,
we evaluate the link between price points and the size of price changes. In section VII, we
discuss the robustness of the findings. Section VIII concludes.
II. Two Datasets
Kashyap’s (1995) price point theory suggests that price points should be most important
to retail firms (Blinder et al. 1998, Stahl 2010). We examine retail prices from two large datasets.
One is Dominick’s weekly price data for 29 different supermarket product categories over an
eight-year period. The other contains daily prices from the Internet on products that include
music CDs, DVDs, hard disks, and notebook PCs, among others.
The two datasets cover a wide variety of products, a wide range of prices, and different
retail formats. In addition, although Dominick’s prices are set on a chain-wide basis, our Internet
data come from many different retailers, which presumably employ different pricing decision
models. Thus, the conclusions that we draw are not specific to a particular retail format, a
retailer, a product, or a price range.
Dominick’s is a large supermarket chain in the Chicago metropolitan area. During the
period of our study, it operated 93 stores with a market share of about 25 percent. The data
consist of up to 400 weekly observations of retail prices in 29 different product categories,
3
covering the period from September 14, 1989 to May 8, 1997. The prices are the actual
transaction prices as recorded by the chain’s checkout scanners. If an item was on sale, then the
price data reflect the sale price of the item.
Although Dominick’s prices are set on a chain-wide basis at the company headquarters,
there are some price variations across the stores depending on the price tiers to which the stores
belong. Dominick’s divides its stores into four price tiers. These are “Cub-fighter,” “low,”
“medium,” and “high.” The stores designated as Cub-fighters are typically located in proximity
to a Cub Foods store and thus compete directly with it. The other three price tier stores employ a
pricing strategy that fits best given their local market structure and competition.
We report results from analyzing the prices in four stores, one from each price tier. The
stores were selected at random and include Store #8 (“low” price tier), #12 (“high” price tier),
#122 (“Cub Fighter”), and #133 (“medium” price tier). To study the behavior of regular prices,
we removed data points if they involved bonus buys, coupon-based sales, or simple price
reductions. For this, we relied on Dominick’s data identifiers which indicated the occurrences of
such promotions. Dominick’s did not use loyalty cards during the time period studied. In total,
the Dominick’s data contain over 98 million weekly price observations on 18,037 different
grocery products in 29 product categories.2 The four-store sample contains 4,910,129 weekly
price observations on 16,105 different products. Barsky et al. (2003), Chevalier et al. (2003), and
Levy et al. (2010) offer more details about the data.3 Table 1 presents descriptive statistics for the
Dominick’s data for the four stores.
Our Internet data were obtained through the use of a price data-gathering software agent.
We programmed it to download price data from BizRate (www.bizrate.com), a popular price
comparison site. It accessed the site for data collection from 3:00 a.m. to 5:00 a.m. over a period
of more than two years from March 26, 2003 to April 15, 2005. We generated a large sample of
product IDs using stratified proportionate random sampling (Wooldridge 2002) from a list of
products available at BizRate. The software agent automatically built a panel of sales prices
given the product IDs.4 The resulting dataset consists of 743 daily price observations for 474
2
The products in Beers and Cigarettes categories are highly regulated, which might skew the results (Besley and
Rosen, 1999). We, therefore, do not discuss the results for these two categories.
3
Dominick’s data are available at http://research.chicagobooth.edu/marketing/databases/dominicks/stores.aspx. The
site contains detailed information about the location of the stores, as well as detailed description of the data files,
product categories included, etc. The site also discusses various measurement issues.
4
When the sellers’ websites were inaccessible or the price information was not available, instances of missing data
4
personal electronic products in 10 product categories from 293 different Internet-based retailers.
The categories include Music CDs, Movie DVDs, Video Games, Notebook PCs, Personal Digital
Assistants (PDAs), Software, Digital Cameras and Camcorders, DVD Players, PC Monitors, and
Hard Drives.5 In total, the Internet data contain over 2.5 million daily price observations. Table
2 presents descriptive statistics for the Internet data.
III. Evidence on the Popularity of 9-Ending and 99-Ending Prices
I asked the best economist I know, at least for such things—my wife, if she
recalled a price not ending in a “9” at our local grocery store. “Not really,” she
said. “Maybe sometimes there are prices ending in a “5,” but not really.”
Jurek Konieczny (2003, Discussant Comment)
We begin by presenting the results on the frequency distribution of price-endings in the
two datasets. In the analysis of Dominick’s data, our focus was on 9¢ and 99¢ price-endings
because the overwhelming majority of the prices in retail grocery stores were well below $10.00
during the study period.6 In the Internet data, the price ranges were different: from a minimum
of $3.99 to a maximum of $6,000.00, with the average prices in different categories spanning
$13.46 to $1,666.68 in the study period. The wider price range in the Internet data enables us to
occurred. The software agent used the following algorithm to address this issue. If 10% or more observations were
missing for a product, then that series was excluded from the data altogether. If less than 10% of the data were
missing, then the algorithm examined if the prices for the day before and the day after were the same. If they were
the same, then the software agent automatically filled in the missing data with that price. Otherwise, it filled in the
missing data with the price for the day after. Only 0.075% of the Internet dataset was interpolated this way because
of missing observations, and thus missing data are unlikely to affect our results.
5
Product categories were selected based on their popularity on the Internet. The products in these categories were
sold by a large number of stores. For example, in the category of Digital Cameras, the “Canon-EOS Digital Rebel
XT” was sold by 63 stores. Our selection of products was random. For example, in the category of Movie DVDs, we
chose products from multiple sub-categories (e.g., Action, Drama, Comedy, etc.). Similarly, in the Music CDs
category, we chose from many different sub-categories (e.g., Blues, Jazz, Country, etc.). However, in some
categories (e.g., Notebook PCs and Hard Drives), we included all of the available products. In other categories (e.g.,
DVD Players, Digital Cameras, PC Monitors, Software), we randomly chose products from all of the sub-categories.
For example, in the DVD Players category, we chose half of the products from among Standard DVD Players, while
the other half came from the more expensive DVD/VCR Combo Players. In the Digital Cameras and Camcorders
categories, we chose half from Regular Digital Cameras while the other half came from Digital Camcorders. For PC
Monitors, we chose half from CRTs and Flat CRTs, and the other half from LCDs and TFTs. In the Software
category, we chose products from multiple genres (e.g., Educational Software, Operating Systems, Programming
Software, Utility Software, etc.). Similarly, for Video Games, we included multiple genres (adventure, action,
sports, etc.). See Figures R8a–R8j in the supplementary appendix for sample price series from our Internet dataset.
6
Indeed, according to Dutta et al. (1999) and Levy et al. (1997, 1998), the average price of an item in large U.S.
supermarket chains during 1991–1992 was about $1.70. Bergen et al. (2008) have noted that the figure increased to
$2.08 by 2001. In our four-store sample, the average price is $2.67. See Table 1.
5
study not only 9¢ and 99¢ price-endings, but also other 9-ending prices in both the cents and the
dollars digits, including $9, $9.99, $99, and $99.99.
In Figure 1, we report the frequency distribution of the last digit of the prices in
Dominick’s data. If a digit’s appearance as a price-ending were random, then we should have
seen 10 percent of the prices ending with each digit. As the figure indicates, however, about 69
percent of the prices ended with a “9.” The next most popular ending was “5,” accounting for
only 12 percent of all price endings. Only a small proportion of the prices ends with other digits.
Next, we consider the frequency distribution of the last two digits. With two digits, there
are 100 possible endings, 00¢, 01¢, …, 98¢, and 99¢. Thus, with a random distribution, the
probability of each ending should be only 1 percent. According to Figure 2, however, most prices
end with either 09¢, 19¢, …, or 99¢. This is not surprising since “9” was the dominant singledigit ending. But of these, more than 15 percent of the prices ended with 99¢. In contrast, only
about 4 percent to 6 percent of the prices ended with 09¢, 19¢, …, and 89¢.
Figure 3 displays the frequency distribution of the last digit in the Internet data. We can
see that “9” was the most popular terminal digit (33.4 percent), followed by “0” (24.1 percent),
and “5” (17.4 percent). The frequency distribution of the last two digits, which is shown on
Figure 4, exhibits a similar pattern, with 99¢ as the most popular price-ending (26.7 percent),
followed by 00¢ (20.3 percent), 95¢ (13.8 percent), and 98¢ (4.8 percent).
As mentioned above, the Internet dataset also includes some high-price product
categories, which allowed us to examine price-endings in dollar digits as well. In Figure 5,
therefore, we present the frequency distribution of the last dollar digit in the Internet data.
According to the figure, “9” was the most popular ending for the dollar digit, with $9 priceendings over-represented with 36.1 percent, followed by $4 price-endings with 9.9 percent, and
$5 price-endings with 9.2 percent.
A similar pattern emerged for the last two dollar digits, as shown in Figure 6. Not
surprisingly, the last two dollar digits of most prices contained “9” also, such as $99, $89, and
$09. But more prices ended with $99 than any other two dollar digit endings. Moreover, almost
10 percent ended with $99 among the 100 possible dollar endings of $0 through $99.
We also examined the frequency distribution of the last three digits of prices in the
Internet data. According to Table 3 (first column), among the 1,000 possible endings $9.99 was
the most popular ending for the last three digits (13.2 percent), followed by $9.00 (10.0 percent),
6
and $9.95 (4.9 percent). When we examined the last four digits of the prices (second column)
among the 10,000 possible endings $99.99 was the most popular ending (3.47 percent), followed
by $99.00 (3.46 percent), and $19.99 (2.16 percent).
To summarize, in both datasets, “9” was the most popular terminal digit overall. But the
popularity of “9” was not limited to the penny digit. Rather, it was popular in the dime, dollar,
and ten-dollar digits too. The fact that our data include a variety of products with wide-ranging
prices and different retail formats further underscores the popularity of “9” and “99” as a
terminal cent and dollar digits.
IV. Frequency Distribution of Price Changes
Having documented the dominance of “9” and “99” price endings as the terminal digits in
both datasets, we next assessed the extent to which the specific price points “9” and “99” may be
contributing to the retail price rigidity. To characterize the price change dynamics, we conducted
a 10-state Markov chain analysis for price changes that affect one digit of a price (the penny digit
and the dollar digit), and a 100-state Markov chain analysis for price changes that affect two
digits of a price (the penny and the dime digits, and the dollar and the 10-dollar digits).
Table 4 displays the 10-state transition probability matrix for the penny digit for the
Dominick’s data at the four sampled stores. For ease of interpretation, the figures in the matrix
(as well as in the remaining matrices) have been normalized, so that the probabilities in all rows
and columns combined add up to 1. Considering all 100 possible transition probabilities, it is
clear that 9¢-ending prices are the most persistent: 37.87 percent of the 9¢-ending prices preserve
the 9¢-ending after the change. Moreover, when non 9¢-ending prices change, they most often
end up with 9¢-ending than with any other ending. Considering the diagonal elements of the
matrix, after 9¢-ending prices, 5¢-ending prices seem to be the second most persistent with a
transition probability of 0.84 percent, followed by 0¢-eding prices, with a transition probability
of 0.64 percent. Overall, however, it seems that most of the transition dynamics takes place in the
movement to and from 9¢-ending prices. Proportionally, there is very little transition from any
particular non-9¢-ending prices to another non-9¢-ending price.
Table 5 displays the 10-state transition probability matrix for the penny digit for the
Internet data. Focusing on the diagonal terms, we find that on the Internet 0¢-ending prices are
the most persistent, with a transition probability of 20.35 percent. 9¢-ending prices are the
7
second most persistent with a transition probability of 17.68 percent, followed by 5¢-ending
prices with a transition probability of 10.63 percent.
Table 6 displays the 10-state transition probability matrix for the dollar digit for the
Internet data. Focusing on the diagonal terms, we find that $9-ending prices are significantly
more persistent than any other dollar-ending prices, with a transition probability of 11.75
percent. $4-eding prices are the second most persistent with a transition probability of 2.73
percent, followed by $5-ending prices with a transition probability of 2.52 percent. The
popularity of $4 and $5 ending prices stems from the fact that the actual prices in the low price
product categories (Music CDs, Movie DVDs, and Video Games) often are in the $14–$15
range, and the $4 and $5 endings persist because the changes take place in the penny and in the
dime digits.
Comparing the figures presented in Tables 5 and 6, it appears that the Internet retailers
tend not to use 9¢-ending proportionally as often. Instead, they use $9-ending more often. Thus,
the use of 9 as a terminal digit increases as we move from the penny and dime digits to the dollar
and the 10-dollar digits. Below we offer more evidence consistent with this behavior.
We next report the results of 100-state Markov chain analysis for the terminal two-digits
of the price, for the penny and the dime digits for both data sets, and for the dollar and the 10dollar digits for the Internet data. The resulting transition probability matrix, however, is 100 
100. We, therefore, present only partial results of these analyses. The figures presented in these
matrices are normalized as before, so that the probabilities in the entire table add up to 1.
Table 7 lists the top 25 transition probabilities for the penny and the dime digits at the
four Dominick’s stores. According to these figures, the most common transitions are from 89¢ending prices to 99¢-ending prices with the transition probabilities of 1.34 percent, 1.09 percent,
0.87 percent, and 0.82 percent, for Stores #8, #12, #122, and #133, respectively. These
probabilities seem quite high considering the fact that in the 100-state Markov chain there are
10,000 possible transitions. The second most common movement is from a 99¢-ending to a 89¢ending with the transition probability of 1.03 percent, 0.86 percent, and 0.70 percent, at Stores
#8, #12, and #122, respectively. In Store #122, the second most common movement is from a
39¢-ending to a 49¢-ending, with a transition probability of 0.65 percent. The third most
common movement in Stores #8 and #122 is from a 99¢-ending to a 19¢-ending with the
transition probability of 0.86 percent and 0.61 percent, respectively, in Store #12 from a 79¢-
8
ending to a 99¢-ending with a transition probability of 0.83 percent, and in Store #133 from a
79¢-ending to a 89¢-ending with a transition probability of 0.62 percent.
The transition from 99¢-ending prices to 99¢-ending prices come only in the 13th, 12th,
15th and 18th places for Stores #8, #12, #122, and #133, respectively, with the corresponding
transition probabilities of 0.66 percent, 0.61 percent, 0.43 percent, and 0.43 percent. While these
figures are quite high, it appears that other movements are more dominant than this particular
transition. The reason for this, we believe, is the fact that the average price in the Dominick’s
data is $2.67. Moreover, in all but two product categories, Analgesics and Laundry Detergents
(Beer and Cigarette categories are not discussed as mentioned in footnote 2), the average prices
are $3.00 or less. A move from a 99¢-ending price to a 99¢-ending price, therefore, will result in
a minimum price increase of 33–50 percent on average and a minimum price decrease of 25–33
percent, on average. Changes of this magnitude seem fairly large and, therefore, we suspect that
they are not as frequent.
Table 8 lists the top 25 transition probabilities for the internet data, for the penny and
dime digits on the left-hand side and for the dollar and the 10-dollar digits on the right-hand side.
The top three transitions for the penny and dime digits are from 00¢-ending prices to 00¢-ending
prices with a transition probability of 18.36 percent, from 99¢-ending prices to 99¢-ending prices
with a transition probability of 11.89 percent, and from 95¢-ending prices to 95¢-ending prices
with a transition probability of 8.83 percent. The top three transitions for the dollar and the 10dollar digits are from $14-ending prices to $14-ending prices with a transition probability of 1.47
percent, from $11-ending prices to $11-ending prices with a transition probability of 1.36
percent, and from $15-ending prices to $15-ending prices with a transition probability of 1.28
percent. The transition from $99-ending price to $99-dollar ending price came in only the 6th.
The frequent use of the $11-, $14-, and $15-ending prices stems from the fact that in the
low-priced product categories which include Music CD’s, Movie DVD’s and Video Games’
categories, these are not just price endings; these are actual prices. In these categories, therefore,
the most common price changes are in the penny and the dime digits, which may leave the dollar
and the 10-dollar digits unchanged.
This finding suggests that price change patterns likely differ between low-priced and
high-priced product categories. To explore this possibility, we separated the Internet data into
two groups: (1) low-priced product categories which include Music CDs, Movie DVDs, and
9
Video Games, and (2) high-priced product categories which include Computer Monitors, Digital
Cameras, DVD Players, Hard Drives, Laptop Computers, PDAs, and Software.
The results of the analyses are reported in Table 9. Beginning with the low-priced product
categories, we find that for the penny and the dime digits, the most common transition is from
99¢-ending to 99¢-ending with a transition probability of 16.32 percent, followed by a
movement from 98¢-ending to 98¢-ending with a transition probability of 1.80 percent, and a
movement from 95¢-ending to 95¢-ending with a transition probability of 1.75 percent. For the
dollar and the $10 digits, we find that $14-, $11-, and $15-ending prices are the most popular.
Next, moving to the high priced product categories, we find that for the penny and the
dime digits, the most common transition is from 00¢-ending to 00¢-ending with a transition
probability of 28.59 percent, followed by a movement from 95¢-ending to 95¢-ending with a
transition probability of 12.77 percent, and a movement from 99¢-ending to 99¢-ending with a
transition probability of 9.42 percent. For the dollar and the 10-dollar digits, we find that the top
three transition probabilities are from $99-ending prices to $99-ending prices with a transition
probability of 1.51 percent, from $99-ending prices to $49-ending prices with a transition
probability of 0.65 percent, and from $49-ending prices to $99-ending prices with a transition
probability of 0.60 percent.
In sum, we find that for the low-priced product categories, price changes that keep the
terminal digits at “9” are the most popular in the penny digit, in the penny and dime digits, and in
the dollar digit. For the high-priced product categories, price changes that keep the terminal
digits at “9” are the most popular in the dollar digit, and in the dollar and 10-dollar digits. These
results suggest that the persistent use of 9-ending prices is more likely to occur in the right-most
digits for low-priced products, but shift to the left as the products became more expensive. This
is consistent with the finding discussed above that “99¢”-to-“99¢” transitions were less common
in the Dominick’s dataset, which consists of mostly low-priced products.
V. The Effect of Price Points on Price Rigidity
To study the link between 9-ending prices and price rigidity more directly, we use a
binomial logit model to estimate price change probabilities. Using the method of maximum
likelihood, we estimated the parameters ,  and  of the following equation:
ln (q/(1 – q)) =  +  9_Endingjt +  Productjt +t
(1)
10
where q is the probability of a price change and 9_Endingjt is a 9-ending dummy variable. For
the Dominick's data, we estimate two versions of the regression. In the first, the 9_Endingjt
dummy equals 1 if the price for product j at time t ends with “9¢” and 0 otherwise. In the second
regression, the 9_Endingjt dummy equals 1 if the price for product j at time t ends with “99¢” and
0 otherwise. For the Internet data, we estimate six versions of the regression, corresponding to
the six different values of the 9_Endingjt dummy variable for 9¢, 99¢, $9, $9.99, $99 and $99.99.
Productjt represents a set of product-specific dummy variables based on universal product
codes (UPCs) in the Dominick’s data and other unique product identifiers in the Internet data.
They permit us to account for product-specific effects. For example, products for which 9-ending
prices are more common, may tend to be more rigid.7
The estimation results for the Dominick’s data are reported in Table 10. In the table, we
present the estimated coefficients of each dummy along with the corresponding odds ratios. For
all 27 product categories, the coefficient estimates for the 9¢-ending dummy are negative (all pvalues < 0.0001). The odds ratios, which equal eCoefficient, are all smaller than 1, indicating that
9¢-ending prices are less likely to change than prices that do not end with 9¢. On average, prices
that ended with 9¢ were 66 percent less likely to change than prices that did not end with 9¢.
We obtained similar results for the 99¢-ending prices. The coefficient estimates for the
99¢-ending dummy are all negative. For 25 out of 27 categories, they are statistically significant,
as shown on the right-hand panel in Table 10. The odds ratios indicate that prices that ended with
99¢ were on average 43 percent less likely to change than prices that did not end with 99¢.
Next, we estimated the same logit regression model for the Internet data, using dummies
for 9¢, 99¢, $9, $9.99, $99, and $99.99, in turn, as the independent variables. As with the
Dominick’s dataset, we included product dummies to account for product-specific effects. The
estimation results are reported in Table 11. Similar to what we found with the Dominick’s
dataset, 9-ending prices were less likely to change than other prices. Overall, 9¢-ending prices
were 25 percent, 99¢-ending prices 36 percent, $9-ending prices 36 percent, $99-ending prices
55 percent, $9.99-ending prices 45 percent, and $99.99-ending prices 64 percent less likely to
7
In an earlier analysis, we ran the above regression without the product dummies and obtained similar results. When
we correlated the proportion of 9-ending prices for each product category with the regression coefficient of the 9dummy from this earlier analysis, we obtained a significantly negative correlation for the 9¢ ending prices,
suggesting the presence of some product specific effects. For the 99¢-ending prices the correlation coefficient was
positive but statistically insignificant. We chose to include the product dummies in the results we report here.
11
change than other prices. We obtained similar results for the individual product categories. In 96
percent (52 out of 54 categories) of all possible cases in the category-level analyses, the effect of
9 price-endings on the probability of price changes was negative and significant.
Thus, prices seem to be “stuck” at 9- and 99-endings, making them more rigid: 9¢- and
99¢-ending prices at Dominick’s as well as on the Internet are less likely to change than other
prices. On the Internet, the findings hold also for $9-, $9.99-, $99-, and $99.99-ending prices.
VI. The Effect of Price Points on the Size of Price Change
If pricing points inhibit price changes, then they might also be expected to affect
the sizes of price increases. Specifically if prices that are at price points are fixed
longer than other prices, then any subsequent price adjustments might be expected
to be larger than average.
Anil Kashyap (1995, p. 267)
If 9-ending prices are less likely to change in comparison to non-9-ending prices, then the
average size of change of 9-ending prices should be larger when they do change, in comparison
to non-9-ending prices. This assumes that the cost of a price change is the same regardless of the
price-ending, which we believe is indeed the case according to the menu cost estimates of Levy
et al. (1997, 1998, 2008) and Dutta et al. (1999) for large U.S. supermarket and drugstore chains.
In Table 12, we report the average size of price changes for 9-ending and non-9-ending
prices for both datasets. In the table, we also report the corresponding results for the low quartile
of the products in terms of the popularity of 9-ending prices. The goal of this analysis is to assess
the possibility that the findings we are documenting in this section may be driven by the frequent
use of 9-endings. By limiting the analysis to the low quartile of the products in terms of the use
of 9-endings, we are offering the most conservative test for this hypothesis.
In the Dominick’s dataset, the average price change was 75¢ if the price ended with 9¢, in
contrast to a 40¢ change when it did not end with 9¢, an 88 percent difference. The findings for
the 99¢-ending prices are also consistent: the average price change was 91¢ if the price ended
with 99¢, in contrast to a 55¢ change when it did not end with 99¢. This amounts to a 65 percent
difference.
Similarly, when we focused on the low quartile of products in terms of the popularity of
9-ending prices, the average price change was 38¢ if the price ended with 9¢, in contrast to a 33¢
change when it did not end with 9¢, a 15 percent difference. For the 99¢-ending prices, the
12
average price change was 49¢ if the price ended with 99¢, in contrast to a 34¢ change when it did
not end with 99¢. This is a 44 percent difference.
With the Internet data, we considered prices ending with 9¢, 99¢, $9, $9.99, $99, and
$99.99, again for the entire dataset, as well as for the low quartile of products. When we
considered the entire Internet dataset, for the 9-ending prices, the average price changes were
$15.54, $22.40, $32.13, $33.97, $66.15, and $63.04 for 9¢-, 99¢-, $9-, $9.99-, $99-, and $99.99ending prices, respectively. The corresponding non-9-ending average price changes were $18.07,
$16.78, $12.83, $16.30, $15.20, and $16.88, respectively. In other words, the 9-ending price
changes were higher than non-9-ending price changes by about -14 percent, 33 percent, 150
percent, 108 percent, 335 percent, and 273 percent, respectively. Only in one case (Notebook
PCc, 9¢- vs. non-9¢-endings), was the average 9-ending price change lower than the average
non-9-ending price change. See Table R22 in supplementary appendix.
When we considered the low quartile data, for 9-ending prices, the average price changes
were $24.02, $27.78, $11.93, $22.47, $49.61, and $38.24 for the 9¢-, 99¢-, $9-, $9.99-, $99-, and
$99.99-ending prices, respectively. The corresponding non-9-ending average price changes were
$21.03, $20.76, $7.21, $7.38, $18.27, and $19.21, respectively. Thus, the 9-ending price changes
for the low quartile products were higher than non-9-ending price changes by about 14 percent,
34 percent, 65 percent, 204 percent, 172 percent, and 99 percent, respectively.
Thus, the average size of the 9¢-ending and 99¢-ending price changes systematically
exceed the average size of the non-9¢-ending and non-99¢-ending price changes, respectively.
The fact that the results are similar for the overall data and the products in the low quartile
suggests that in terms of the 9¢ use, the difference is unlikely to be driven by product-specific
effects that could simultaneously increase the prevalence of 9-ending prices and the magnitude
of the price changes. If that were the case, we should not have observed larger price changes for
9-ending and 99-ending prices in the low quartile of products for which 9-ending prices are less
common. These findings are consistent with our predictions: since 9-ending and 99-ending prices
are less likely to change, the average sizes of the changes of the 9-ending and 99-ending prices
are systematically larger when they do change, in comparison to the non-9-ending and non-99ending prices, respectively.
13
VII. Robustness
To explore the robustness of the findings, we conducted several additional analyses,
much of them following the referees’ comments and suggestions. The findings we have reported
for the Dominick’s data were based on the analysis of the price data from the chain’s four stores.
We, however, have also analyzed the data for each of the four sampled stores individually, as
well as the chain's entire dataset which include the price information from all 93 stores. In each
case, we have considered the data for all 27 categories combined, as well as for each individual
product category. For the Internet data, we have primarily reported the results of the aggregate
data analysis. However, most of the analyses were repeated for each product category. In
general, the results of these additional analyses are similar to the results that we have reported.
Here we offer some details about these analyses and the findings. More detailed presentation of
these analyses is included in the supplementary appendix.
A. Evidence on the Frequency Distribution of 9- and 99-Ending Prices
We found that 9¢- and 99¢-ending prices were more popular than other endings at the
Dominick's data (for all 93 stores combined), and at each one of the four individual stores
sampled. At the category level, we found that 9¢-ending prices were more popular than other
endings at all 27 product categories, while 99¢-ending prices were more popular than other
endings in 23 of the 27 product categories.
For the Internet data, we found that 9¢-ending and 99¢-ending prices were more popular
than other endings for four product categories, while the 0¢-ending was the most popular for the
remaining six categories. For the dollar digit, 9-endings were more popular than other endings in
8 of the 10 categories. For the last two dollar digits, $99-ending prices were more popular than
the other price-endings in 6 of the 10 categories.8
We have also considered the possibility that the use of 9- and 99-ending prices is related
to the sales volume. The analysis of 9- and 99-ending prices by sales volume, however, suggests
no such systematic relationship. The results suggest that 9-ending prices are popular for both
8
Three individual product categories with low average prices exhibited some variation in their price endings. For
example, for the dollar digit, the $3, $4 and $5 price-endings were the most common for CDs and DVDs. That is
because the prices in these categories usually range between $13 and $16. Also, the $99 and $99.99 endings were
not common in those two categories or the category of Video Games, because the average prices in these categories
are less than $100. We, therefore, did not see frequent 9-endings for the dollar and ten-dollar digits in these
categories.
14
products that have a large sales volume and products that have a small sales volume.
B. Evidence on the Frequency Distribution of Price Changes
Similar to the other results that we have reported in this paper, we found that for regular
prices in each of the four Dominick’s stores, as well as for all 93 stores combined and for all
prices, “9”-to-“9” was the most popular price change. For example, 37.74 percent of the
transition takes place from 9¢-ending to 9¢-ending prices. 5¢-to-5¢ and 0¢-to-0¢ ending
transitions only occur with 0.90 percent and 0.66 percent probabilities. The 9¢-ending prices are
the most persistent if we consider the entire Dominick’s data as well. “99”-to-“99” is not the
most popular price change for any of the four stores, similar to the results reported earlier in the
paper, but it is the most popular when all prices from all stores are considered. For the
Dominick's dataset, in all but one category (Front-End Candies), there were considerably more
price changes that were multiples of dimes and dollars for 9-ending prices.
For the Internet data, in the low-priced product categories, we found considerably more
price changes that were multiples of dimes and dollars for 9-ending prices. For high-priced
product categories, we found more price changes that were multiples of $10 and $100 for 9ending prices.
C. Evidence on the Link between 9- and 99-Ending Prices and Price Rigidity
We find a strong positive link between price points and price rigidity at the level of the
entire Dominick's chain, as well at each one of the four sampled stores examined. Beginning
with Store #8, we find that the probability of a change of a 9¢-ending and a 99¢-ending prices
are on average 60 percent and 28 percent lower than non-9¢-ending and non-99¢-ending prices,
respectively. The result holds true for most product categories: overall, in 50 of the 54 cases (27
coefficients for the 9¢-ending dummy and 27 coefficients for the 99¢-ending dummy) the
coefficient of the 9-ending dummy was negative. In 48 of these 50 cases, they were statistically
significant. We found similar results for the remaining 3 stores. For example, at Store #12, the
estimated coefficient was negative in 51 of the 54 cases, with 48 of them being statistically
significant. At Store #122, the estimated coefficient was negative in 53 of the 54 cases, with 50
of them being statistically significant. At Store #133, the estimated coefficient was negative in 53
of the 54 cases, with 51 of them being statistically significant. The findings for the entire
15
Dominick’s dataset are even stronger: all 54 estimated coefficients were negative and statistically
significant.
D. Evidence on the Link between 9- and 99-Endings and the Size of Price Changes
In the Dominick’s dataset, in 23 of the 27 categories the average price change was higher
for 9¢-ending than for non-9¢-ending prices. The findings that we obtained for the 99¢-ending
prices are even stronger. In 26 categories (the exception is Frozen Entries), the average change
was higher for 99¢-ending than for non-99¢-ending prices. Similarly, when we focused on the
low quartile of products in terms of the popularity of 9-ending prices, we found that in 21
categories the average change was higher for 9¢-ending than for non-9¢-ending prices. For the
99¢-ending prices, in 25 categories the average price change was higher for the 99¢-ending than
for non-99¢-ending prices.
With the Internet data, we considered prices ending with 9¢, 99¢, $9, $9.99, $99, and
$99.99, again for the entire dataset, as well as for the low quartile of products. For the entire
dataset we find that the average price change was higher if the price ended with 9 in comparison
to non-9 ending prices in 8, 9, 9, 9, 8, and 7 categories for 9¢, 99¢, $9, $9.99, $99, and $99.99
ending prices, respectively.9 Thus, in 50 of the 56 cases, the average size of the price change was
higher if the price ended with a 9-ending price point in comparison to non-9¢-ending prices.
The results for the low quartile of products are similar. Specifically, we find that the
average price change was higher if the price ended with 9 in comparison to non-9 ending prices
in 7, 10, 9, 9, 6, and 6 categories for 9¢, 99¢, $9, $9.99, $99, and $99.99 ending prices,
respectively.10 Overall, in 47 of the 54 cases the average size of the price change was higher if
the price ended with a 9-ending price point than with a non-9-ending price.
VIII. Conclusion
To our knowledge, this is the first study that directly examines the effect of price points
on price rigidity across a broad range of product categories, price levels, and retailers, in the
traditional retailing and the Internet-based selling formats, using data from the U.S. We found
that 9-ending prices were the most popular and were less likely to change compared to non-99
Two categories, Music CDs and Video Games, contained no prices with a $99-and $99.00 endings.
There were no Music CDs, Music DVDs or Video Games with $99- or with $99.99-ending prices.
10
16
ending prices. Further, the most common price changes preserve the terminal digits at “9” and
the size of the price changes was larger for these 9-ending prices than for non-9-ending prices.
We also discovered that there is a shift in this preservation of 9-ending prices with the price
level: for more expensive product categories we saw less frequent persistence of 9’s in the penny
and the dime digits, but more frequent persistence of 9’s in the dollar, $10, and $100 digits.
Overall, we find that for the Dominick’s data 9-ending prices are at least 43–66 percent
less likely to change than non-9-ending prices. For the Internet data, these probabilities are in the
range of 25–64 percent. These figures seem to us quite substantial. We conclude therefore, that
9-ending and 99-ending prices form a considerable barrier to price changes, offering direct
evidence on the link between price points and price rigidity. Combining this with the robustness
of the findings—occurring in both datasets, across a wide range of product categories with a
wide range of prices, products, retail formats and retailers, suggests that price points might be
substantial enough to have broader macro implications. This is reinforced by the finding that the
use of 9s shifts leftwards as the products’ average price increases, which suggest that the
phenomenon of 9-ending prices rigidity may exist in markets for other goods and services in
more expensive product categories where the use of 9-endings in $1, $10, $100 digits, etc. is
quite common. These include prices of the goods sold at department stores such as clothes,
shoes, fragrances, jewelry, and high tech equipment, as well as other high priced products and
services such as musical instruments, furniture, cars, home appliances, hotels, air travel, car
rentals, and even in pricing of homes and apartments. Taken together, these goods and services
comprise a substantial proportion of the aggregate consumption and thus may have a
considerable economic significance.
The use of 9-ending prices seems to be relevant in the context of public policy issues as
well. For example, the use of 9-ending prices is often debated in countries where lowdenomination coins have been abolished. When small denomination coins are no longer used,
transactions involving small changes must rely on rounding, as is the case in Israel, Hungary, or
Singapore. In Israel, for example, the 1¢ (“1-Agora”) coin was abolished in 1991, and the 5¢
coin was eliminated in 2008. The law, therefore, requires that the final bills be rounded up (if it
ends with 5¢–9¢) or down (if it ends with 1¢–4¢) to the nearest 10¢. It turns out, however, that
the Israeli retailers use 9-ending prices extensively, which irritates consumers, who claim that 9ending prices are unethical given the absence of 1¢ coin. The Israeli Parliament has twice
17
rejected a proposed law which would outlaw the use of 9-ending prices.11 This may extend to
other countries soon. For example, dropping the smallest currency unit has been a recent topic of
debate in the U.S., Canada and Europe.12 Australia has stopped issuing 1¢ and 2¢ coins in 1989.
New Zealand ceased issuing the 1¢ and 2¢ coins in 1989. Denmark stopped issuing the 5- and
10-ores in 1989. The Dutch eliminated the 1¢ of the guilder in 1980 and ceased issuing the 1¢
and 2¢ of Dutch euro coins in 2006. In Finland, the 1¢ and 2¢ of Finnish euro coins are not in
general use any longer. In 2008, Hungary eliminated the 1 and 2 forint coins. France, Norway,
Britain and Singapore have also eliminated low-denomination coins.
The common use of price points has also received considerable attention in some
European Union countries in the context of the conversion of prices from local currencies to the
euro. The concern has been about the possibility that retailers may have acted opportunistically
by rounding their prices upward after conversion to the euro in their attempt to preserve the price
points. This appears to be true, for example, in the case of products that are sold through
automated devices, such as soda and candy bar vending machines, parking meters, coin-operated
laundry machines, etc. (Bils and Klenow 2004, Levy and Young 2004, and Campbell and Eden
2005, Ehrmann 2005, Hoffmann and Kurz-Kim 2010).
In our data, 9 is the most popular terminal digit overall. The use of price points, however,
seems to vary across countries. For example, Konieczny and Skrzypacz (2003, 2004) and
Konieczny and Rumler (2007) note that 9-ending prices are particularly popular in the U.S.,
Canada, Germany, and Belgium, but they are rare in Spain, Italy, Poland, and Hungary.
According to Heeler and Nguyen (2001), in the Chinese culture, numbers have special
significance and symbolism. The number 8, for example, is associated with “success.”13 They
11
See, for example, http://www.globes.co.il/news/article.aspx?did=1000403091 (in Hebrew).
In the July 19, 2001 issue of the USA Today, L. Copland reported that “France, Spain and Britain quit producing
low-denomination coins in recent decades because production costs kept going up while the coins’ purchasing
power went down.” More recently, it has been reported that in many European countries which have adopted the
Euro, the public seems to be exhibiting resistance to the use of 1-cent and 2-cent denomination coins. This is due to
the inconvenience their use entails. In the March 22, 2002 issue of the International Herald Tribune (Tel-Aviv
Edition), E. Pfanner suggested that these coins are “small, nearly valueless—and a nuisance to millions of
Europeans. The tiny denominations of the 1-cent and 2-cent Euro coins are annoying shoppers and disrupting
business from Paris to Milan.” According to the above USA Today report, in 2001, Rep. Jim Kolbe (R-Arizona)
introduced the “Legal Tender Modernization Act,” to make the U.S. penny obsolete. The bill was defeated. Previous
attempts made in 1990 and 1996 also died in Congress.
13
Even the sounds of the numbers can suggest good or bad luck. For example, the number 8 represents luck to
Cantonese Chinese because it sounds like multiply or get rich (fa in Cantonese). In Japan, 8 also has great symbolic
significance because the writing of the number 8 looks like a mountain (“八”), and thus the number 8 signifies
growth and prosperity.
12
18
find that close to 50 percent of restaurant menu prices sampled in Hong Kong had 8-endings,
which they refer to as “happy endings.” Also, a Time Magazine article (Rawe, 2004) reports that
at the casino of the recently-built $240 million Sands Macao hotel in Macao, China, the slot
machines’ winning trios of 7’s have been replaced with trios of 8’s. Consistent with these
observations, the opening ceremony of the Beijing Olympic Games, held in the Beijing National
Stadium, began exactly at 08:08:08 p.m. on 8/8/2008.14
Knotek (2008, 2010) has focused on other types of pricing practices, especially the
common use of round prices, which he terms “convenient prices” because their use reduces the
amount of the change used in a transaction. Levy and Young (2004, 2008) reported that the
nominal price of Coca Cola was fixed for almost 70 years at 5¢, also a convenient price.
Future work might study such pricing practices across other products, industries, retailers,
and countries to assess the generalizability of these findings and observations. Beyond
documenting these facts, this study raises interesting questions concerning the importance of
price points for monetary non-neutrality. For example, how much monetary non-neutrality could
be generated by pricing points? How are pricing points determined? To answer these questions,
one would need a monetary economy model with pricing points. These remain interesting
avenues for future research.
We end by noting that the Internet provides a unique context for micro-level studies of
price setting behavior (Bergen et al. 2005). The ability to access transaction price data using
software agents has allowed us to explore pricing and price adjustment patterns at a low cost and
with a previously unimaginable level of microeconomic detail. This approach also allows
empirical research methods to take advantage of natural experiments in the real world (Kauffman
and Wood 2007, 2009). With the expanding retail activities on the Internet, and new techniques
and tools that have become available, we expect such opportunities to increase further in the
future.
14
The cultural importance of numbers is not limited to “happy endings.” For example, according to Mirhadi (2000),
when the Masquerade Tower was added to Hotel Rio in Las Vegas in 1997, the architects decided to skip the 40th to
the 49th floors because the Arabic numeral “4” in Chinese sounds similar to the word “death.” The elevators in the
building went directly from the 39th floor to the 50th floor.
19
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Warner, E. and R. Barsky (1995), “The Timing and Magnitude of Retail Store Markdowns:
Evidence from Weekends and Holidays,” Quarterly Journal of Economics 110(2), 321–352.
Willis, J. (2003), “Implications of Structural Changes in the U.S. Economy for Pricing Behavior
and Inflation Dynamics,” Federal Reserve Bank of Kansas City Economic Review, Kansas
City, MO (1st quarter), 5–26.
Wolman, A. L. (2007), “The Frequency and Costs of Individual Price Adjustment: A Survey,”
Managerial and Decision Economics 28(6), 531–552.
Wooldridge, J. (2002), Econometric Analysis of Cross Section and Panel Data (Cambridge, MA:
MIT Press).
22
Table 1. Descriptive Statistics for the Dominick’s Price Data,
Regular Prices, Stores #8, #12, #122 and #133
Category
Analgesics
Bath Soap
Bathroom Tissue
Beer
Bottled Juice
Canned Soup
Canned Tuna
Cereals
Cheeses
Cigarettes
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End-Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Toothbrushes
Toothpastes
Total
Number of
Observations
174,132
31,859
52,856
126,295
204,967
251,505
111,142
213,771
312,455
80,637
355,388
107,527
101,077
108,050
208,322
84,942
340,123
109,916
244,043
156,156
47,584
43,389
102,221
306,053
163,346
94,722
516,692
99,921
161,038
4,910,129
Number of
Products
599
492
119
595
460
400
247
447
594
599
1,018
290
270
308
443
239
825
160
1,237
556
94
150
213
2,615
390
313
1,411
447
574
16,105
Mean
Price
$5.32
$3.31
$2.14
$5.69
$2.24
$1.15
$1.82
$3.17
$2.43
$8.23
$2.11
$2.03
$2.37
$2.85
$0.61
$2.35
$2.31
$1.36
$2.95
$5.67
$2.66
$1.55
$2.20
$3.06
$2.19
$2.60
$2.35
$2.24
$2.49
$2.67
Std.
Dev.
$2.51
$1.76
$1.71
$2.69
$0.97
$0.49
$1.07
$0.78
$1.12
$8.40
$0.63
$0.57
$0.92
$1.47
$0.24
$0.88
$1.06
$0.43
$1.39
$3.24
$0.67
$1.51
$0.88
$1.87
$0.59
$1.58
$1.90
$0.93
$0.97
$2.22
Min.
Price
$0.47
$0.47
$0.25
$0.99
$0.32
$0.23
$0.25
$0.29
$0.10
$0.89
$0.25
$0.25
$0.39
$0.10
$0.01
$0.28
$0.25
$0.22
$0.49
$0.39
$0.49
$0.33
$0.39
$0.27
$0.10
$0.25
$0.10
$0.39
$0.31
$0.01
Max.
Price
$23.69
$18.99
$11.99
$26.99
$8.00
$5.00
$11.19
$7.49
$11.50
$25.65
$8.79
$6.85
$7.00
$9.99
$6.99
$9.99
$15.99
$5.00
$11.29
$24.49
$5.00
$12.59
$7.05
$29.99
$8.00
$9.99
$26.02
$9.99
$10.99
$29.99
Note: The data are weekly. The sampled stores belong to four price tiers as follows: Store #8 - “low”
price tier, #12 - “high” price tier, #122 - “Cub Fighter,” and #133 - “medium” price tier. See section II
for details.
23
Table 2. Descriptive Statistics for the Internet Price Data
Category
Music CDs
Movie DVDs
Video Games
Software
Hard Drives
PDAs
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Number of
Observations
302,914
447,519
244,625
382,297
263,244
148,731
220,236
319,369
247,917
79,386
2,656,238
Number of
Products
46
49
49
48
46
45
49
51
46
45
474
Number of
Retailers
15
22
38
83
73
92
104
87
143
45
293
Mean
Price
Std. Dev.
$13.46
$3.50
$27.42
$26.70
$30.83
$12.57
$294.07
$417.60
$330.67
$556.29
$346.60
$193.24
$369.51
$247.75
$682.89
$659.13
$760.12
$688.76
$1,666.68
$475.80
$337.06
$536.13
Min.
Price
Max. Price
$3.99
$26.98
$4.95
$144.99
$4.90
$57.99
$4.95 $5,695.00
$39.00 $3,670.98
$32.99
$956.95
$57.99 $1,489.00
$85.78 $3,010.41
$175.95 $6,000.00
$699.00 $3,199.00
$3.99 $6,000.00
Note: The table covers 743 daily price observations from March 26, 2003 to April 15, 2005, from 293 Internet retailers for
474 products. The retailers have many different product categories (e.g., Amazon.com sells books, CDs, DVDs, computer
products and electronics, etc.). Consequently, the sum of the number of retailers in each product category will not
necessarily be consistent with the total number of stores in all product categories. In addition, some retailers do not have all
products (e.g., in our sample, Amazon has 15 Music CDs while Barnes & Noble has 20). Also, the length of individual
product’s price time series varies due to different life cycle of products. Thus, the number of observations in the Music CDs
category, for example, 302,914, is less than total available combinations (i.e., 46  15  743 = 512,670.)
Table 3. Top 10 Highest Frequencies in the Internet Data
Rank
Last 3 Digits of
Price Endings
Last 4 Digits of Price
Endings
Price Changes
1
2
3
4
5
6
7
8
9
10
$9.99 (13.17%)
$9.00 (9.98%)
$9.95 (4.86%)
$4.99 (3.24%)
$5.00 (2.48%)
$2.99 (1.46%)
$8.95 (1.45%)
$8.00 (1.44%)
$7.99 (1.43%)
$4.95 (1.42%)
$99.99 (3.47%)
$99.00 (3.46%)
$19.99 (2.16%)
$49.99 (2.00%)
$29.99 (1.55%)
$49.00 (1.43%)
$14.99 (1.40%)
$99.95 (1.09%)
$09.99 (0.97%)
$79.00 (0.87%)
$1.00 (6.74%)
$2.00 (4.49%)
$10.00 (3.24%)
$3.00 (3.09%)
$5.00 (2.72%)
$4.00 (2.30%)
$20.00 (1.80%)
$6.00 (1.55%)
$0.10 (1.38%)
$0.01 (1.38%)
Price Changes with
Three Categories
Left Out
$1.00 (5.63%)
$2.00 (4.66%)
$10.00 (4.31%)
$3.00 (3.60%)
$5.00 (3.38%)
$4.00 (2.90%)
$20.00 (2.56%)
$6.00 (2.18%)
$30.00 (1.50%)
$7.00 (1.47%)
Note: The figures in each column are ordered from the most frequent to the least frequent. Bold-marked
prices in the first three rows indicate that they are in the top three most frequent in each category. The rightmost column shows the top ten most frequent price changes after three product categories (Music CDs,
Movie DVDs, and Video Games) are excluded from the analysis.
24
Current Ending Digit (¢)
Table 4. Transition Probability Matrix Conditional on a Price Change for a 10-State
Markov Chain, Dominick’s Data, Stores #8, #12, #122, #133, Regular Prices Only, for the
Penny Digit
0
1
2
3
4
5
6
7
8
9
0
0.64
0.26
0.25
0.28
0.30
0.72
0.26
0.23
0.15
3.40
1
0.25
0.14
0.13
0.20
0.12
0.30
0.15
0.14
0.10
1.58
2
0.29
0.18
0.15
0.16
0.17
0.32
0.18
0.15
0.11
1.45
Next Period Ending Digit (¢)
3
4
5
6
0.31
0.33
0.79
0.26
0.21
0.14
0.44
0.14
0.18
0.19
0.36
0.18
0.33
0.22
0.47
0.20
0.18
0.29
0.40
0.23
0.42
0.33
0.43
0.84
0.21
0.26
0.37
0.20
0.28
0.21
0.41
0.25
0.14
0.14
0.29
0.13
1.88
2.34
3.15
1.85
7
0.23
0.13
0.15
0.24
0.17
0.49
0.29
0.24
0.13
1.77
8
0.16
0.09
0.09
0.15
0.11
0.26
0.14
0.13
0.12
0.85
9
3.68
2.98
1.81
2.47
2.93
3.81
2.15
2.17
1.43
37.87
Note: Each cell contains the percentage of the price change compared to the total price change (i.e.,
1,374,142). The top three highest transition probabilities on the matrix diagonal are indicated in
boldface.
Current Ending Digit (¢)
Table 5. Transition Probability Matrix Conditional on a Price Change
for a 10-State Markov Chain, Internet Data, for the Penny Digit
0
1
2
3
4
5
6
7
8
9
0
20.35
0.32
0.40
0.34
0.37
1.45
0.34
0.39
0.54
1.54
1
0.35
0.39
0.33
0.29
0.34
0.33
0.29
0.27
0.33
0.42
2
0.35
0.33
0.47
0.32
0.37
0.30
0.31
0.27
0.30
0.42
Next Period Ending Digit (¢)
3
4
5
6
0.34
0.33
1.40
0.39
0.32
0.34
0.29
0.30
0.34
0.34
0.27
0.24
0.47
0.33
0.35
0.32
0.31
0.66
0.52
0.40
0.34
0.48
0.45
10.63
0.34
0.43
0.48
0.86
0.37
0.36
0.32
0.33
0.37
0.44
0.58
0.41
0.48
0.87
2.19
0.54
7
0.38
0.28
0.31
0.30
0.38
0.34
0.41
0.66
0.48
0.56
8
0.52
0.30
0.34
0.41
0.37
0.53
0.30
0.49
2.95
1.47
9
1.69
0.40
0.32
0.43
0.87
2.04
0.66
0.58
1.21
17.68
Note: Each cell contains the percentage of the price changes compared to the total number of price
changes (41,034). The top three highest transition probabilities on the matrix diagonal are indicated in
boldface.
25
Current Ending Digit ($)
Table 6. Transition Probability Matrix Conditional on a Price Change
for a 10-State Markov Chain, Internet Data, for the Dollar Digit
0
1
2
3
4
5
6
7
8
9
0
1.58
0.98
0.58
0.46
0.55
0.49
0.36
0.33
0.49
1.08
1
0.85
2.18
1.19
0.67
0.49
0.44
0.37
0.30
0.39
0.83
2
0.45
1.06
1.72
1.23
0.87
0.61
0.42
0.41
0.38
0.81
Next Period Ending Digit ($)
3
4
5
6
0.40
0.42
0.43
0.35
0.49
0.40
0.35
0.33
1.01
0.76
0.56
0.34
1.99
1.12
0.65
0.50
1.30
1.32
0.69
2.73
0.90
1.50
1.01
2.52
0.52
0.88
1.15
1.47
0.48
0.79
0.79
1.14
0.57
0.56
0.72
0.71
0.91
1.98
1.56
1.25
7
0.41
0.40
0.32
0.42
0.65
0.67
0.86
1.27
1.11
1.47
8
0.68
0.43
0.48
0.51
0.62
0.54
0.64
0.88
1.73
2.09
9
1.38
0.97
1.12
1.00
1.98
1.45
1.04
1.22
1.79
11.75
Note: Each cell contains the percentage of the price changes compared to the total number of price
changes (41,034). The top three highest transition probabilities on the matrix diagonal are indicated in
boldface.
Table 7. Top 25 Transition Probabilities Conditional on a Price Change for a 100-State Markov
Chain, Dominick’s Data, by Store, Regular Prices Only, for the Penny and Dime Digits
Current
Rank Ending
1
89
2
99
3
99
4
39
5
79
6
49
7
79
8
99
9
99
10
19
11
99
12
29
13
99
14
29
15
99
16
99
17
69
18
69
19
49
20
09
21
19
22
59
23
09
24
99
25
39
Store 8
Next
Ending
99
89
19
49
99
99
89
49
29
99
09
99
99
39
79
39
99
79
59
19
29
69
99
69
99
%
1.34
1.03
0.86
0.79
0.78
0.75
0.73
0.73
0.72
0.71
0.70
0.70
0.66
0.60
0.60
0.55
0.53
0.52
0.51
0.50
0.50
0.49
0.49
0.48
0.46
Current
Ending
89
99
79
79
99
99
59
99
49
99
99
99
49
29
39
19
29
59
99
69
69
09
19
99
99
Store 12
Next
Ending
99
89
99
89
19
49
99
29
99
59
79
99
59
99
49
99
39
69
09
99
79
19
29
39
69
%
1.09
0.86
0.83
0.71
0.70
0.69
0.68
0.68
0.67
0.64
0.63
0.61
0.59
0.58
0.56
0.55
0.54
0.52
0.52
0.50
0.49
0.48
0.45
0.43
0.42
Current
Ending
89
99
99
79
79
39
29
99
99
69
19
19
59
49
99
99
29
69
99
49
99
09
09
99
39
Store 122
Next
Ending
99
89
19
89
99
49
39
09
29
99
29
99
69
99
99
49
99
79
79
59
39
99
19
69
29
%
0.87
0.70
0.61
0.58
0.58
0.57
0.55
0.55
0.50
0.49
0.48
0.47
0.46
0.45
0.43
0.42
0.42
0.42
0.41
0.40
0.40
0.40
0.38
0.37
0.35
Current
Ending
89
39
79
99
79
99
99
99
29
49
49
29
19
59
19
69
99
99
69
09
99
29
59
94
99
Store 133
Next
Ending
99
49
89
19
99
29
89
09
39
99
59
99
29
69
99
99
49
99
79
19
79
49
99
99
69
%
0.82
0.65
0.62
0.61
0.60
0.60
0.60
0.54
0.53
0.50
0.48
0.47
0.45
0.45
0.44
0.44
0.44
0.43
0.42
0.41
0.39
0.36
0.35
0.33
0.32
26
Table 8. Top 25 Transition Probabilities Conditional on a Price Change
for a 100-State Markov Chain, Internet Dataset, for the Penny and Dime Digits (LHS) and
for the Dollar and $10 Digits (RHS)
Cents
Dollars
Current
Next
Current
Next
Rank
Ending
Ending
%
Ending
Ending
1
00
00
18.36
14
14
2
99
99
11.89
11
11
3
95
95
8.83
15
15
4
98
98
1.13
09
09
5
00
99
0.89
13
13
6
99
00
0.85
99
99
7
99
95
0.72
12
12
8
00
95
0.66
10
10
9
99
98
0.64
08
08
10
99
49
0.62
14
15
11
49
99
0.62
16
16
12
95
00
0.62
15
14
13
95
99
0.57
14
13
14
98
99
0.54
12
11
15
49
49
0.28
13
14
16
00
50
0.25
11
12
17
88
88
0.24
22
22
18
50
00
0.23
12
13
19
85
85
0.20
13
12
20
96
96
0.19
99
49
21
89
99
0.19
19
19
22
00
90
0.18
11
10
23
96
99
0.18
21
21
24
24
99
0.17
49
99
25
97
97
0.16
10
11
Note: Total number of price changes = 41,034
%
1.47
1.36
1.28
1.23
1.16
1.01
0.80
0.67
0.63
0.59
0.58
0.54
0.49
0.48
0.48
0.44
0.43
0.42
0.42
0.42
0.41
0.39
0.39
0.38
0.35
27
Table 9. Top 25 Transition Probabilities Conditional on a Price Change
for a 100-State Markov Chain, by Price Level, Internet Data, for the Penny and Dime
Digits (LHS) and for the Dollar and $10 Digits (RHS)
Low-Priced Categories
Current Next
%
Rank Ending Ending
1
99
99
16.32
2
98
98
1.80
3
95
95
1.75
4
99
98
1.19
5
49
99
1.04
6
98
99
0.97
7
99
49
0.95
8
96
96
0.50
9
24
99
0.45
10
99
24
0.42
11
96
99
0.40
12
89
99
0.37
13
88
88
0.37
14
99
95
0.34
15
99
19
0.33
16
82
82
0.28
17
99
89
0.27
18
19
99
0.26
19
95
99
0.26
20
99
39
0.25
21
99
29
0.25
22
49
59
0.24
23
49
49
0.22
24
09
95
0.21
25
59
69
0.21
Cents
High-Priced Categories
Current
Next
%
Ending
Ending
00
00
28.59
95
95
12.77
99
99
9.42
00
99
1.34
99
00
1.29
00
95
1.02
95
00
0.96
99
95
0.94
98
98
0.76
95
99
0.75
99
49
0.44
00
50
0.39
49
99
0.39
50
00
0.35
99
98
0.33
49
49
0.32
98
99
0.30
85
85
0.29
00
90
0.27
97
97
0.22
90
00
0.20
94
99
0.18
90
90
0.17
99
94
0.17
88
88
0.17
Dollars
Low-Priced Categories
High-Priced Categories
Current
Next
Current
Next
%
%
Ending
Ending
Ending
Ending
14
14
4.03
99
99
1.51
11
11
3.72
99
49
0.65
15
15
3.53
49
99
0.60
09
09
3.31
99
79
0.54
13
13
3.21
79
99
0.40
12
12
2.18
99
89
0.39
10
10
1.84
49
39
0.33
08
08
1.62
49
49
0.28
14
15
1.59
89
79
0.28
16
16
1.55
79
69
0.28
15
14
1.40
39
29
0.27
13
14
1.26
49
29
0.25
14
13
1.25
29
99
0.25
12
11
1.17
99
69
0.25
11
12
1.16
99
94
0.24
22
22
1.15
59
49
0.23
12
13
1.12
99
98
0.23
13
12
1.06
79
49
0.22
19
19
1.06
19
99
0.22
21
21
1.01
69
59
0.21
11
10
0.94
89
99
0.21
10
11
0.90
99
29
0.20
23
23
0.84
29
19
0.20
16
17
0.78
09
99
0.20
17
16
0.74
19
09
0.18
Note: Low-priced categories include CDs, DVDs, and Video Games. High-priced categories include Computer Monitors,
Digital Cameras, DVD Players, Hard Drives, Laptop Computers, PDAs, and Software.
28
Table 10. Results of the Logit Regression (Equation 1) Estimation
for the Dominick’s Data, Regular Prices, Stores #8, #12, #122 and #133
9¢-Ending
(9-Ending9 = 1)
Category
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Average
99¢-Ending
(9-Ending99 = 1)
Coefficient
Odds Ratio
Coefficient
Odds Ratio
 1.4820
 1.6871
 0.4763
 0.7232
 0.4553
 0.7692
 0.5013
 1.7457
 2.1156
 1.8639
 1.0433
 0.6951
 0.8917
 1.3773
 1.1704
 0.3795
 2.2234
 1.5275
 1.0142
 0.6164
 0.8902
 2.1695
 1.9320
 1.6669
 3.1645
 0.9833
 0.6796
0.23
0.19
0.62
0.49
0.63
0.46
0.61
0.17
0.12
0.16
0.35
0.50
0.41
0.25
0.31
0.68
0.11
0.22
0.36
0.54
0.41
0.11
0.14
0.19
0.04
0.37
0.51
0.34
 0.3599
 0.7683
 0.0353
 0.4984
 0.6055
 0.5518
 0.3582
 1.1008
 1.1052
 0.9784
 0.7082
 0.3909
 1.5532
 0.6168
 0.6649
 0.0395
 0.6918
 0.5607
 0.2450
 0.7879
 0.4119
 0.3264
 0.8181
 0.6347
 0.6425
 0.5719
 0.6291
0.70
0.46
0.97
0.61
0.55
0.58
0.70
0.33
0.33
0.38
0.49
0.68
0.21
0.54
0.51
0.96
0.50
0.57
0.78
0.45
0.66
0.72
0.44
0.53
0.53
0.56
0.53
0.57
Note: 9-Endingj are dummy variables, which equal 1 if the price ends with 9 or 99, and 0 otherwise.
All p-values < 0.0001, except for the coefficients formatted in italic (Bathroom Tissues and Frozen
Juices, for 99¢-ending dummy), for which p > .10. The average odds ratios reported in the last row of
the table are the simple averages of the odds ratios for each product category.
29
Table 11. Results of Logit Regression (Equation 1) Estimation for the Internet Dataset
9¢Endings
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
99¢Endings
-0.0727***
(0.9299)
-0.4716***
(0.6240)
0.1630***
(1.1770)
-0.3185***
(0.7272)
-0.1496***
(0.8611)
-0.2276***
(0.7964)
-0.5161***
(0.5968)
-0.1893***
(0.8275)
-0.3634***
(0.6953)
-0.3583***
(0.6989)
-0.2800***
(0.7558)
-0.5463***
(0.5791)
-0.5827***
(0.5584)
0.0729***
(1.0756)
-0.4998***
(0.6067)
-0.2253***
(0.7983)
-0.2777***
(0.7575)
-0.5808***
(0.5595)
-0.3734***
(0.6884)
-0.4199***
(0.6571)
-0.5335***
(0.5865)
-0.4330***
(0.6486)
$9Endings
-0.0125***
(0.9876)
-0.3551***
(0.7011)
-0.3572***
(0.6996)
-0.5892***
(0.5548)
-0.4370***
(0.6460)
-0.3368***
(0.7141)
-0.7455***
(0.4745)
-0.5445***
(0.5801)
-0.4464***
(0.6339)
-0.7383***
(0. 4779)
-0.4378***
(0.6455)
$99Endings
-1.0831***
(0.3385)
-0.5944***
(0.5519)
-0.3242***
(0.7231)
-0.5246***
(0. 5918)
-0.7598***
(0.4678)
-0.9363***
(0.3921)
-0.5533***
(0. 5750)
-0.7787***
(0.4590)
$9.99Endings
$99.99Endings
-0.4430***
(0.6421)
-0.9068***
(0.4038)
-0.2807***
(0.7553)
-0.8032***
(0.4479)
-0.4041***
(0.6676)
-0.5197***
(0.5947)
-0.6718***
(0.5108)
-0.7457***
(0.4744)
-0.5052***
(0.6034)
-0.7014***
(0.4959)
-0. 5841***
(0.5576)
-1.4014***
(0.2463)
-0.8986***
(0.4071)
-0. 6072***
(0. 5449)
-0.6074***
(0.5448)
-1.3102***
(0.2698)
-1.1454***
(0.3181)
-0.7149***
(0.4892)
-1.0201***
(0.3606)
Note: Each cell contains a coefficient and odds ratio in parenthesis; significance levels: *** < 0.01, ** < 0.05, * <
0.10. The estimated coefficients in italics indicate unsupportive results.
Table 12. Comparing Average Size of Price Change Between 9- and Non-9-Ending Prices:
for Dominick’s (Regular Prices; Stores #8, #12, #122 and #133) and for the Internet
Low Quartile of Products in Terms of
Popularity of 9-Ending Prices
All Products
9-Endings
Non-9Endings
t-Stat
p-Value
9-Endings
Non-9Endings
t-Stat
p-Value
9¢
99¢
$0.75
$0.91
$0.40
$0.55
934.87
721.24
.000
.000
$0.38
$0.49
$0.33
$0.34
27.61
53.64
.000
.000
9¢
99¢
$9
$9.99
$99
$99.99
$15.54
$22.40
$32.13
$33.97
$66.15
$63.04
$18.07
$16.78
$12.83
$16.30
$15.20
$16.88
-4.50
5.55
33.65
17.34
42.89
19.93
.000
.000
.000
.000
.000
.000
$24.02
$27.78
$11.93
$22.47
$49.61
$38.24
$21.03
$20.76
$7.21
$7.38
$18.27
$19.21
2.75
4.56
5.67
5.99
8.56
4.78
.006
.000
.000
.000
.000
.000
Dominick’s
Internet
30
Figure 1. Frequency Distribution of the Last Digit
in the Dominick’s Data, Regular Prices, Stores #8, #12, #122 and #133
Figure 2. Frequency Distribution of the Last Two Digits
in the Dominick’s Data, Regular Prices; Stores #8, #12, #122 and #133
31
Figure 3. Frequency Distribution of the Last Digit in the Internet Data
Figure 4. Frequency Distribution of the Last Two Digits in the Internet Data
32
Figure 5. Frequency Distribution of the Last Dollar Digit in the Internet Data
Figure 6. Frequency Distribution of the Last Two Dollar Digits in the Internet Data
1
Price Points and Price Rigidity: Reviewer’s Appendix
Last revised: April 29, 2010
______________________________________________________________________________
A. Detailed Results on Price Endings
Similar to the aggregate results reported in the paper, the following figures show that 9¢
and 99¢ are the most popular price-endings for each of the four stores in the Dominick’s dataset
and most of the individual product categories in both the Dominick’s and the Internet dataset.
 Figure R1a. Frequency Distribution of the Last Digit of Regular Prices – for the
Dominick’s Dataset, by Store
 Figures R1b–R1d. Frequency Distribution of the Last Digit – for the Dominick’s Dataset,
by Product Category
 Figure R2a. Frequency Distribution of the Last Two Digits of Regular Prices – for the
Dominick’s Dataset, by Store
 Figures R2b–R2d. Frequency Distribution of the Last Two Digits – for the Dominick’s
Dataset, by Product Category
 Figure R3. Frequency Distribution of the Last Digit – for the Internet Dataset, by Product
Category
 Figure R4. Frequency Distribution of the Last Two Digits – for the Internet Dataset, by
Product Category
 Figure R5. Frequency Distribution of the Last Dollar Digit – for the Internet Dataset, by
Product Category
 Figure R6. Frequency Distribution of the Last Two Dollar Digits – for the Internet Dataset,
by Product Category
B. Results on Price Endings by Sales Volume
The results in the following table show the popularity of 9-ending prices for both
products that had a large sales volume and products that had a small sales volume.
 Table R0. Popularity of 9-Ending Prices - for the Dominick’s Dataset, for the Low and
High Quartile of Products in Terms of Sales Volume
C. Detailed Results from Markov-Chain Analyses
Similar to the aggregate results reported in the paper, the following tables show that for
regular prices in each of the four stores for the Dominick’s dataset, as well as for all stores
combined and all prices, “9” to “9” was the most popular price change. While “99” to “99” is not
the most popular price change for any of the four stores, similar to the aggregate results reported
in the paper, it is the most popular price change when all prices from all stores are analyzed
together.
2
 Tables R1a–R1d. Transition Probabilities Conditional on a Price Change from a 10-State
Markov Chain Analysis – for the Dominick’s Dataset, by Store, Regular Prices Only, in
Cents
 Table R1e. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Dominick’s Dataset, in Cents
 Table R1f. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Dominick’s Dataset, Stores #8, #12, #122 and #133, Regular
Prices Only, in Cents, for the Low Quartile of Products in Terms of the Prevalence of 9Ending Prices
 Table R1g–R1j. Transition Probabilities Conditional on a Price Change from a 10-State
Markov Chain Analysis – for the Dominick’s Dataset, by Store, Regular Prices Only, in
Cents, for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
 Table R1k. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Internet Dataset, in Cents
 Table R1l. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Internet Dataset, in Dollars
 Table R1m. Transition Probabilities Conditional on a Price Change from a 10-State
Markov Chain Analysis – for the Internet Dataset, Low Priced Product Categories, in Cent
 Table R1n. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Internet Dataset, High Priced Product Categories, in Cent
 Table R1o. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Internet Dataset, Low Priced Product Categories, in Dollar
 Table R1p. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Internet Dataset, Low Priced Product Categories, in Dollar
 Table R2a. Top 50 Transition Probabilities Conditional on a Price Change from a 100State Markov Chain Analysis – for the Dominick’s Dataset, by Store, Regular Prices Only,
in Cents
 Table R2b. Top 50 Transition Probabilities Conditional on a Price Change from a 100State Markov Chain Analysis – for the Dominick’s Dataset, in Cents
 Table R2c. Top 50 Transition Probabilities Conditional on a Price Change from a 100State Markov Chain Analysis – for the Dominick’s Dataset, Stores #8, #12, #122 and #133,
Regular Prices Only, in Cents, for the Low Quartile of Products in Terms of the Prevalence
of 9-Ending Prices
 Table R2d. Top 50 Transition Probabilities Conditional on a Price Change from a 100State Markov Chain Analysis – for the Dominick’s Dataset, by Store, Regular Prices Only,
in Cents, for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
 Table R2e. Top 50 Transition Probabilities Conditional on a Price Change from a 100State Markov Chain Analysis – for the Internet Dataset
 Table R2f. Top 50 Transition Probabilities by Price Level Conditional on a Price Change
from a 100-State Markov Chain Analysis – for the Internet Dataset
Taking stock of the results from the Markov-chain analyses, in the following figures we
show that price changes in multiples of dimes are most common among all price changes in the
Dominick’s dataset. The following tables report in detail the proportion of 9-ending-preserving
3
price changes, that is, price changes of 10¢, $1, $10, $100, etc. For the Dominick's dataset, in all
but one category (Front-End Candies), there were considerably more price changes that were
multiples of dimes and dollars for 9-ending prices. For the Internet dataset, in the low-priced
product categories (Music CDs, Movie DVDs, Video Games), we found considerably more price
changes that were multiples of dimes and dollars for 9-ending prices. For high-priced product
categories (DVD Players, PC Monitors, Digital Cameras, Notebook PCs), we found more price
changes that were multiples of $10 and $100 for 9-ending prices.
 Figures R7a–R7c. Frequency Distribution of the Price Changes by Category – for the
Dominick’s
 Table R3. Price Changes in Multiples of Dimes in the Dominick’s Dataset: 9¢-Ending vs.
Non-9¢-Ending Prices
 Table R4: Price Changes in Multiples of Dollars in the Dominick’s Dataset: 99¢-Ending vs.
Non-99¢-Ending Prices
 Table R5. Price Changes in Multiples of Dimes in the Internet Dataset: 9¢-Endings vs.
Non-9¢-Endings
 Table R6. Price Changes in Multiples of Dollars in the Internet Dataset: 99¢-Endings vs.
Non-99¢-Endings
 Table R7. Price Changes in Multiples of $10 in the Internet Dataset: $9-Endings vs. Non$9-Endings
 Table R8. Price Changes in Multiples of $10 in the Internet Dataset: $9.99-Endings vs.
Non-$9.99-Endings
 Table R9. Price Changes in Multiples of $100 in the Internet Dataset: $99-Endings vs.
Non-$99-Endings
 Table R10. Price Changes in Multiples of $100 in the Internet Dataset: $99.99-Endings vs.
Non-$99.99-Endings
D. Detailed Results on Price Rigidity
 Tables R11a–R11e. Results of the Logit Regression (Equation 1) Estimation with Product
Fixed Effects – for the Dominick’s Dataset, by Store, and for the entire chain
E. Detailed Results on the Size of Price Change
Similar to the aggregate results reported in the paper, the following tables show that the
average price change was larger for 9- and 99-ending prices for most of the product categories in
each of the four stores in the Dominick’s dataset. This is especially true for all stores combined,
when we focused on the low quartile of the products in terms of 9-ending popularity, and for 9¢,
$9, $9.99 and $99.99-ending prices for each of the product categories when we focuses on the
low quartile of the products in terms of 9-ending popularity. It is also true when we included all
of our Internet dataset.
4
 Table R12. Average Price Change for 9- and Non-9-Ending Prices – for the Dominick’s
Dataset, Stores #8, #12, #122 and #133, for the Low Quartile of the Products in Terms of
9-Ending Popularity
 Table R13. Average Price Change for 99- and Non-99-Ending Prices – for the Dominick’s
Dataset, Stores #8, #12, #122 and 3133, for the Low Quartile of the Products in Terms of
9-Ending Popularity
 Tables R14–R19. Average Price Change for 9- and Non-9-Ending Prices – for the Internet
Dataset, for the Low Quartile of the Products In Terms of 9-Ending Popularity by Product
Category
 Tables R20–R21. Average Price Change for 9- and Non-9-Ending Prices – for the
Dominick’s Dataset
 Tables R22–R27. Average Price Change for 9- and Non-9-Ending Prices by Product
Category – for the Internet Dataset
F. Sample Price Series for the Internet Dataset
The following figures provide sample price series for ten randomly-selected products,
one from each of the ten product categories in our Internet dataset. All data are for 743 days,
from March 26, 2005 to April 15, 2005.










Figure R8a. Price of a Music CD (Product #3, Store #194)
Figure R8b. Price of a Movie DVD (Product #23, Store #194)
Figure R8c. Price of a Notebook PC (Product #422, Store #258)
Figure R8d. Price of a Hard Drive (Product #71, Store #324)
Figure R8e. Price of a DVD Player (Product #262, Store #230)
Figure R8f. Price of a Digital Camera (Product #273, Store #108)
Figure R8g. Price of a PC Monitor (Product #189, Store #17)
Figure R8h. Price of a PDA (Product #490, Store #207)
Figure R8i. Price of a Software Product (Product #96, Store #292)
Figure R8j. Price of a Video Game (Product #205, Store #68)
5
Figure R1a. Frequency Distribution of the Last Digit of Regular Prices
– for the Dominick’s Dataset, by Store
Store 12
Store 8
80
Percentage of Price Ending (%)
Percentage of Price Ending (%)
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
0
1
2
3
4
5
6
Price Ending in Cent (¢)
7
8
0
9
1
2
3
4
5
6
Price Ending in Cent (¢)
7
8
9
7
8
9
Store 133
Store 122
80
Percentage of Price Ending (%)
Percentage of Price Ending (%)
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
0
1
2
3
4
5
6
Price Ending in Cent (¢)
7
8
9
0
1
2
3
4
5
6
Price Ending in Cent (¢)
6
Figure R1b. Frequency Distribution of the Last Digit
– for the Dominick’s Dataset, by Product Category
90
90
Analgesics
Bath Soap
80
Percentage of Price Ending (%)
Percentage of Price Ending (%)
80
70
60
50
40
30
20
10
70
60
50
40
30
20
10
0
0
0
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
100
Bathroom Tissues
4
5
6
7
8
9
7
8
9
7
8
9
7
8
9
7
8
9
Beer
90
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
3
Price Ending in Cents (¢)
50
40
30
20
10
80
70
60
50
40
30
20
10
0
0
0
1
2
3
4
5
6
7
8
0
9
1
2
Price Ending in Cents (¢)
35
Bottled Juices
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
50
40
30
20
10
0
5
6
Canned Soup
30
25
20
15
10
5
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
50
3
4
5
6
Price Ending in Cents (¢)
40
Canned Tuna
Percentage of Price Ending (%)
45
Percentage of Price Ending (%)
4
0
0
40
35
30
25
20
15
10
Cereals
35
30
25
20
15
10
5
5
0
0
0
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
70
3
4
5
6
Price Ending in Cents (¢)
25
Cheeses
60
Percentage of Price Ending (%)
Percentage of Price Ending (%)
3
Price Ending in Cents (¢)
50
40
30
20
10
0
Cigarettes
20
15
10
5
0
0
1
2
3
4
5
6
Price Ending in Cents (¢)
7
8
9
0
1
2
3
4
5
6
Price Ending in Cents (¢)
7
Figure R1c. Frequency Distribution of the Last Digit
– for the Dominick’s Dataset, by Product Category
70
Cookies
70
Percentage of Price Ending (%)
Percentage of Price Ending (%)
80
60
50
40
30
20
10
0
Crackers
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
60
Dish Detergent
60
Percentage of Price Ending (%)
Percentage of Price Ending (%)
70
50
40
30
20
10
0
5
6
7
8
9
7
8
9
7
8
9
7
8
9
7
8
9
Fabric Softeners
50
40
30
20
10
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
40
3
4
5
6
Price Ending in Cents (¢)
60
Front-End-Candies
35
Percentage of Price Ending (%)
Percentage of Price Ending (%)
4
0
0
30
25
20
15
10
5
0
Frozen Dinners
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
60
3
4
5
6
Price Ending in Cents (¢)
50
Frozen Entrees
Frozen Juices
45
Percentage of Price Ending (%)
Percentage of Price Ending (%)
3
Price Ending in Cents (¢)
50
40
30
20
10
40
35
30
25
20
15
10
5
0
0
0
1
2
3
4
5
6
7
8
0
9
1
2
Price Ending in Cents (¢)
100
Percentage of Price Ending (%)
Percentage of Price Ending (%)
80
Grooming Products
90
3
4
5
6
Price Ending in Cents (¢)
80
70
60
50
40
30
20
Laundry Detergents
70
60
50
40
30
20
10
10
0
0
0
1
2
3
4
5
6
Price Ending in Cents (¢)
7
8
9
0
1
2
3
4
5
6
Price Ending in Cents (¢)
8
Figure R1d. Frequency Distribution of the Last Digit
– for the Dominick’s Dataset, by Product Category
60
Oatmeal
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
50
40
30
20
10
0
Paper Towels
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
100
Refrigerated Juices
4
5
6
7
8
9
7
8
9
7
8
9
7
8
9
Shampoos
90
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
3
Price Ending in Cents (¢)
50
40
30
20
10
80
70
60
50
40
30
20
10
0
0
0
1
2
3
4
5
6
7
8
0
9
1
2
Price Ending in Cents (¢)
70
Snack Crackers
70
Percentage of Price Ending (%)
Percentage of Price Ending (%)
80
60
50
40
30
20
10
0
5
6
Soaps
60
50
40
30
20
10
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
90
3
4
5
6
Price Ending in Cents (¢)
80
Soft Drinks
Percentage of Price Ending (%)
80
Percentage of Price Ending (%)
4
0
0
70
60
50
40
30
20
Toothbrushes
70
60
50
40
30
20
10
10
0
0
0
1
2
3
4
5
6
7
8
9
Price Ending in Cents (¢)
70
Percentage of Price Ending (%)
3
Price Ending in Cents (¢)
Toothpastes
50
40
30
20
10
0
1
2
3
4
5
6
Price Ending in Cents (¢)
1
2
3
4
5
6
Price Ending in Cents (¢)
60
0
0
7
8
9
9
Figure R2a. Frequency Distribution of the Last Two Digits of Regular Prices
– for the Dominick’s Dataset, by Store
Store 12
Store 8
16
Percentage of Price Ending (%)
Percentage of Price Ending (%)
16
14
12
10
8
6
4
2
14
12
10
8
6
4
2
0
0
0
10
20
30
40
50
60
Price Ending in Cent (¢)
70
80
0
90
10
20
30
70
80
90
70
80
90
Store 133
Store 122
18
Percentage of Price Ending (%)
16
Percentage of Price Ending (%)
40
50
60
Price Ending in Cent (¢)
14
12
10
8
6
4
2
16
14
12
10
8
6
4
2
0
0
0
10
20
30
40
50
60
Price Ending in Cent (¢)
70
80
90
0
10
20
30
40
50
60
Price Ending in Cent (¢)
10
Figure R2b. Frequency Distribution of the Last Two Digits
- for the Dominick’s Dataset, by Product Category
25
Analgesics
Percentage of Price Ending (%)
Percentage of Price Ending (%)
25
20
15
10
5
0
Bath Soap
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
0
10
20
30
Price Ending in Cents (¢)
50
Bathroom Tissues
Percentage of Price Ending (%)
Percentage of Price Ending (%)
12
40
50
60
70
80
90
70
80
90
70
80
90
70
80
90
70
80
90
Price Ending in Cents (¢)
10
8
6
4
2
Beer
45
40
35
30
25
20
15
10
5
0
0
0
10
20
30
40
50
60
70
80
0
90
10
20
30
Price Ending in Cents (¢)
6
Bottled Juices
Percentage of Price Ending (%)
Percentage of Price Ending (%)
10
8
6
4
2
0
60
Canned Soup
5
4
3
2
1
10
20
30
40
50
60
70
80
90
0
10
20
Price Ending in Cents (¢)
7
30
40
50
60
Price Ending in Cents (¢)
7
Canned Tuna
Percentage of Price Ending (%)
Percentage of Price Ending (%)
50
0
0
6
5
4
3
2
1
0
Cereals
6
5
4
3
2
1
0
0
10
20
30
40
50
60
70
80
90
0
10
20
Price Ending in Cents (¢)
14
30
40
50
60
Price Ending in Cents (¢)
6
Cheeses
Percentage of Price Ending (%)
Percentage of Price Ending (%)
40
Price Ending in Cents (¢)
12
10
8
6
4
2
0
Cigarettes
5
4
3
2
1
0
0
10
20
30
40
50
60
Price Ending in Cents (¢)
70
80
90
0
10
20
30
40
50
60
Price Ending in Cents (¢)
11
Figure R2c. Frequency Distribution of the Last Two Digits
– for the Dominick’s Dataset, by Product Category
15
Cookies
Percentage of Price Ending (%)
Percentage of Price Ending (%)
18
15
12
9
6
3
Crackers
12
9
6
3
0
0
0
10
20
30
40
50
60
70
80
90
0
10
20
30
Price Ending in Cents (¢)
15
Dish Detergent
Percentage of Price Ending (%)
Percentage of Price Ending (%)
15
12
9
6
3
0
10
20
15
30
40
50
60
70
80
70
80
90
70
80
90
70
80
90
70
80
90
70
80
90
Fabric Softeners
9
6
3
90
0
10
20
30
40
50
60
Price Ending in Cents (¢)
15
Front-End-Candies
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
12
Price Ending in Cents (¢)
12
9
6
3
0
Frozen Dinners
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90
0
10
20
30
Price Ending in Cents (¢)
12
40
50
60
Price Ending in Cents (¢)
8
Frozen Entrees
Percentage of Price Ending (%)
Percentage of Price Ending (%)
50
0
0
10
8
6
4
2
0
Frozen Juices
7
6
5
4
3
2
1
0
0
10
20
30
40
50
60
70
80
0
90
10
20
Price Ending in Cents (¢)
25
30
40
50
60
Price Ending in Cents (¢)
25
Grooming Products
Percentage of Price Ending (%)
Percentage of Price Ending (%)
40
Price Ending in Cents (¢)
20
15
10
5
0
Laundry Detergents
20
15
10
5
0
0
10
20
30
40
50
60
Price Ending in Cents (¢)
70
80
90
0
10
20
30
40
50
60
Price Ending in Cents (¢)
12
Figure R2d. Frequency Distribution of the Last Two Digits
for the Dominick’s Dataset, by Product Category
10
Oatmeal
Percentage of Price Ending (%)
Percentage of Price Ending (%)
12
10
8
6
4
2
0
Paper Towels
8
6
4
2
0
0
10
20
30
40
50
60
70
80
0
90
10
20
Price Ending in Cents (¢)
25
Refrigerated Juices
10
8
6
4
2
0
10
20
15
30
40
50
60
70
80
70
80
90
70
80
90
70
80
90
70
80
90
Shampoos
15
10
5
0
90
10
20
30
40
50
60
Price Ending in Cents (¢)
15
Snack Crackers
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
20
Price Ending in Cents (¢)
12
9
6
3
0
Soaps
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90
0
10
20
Price Ending in Cents (¢)
30
30
40
50
60
Price Ending in Cents (¢)
25
Soft Drinks
Percentage of Price Ending (%)
Percentage of Price Ending (%)
50
0
0
25
20
15
10
5
0
Toothbrushes
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
Price Ending in Cents (¢)
18
Percentage of Price Ending (%)
40
Price Ending in Cents (¢)
Percentage of Price Ending (%)
Percentage of Price Ending (%)
12
30
Toothpastes
12
9
6
3
0
10
20
30
40
50
60
Price Ending in Cents (¢)
10
20
30
40
50
60
Price Ending in Cents (¢)
15
0
0
70
80
90
13
Figure R3. Frequency Distribution of the Last Digit for the Internet Dataset, by Product Category
50
Music CDs
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
50
40
30
20
10
0
Movie DVDs
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Cents (¢)
40
Video Games
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
50
40
30
20
10
0
1
2
3
50
4
5
6
7
8
6
7
8
9
7
8
9
7
8
9
7
8
9
7
8
9
30
20
10
0
9
1
2
3
4
5
6
Price Ending In Cents (¢)
30
PDAs
Percentage of Price Ending (%)
Percentage of Price Ending (%)
5
Software
Price Ending in Cents (¢)
40
30
20
10
0
Hard Drives
20
10
0
0
1
2
3
4
5
6
7
8
9
0
1
2
40
DVD Players
Percentage of Price Ending (%)
30
20
10
0
0
1
2
3
4
5
6
3
4
5
6
Price Ending in Cents (¢)
Price Ending in Cents (¢)
Percentage of Price Ending (%)
4
0
0
7
8
PC Monitors
30
20
10
0
9
0
1
2
Price Ending in Cents (¢)
60
Digital Cameras/Camcorders
40
Percentage of Price Ending (%)
Percentage of Price Ending (%)
3
Price Ending in Cents (¢)
30
20
10
0
3
4
5
6
Price Ending in Cents (¢)
Notebook PCs
50
40
30
20
10
0
0
1
2
3
4
5
6
Price Ending in Cents (¢)
7
8
9
0
1
2
3
4
5
6
Price Ending in Cents (¢)
14
Figure R4. Frequency Distribution of the Last Two Digits
– for the Internet Dataset, by Product Category
35
Music CDs
30
Percentage of Price Ending (%)
Percentage of Price Ending (%)
35
25
20
15
10
5
0
Movie DVDs
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
0
10
20
Price Ending in Cents (¢)
35
Video Games
50
40
30
20
10
0
10
20
30
40
40
50
60
70
80
70
80
90
70
80
90
70
80
90
70
80
90
70
80
90
Software
25
20
15
10
5
0
90
10
20
30
40
50
60
Price Ending in Cents (¢)
25
PDAs
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
30
Price Ending in Cents (¢)
30
20
10
0
Hard Drives
20
15
10
5
0
0
10
20
30
40
50
60
70
80
0
90
10
20
35
30
40
50
60
Price Ending in Cents (¢)
Price Ending in Cents (¢)
35
DVD Players
Percentage of Price Ending (%)
Percentage of Price Ending (%)
50
0
0
30
25
20
15
10
5
PC Monitors
30
25
20
15
10
5
0
0
0
10
20
30
40
50
60
70
80
0
90
10
20
Price Ending in Cents (¢)
40
30
40
50
60
Price Ending in Cents (¢)
60
Digital Cameras/Camcorders
35
Percentage of Price Ending (%)
Percentage of Price Ending (%)
40
Price Ending in Cents (¢)
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
30
30
25
20
15
10
5
0
Notebook PCs
50
40
30
20
10
0
0
10
20
30
40
50
60
Price Ending in Cents (¢)
70
80
90
0
10
20
30
40
50
60
Price Ending in Cents (¢)
15
Figure R5. Frequency Distribution of the Last Dollar Digit
– for the Internet Dataset, by Product Category
16
Music CDs
Percentage of Price Ending (%)
Percentage of Price Ending (%)
25
20
15
10
5
0
Movie DVDs
12
8
4
0
0
1
2
3
4
5
6
7
8
0
9
1
2
40
Video Games
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
50
40
30
20
10
0
1
2
3
60
4
5
6
7
8
6
7
8
9
7
8
9
7
8
9
7
8
9
7
8
9
30
20
10
0
9
1
2
3
4
5
6
Price Ending in Dollars ($)
25
PDAs
Percentage of Price Ending (%)
Percentage of Price Ending (%)
5
Software
Price Ending in Dollars ($)
50
40
30
20
10
0
Hard Drives
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9
0
1
2
60
3
4
5
6
Price Ending in Dollars ($)
Price Ending in Dollars ($)
40
DVD Players
Percentage of Price Ending (%)
Percentage of Price Ending (%)
4
0
0
50
40
30
20
10
0
PC Monitors
30
20
10
0
0
1
2
3
4
5
6
7
8
9
0
1
2
Price Ending in Dollars ($)
60
3
4
5
6
Price Ending in Dollars ($)
80
Digital Cameras/Camcorders
Percentage of Price Ending (%)
Percentage of Price Ending (%)
3
Price Ending in Dollars ($)
Price Ending in Dollars ($)
50
40
30
20
10
0
Notebook PCs
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Price Ending in Dollars ($)
7
8
9
0
1
2
3
4
5
6
Price Ending in Dollars ($)
16
Figure R6. Frequency Distribution of the Last Two Dollar Digits
– for the Internet Dataset, by Product Category
10
Music CDs
Percentage of Price Ending (%)
Percentage of Price Ending (%)
25
20
15
10
5
Movie DVDs
8
6
4
2
0
0
0
10
20
30
40
50
60
70
80
0
90
10
20
15
12
9
6
3
0
10
20
30
15
40
50
60
70
80
70
80
90
80
90
80
90
80
90
80
90
9
6
3
90
0
10
20
30
40
50
60
70
Price Ending in Dollars ($)
4
PDAs
Percentage of Price Ending (%)
Percentage of Price Ending (%)
60
Software
Price Ending in Dollars ($)
12
9
6
3
0
Hard Drives
3
2
1
0
0
10
20
30
40
50
60
70
80
90
0
10
20
Price Ending in Dollars ($)
15
30
40
50
60
70
Price Ending in Dollars ($)
12
DVD Players
Percentage of Price Ending (%)
Percentage of Price Ending (%)
50
0
0
12
9
6
3
0
PC Monitors
9
6
3
0
0
10
20
30
40
50
60
70
80
0
90
10
20
35
30
40
50
60
70
Price Ending in Dollars ($)
Price Ending in Dollars ($)
40
Digital Cameras/Camcorders
Percentage of Price Ending (%)
Percentage of Price Ending (%)
40
12
Video Games
Percentage of Price Ending (%)
Percentage of Price Ending (%)
18
30
Price Ending in Dollars ($)
Price Ending in Dollars ($)
30
25
20
15
10
5
Notebook PCs
35
30
25
20
15
10
5
0
0
0
10
20
30
40
50
60
70
Price Ending in Dollars ($)
80
90
0
10
20
30
40
50
60
70
Price Ending in Dollars ($)
17
Figure R7a. Frequency Distribution of the Price Changes
– for the Dominick’s Dataset, by Category
14
Analgesics
Percentage of Price Change (%)
Percentage of Price Change (%)
12
10
8
6
4
2
0
Bath Soap
12
10
8
6
4
2
0
0
10
20
30
40
50
0
10
Price Change in Cents (¢)
35
Bathroom Tissues
Percentage of Price Change (%)
Percentage of Price Change (%)
12
10
8
6
4
2
0
40
50
40
50
40
50
Beer
30
25
20
15
10
5
10
20
30
40
50
0
10
Price Change in Cents (¢)
7
20
30
Price Change in Cents (¢)
12
Bottled Juices
6
Percentage of Price Change (%)
Percentage of Price Change (%)
30
0
0
5
4
3
2
1
0
Canned Soup
10
8
6
4
2
0
0
10
20
30
40
50
0
10
Price Change in Cents (¢)
10
20
30
Price Change in Cents (¢)
8
Canned Tuna
Percentage of Price Change (%)
Percentage of Price Change (%)
20
Price Change in Cents (¢)
8
6
4
2
Cereals
7
6
5
4
3
2
1
0
0
0
10
20
12
40
50
0
10
20
10
8
6
4
2
0
30
Price Change in Cents (¢)
10
Cheeses
Percentage of Price Change (%)
Percentage of Price Change (%)
30
Price Change in Cents (¢)
40
50
40
50
Cigarettes
8
6
4
2
0
0
10
20
30
Price Change in Cents (¢)
40
50
0
10
20
30
Price Change in Cents (¢)
18
Figure R7b. Frequency Distribution of the Price Changes
– for the Dominick’s Dataset, by Category
12
Cookies
Percentage of Price Change (%)
Percentage of Price Change (%)
12
10
8
6
4
2
0
10
20
40
6
4
2
50
0
10
20
12
10
8
6
4
2
0
30
40
Price Change in Cents (¢)
14
Dish Detergent
Percentage of Price Change (%)
Percentage of Price Change (%)
30
Price Change in Cents (¢)
14
50
Fabric Softeners
12
10
8
6
4
2
0
0
10
20
30
Price Change in Cents (¢)
14
40
50
0
10
20
10
8
6
4
2
0
30
40
50
40
50
40
50
Price Change in Cents (¢)
6
Front-End-Candies
12
Percentage of Price Change (%)
Percentage of Price Change (%)
8
0
0
Frozen Dinners
5
4
3
2
1
0
0
10
20
30
Price Change in Cents (¢)
8
40
0
50
10
20
6
5
4
3
2
30
Price Change in Cents (¢)
12
Frozen Entrees
7
Percentage of Price Change (%)
Percentage of Price Change (%)
Crackers
10
Frozen Juices
10
8
6
4
2
1
0
0
0
10
20
15
40
50
0
10
20
12
9
6
3
0
30
Price Change in Cents (¢)
10
Grooming Products
Percentage of Price Change (%)
Percentage of Price Change (%)
30
Price Change in Cents (¢)
Laundry Detergents
8
6
4
2
0
0
10
20
30
Price Change in Cents (¢)
40
50
0
10
20
30
Price Change in Cents (¢)
40
50
19
Figure R7c. Frequency Distribution of the Price Changes
– for the Dominick’s Dataset, by Category
12
Oatmeal
Percentage of Price Change (%)
Percentage of Price Change (%)
12
10
8
6
4
2
0
8
6
4
2
0
0
10
20
30
Price Change in Cents (¢)
8
40
50
0
10
20
6
5
4
3
2
30
Price Change in Cents (¢)
18
Refrigerated Juices
7
Percentage of Price Change (%)
Percentage of Price Change (%)
Paper Towels
10
40
50
40
50
40
50
40
50
Shampoos
15
12
9
6
3
1
0
0
0
10
20
10
40
0
50
8
6
4
2
0
10
20
30
Price Change in Cents (¢)
18
40
30
Soaps
8
6
4
2
50
0
10
20
15
12
9
6
3
0
30
Price Change in Cents (¢)
12
Soft Drinks
Percentage of Price Change (%)
Percentage of Price Change (%)
20
Price Change in Cents (¢)
0
0
Toothbrushes
10
8
6
4
2
0
0
10
20
30
Price Change in Cents (¢)
10
Percentage of Price Change (%)
10
10
Snack Crackers
Percentage of Price Change (%)
Percentage of Price Change (%)
30
Price Change in Cents (¢)
40
50
40
50
Toothpastes
8
6
4
2
0
0
10
20
30
Price Change in Cents (¢)
0
10
20
30
Price Change in Cents (¢)
20
Table R0. Popularity of 9-Ending Prices – for the Dominick’s Data Set,
for Low and High Quartile of Products with Respect to Sales Volume
Category
Analgesics
Bath Soap
Bathroom Tissue
Beer
Bottled Juice
Canned Soup
Canned Tuna
Cereals
Cheeses
Cigarettes
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Toothbrushes
Toothpastes
Total
Low Quartile
9-Ending
99-Ending
Rank
%
Rank
%
1
78.69
1
26.63
1
66.35
1
23.79
1
78.53
1
35.87
1
99.20
1
52.04
1
65.94
1
11.67
1
53.65
7
4.79
1
66.12
2
10.25
2
29.55
6
5.49
1
72.34
2
11.17
1
24.39
1
9.19
1
76.27
1
13.28
1
73.03
1
14.74
1
81.81
1
26.67
1
75.80
1
20.58
1
59.49
7
6.10
1
80.37
1
23.61
1
86.70
1
34.13
1
59.25
4
7.91
1
85.99
1
22.35
1
82.01
1
29.15
1
44.28
13
2.20
1
99.25
3
4.36
1
67.37
4
9.25
1
91.10
1
36.30
1
71.53
1
18.60
1
80.19
1
25.68
1
84.07
1
29.89
1
77.56
1
28.68
1
77.81
1
30.18
1
74.48
1
20.44
High Quartile
9-Ending
99-Ending
Rank
%
Rank
%
1
85.53
1
20.09
1
88.83
1
23.34
1
43.06
1
8.07
1
94.83
1
41.12
1
48.09
1
8.75
1
27.98
3
4.35
1
42.03
1
5.90
1
34.58
5
4.38
1
60.06
1
12.33
3
15.83
8
3.69
1
73.60
1
15.22
1
61.88
1
13.96
1
64.91
1
11.02
1
55.27
1
14.01
1
43.04
3
9.12
1
54.31
1
13.08
1
55.35
1
9.61
1
46.92
1
8.23
1
86.83
1
25.03
1
75.53
1
19.10
1
50.70
5
6.06
1
41.41
4
5.08
1
54.68
1
11.96
1
90.83
2
18.29
1
70.66
2
13.54
1
56.99
1
11.67
1
77.70
1
24.00
1
77.29
1
18.87
1
68.28
1
15.07
1
61.53
1
14.12
21
Current Ending Digit (¢)
Table R1a. Transition Probabilities Conditional on a Price Change for a 10-State Markov
Chain Analysis – for the Dominick’s Dataset, Store #8, Regular Prices Only, in Cents
0
1
2
3
4
5
6
7
8
9
0
0.46
0.16
0.21
0.25
0.19
0.89
0.17
0.21
0.14
2.94
1
0.15
0.08
0.14
0.29
0.17
0.55
0.17
0.19
0.14
2.03
2
0.22
0.17
0.14
0.20
0.20
0.55
0.21
0.18
0.12
2.10
Next Period Ending Digit (¢)
3
4
5
6
0.26
0.22
0.98
0.15
0.31
0.16
0.63
0.17
0.21
0.21
0.63
0.20
0.32
0.23
0.78
0.18
0.21
0.17
0.53
0.17
0.67
0.48
1.17
0.52
0.19
0.16
0.38
0.09
0.28
0.23
0.57
0.31
0.17
0.11
0.40
0.10
2.31
3.05
4.60
1.97
7
0.20
0.17
0.18
0.30
0.23
0.65
0.37
0.21
0.16
2.55
8
0.17
0.11
0.11
0.15
0.13
0.43
0.13
0.16
0.09
1.34
9
2.82
1.97
2.06
2.38
3.05
4.66
2.00
2.80
1.43
30.92
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (113,615).
Current Ending Digit (¢)
Table R1b. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Dominick’s Dataset, Store #12, Regular Prices Only, in Cents
0
1
2
3
4
5
6
7
8
9
0
0.53
0.14
0.23
0.23
0.21
0.81
0.17
0.18
0.16
3.36
1
0.15
0.11
0.11
0.23
0.12
0.47
0.14
0.15
0.10
2.13
2
0.25
0.16
0.11
0.17
0.17
0.50
0.18
0.19
0.12
2.23
Next Period Ending Digit (¢)
3
4
5
6
0.25
0.25
0.90
0.17
0.24
0.14
0.59
0.15
0.19
0.19
0.62
0.19
0.32
0.23
0.73
0.19
0.19
0.17
0.45
0.17
0.63
0.41
0.91
0.48
0.22
0.16
0.37
0.15
0.25
0.20
0.54
0.37
0.17
0.10
0.38
0.14
2.59
3.17
4.31
2.33
7
0.18
0.15
0.21
0.26
0.23
0.58
0.43
0.18
0.12
2.62
8
0.15
0.10
0.12
0.18
0.12
0.35
0.14
0.15
0.11
1.27
9
3.19
1.97
2.18
2.62
3.22
4.32
2.40
2.84
1.34
30.20
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (113,012).
22
Current Ending Digit (¢)
Table R1c. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Dominick’s Dataset, Store #122, Regular Prices Only, in Cents
0
1
2
3
4
5
6
7
8
9
0
0.32
0.24
0.29
0.32
0.20
0.73
0.21
0.24
0.17
2.54
1
0.25
0.09
0.22
0.31
0.20
0.53
0.16
0.22
0.18
2.64
2
0.32
0.26
0.11
0.26
0.24
0.60
0.18
0.24
0.14
2.58
Next Period Ending Digit (¢)
3
4
5
6
0.35
0.24
0.83
0.16
0.38
0.21
0.70
0.17
0.30
0.31
0.67
0.22
0.39
0.32
0.88
0.27
0.28
0.16
0.66
0.24
0.75
0.59
0.67
0.60
0.24
0.22
0.43
0.10
0.35
0.27
0.54
0.41
0.18
0.14
0.44
0.17
2.66
3.51
4.12
2.47
7
0.23
0.20
0.23
0.41
0.26
0.63
0.48
0.23
0.21
3.00
8
0.17
0.14
0.15
0.20
0.14
0.42
0.18
0.26
0.11
1.78
9
2.39
2.43
2.45
2.69
3.56
4.25
2.64
3.30
1.86
23.47
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (122,877).
Current Ending Digit (¢)
Table R1d. Transition Probabilities Conditional on a Price Change
from a 10-State Markov Chain Analysis – for the Dominick’s Dataset,
Store #133, Regular Prices Only, in Cents
0
1
2
3
4
5
6
7
8
9
0
0.11
0.19
0.25
0.20
0.18
0.66
0.20
0.18
0.13
2.43
1
0.23
0.10
0.22
0.25
0.18
0.62
0.18
0.20
0.15
2.60
2
0.27
0.26
0.11
0.23
0.26
0.77
0.23
0.21
0.13
2.68
Next Period Ending Digit (¢)
3
4
5
6
0.20
0.24
0.79
0.19
0.30
0.20
0.84
0.18
0.24
0.25
0.92
0.23
0.17
0.29
0.93
0.25
0.25
0.16
0.80
0.28
0.84
0.70
0.94
0.75
0.21
0.24
0.54
0.12
0.25
0.22
0.75
0.51
0.16
0.14
0.51
0.15
2.30
3.94
4.54
2.48
7
0.19
0.20
0.18
0.28
0.22
0.85
0.58
0.14
0.19
3.11
8
0.12
0.13
0.13
0.17
0.15
0.50
0.15
0.22
0.07
1.73
9
2.14
2.37
2.64
2.37
3.93
4.62
2.73
3.37
1.75
22.34
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (85,943).
23
Current Ending Digit (¢)
Table R1e. Transition Probabilities Conditional on a Price Change
from a 10-State Markov Chain Analysis – for the Dominick’s Dataset, in Cents
0
1
2
3
4
5
6
7
8
9
0
0.66
0.28
0.26
0.30
0.30
0.77
0.26
0.24
0.15
3.47
1
0.25
0.12
0.14
0.22
0.13
0.33
0.15
0.14
0.10
1.56
2
0.29
0.17
0.15
0.16
0.17
0.35
0.18
0.16
0.11
1.45
Next Period Ending Digit (¢)
3
4
5
6
0.32
0.33
0.83
0.27
0.22
0.14
0.47
0.14
0.17
0.18
0.38
0.18
0.31
0.22
0.49
0.19
0.19
0.26
0.42
0.22
0.45
0.35
0.90
0.43
0.19
0.26
0.38
0.17
0.25
0.23
0.45
0.25
0.14
0.15
0.29
0.13
1.91
2.38
3.32
1.84
7
0.23
0.14
0.15
0.24
0.18
0.50
0.28
0.23
0.12
1.79
8
0.15
0.10
0.09
0.14
0.10
0.26
0.13
0.12
0.12
0.82
9
3.75
2.76
1.75
2.42
2.88
3.88
2.09
2.11
1.31
37.74
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
change (27,524,476).
Current Ending Digit (¢)
Table R1f. Transition Probability Matrix
10-State Markov Chain Conditional on a Price Change
– for the Dominick’s Dataset, Regular Prices; Stores #8, #12, #122 and #133, in Cents,
for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
0
1
2
3
4
5
6
7
8
9
0
0.37
0.18
0.25
0.25
0.19
0.78
0.19
0.21
0.15
2.83
1
0.20
0.09
0.17
0.28
0.17
0.54
0.16
0.19
0.14
2.34
2
0.27
0.21
0.12
0.22
0.21
0.60
0.20
0.20
0.13
2.38
Next Period Ending Digit (¢)
3
4
5
6
0.27
0.24
0.88
0.16
0.31
0.17
0.68
0.17
0.24
0.24
0.70
0.21
0.31
0.27
0.83
0.22
0.23
0.17
0.60
0.21
0.72
0.54
0.92
0.58
0.22
0.19
0.42
0.12
0.29
0.23
0.59
0.39
0.17
0.12
0.43
0.14
2.48
3.39
4.37
2.30
7
0.20
0.18
0.20
0.32
0.24
0.66
0.46
0.19
0.17
2.81
8
0.16
0.12
0.12
0.18
0.13
0.42
0.15
0.20
0.09
1.52
9
2.66
2.18
2.32
2.53
3.41
4.45
2.43
3.07
1.59
26.93
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (434,997).
24
Current Ending Digit (¢)
Table R1g. Transition Probabilities Conditional on a Price Change from a 10-State
Markov Chain Analysis – for the Dominick’s Dataset, Store #8, Regular Prices Only,
in Cents, for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
0
1
2
3
4
5
6
7
8
9
0
0.87
0.29
0.20
0.22
0.31
0.87
0.28
0.21
0.11
3.95
1
0.22
0.06
0.11
0.19
0.08
0.26
0.11
0.09
0.04
1.30
2
0.22
0.10
0.13
0.13
0.16
0.25
0.13
0.11
0.08
1.15
Next Period Ending Digit (¢)
3
4
5
6
0.24
0.31
0.93
0.27
0.20
0.09
0.34
0.09
0.15
0.13
0.27
0.13
0.31
0.20
0.40
0.13
0.16
0.25
0.27
0.12
0.31
0.20
0.72
0.27
0.17
0.15
0.23
0.13
0.22
0.13
0.33
0.14
0.10
0.07
0.21
0.06
1.67
2.28
3.00
1.57
7
0.21
0.12
0.13
0.20
0.13
0.38
0.16
0.14
0.08
1.53
8
0.13
0.04
0.05
0.10
0.08
0.21
0.07
0.07
0.08
0.67
9
4.18
2.04
1.42
1.99
2.56
3.48
1.70
1.84
1.22
45.81
Note: Each cell contains the percentage (%) of the price change compared to the total number of price
changes (44,773).
0.09Current Ending
Digit (¢)
Table R1h. Transition Probabilities Conditional on a Price Change from a 10-State
Markov Chain Analysis – for the Dominick’s Dataset, Store #12, Regular Prices Only,
in Cents for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
0
1
2
3
4
5
6
7
8
9
0
0.73
0.21
0.24
0.30
0.41
0.88
0.23
0.18
0.19
4.27
1
0.26
0.09
0.11
0.22
0.10
0.26
0.10
0.12
0.07
1.60
2
0.27
0.14
0.06
0.14
0.13
0.31
0.12
0.12
0.05
1.48
Next Period Ending Digit (¢)
3
4
5
6
0.36
0.41
0.89
0.23
0.18
0.13
0.36
0.10
0.17
0.14
0.35
0.12
0.26
0.22
0.42
0.15
0.17
0.15
0.32
0.19
0.34
0.26
0.72
0.29
0.18
0.20
0.25
0.07
0.22
0.15
0.41
0.15
0.13
0.06
0.22
0.10
2.06
2.62
3.22
1.75
7
0.20
0.12
0.14
0.24
0.15
0.41
0.20
0.11
0.06
1.63
8
0.20
0.05
0.06
0.14
0.10
0.19
0.11
0.09
0.08
0.88
9
4.19
1.67
1.49
2.05
2.68
3.36
1.72
1.72
1.01
42.86
Note: Each cell contains the percentage (%) of the price change compared to the total number of price
changes (42,377).
25
Current Ending Digit (¢)
Table R1i. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Dominick’s Dataset, Store #122, Regular Prices Only, in Cents
for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
0
1
2
3
4
5
6
7
8
9
0
0.89
0.42
0.21
0.25
0.26
0.61
0.23
0.21
0.18
2.57
1
0.30
0.18
0.15
0.17
0.10
0.26
0.10
0.10
0.07
1.30
2
0.25
0.18
0.17
0.18
0.15
0.24
0.13
0.12
0.10
1.19
Next Period Ending Digit (¢)
3
4
5
6
0.21
0.25
0.68
0.22
0.18
0.13
0.50
0.10
0.19
0.21
0.28
0.14
0.42
0.21
0.43
0.18
0.19
0.34
0.36
0.16
0.36
0.25
0.86
0.31
0.15
0.18
0.26
0.27
0.22
0.19
0.32
0.22
0.12
0.11
0.25
0.12
1.52
1.83
2.62
1.28
7
0.21
0.12
0.12
0.23
0.12
0.41
0.23
0.27
0.11
1.48
8
0.14
0.07
0.08
0.12
0.10
0.20
0.09
0.13
0.16
0.69
9
3.37
3.41
1.74
2.34
2.89
3.13
1.96
2.04
1.68
44.27
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (57,668).
Current Ending Digit (¢)
Table R1j. Transition Probabilities Conditional on a Price Change from a 10-State Markov
Chain Analysis – for the Dominick’s Dataset, Store #133, Regular Prices Only, in Cents
for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
0
1
2
3
4
5
6
7
8
9
0
0.80
0.30
0.20
0.27
0.25
0.63
0.22
0.21
0.17
2.60
1
0.30
0.18
0.13
0.13
0.13
0.24
0.13
0.09
0.06
1.31
2
0.26
0.13
0.23
0.14
0.19
0.29
0.15
0.12
0.13
1.20
Next Period Ending Digit (¢)
3
4
5
6
0.20
0.31
0.69
0.21
0.16
0.12
0.49
0.11
0.17
0.19
0.32
0.15
0.34
0.20
0.43
0.18
0.18
0.40
0.39
0.22
0.35
0.32
0.83
0.36
0.17
0.25
0.28
0.25
0.17
0.21
0.31
0.15
0.12
0.15
0.23
0.14
1.30
1.94
2.49
1.38
7
0.22
0.11
0.08
0.20
0.16
0.38
0.21
0.27
0.10
1.29
8
0.10
0.07
0.07
0.13
0.08
0.20
0.11
0.09
0.13
0.65
9
3.59
3.86
1.94
2.72
3.03
4.02
2.10
2.05
1.70
42.25
Note: Each cell contains the percentage (%) of the price change compared to the total number of price
changes (47,097).
26
Current Ending Digit (¢)
Table R1k. Transition Probability Matrix
for a 10-State Markov Chain Conditional on a Price Change
– for the Internet Dataset, in Cents
0
1
2
3
4
5
6
7
8
9
0
20.35
0.32
0.40
0.34
0.37
1.45
0.34
0.39
0.54
1.54
1
0.35
0.39
0.33
0.29
0.34
0.33
0.29
0.27
0.33
0.42
2
0.35
0.33
0.47
0.32
0.37
0.30
0.31
0.27
0.30
0.42
Next Period Ending Digit (¢)
3
4
5
6
0.34
0.33
1.40
0.39
0.32
0.34
0.29
0.30
0.34
0.34
0.27
0.24
0.47
0.33
0.35
0.32
0.31
0.66
0.52
0.40
0.34
0.48
10.63
0.45
0.34
0.43
0.48
0.86
0.37
0.36
0.32
0.33
0.37
0.44
0.58
0.41
0.48
0.87
2.19
0.54
7
0.38
0.28
0.31
0.30
0.38
0.34
0.41
0.66
0.48
0.56
8
0.52
0.30
0.34
0.41
0.37
0.53
0.30
0.49
2.95
1.47
9
1.69
0.40
0.32
0.43
0.87
2.04
0.66
0.58
1.21
17.68
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (41,034).
Current Ending Digit ($)
Table R1l. Transition Probability Matrix
for a 10-State Markov Chain Conditional on a Price Change
– for the Internet Dataset, in Dollars
0
1
2
3
4
5
6
7
8
9
0
1.58
0.98
0.58
0.46
0.55
0.49
0.36
0.33
0.49
1.08
1
0.85
2.18
1.19
0.67
0.49
0.44
0.37
0.30
0.39
0.83
2
0.45
1.06
1.72
1.23
0.87
0.61
0.42
0.41
0.38
0.81
Next Period Ending Digit ($)
3
4
5
6
0.40
0.42
0.43
0.35
0.49
0.40
0.35
0.33
1.01
0.76
0.56
0.34
1.99
1.12
0.65
0.50
1.30
2.73
1.32
0.69
0.90
1.50
2.52
1.01
0.52
0.88
1.15
1.47
0.48
0.79
0.79
1.14
0.57
0.56
0.72
0.71
0.91
1.98
1.56
1.25
7
0.41
0.40
0.32
0.42
0.65
0.67
0.86
1.27
1.11
1.47
8
0.68
0.43
0.48
0.51
0.62
0.54
0.64
0.88
1.73
2.09
9
1.38
0.97
1.12
1.00
1.98
1.45
1.04
1.22
1.79
11.75
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (41,034).
27
Table R1m: Transition Frequency Matrix
for a 10-State Markov Chain Conditional on a Price Change
– for the Internet Dataset, Low Price Product Categories, in Cents
Current Ending Digit (¢)
Next Period Ending Digit (¢)
0
1
2
3
4
5
6
7
8
9
0.73
0.44
0.39
0.38
0.42
0.42
0.50
0.40
0.48
1.14
0
0.37
0.35
0.37
0.35
0.42
0.32
0.31
0.36
0.41
0.52
1
0.50
0.38
0.68
0.44
0.55
0.33
0.29
0.33
0.39
0.44
2
0.43
0.33
0.37
0.59
0.49
0.48
0.54
0.36
0.58
0.62
3
0.44
0.42
0.58
0.47
0.75
0.54
0.63
0.53
0.50
1.31
4
0.57
0.37
0.35
0.48
0.44
3.20
0.58
0.33
0.59
3.51
5
0.32
0.32
0.49
0.49
0.67
0.72
1.83
0.61
0.46
1.19
6
0.41
0.26
0.40
0.51
0.50
0.35
0.52
0.72
0.72
0.76
7
0.63
0.38
0.39
0.55
0.54
0.67
0.65
0.73
5.40
2.10
8
1.00
0.67
0.58
0.72
1.35
3.56
0.82
0.89
2.64
28.68
9
Note: Each cell contains the percentage (%) of the price changes compared to the total number
of price changes (14,685). Low price categories include Music CDs, Movie DVDs, and Video
Games.
Table R1n: Transition Frequency Matrix
for a 10-State Markov Chain Conditional on a Price Change
– for the Internet Dataset, High Price Product Categories, in Cents
Current Ending Digit (¢)
Next Period Ending Digit (¢)
0
1
2
3
4
5
6
7
8
9
31.28
0.30
0.33
0.32
0.28
1.95
0.33
0.37
0.54
1.99
0
0.30
0.41
0.30
0.30
0.30
0.27
0.30
0.23
0.24
0.33
1
0.35
0.30
0.35
0.28
0.22
0.24
0.20
0.30
0.31
0.26
2
0.29
0.26
0.29
0.41
0.24
0.27
0.20
0.26
0.32
0.32
3
0.33
0.30
0.25
0.22
0.61
0.51
0.27
0.30
0.30
0.63
4
1.94
0.31
0.28
0.25
0.50 14.77
0.37
0.35
0.50
1.22
5
0.35
0.27
0.22
0.25
0.30
0.36
0.32
0.30
0.21
0.36
6
0.38
0.28
0.20
0.29
0.28
0.30
0.22
0.62
0.37
0.49
7
0.49
0.30
0.24
0.26
0.39
0.52
0.28
0.34
1.59
0.72
8
1.84
0.29
0.33
0.35
0.61
1.43
0.38
0.38
0.81
11.55
9
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price changes
(26,349). High price categories include Computer Monitors, Digital Cameras, DVD Players, Hard Drives, Laptop
Computers, PDAs, and Software.
28
Table R1o: Transition Frequency Matrix
for a 10-State Markov Chain Conditional on a Price Change
– for the Internet Dataset, Low Price Product Categories, in Dollars
Current Ending Digit ($)
Next Period Ending Digit ($)
0
1
2
3
4
5
6
7
8
9
2.96
1.38 0.39
0.40
0.35
0.16
0.21
0.25
0.37
1.06
0
1.40
5.03 1.90
0.46
0.30
0.23
0.16
0.22
0.26
0.74
1
0.36
1.89 3.62
1.72
0.93
0.40
0.22
0.15
0.22
0.52
2
0.37
0.54 1.70
4.41
1.82
0.71
0.36
0.24
0.23
0.52
3
0.41
0.43 0.89
1.71
5.17
2.25
0.90
0.59
0.29
1.11
4
0.22
0.33 0.33
0.85
1.97
4.56
1.40
0.55
0.21
0.34
5
0.16
0.22 0.20
0.32
0.92
1.23
2.64
1.21
0.52
0.85
6
0.15
0.13 0.22
0.22
0.59
0.50
1.35
1.87
0.96
0.96
7
0.31
0.27 0.12
0.27
0.26
0.19
0.37
0.88
2.40
1.55
8
0.99
0.69 0.42
0.47
1.11
0.29
0.95
0.97
1.48
7.13
9
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price
changes (14,685). Low price categories include CDs, DVDs, and Video Games.
Current Ending Digit ($)
Table R1p: Transition Frequency Matrix
for a 10-State Markov Chain Conditional on a Price Change
– for the Internet Dataset, High Price Product Categories, in Dollars
0
1
2
3
4
5
6
7
8
9
0
0.82
0.74
0.71
0.50
0.62
0.63
0.47
0.43
0.59
1.13
1
0.55
0.60
0.80
0.73
0.53
0.50
0.45
0.40
0.46
0.90
2
0.48
0.59
0.66
0.96
0.85
0.77
0.54
0.52
0.53
1.02
Next Period Ending Digit ($)
3
4
5
6
0.40
0.46
0.58
0.43
0.50
0.46
0.41
0.42
0.62
0.67
0.64
0.41
0.64
0.73
0.62
0.58
1.07
1.38
0.80
0.58
0.92
1.24
1.39
0.80
0.63
0.87
1.11
0.82
0.63
0.90
0.96
1.02
0.73
0.73
1.01
0.90
1.16
2.46
2.27
1.41
7
0.50
0.51
0.42
0.52
0.69
0.73
0.66
0.93
1.24
1.74
8
0.86
0.52
0.62
0.67
0.81
0.72
0.71
0.84
1.35
2.44
9
1.56
1.09
1.45
1.26
2.47
2.07
1.14
1.36
1.92
14.32
Note: Each cell contains the percentage (%) of the price changes compared to the total number of price changes
(26,349). High price categories include Computer Monitors, Digital Cameras, DVD Players, Hard Drives,
Laptop Computers, PDAs, and Software.
29
Table R2a. Top 50 Transition Probabilities Conditional on a Price Change
for a 100-State Markov Chain Analysis –
for the Dominick’s Dataset, by Store, Regular Prices Only, in Cents
Current
Rank
Ending
1
89
2
99
3
99
4
39
5
79
6
49
7
79
8
99
9
99
10
19
11
99
12
29
13
99
14
29
15
99
16
99
17
69
18
69
19
49
20
09
21
19
22
59
23
09
24
99
25
39
26
89
27
49
28
99
29
00
30
59
31
89
32
29
33
39
34
49
35
59
36
79
37
69
38
19
39
19
40
59
41
89
42
99
43
29
44
49
45
29
46
69
47
19
48
39
49
69
50
49
Store 8
Next
Ending
99
89
19
49
99
99
89
49
29
99
09
99
99
39
79
39
99
79
59
19
29
69
99
69
99
79
39
59
89
99
00
49
29
69
49
69
89
09
39
79
69
00
19
29
69
59
59
59
29
19
%
1.34
1.03
0.86
0.79
0.78
0.75
0.73
0.73
0.72
0.71
0.70
0.70
0.66
0.60
0.60
0.55
0.53
0.52
0.51
0.50
0.50
0.49
0.49
0.48
0.46
0.46
0.43
0.40
0.39
0.38
0.38
0.36
0.36
0.35
0.33
0.33
0.32
0.32
0.31
0.29
0.28
0.28
0.28
0.27
0.27
0.27
0.26
0.26
0.26
0.25
Current
Ending
89
99
79
79
99
99
59
99
49
99
99
99
49
29
39
19
29
59
99
69
69
09
19
99
99
59
89
39
29
69
59
29
39
09
19
79
00
39
59
89
19
49
19
49
99
79
49
69
79
79
Store 12
Next
Ending
99
89
99
89
19
49
99
29
99
59
79
99
59
99
49
99
39
69
09
99
79
19
29
39
69
79
79
99
49
59
49
59
59
99
79
19
89
29
29
00
39
69
59
39
00
69
29
89
29
59
%
1.09
0.86
0.83
0.71
0.70
0.69
0.68
0.68
0.67
0.64
0.63
0.61
0.59
0.58
0.56
0.55
0.54
0.52
0.52
0.50
0.49
0.48
0.45
0.43
0.42
0.41
0.41
0.40
0.37
0.35
0.34
0.33
0.33
0.32
0.32
0.32
0.31
0.31
0.31
0.31
0.31
0.30
0.30
0.30
0.29
0.29
0.29
0.27
0.26
0.26
Current
Ending
89
99
99
79
79
39
29
99
99
69
19
19
59
49
99
99
29
69
99
49
99
09
09
99
39
89
29
39
49
49
95
59
94
69
29
97
79
19
69
19
99
59
89
69
99
99
39
96
29
69
Store 122
Next
Ending
99
89
19
89
99
49
39
09
29
99
29
99
69
99
99
49
99
79
79
59
39
99
19
69
29
79
49
99
69
39
99
79
99
89
19
99
69
39
59
09
97
99
69
49
94
95
59
99
69
29
%
0.87
0.70
0.61
0.58
0.58
0.57
0.55
0.55
0.50
0.49
0.48
0.47
0.46
0.45
0.43
0.42
0.42
0.42
0.41
0.40
0.40
0.40
0.38
0.37
0.35
0.31
0.31
0.31
0.29
0.29
0.28
0.28
0.27
0.27
0.27
0.27
0.26
0.26
0.26
0.26
0.26
0.25
0.24
0.24
0.24
0.23
0.23
0.23
0.23
0.23
Current
Ending
89
39
79
99
79
99
99
99
29
49
49
29
19
59
19
69
99
99
69
09
99
29
59
94
99
95
49
97
19
89
66
99
99
49
09
67
99
39
59
99
96
99
99
59
69
39
19
29
59
29
Store 133
Next
Ending
99
49
89
19
99
29
89
09
39
99
59
99
29
69
99
99
49
99
79
19
79
49
99
99
69
99
69
99
39
79
67
97
39
39
99
66
59
29
79
95
99
94
96
29
59
59
09
19
49
69
%
0.82
0.65
0.62
0.61
0.60
0.60
0.60
0.54
0.53
0.50
0.48
0.47
0.45
0.45
0.44
0.44
0.44
0.43
0.42
0.41
0.39
0.36
0.35
0.33
0.32
0.32
0.31
0.31
0.31
0.31
0.30
0.30
0.30
0.30
0.30
0.30
0.29
0.29
0.29
0.26
0.26
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.24
0.24
30
Table R2b. Top 50 Transition Probabilities Conditional on a Price Change
from a 100-State Markov Chain Analysis – for the Dominick’s Dataset, in Cents
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Current Ending
99
49
99
89
59
29
79
99
19
99
99
39
69
99
99
99
99
09
79
39
99
89
29
69
49
49
29
19
50
59
49
79
99
79
69
09
19
59
59
39
79
29
39
79
29
49
19
59
19
59
Next Ending
99
99
49
99
99
99
99
89
99
29
59
99
99
79
19
69
39
99
89
49
09
79
49
79
29
39
39
59
99
29
59
39
50
69
29
19
29
79
69
29
49
69
79
49
59
79
79
49
49
19
Note: Total number of price changes = 27,524,476.
%
1.91
1.50
1.35
1.10
0.97
0.97
0.95
0.92
0.88
0.83
0.83
0.83
0.82
0.78
0.71
0.64
0.63
0.61
0.53
0.46
0.45
0.43
0.41
0.39
0.37
0.37
0.37
0.36
0.36
0.35
0.34
0.34
0.34
0.34
0.33
0.33
0.33
0.32
0.31
0.31
0.31
0.30
0.30
0.29
0.29
0.29
0.29
0.29
0.29
0.28
31
Table R2c. Top 50 Transition Probabilities
for a 100-State Markov Chain Conditional on a Price Change
– for the Dominick’s Dataset, Regular Prices; Stores #8, #12, #122 and #133, in Cents
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Current Ending
89
99
79
99
79
39
99
49
99
99
29
19
29
99
99
49
69
59
19
69
09
99
59
99
99
09
89
39
29
49
39
59
49
19
69
59
79
69
95
39
19
94
29
49
29
99
59
29
97
69
Next Ending
99
89
99
19
89
49
29
99
09
49
39
99
99
99
79
59
99
69
29
79
19
39
99
69
59
99
79
99
49
39
29
79
69
39
59
49
69
89
99
59
09
99
19
29
59
00
29
69
99
49
Note: Total number of price changes = 434,997.
%
1.04
0.80
0.70
0.70
0.66
0.64
0.62
0.60
0.58
0.57
0.56
0.55
0.54
0.54
0.51
0.50
0.49
0.48
0.47
0.46
0.44
0.43
0.42
0.40
0.39
0.38
0.37
0.35
0.35
0.33
0.33
0.32
0.31
0.29
0.28
0.28
0.28
0.27
0.27
0.27
0.27
0.27
0.26
0.24
0.24
0.24
0.24
0.23
0.23
0.23
32
Table R2d. Top 50 Transition Probabilities Conditional on a Price Change for a 100-State
Markov Chain Analysis – for the Dominick’s Dataset, by Store, Regular Prices Only, in Cents,
for the Low Quartile of Products in Terms of the Prevalence of 9-Ending Prices
Current
Rank
Ending
1
99
2
89
3
49
4
99
5
99
6
19
7
79
8
99
9
99
10
29
11
69
12
39
13
59
14
99
15
99
16
99
17
09
18
99
19
79
20
39
21
89
22
69
23
50
24
19
25
69
26
49
27
89
28
00
29
89
30
99
31
99
32
79
33
19
34
59
35
79
36
29
37
19
38
29
39
69
40
49
41
09
42
49
43
59
44
49
45
29
46
79
47
99
48
79
49
29
50
69
Store #8
Next
Ending
99
99
99
49
89
99
99
19
79
99
99
99
99
59
39
29
99
69
89
49
79
79
99
49
89
39
69
89
00
50
09
39
59
19
69
49
29
39
29
19
19
19
29
79
59
19
00
49
19
49
%
2.79
1.84
1.68
1.62
1.60
1.32
1.20
1.15
1.06
0.99
0.99
0.95
0.89
0.84
0.81
0.79
0.77
0.75
0.69
0.58
0.58
0.54
0.50
0.50
0.49
0.48
0.47
0.46
0.46
0.46
0.45
0.45
0.45
0.42
0.41
0.40
0.39
0.38
0.37
0.37
0.36
0.36
0.36
0.36
0.35
0.35
0.35
0.34
0.34
0.34
Current
Ending
99
99
49
59
89
99
99
79
19
99
29
99
99
69
39
99
99
39
79
50
99
99
19
49
89
79
29
49
09
49
69
59
19
69
19
89
79
29
49
59
49
69
49
99
39
00
39
49
29
00
Store #12
Next
Ending
99
49
99
99
99
89
59
99
99
79
99
19
29
99
99
69
39
49
89
99
50
09
79
29
79
19
49
59
99
39
89
19
49
79
59
69
39
59
19
29
49
49
69
00
79
89
89
79
29
09
%
2.21
1.77
1.77
1.52
1.51
1.50
1.29
1.11
0.97
0.92
0.91
0.84
0.80
0.78
0.75
0.74
0.58
0.54
0.52
0.51
0.50
0.50
0.50
0.49
0.48
0.47
0.46
0.45
0.44
0.43
0.42
0.40
0.40
0.39
0.38
0.38
0.38
0.38
0.37
0.37
0.37
0.36
0.36
0.36
0.35
0.34
0.33
0.33
0.33
0.32
Store #122
Current
Next
Ending
Ending
99
99
49
99
99
49
89
99
19
99
99
89
79
99
69
99
39
99
29
99
09
99
99
19
59
99
99
69
99
79
79
89
99
39
99
29
39
49
99
59
89
79
49
39
29
49
99
09
69
79
39
89
79
39
29
39
49
89
69
89
69
49
89
69
49
49
19
89
89
49
59
89
19
59
49
29
19
49
39
19
19
29
59
79
19
39
50
99
59
69
49
79
79
19
09
19
69
29
59
49
%
2.33
1.78
1.73
1.31
1.25
1.11
1.11
1.04
0.96
0.95
0.92
0.82
0.79
0.75
0.70
0.69
0.64
0.60
0.58
0.55
0.53
0.52
0.48
0.48
0.46
0.45
0.45
0.44
0.44
0.43
0.42
0.42
0.41
0.41
0.40
0.39
0.39
0.38
0.38
0.37
0.36
0.36
0.35
0.35
0.35
0.34
0.34
0.34
0.33
0.33
Store #133
Current
Next
Ending
Ending
99
99
49
99
99
49
89
99
79
99
29
99
19
99
69
99
99
89
59
99
39
99
99
29
09
99
99
79
99
19
79
89
99
69
99
59
39
49
99
39
89
79
50
99
49
49
29
49
79
39
89
49
49
29
19
49
99
50
49
39
79
49
49
79
39
89
49
89
19
59
39
69
59
29
69
29
69
79
69
49
09
49
79
19
09
19
79
29
29
89
59
49
19
89
19
79
89
39
19
39
%
2.40
1.78
1.69
1.28
1.08
1.07
1.05
1.03
0.98
0.98
0.89
0.71
0.71
0.70
0.66
0.66
0.64
0.63
0.55
0.54
0.54
0.52
0.50
0.49
0.46
0.45
0.45
0.44
0.44
0.40
0.40
0.39
0.38
0.38
0.37
0.35
0.35
0.35
0.35
0.34
0.34
0.34
0.34
0.33
0.33
0.32
0.32
0.32
0.32
0.31
33
Table R2e. Top 50 Transition Probabilities
for a 100-State Markov Chain Conditional on a Price Change
– for the Internet Dataset
Cents
Dollars
Current
Next
Current
Next
Rank Ending
Ending
%
Ending
Ending
1
00
00
18.36
14
14
2
99
99
11.89
11
11
3
95
95
8.83
15
15
4
98
98
1.13
09
09
5
00
99
0.89
13
13
6
99
00
0.85
99
99
7
99
95
0.72
12
12
8
00
95
0.66
10
10
9
99
98
0.64
08
08
10
99
49
0.62
14
15
11
49
99
0.62
16
16
12
95
00
0.62
15
14
13
95
99
0.57
14
13
14
98
99
0.54
12
11
15
49
49
0.28
13
14
16
00
50
0.25
11
12
17
88
88
0.24
22
22
18
50
00
0.23
12
13
19
85
85
0.20
13
12
20
96
96
0.19
99
49
21
89
99
0.19
19
19
22
00
90
0.18
11
10
23
96
99
0.18
21
21
24
24
99
0.17
49
99
25
97
97
0.16
10
11
26
99
24
0.15
29
19
27
94
99
0.14
99
79
28
99
19
0.14
23
23
29
99
89
0.14
17
16
30
90
00
0.13
16
17
31
99
88
0.13
10
09
32
99
94
0.13
49
29
33
50
50
0.12
09
08
34
19
99
0.11
49
39
35
90
90
0.11
07
07
36
82
82
0.10
16
14
37
88
99
0.10
17
17
38
95
75
0.10
15
16
39
99
39
0.10
99
89
40
97
99
0.10
79
99
41
99
29
0.10
08
09
42
99
97
0.10
15
13
43
89
89
0.10
24
24
44
49
59
0.09
25
25
45
75
95
0.09
49
49
46
75
75
0.09
09
10
47
99
79
0.09
16
15
48
75
00
0.08
39
29
49
59
69
0.08
14
16
50
59
99
0.08
14
12
Note: Total number of price changes = 41,034
%
1.47
1.36
1.28
1.23
1.16
1.01
0.80
0.67
0.63
0.59
0.58
0.54
0.49
0.48
0.48
0.44
0.43
0.42
0.42
0.42
0.41
0.39
0.39
0.38
0.35
0.35
0.35
0.32
0.31
0.30
0.29
0.29
0.29
0.29
0.28
0.28
0.27
0.27
0.26
0.26
0.25
0.24
0.24
0.24
0.24
0.24
0.23
0.23
0.22
0.21
34
Table R2f. Top 50 Transition Probabilities by Price Level
for a 100-State Markov Chain Conditional on a Price Change – for the Internet Dataset
Low-Priced Categories
Current Next
Rank
%
Ending Ending
1
99
99
16.32
2
98
98
1.80
3
95
95
1.75
4
99
98
1.19
5
49
99
1.04
6
98
99
0.97
7
99
49
0.95
8
96
96
0.50
9
24
99
0.45
10
99
24
0.42
11
96
99
0.40
12
89
99
0.37
13
88
88
0.37
14
99
95
0.34
15
99
19
0.33
16
82
82
0.28
17
99
89
0.27
18
19
99
0.26
19
95
99
0.26
20
99
39
0.25
21
99
29
0.25
22
49
59
0.24
23
49
49
0.22
24
09
95
0.21
25
59
69
0.21
26
99
05
0.21
27
29
39
0.20
28
79
59
0.20
29
79
89
0.20
30
19
89
0.20
31
99
79
0.20
32
29
49
0.19
33
39
49
0.19
34
99
88
0.19
35
29
99
0.18
36
36
16
0.18
37
95
89
0.18
38
16
36
0.18
39
49
79
0.18
40
58
98
0.18
41
98
48
0.18
42
39
99
0.17
43
46
99
0.17
44
48
98
0.17
45
65
53
0.17
46
88
99
0.17
47
05
99
0.16
48
69
79
0.16
49
69
99
0.16
50
95
09
0.16
Cents
High-Priced Categories
Current
Next
%
Ending
Ending
00
00
28.59
95
95
12.77
99
99
9.42
00
99
1.34
99
00
1.29
00
95
1.02
95
00
0.96
99
95
0.94
98
98
0.76
95
99
0.75
99
49
0.44
00
50
0.39
49
99
0.39
50
00
0.35
99
98
0.33
49
49
0.32
98
99
0.30
85
85
0.29
00
90
0.27
97
97
0.22
90
00
0.20
94
99
0.18
90
90
0.17
99
94
0.17
88
88
0.17
50
50
0.16
75
00
0.13
75
75
0.13
95
75
0.13
75
95
0.12
00
75
0.11
89
89
0.11
99
88
0.10
94
94
0.09
00
98
0.09
95
50
0.09
97
99
0.09
25
25
0.08
89
99
0.08
75
50
0.08
50
95
0.07
90
99
0.07
95
94
0.07
99
90
0.07
99
97
0.07
90
50
0.07
80
00
0.06
88
00
0.06
88
99
0.06
94
95
0.06
Dollars
Low-Priced Categories
High-Priced Categories
Current
Next
Current
Next
%
%
Ending
Ending
Ending
Ending
14
14
4.03
99
99
1.51
11
11
3.72
99
49
0.65
15
15
3.53
49
99
0.60
09
09
3.31
99
79
0.54
13
13
3.21
79
99
0.40
12
12
2.18
99
89
0.39
10
10
1.84
49
39
0.33
08
08
1.62
49
49
0.28
14
15
1.59
89
79
0.28
16
16
1.55
79
69
0.28
15
14
1.40
39
29
0.27
13
14
1.26
49
29
0.25
14
13
1.25
29
99
0.25
12
11
1.17
99
69
0.25
11
12
1.16
99
94
0.24
22
22
1.15
59
49
0.23
12
13
1.12
99
98
0.23
13
12
1.06
79
49
0.22
19
19
1.06
19
99
0.22
21
21
1.01
69
59
0.21
11
10
0.94
89
99
0.21
10
11
0.90
99
29
0.20
23
23
0.84
29
19
0.20
16
17
0.78
09
99
0.20
17
16
0.74
19
09
0.18
17
17
0.74
89
89
0.18
10
09
0.71
69
89
0.18
07
07
0.70
69
99
0.18
16
14
0.69
79
79
0.18
09
08
0.68
79
78
0.17
24
24
0.65
99
19
0.17
09
10
0.63
99
97
0.17
15
13
0.63
69
79
0.17
15
16
0.63
99
59
0.16
25
25
0.62
39
99
0.16
08
09
0.61
89
69
0.15
29
19
0.61
29
49
0.15
14
16
0.59
88
88
0.15
20
20
0.57
94
94
0.15
16
15
0.54
97
97
0.15
21
22
0.54
89
88
0.14
13
15
0.52
94
99
0.14
14
12
0.51
69
49
0.14
22
21
0.50
49
79
0.14
26
26
0.46
90
89
0.14
13
11
0.45
95
94
0.14
19
17
0.42
98
99
0.13
06
06
0.42
39
49
0.13
25
26
0.40
96
95
0.13
19
16
0.39
00
99
0.13
Note: Low-priced categories include CDs, DVDs, and Video Games. High-priced categories include Computer
Monitors, Digital Cameras, DVD Players, Hard Drives, Laptop Computers, PDAs, and Software.
35
Table R3: Price Changes in Multiples of Dimes in the Dominick’s Dataset:
9¢- vs. Non-9¢-Ending Prices
Category
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Total
9¢-Ending
Multiples of
Sample
Dimes
Size
78.25%
367,969
74.93%
58,735
47.97%
156,863
42.10%
457,490
26.14%
304,439
36.10%
170,023
37.21%
271,757
46.49%
872,489
58.73%
1,135,112
46.99%
283,278
56.10%
240,532
51.41%
212,288
18.47%
137,453
32.72%
230,423
42.49%
883,284
46.75%
301,114
71.30%
1,017,513
68.07%
446,767
36.27%
72,753
37.01%
109,596
46.25%
405,144
80.84%
1,916,061
48.53%
488,341
48.23%
180,935
76.54%
4,614,455
74.22%
350,705
61.64%
468,688
62.81% 16,154,207
Non-9¢-Ending
Multiples of
Sample
Dimes
Size
5.60%
102,550
12.65%
18,298
4.09%
184,414
5.33%
583,025
4.12%
741,357
6.15%
281,703
8.32%
494,597
4.57%
1,039,738
9.01%
709,697
7.31%
279,353
4.75%
183,222
5.96%
191,319
11.66%
385,234
5.70%
336,201
5.93%
1,183,557
5.40%
395,344
10.22%
287,969
4.68%
210,342
7.17%
107,971
4.26%
152,846
4.59%
418,402
29.23%
238,976
4.61%
405,005
4.79%
190,632
15.36%
1,219,151
2.46%
123,840
6.18%
291,045
7.64% 10,755,788
Note: The column heading p-Value is an asymptotic significance level derived from the Pearson 2 test.
p-Value
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
36
Table R4: Price Changes in Multiples of Dollars in the Dominick’s Data:
99¢- vs. Non-99¢-Ending Prices
Category
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Total
99¢-Ending
Multiples of
Sample
Dollars
Size
17.09%
106,038
21.06%
15,608
1.66%
36,944
2.02%
104,451
0.19%
56,527
2.96%
19,566
6.60%
56,437
3.03%
160,237
5.41%
270,448
9.79%
62,297
1.83%
52,117
10.67%
62,370
0.00%
11,923
3.38%
56,617
8.47%
188,496
0.21%
67,862
5.21%
247,298
20.15%
158,974
1.28%
12,921
8.38%
15,137
4.76%
101,063
12.99%
503,157
3.23%
97,690
4.43%
43,874
12.87% 1,385,935
19.06%
108,407
4.85%
117,086
9.86% 4,119,480
Non-99¢-Ending
Multiples of
Sample
Dollars
Size
1.39%
364,481
3.11%
61,425
0.04%
304,333
0.27%
936,064
0.01%
989,269
0.03%
432,160
0.99%
709,917
0.16%
1,751,990
1.01%
1,574,361
0.06%
500,334
0.22%
371,637
0.31%
341,237
0.01%
510,764
0.65%
510,007
0.53%
1,878,345
0.04%
628,596
1.63%
1,058,184
2.53%
498,135
0.82%
167,806
0.03%
247,305
0.25%
722,522
5.86%
1,651,880
0.13%
795,656
0.20%
327,693
2.86%
4,447,671
0.89%
366,138
0.57%
642,647
1.39% 22,790,515
p-Value
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.1887
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
Note: Categories with unsupportive results are indicated by italics. The column heading p-Value is an asymptotic
significance level derived from the Pearson 2 test.
37
Table R5. Price Changes in Multiples of Dimes in the Internet Dataset:
9¢- vs. Non-9¢-Endings
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
9¢-Endings
Multiples of
Sample
Dimes
Size
73.32%
2,268
66.90%
2,813
80.05%
832
57.32%
778
66.76%
355
74.36%
1,435
57.18%
383
47.71%
809
72.77%
852
73.91%
92
68.32%
10,617
Non-9¢-Endings
Multiples of
Sample
Dimes
Size
21.17%
2,352
23.08%
5,888
44.17%
532
60.43%
4,751
59.40%
1,436
57.39%
5,517
59.83%
1,210
56.08%
5,150
77.07%
3,018
78.51%
563
50.50%
30,417
p-Value
.0000
.0000
.0000
.1015
.0110
.0000
.3569
.0000
.0093
.3250
.0000
Note: Categories with unsupportive results are indicated by italics. The column heading p-Value is an
asymptotic significance level derived from the Pearson 2 test.
Table R6. Price Changes in Multiples of Dollars in the Internet Data:
99¢- vs. Non-99¢-Endings
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
99¢-Endings
Multiples of
Sample
Dollars
Size
62.43%
1,142
72.19%
1,532
77.69%
744
56.42%
553
70.33%
300
84.95%
1,083
59.27%
329
47.98%
544
65.02%
852
84.38%
64
69.13%
7,056
Non-99¢-Endings
Multiples of
Sample
Dollars
Size
5.69%
3,478
6.89%
7,169
33.71%
620
50.18%
4,976
52.45%
1,491
45.14%
5,869
50.08%
1,264
47.17%
5,415
74.12%
3,018
72.76%
591
37.40%
33,978
p-Value
.0000
.0000
.0000
.0054
.0000
.0000
.0030
.7174
.0000
.0444
.0000
Note: Categories with unsupportive results are indicated by italics. The column heading p-Value is an
asymptotic significance level derived from the Pearson 2 test.
38
Table R7. Price Changes in Multiples of $10
in the Internet Dataset: $9- vs. Non-$9-Endings
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
$9-Endings
Multiples of
Sample
$10
Size
0.00%
587
2.92%
926
32.78%
659
29.62%
1,347
43.38%
710
22.50%
1,169
33.23%
641
33.43%
1,436
48.98%
1,899
74.13%
344
31.65%
9,718
Non-$9-Endings
Multiples of
Sample
$10
Size
0.25%
4,033
0.35%
7,775
11.99%
705
3.25%
4,182
4.07%
1,081
2.11%
5,783
7.35%
952
4.13%
4,523
9.84%
1,971
19.29%
311
2.76%
31,316
p-Value
.2271
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
Note: Categories with unsupportive results are indicated by italics. The column heading p-Value is an
asymptotic significance level derived from the Pearson 2 test.
Table R8. Price Changes in Multiples of $10 in the Internet Dataset:
$9.99- vs. Non-$9.99-Endings
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
$9.99-Endings
Multiples of
Sample
$10
Size
0.00%
76
11.70%
188
42.26%
433
44.62%
186
38.82%
170
50.45%
335
42.47%
219
34.41%
247
55.48%
566
78.72%
47
42.64%
2,467
Non-$9.99-Endings
Multiples of
Sample
$10
Size
0.22%
4,544
0.38%
8,513
5.05%
931
8.46%
5,343
17.64%
1,621
3.26%
6,617
13.83%
1,374
10.19%
5,712
24.06%
3,304
9.63%
608
7.49%
38,567
p-Value
.6822
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
Note: Categories with unsupportive results are indicated by italics. The column heading p-Value is an
asymptotic significance level derived from the Pearson 2 test.
39
Table R9. Price Changes in Multiples of $100 in the Internet Dataset:
$99- vs. Non-$99-Endings
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
$99-Endings
Multiples of
Sample
$100
Size
Non-$99-Endings
Multiples of
Sample
$100
Size
p-Value
N/A
1.59%
10.66%
0.00%
6.06%
15.36%
19.12%
38.51%
13.70%
251
122
197
132
332
476
161
1,671
0.23%
0.30%
0.06%
0.41%
0.32%
0.77%
6.07%
0.26%
5,278
1,669
6815
1,461
5,627
3,394
494
39,363
.0000
.0000
.7993
.0000
.0000
.0000
.0000
.0000
Note: Categories with unsupportive results are indicated by italics. The column heading p-Value is an
asymptotic significance level derived from Pearson 2 test.
Table R10. Price Changes in Multiples of $100 for the Internet Data:
$99.99- vs. Non-$99.99-Endings
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
$99.99-Endings
Multiples of
Sample
$100
Size
Non-$99.99-Endings
Multiples of
Sample
$100
Size
p-Value
N/A
0.00%
2.94%
0.00%
8.93%
12.50%
14.39%
41.18%
10.07%
37
34
36
56
64
139
17
407
0.29%
0.97%
0.06%
0.59%
1.03%
2.60%
13.32%
0.71%
5,492
1,757
6,916
1,537
5,895
3,731
638
40,627
.7423
.2531
.8852
.0000
.0000
.0000
.0011
.0000
Note: Categories with unsupportive results are indicated by italics. The column heading p-Value is an
asymptotic significance level derived from the Pearson 2 test.
40
Table 11a. Logit Regression Estimation with Product-Level Fixed Effects
for Regular Prices – for the Dominick’s Dataset, Store #8
Category
9¢-Ending
(9-Ending9 = 1)
Coeff.
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Average
 1.1677
 2.2213
 0.3398
 0.4762
 0.3535
 0.5950
 0.3094
 1.6407
 1.6438
 1.5476
 0.8510
 0.4802
 0.7422
 1.4322
 1.2126
 0.2585
 1.8585
 1.4641
 0.9740
 0.4516
 0.8390
 1.7033
 1.4559
 1.6553
 2.3835
 0.5696
 0.4523
Odds
Ratio
0.31
0.11
0.71
0.62
0.70
0.55
0.73
0.19
0.19
0.21
0.43
0.62
0.48
0.24
0.30
0.77
0.16
0.23
0.38
0.64
0.43
0.18
0.23
0.19
0.09
0.57
0.64
0.40
99¢-Ending
(9-Ending99 = 1)
Coeff.
 0.2411
 1.2291
0.2493
 0.4973
 0.4861
 0.4069
 0.1644
 1.2511
 0.9056
 0.7460
 0.7509
 0.1294
 1.1140
 0.4512
 0.5371
0.1160
 0.5076
 0.4155
0.6991
 0.7464
 0.3572
0.0484
 0.4156
 0.5254
 0.3610
 0.1025
 0.3599
Odds
Ratio
0.79
0.29
1.28
0.61
0.62
0.67
0.85
0.29
0.40
0.47
0.47
0.88
0.33
0.64
0.58
1.12
0.60
0.66
2.01
0.47
0.70
1.05
0.66
0.59
0.70
0.90
0.70
0.72
Note: 9-Ending9 and 9-Ending99 are 9-ending dummy variables, which equal 1 if
the price ends with “9” or “99,” and 0 otherwise. All p-values < 0.0001, except for
the italicized coefficients, for which p > .10. The average odds ratios reported in
the last row of the table are the simple averages of the odds ratios for each product
category.
41
Table 11b. Logit Regression Estimation with Product-Level Fixed Effects for Regular
Prices – for the Dominick’s Dataset, Store #12
Category
9¢-Ending
(9-Ending9 = 1)
Coeff.
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Average
 1.5589
 1.8097
 0.2056
 0.6767
 0.5149
 0.8264
 0.2885
 1.6640
 1.8859
 1.5576
 0.7660
 0.6354
 0.8269
 1.3782
 1.3498
 0.4710
 2.4000
 1.1451
 0.5015
 0.2459
 0.9773
 3.8464
 1.8120
 1.2851
 3.2185
 1.1053
 0.8223
Odds
Ratio
0.21
0.16
0.81
0.51
0.60
0.44
0.75
0.19
0.15
0.21
0.46
0.53
0.44
0.25
0.26
0.62
0.09
0.32
0.61
0.78
0.38
0.02
0.16
0.28
0.04
0.33
0.44
0.37
99¢-Ending
(9-Ending99 = 1)
Coeff.
 0.3367
 0.6650
 0.0397
0.1706
 0.6610
 0.8210
0.0288
 1.1023
 1.0973
 0.7035
 0.3160
 0.5837
 1.2994
 0.4012
 0.7926
0.2026
 0.6572
 0.0734
 1.1298
 1.1351
 0.5579
 0.3303
 0.7312
 0.1802
 0.5519
 0.5290
 0.6423
Odds
Ratio
0.71
0.51
0.96
1.19
0.52
0.44
1.03
0.33
0.33
0.49
0.73
0.56
0.27
0.67
0.45
1.22
0.52
0.93
0.32
0.32
0.57
0.72
0.48
0.84
0.58
0.59
0.53
0.62
Note: 9-Ending9or 9-Ending99 are 9-ending dummy variables, which equal 1 if the
price ends with “9” or “99,” and 0 otherwise. All p-values are less than 0.0001,
except for the italicized coefficients, for which p > .10. The average odds ratios
reported in the last row of the table are the simple averages of the odds ratios for
each product category.
42
Table 11c. Logit Regression Estimation with Product-Level Fixed Effects
for Regular Prices – for the Dominick’s Dataset, Store #122
9¢-Ending
(9-Ending9 = 1)
Category
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Average
Coeff.
 1.8527
 1.6792
 0.5936
 1.0835
 0.5211
 0.8724
 0.7885
 1.8737
 2.2580
 2.2165
 1.3232
 1.0728
 0.8878
 2.0393
 1.1912
 0.4213
 2.9716
 2.6676
 1.1534
 1.0415
 0.9071
 2.6157
 2.1846
 2.3531
 3.4715
 1.3230
 0.7877
Odds
Ratio
0.16
0.19
0.55
0.34
0.59
0.42
0.45
0.15
0.10
0.11
0.27
0.34
0.41
0.13
0.30
0.66
0.05
0.07
0.32
0.35
0.40
0.07
0.11
0.10
0.03
0.27
0.45
0.27
99¢-Ending
(9-Ending99 = 1)
Coeff.
 0.4197
 0.7045
 0.1470
 0.7830
 0.6410
 0.6300
 0.6695
 1.1211
 1.1750
 1.2748
 0.7658
 0.6999
 1.5105
 0.8201
 0.7857
 0.4161
 0.8471
 1.0936
0.1812
 0.7675
 0.1166
 0.7229
 0.9171
 0.7919
 0.7920
 0.8326
 0.7520
Odds
Ratio
0.66
0.49
0.86
0.46
0.53
0.53
0.51
0.33
0.31
0.28
0.46
0.50
0.22
0.44
0.46
0.66
0.43
0.34
1.20
0.46
0.89
0.49
0.40
0.45
0.45
0.43
0.47
0.51
Note: 9-Ending9 or 9-Ending99 are 9-ending dummy variables, which equal 1 if the
price ends with “9” or “99,” and 0 otherwise. All p-values are less than 0.0001,
except for italicized coefficients, for which p > .10. The average odds ratios
reported in the last row of the table are the simple averages of the odds ratios for
each product category.
43
Table 11d. Logit Regression Estimation with Product-Level Fixed Effects
for Regular Prices – for the Dominick’s Dataset, Store #133
Category
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-End Candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Average
9¢-Ending
(9-Ending9 = 1)
99¢-Ending
(9-Ending99 = 1)
Coeff.
Odds
Ratio
Coeff.
Odds
Ratio
 1.6394
 1.6398
 1.2778
 1.2537
 0.6521
 1.5447
 0.8816
 2.5728
 3.1094
 2.1196
 1.8553
 1.0582
 1.1614
 1.9305
 1.8965
 0.5149
 2.2651
 2.0479
 1.2421
 1.0388
 1.2913
 2.0740
 2.3402
 1.9898
 4.7696
 0.9789
 0.8136
0.19
0.19
0.28
0.29
0.52
0.21
0.41
0.08
0.04
0.12
0.16
0.35
0.31
0.15
0.15
0.60
0.10
0.13
0.29
0.35
0.27
0.13
0.10
0.14
0.01
0.38
0.44
 0.4019
 0.6139
 0.1916
 1.0469
 0.8803
 0.6787
 0.7887
 1.0503
 1.3447
 1.1906
 1.5776
 0.9088
 3.0656
 1.3401
 1.0437
 0.0027
 0.7322
 0.9456
0.5850
 0.8423
 1.3291
 0.5356
 1.2890
 0.9234
 1.1849
 0.7516
 0.8738
0.67
0.54
0.83
0.35
0.41
0.51
0.45
0.35
0.26
0.30
0.21
0.40
0.05
0.26
0.35
1.00
0.48
0.39
1.79
0.43
0.26
0.59
0.28
0.40
0.31
0.47
0.42
0.24
0.47
Note: 9-Ending9 and 9-Ending99 are 9-ending dummy variables, which equal 1 if
the price ends with “9” or “99,” and 0 otherwise. All p-values are less than
0.0001, except for the italicized coefficients, for which p > .10. The average odds
ratios reported in the last row of the table are the simple averages of the odds ratios
for each product category.
44
Table 11e. Results of the Logit Regression (Equation 1) Estimation
for the Entire Dominick’s Data
1.
Analgesics
Bath Soap
Bathroom Tissues
Bottled Juices
Canned Soup
Canned Tuna
Cereals
Cheeses
Cookies
Crackers
Dish Detergent
Fabric Softeners
Front-end-candies
Frozen Dinners
Frozen Entrees
Frozen Juices
Grooming Products
Laundry Detergents
Oatmeal
Paper Towels
Refrigerated Juices
Shampoos
Snack Crackers
Soaps
Soft Drinks
Tooth Brushes
Tooth Pastes
Average
9¢-Ending
99¢-Ending
D9 (9-Ending = 1)
D99 (9-Ending = 1)
Coeff.
O/R
Coeff.
O/R
 0.6781
 0.8155
 0.5036
 0.2891
 0.1112
 0.5331
 0.2558
 0.9142
 0.8173
 0.4412
 0.6283
 0.3779
 0.4477
 0.5808
 0.5642
 0.2451
 0.9030
 0.5783
 0.5805
 0.5186
 0.5042
 0.7868
 0.8517
 0.6709
 0.6709
 0.3154
 0.2343
0.51
0.44
0.60
0.75
0.89
0.59
0.77
0.40
0.44
0.64
0.53
0.69
0.64
0.56
0.57
0.78
0.41
0.56
0.56
0.60
0.60
0.46
0.43
0.51
0.51
0.73
0.79
0.59
 0.1847
 0.2273
 0.3426
 0.2042
 0.1629
 0.4714
 0.1603
 0.6098
 0.1876
 0.0441
 0.6024
 0.1980
 1.3781
 0.4377
 0.1291
 0.1008
 0.2406
 0.1446
 0.2548
 0.1546
 0.2908
 0.2957
 0.3930
 0.3583
 0.3583
 0.0709
 0.2760
0.83
0.80
0.71
0.81
0.85
0.62
0.85
0.54
0.83
0.96
0.55
0.82
0.25
0.65
0.88
0.90
0.79
0.87
0.78
0.86
0.75
0.74
0.68
0.70
0.70
0.93
0.76
0.76
45
Table R12. Average Price Change for 9- and Non-9-Ending Prices
– in the Dominick’s Dataset, Stores #8, #12, #122 and #133,
for the Low Quartile of the Products in Terms of 9-Ending Popularity
9¢-Ending
Non-9¢-Ending
Category
Mean Price
Sample
Mean Price
Sample
Change
Size
Change
Size
Analgesics
$0.4348
499
$0.3583
519
Bath Soap
$0.5078
92
$0.6090
90
Bathroom Tissues
$0.2197
3,737
$0.2175
6,201
Bottled Juices
$0.3137
12,021
$0.2610
19,670
Canned Soup
$0.2244
13,251
$0.1870
32,121
Canned Tuna
$0.2017
4,616
$0.1399
9,602
Cereals
$0.5445
9,236
$0.4959
21,680
Cheeses
$0.2721
14,076
$0.1755
29,765
Cookies
$0.3448
6,407
$0.3602
12,551
Crackers
$0.1946
2,423
$0.1630
4,877
Dish Detergent
$0.2774
3,639
$0.2231
4,704
Fabric Softeners
$0.3873
4,556
$0.2713
5,458
Front-End Candies
$0.1343
4,583
$0.2073
15,491
Frozen Dinners
$0.4821
5,596
$0.5615
11,228
Frozen Entrees
$0.6801
20,816
$0.6766
41,792
Frozen Juices
$0.2773
9,555
$0.2584
15,428
Grooming Products
$0.5061
1,331
$0.4886
1,640
Laundry Detergents
$0.7462
1,850
$0.4203
1,921
Oatmeal
$0.4895
1,867
$0.4774
3,409
Paper Towels
$0.1433
3,018
$0.1571
5,875
Refrigerated Juices
$0.3638
10,338
$0.3030
12,737
Shampoos
$0.3830
493
$0.3001
437
Snack Crackers
$0.3136
4,078
$0.3294
5,534
Soaps
$0.1940
1,692
$0.1423
3,703
Soft Drinks
$0.3767
6,329
$0.2046
15,270
Tooth Brushes
$0.4364
1,706
$0.3577
1,207
Tooth Pastes
$0.3964
9,445
$0.3363
8,852
$0.3754
157,250
$0.3314
291,762
Total
$0.3647
$0.3216
Average
$0.3293
$0.2662
Median
t-Stat p-Value
2.15
-0.79
0.28
12.06
11.36
11.70
6.86
33.20
-2.25
5.066
10.60
14.86
-16.08
-8.37
0.49
-3.44
1.60
14.46
0.93
-2.07
13.62
4.60
-1.99
8.606
24.09
6.75
14.64
27.61
0.032
0.431
0.783
0.000
0.000
0.000
0.000
0.000
0.025
0.000
0.000
0.000
0.000
0.000
0.622
0.000
0.110
0.000
0.355
0.038
0.000
0.000
0.47
0.000
0.000
0.000
0.000
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t26 = 2.728, p = .011).
46
Table R13. Average Price Change for 99- and Non-99-Ending Prices
– for the Dominick’s Dataset, Stores #8, #12, #122 and #133,
for the Low Quartile of the Products in Terms of 9-Ending Popularity
9¢-Ending
Non-9¢-Ending
Category
Mean Price
Sample
Mean Price
Sample
Change
Size
Change
Size
Analgesics
$0.5369
122
$0.3766
896
Bath Soap
$1.1410
20
$0.4859
162
Bathroom Tissues
$0.2733
901
$0.2129
9,037
Bottled Juices
$0.3754
2,909
$0.2715
28,782
Canned Soup
$0.2817
2,640
$0.1928
42,732
Canned Tuna
$0.3976
489
$0.1515
13,729
Cereals
$0.7164
1,948
$0.4966
28,968
Cheeses
$0.3901
2,346
$0.1961
41,495
Cookies
$0.4550
1,771
$0.3447
17,187
Crackers
$0.2330
511
$0.1690
6,789
Dish Detergent
$0.3678
798
$0.2340
7,545
Fabric Softeners
$0.5809
1,333
$0.2846
8,681
Front-End Candies
$0.4763
105
$0.1891
19,969
Frozen Dinners
$0.4848
1,507
$0.5401
15,317
Frozen Entrees
$0.6936
4,537
$0.6765
58,071
Frozen Juices
$0.3169
2,077
$0.2610
22,906
Grooming Products
$0.5512
414
$0.4863
2,557
Laundry Detergents
$1.1455
666
$0.4590
3,105
Oatmeal
$0.6356
311
$0.4700
4,965
Paper Towels
$0.1877
241
$0.1515
8,652
Refrigerated Juices
$0.4717
2,631
$0.3121
20,444
Shampoos
$0.4576
108
$0.3292
822
Snack Crackers
$0.2380
604
$0.3284
9,008
Soaps
$0.2651
317
$0.1518
5,078
Soft Drinks
$0.9923
765
$0.2280
20,834
Tooth Brushes
$0.4395
246
$0.4005
2,667
Tooth Pastes
$0.4943
2,763
$0.3447
15,534
$0.4909
33,080
$0.3353
415,932
Total
$0.5037
$0.3239
Average
$0.4473
$0.2781
Median
t-Stat p-Value
2.92
3.28
4.50
14.16
13.90
18.25
16.54
32.09
9.93
5.56
15.59
26.50
10.84
-3.53
1.33
5.79
3.72
24.33
5.03
1.87
23.01
4.58
-5.60
9.57
44.83
1.88
26.49
53.64
0.004
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.184
0.000
0.000
0.000
0.000
0.062
0.000
0.000
0.000
0.000
0.000
0.061
0.000
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t26 = 4.468, p = .000).
47
Table R14. Average Size of Price Change in Internet Data: 9¢- vs. Non-9¢-Ending Prices –
for the Internet Dataset, for the Low Quartile of the Products
in Terms of 9-Ending Popularity
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
9¢-Ending
Mean Price
Sample
Change
Size
$1.13
476
$4.00
677
$8.47
90
$23.77
217
$24.35
96
$16.99
836
$27.97
97
$29.06
208
$54.22
245
$76.30
70
$24.02
3,012
$26.63
$24.06
Non-9¢-Ending
Mean Price
Sample
Change
Size
$1.13
569
$2.57
1,579
$6.50
87
$18.49
1,488
$29.48
646
$9.80
4,196
$27.43
448
$22.39
1,802
$43.50
1,204
$93.60
495
$21.03
12,514
$25.49
$20.44
t-Stat.
p-Value
0.11
7.34
1.84
2.59
-2.60
5.66
0.12
2.75
3.37
-0.75
2.75
0.908
0.000
0.066
0.009
0.009
0.000
0.907
0.006
0.001
0.454
0.006
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level derived from
an independent samples t-test assuming equal variances. Cross-category paired t-tests showed that the price changes
are of a larger magnitude when prices end with “9”, but not significantly so (t9 = 0.457, p = .669).
Table R15. Average Size of Price Change in Internet Data: 99¢- vs. Non-99¢-Ending Prices
– for Internet Dataset, for the Low Quartile of the Products
in Terms of 9-Ending Popularity
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
9¢-Ending
Mean Price
Sample
Change
Size
$1.86
205
$5.41
307
$8.47
76
$28.51
137
$30.02
65
$19.39
585
$31.98
84
$39.68
116
$56.37
217
$99.69
44
$27.78
1,836
$32.14
$29.27
Non-9¢-Ending
Mean Price
Sample
Change
Size
$0.95
840
$2.62
1,949
$6.77
101
$18.34
1,568
$28.70
677
$9.89
4,447
$26.72
461
$22.06
1,894
$43.36
1,232
$90.76
521
$20.76
13,690
$25.02
$20.20
t-Stat.
p-Value
6.96
7.59
2.58
8.12
1.32
6.45
1.94
5.37
2.60
1.51
5.67
0.000
0.000
0.010
0.000
0.190
0.000
0.051
0.000
0.009
0.130
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level derived from
an independent samples t-test assuming equal variances. Cross-category paired t-tests showed that the price changes
are of a larger magnitude when prices end with “9” (t9 = 3.988, p = .003).
48
Table R16. Average Size of Price Change in Internet Data: $9- vs. Non-$9-Endings – in the
Internet Dataset, for the Low Quartile of the Products in Terms of 9-Ending Popularity
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$9-Ending
Mean Price
Sample
Change
Size
$4.04
13
$2.68
57
$8.75
88
$21.22
278
$29.84
252
$13.42
625
$25.17
168
$22.93
532
$30.52
751
$178.41
97
$11.93
2,861
$33.70
$29.27
Non-$9-Ending
Mean Price
Sample
Change
Size
$1.08
1,939
$1.42
2,078
$5.78
143
$14.49
1,120
$21.34
456
$15.30
3,426
$16.70
340
$12.49
2,629
$21.22
893
$80.91
153
$7.21
13,177
$19.07
$20.20
t-Stat.
p-Value
6.96
4.59
2.58
8.12
2.53
-1.84
4.94
5.35
3.60
2.27
4.56
0.000
0.000
0.010
0.000
0.012
0.066
0.000
0.000
0.000
0.023
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level derived from
an independent samples t-test assuming equal variances. Cross-category paired t-tests showed that the price changes
are of a larger magnitude when prices end with “9”, but not significantly so (t9 = 1.574, p = .150).
Table R17. Average Size of Price Change: $9.99- vs. Non-$9.99-Endings – in the Internet
Dataset, for the Low Quartile of the Products in Terms of 9-Ending Popularity
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$9.99-Ending
Mean Price
Sample
Change
Size
$3.95
11
$2.72
19
$9.83
51
$22.34
27
$23.72
73
$18.38
174
$24.19
59
$35.80
78
$32.81
205
$149.07
7
$22.47
704
$32.28
$29.27
Non-$9.99-Ending
Mean Price
Sample
Change
Size
$1.09
1,941
$1.44
2,116
$6.08
180
$15.70
5,343
$24.44
635
$14.86
3,877
$18.88
449
$13.70
3,083
$24.42
1,439
$117.86
243
$7.38
19,306
$23.85
$20.20
t-Stat.
p-Value
6.96
4.59
2.58
8.12
-0.55
3.89
4.94
5.35
3.60
1.96
5.99
0.000
0.000
0.010
0.000
0.585
0.000
0.000
0.000
0.000
0.050
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level derived from
an independent samples t-test assuming equal variances. Cross-category paired t-tests showed that the price changes
are of a larger magnitude when prices end with “9” (t9 = 2.623, p = .028).
49
Table R18. Average Size of Price Change in Internet Data: $99- vs. Non-$99-Endings – for
the Internet Dataset, for the Low Quartile of the Products in Terms of 9-Ending Popularity
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$99-Ending
Mean Price
Sample
Change
Size
N/A
0
N/A
0
N/A
0
$21.97
55
$37.65
34
$13.76
45
$41.20
22
$25.59
50
$49.75
152
$163.65
43
$49.61
401
$50.51
$37.65
Non-$99-Ending
Mean Price
Sample
Change
Size
$1.10
1,952
$1.45
2,135
$6.91
231
$15.57
1,343
$23.69
674
$15.03
4,006
$18.52
486
$14.07
3,111
$22.99
1,492
$109.41
207
$18.27
11,319
$31.33
$19.36
t-Stat.
p-Value
N/A
N/A
N/A
5.32
4.38
-0.88
4.85
5.37
4.60
1.78
8.56
N/A
N/A
N/A
0.000
0.000
0.388
0.000
0.000
0.000
0.076
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level derived from
an independent samples t-test assuming equal variances. Cross-category paired t-tests showed that the price changes
are of a larger magnitude when prices end with “9” (t6 = 2.804, p = .031).
Table R19. Average Size of Price Change: $99.99- vs. Non-$99.99-Endings – for the
Internet Dataset, for the Low Quartile of Products in Terms of 9-Ending Popularity
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$99.99-Ending
Mean Price
Sample
Change
Size
N/A
0
N/A
0
N/A
0
$26.25
4
$23.42
12
$23.11
12
$23.69
10
$63.60
4
$36.80
41
$549.01
1
$38.24
84
$106.55
$26.25
Non-$9.999-Ending
Mean Price
Sample
Change
Size
$1.10
1,952
$1.45
2,135
$6.91
231
$15.79
1,394
$24.38
696
$14.99
4,039
$19.42
498
$14.19
3,157
$25.18
1,603
$117.01
249
$19.21
11,636
$32.99
$19.69
t-Stat.
p-Value
N/A
N/A
N/A
5.32
-0.58
1.78
3.85
3.36
3.60
1.31
4.78
N/A
N/A
N/A
0.000
0.562
0.076
0.000
0.000
0.000
0.191
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level derived from
an independent samples t-test assuming equal variances. Cross-category paired t-tests showed that the price changes
are of a larger magnitude when prices end with “9”, but not significantly so. (t6 = 1.225, p = .267).
50
Table R20. Average Size of Price Change for 9¢- vs. Non-9¢-Ending Prices
– for the Dominick’s Dataset
9¢-Ending
Non-9¢-Ending
Mean Price
Sample
Mean Price
Sample
Change
Size
Change
Size
Analgesics
$0.7625
367,969
$0.4672
102,550
Bath Soap
$0.5786
58,735
$0.5473
18,298
Bathroom Tissues
$0.2499
156,863
$0.2260
184,414
Bottled Juices
$0.3121
457,490
$0.2650
583,025
Canned Soup
$0.2196
304,439
$0.1948
741,357
Canned Tuna
$0.1946
170,023
$0.1421
281,703
Cereals
$0.5010
271,757
$0.4701
494,597
Cheeses
$0.2943
872,489
$0.2128
1,039,738
Cookies
$0.4947
1,135,112
$0.3656
709,697
Crackers
$0.2964
283,278
$0.2366
279,353
Dish Detergent
$0.2798
240,532
$0.2119
183,222
Fabric Softeners
$0.3955
212,288
$0.2597
191,319
Front-End Candies
$0.1454
137,453
$0.2164
385,234
Frozen Dinners
$0.5008
230,423
$0.5452
336,201
Frozen Entrees
$0.7031
883,284
$0.7551
1,183,557
Frozen Juices
$0.2567
301,114
$0.2816
395,344
Grooming Products
$0.6285
1,017,513
$0.4849
287,969
Laundry Detergents
$0.9036
446,767
$0.5548
210,342
Oatmeal
$0.4239
72,753
$0.4115
107,971
Paper Towels
$0.1913
109,596
$0.1702
152,846
Refrigerated Juices
$0.3780
405,144
$0.2987
418,402
Shampoos
$1.4476
1,916,061
$1.0888
238,976
Snack Crackers
$0.3251
488,341
$0.2903
405,005
Soaps
$0.3147
180,935
$0.1700
190,632
Soft Drinks
$1.0409
4,614,455
$0.6155
1,219,151
Tooth Brushes
$0.5063
350,705
$0.3653
123,840
Tooth Pastes
$0.4255
468,688
$0.3497
291,045
$0.7452 16,154,207
$0.4033 10,755,788
Total
$0.4730
$0.3777
Average
$0.3955
$0.2987
Median
Category
t-Stat p-Value
120.54
5.18
18.16
60.98
33.77
61.43
23.47
169.83
176.67
73.77
87.10
108.29
-82.14
-25.10
-42.37
-24.11
97.71
160.26
5.00
15.41
104.89
96.30
44.70
136.15
341.14
134.28
94.32
934.87
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t26 = 3.911, p = .001).
51
Table R21. Average Size of Price Changes for 99¢- vs. Non-99¢-Ending Prices
– for the Dominick’s Dataset
99¢-Ending
Non-99¢-Ending
Mean Price
Sample
Mean Price
Sample
Change
Size
Change
Size
Analgesics
$0.8931
106,038
$0.6415
364,481
Bath Soap
$0.7149
15,608
$0.5346
61,425
Bathroom Tissues
$0.3302
36,944
$0.2257
304,333
Bottled Juices
$0.3760
104,451
$0.2756
936,064
Canned Soup
$0.2703
56,527
$0.1981
989,269
Canned Tuna
$0.3303
19,566
$0.1543
432,160
Cereals
$0.6374
56,437
$0.4686
709,917
Cheeses
$0.3563
160,237
$0.2403
1,751,990
Cookies
$0.5612
270,448
$0.4251
1,574,361
Crackers
$0.4902
62,297
$0.2489
500,334
Dish Detergent
$0.3273
52,117
$0.2397
371,637
Fabric Softeners
$0.5585
62,370
$0.2896
341,237
Front-End Candies
$0.2326
11,923
$0.1969
510,764
Frozen Dinners
$0.5585
56,617
$0.5237
510,007
Frozen Entrees
$0.7229
188,496
$0.7339
1,878,345
Frozen Juices
$0.2794
67,862
$0.2699
628,596
Grooming Products
$0.6756
247,298
$0.5785
1,058,184
Laundry Detergents
$1.1475
158,974
$0.6785
498,135
Oatmeal
$0.5420
12,921
$0.4068
167,803
Paper Towels
$0.3555
15,137
$0.1682
247,305
Refrigerated Juices
$0.4874
101,063
$0.3168
722,483
Shampoos
$1.6000
503,157
$1.3492
1,651,880
Snack Crackers
$0.3673
97,690
$0.3022
795,656
Soaps
$0.3907
43,874
$0.2203
327,693
Soft Drinks
$1.2138
1,385,935
$0.8704
4,447,671
Tooth Brushes
$0.5972
108,407
$0.4317
366,138
Tooth Pastes
$0.5097
117,086
$0.3758
642,647
$0.9144
4,119,480
$0.5532 22,790,515
Total
$0.5750
$0.4209
Average
$0.5097
$0.3168
Median
Category
t-Stat p-Value
103.50
28.32
49.74
78.78
49.02
89.97
70.05
134.10
134.91
125.25
74.31
157.63
13.90
12.03
-5.23
5.50
62.33
199.81
28.83
65.28
149.05
90.65
52.33
102.49
287.43
151.36
124.32
721.24
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t26 = 7.657, p = .000).
52
Table R22. Average Size of Price Changes for 9¢- vs. Non-9¢-Ending Prices
– for the Internet Dataset
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
9¢-Ending
Mean Price
Sample
Change
Size
$1.27
2,275
$2.63
2,881
$7.96
851
$15.30
775
$20.71
363
$26.19
1,438
$37.71
385
$40.57
814
$42.46
872
$89.34
91
$15.54
10,745
$28.41
$23.45
Non-9¢-Ending
Mean Price
Sample
Change
Size
$1.04
2,345
$1.71
5,820
$7.18
513
$13.45
4,754
$26.28
1,428
$14.66
5,514
$27.88
1,208
$28.56
5,145
$37.87
2,998
$97.09
564
18.07
30,289
$25.57
$20.47
t-Stat.
p-Value
5.37
10.34
1.84
1.31
-2.60
6.97
3.38
5.20
1.51
-0.55
-4.50
0.000
0.000
0.066
0.191
0.009
0.000
0.001
0.000
0.130
0.585
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t9 = 1.603, p = .143).
Table R23. Average Size of Price Changes for 99¢- vs. Non-99¢-Ending Prices
– for the Internet Dataset
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
99¢-Ending
Mean Price
Sample
Change
Size
$1.89
1,114
$3.27
1,564
$8.19
755
$17.43
551
$21.88
308
$30.48
1,098
$40.55
340
$47.63
554
$44.60
782
$110.40
65
$20.40
7,131
$32.63
$26.18
Non-99¢-Ending
Mean Price
Sample
Change
Size
$0.92
3,506
$1.74
7,137
$7.01
609
$13.29
4,978
$25.83
1,483
$14.53
5,854
$27.47
1,253
$28.42
5,405
$37.46
3,088
$94.43
590
$16.78
33,903
$25.11
$20.18
t-Stat.
p-Value
19.68
14.05
2.87
2.53
-1.73
8.71
4.32
7.05
2.27
0.98
5.55
0.000
0.000
0.001
0.012
0.084
0.000
0.000
0.000
0.023
0.330
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t9 = 2.983, p = .015).
53
Table R24. Average Size of Price Changes for $9- vs. Non-$9-Ending Prices
– for the Internet Dataset
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$9-Ending
Mean Price
Sample
Change
Size
$1.05
588
$3.08
890
$8.64
652
$19.07
1,368
$31.53
730
$19.43
1,192
$41.72
649
$52.13
1,450
$47.02
1,875
$118.89
343
$32.13
9,737
$34.26
$25.48
Non-$9-Ending
Mean Price
Sample
Change
Size
$1.17
4,032
$1.89
7,811
$6.77
712
$11.94
4,161
$20.77
1,061
$16.55
5,760
$22.38
944
$23.15
4,509
$31.28
1,995
$70.86
312
$12.83
31,927
$20.68
$18.66
t-Stat.
p-Value
-1.83
8.53
4.58
6.27
6.19
1.78
7.76
15.97
6.25
4.99
33.65
0.067
0.000
0.000
0.000
0.000
0.076
0.000
0.000
0.000
0.000
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t9 = 2.809, p = .020).
Table R25. Average Size of Price Changes for $9.99- vs. Non-$9.99-Ending Prices
– for the Internet Dataset
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$9.99-Ending
Mean Price
Sample
Change
Size
$2.42
76
$5.41
190
$9.19
449
$23.08
198
$23.05
181
$32.09
352
$48.42
235
$66.52
254
$49.28
580
$105.33
45
$33.97
2,560
$36.48
$27.59
Non-$9.99-Ending
Mean Price
Sample
Change
Size
$1.13
4,544
$1.94
8,511
$6.92
915
$13.36
5,331
$25.39
1,610
$16.24
6,600
$27.12
1,358
$28.58
5,705
$37.08
3,290
$95.33
610
$16.30
38,474
$25.31
$20.82
t-Stat.
p-Value
7.45
12.07
5.27
3.68
-0.82
5.18
6.12
9.72
3.45
0.52
17.34
0.000
0.000
0.000
0.000
0.414
0.000
0.000
0.000
0.001
0.606
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t9 = 2.980, p = .015).
54
Table R26. Average Size of Price Changes for $99- vs. Non-$99-Ending Prices
– for the Internet Dataset
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$99-Ending
Mean Price
Sample
Change
Size
N/A
0
$6.04
62
N/A
0
$20.26
271
$42.90
155
$19.75
141
$57.33
143
$96.28
337
$80.54
519
$131.13
153
$66.15
1,781
$56.78
$50.12
Non-$99-Ending
Mean Price
Sample
Change
Size
$1.15
4,620
$1.98
8,639
$7.66
1,669
$13.37
5,258
$23.47
1,636
$16.99
6,811
$27.59
1,450
$26.24
5,622
$32.46
3,351
$85.31
502
$15.20
39,253
$28.43
$24.86
t-Stat.
p-Value
N/A
8.07
N/A
3.03
6.40
0.58
6.91
21.09
13.25
4.00
42.89
N/A
0.000
N/A
0.002
0.000
0.562
0.000
0.000
0.000
0.000
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t7 = 3.266, p = .014).
Table R27. Average Size of Price Changes for $99.99 vs. Non-$99.99-Ending Prices
– for the Internet Dataset
Category
Music CDs
Movie DVDs
Video Games
Software
PDAs
Hard Drives
DVD Players
PC Monitors
Digital Cameras
Notebook PCs
Total
Average
Median
$99.99-Ending
Mean Price
Sample
Change
Size
N/A
0
$11.15
25
N/A
0
$24.18
50
$20.21
40
$34.45
40
$69.68
71
$124.94
62
$67.02
168
$139.93
13
$63.04
469
$61.45
$50.74
Non-$99.99-Ending
Mean Price
Sample
Change
Size
$1.15
4,620
$1.99
8,676
$7.66
1,364
$13.61
5,479
$25.27
1,751
$16.93
6,912
$28.42
1,522
$29.21
5,897
$37.63
3,702
$95.13
642
$16.88
40,565
$31.02
$26.85
t-Stat.
p-Value
N/A
11.65
N/A
3.03
-0.87
2.31
6.92
12.37
4.75
1.28
19.93
N/A
0.000
N/A
0.002
0.387
0.021
0.000
0.000
0.000
0.202
0.000
Note: Categories with unsupportive results are indicated by italics. The p-value is a significance level
derived from an independent samples t-test assuming equal variances. Cross-category paired t-tests
showed that the price changes are of a larger magnitude when prices end with “9” (t7 = 2.748, p = .029).
55
Figure R8a. Price of a CD (Product #3, Store #194)
743 Days (March 26, 2003 –April 15, 2005)
9.99
Price
8.99
7.99
6.99
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
Figure R8b. Price of a DVD (Product #23, Store #194)
743 Days (March 26, 2003 – April 15, 2005)
22.99
21.99
20.99
19.99
18.99
Price
17.99
16.99
15.99
14.99
13.99
12.99
11.99
10.99
9.99
8.99
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
56
Figure R8c. Price of a Notebook PC (Product #422, Store #258)
743 Days (March 26, 2003 – April 15, 2005)
1149.00
1099.00
Price
1049.00
999.00
949.00
899.00
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
Figure R8d. Price of a Hard Drive (Product #71, Store #324)
743 Days (March 26, 2003 – April 15, 2005)
84.99
79.99
Price
74.99
69.99
64.99
59.99
54.99
49.99
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
57
Figure R8e. Price of a DVD Player (Product #262, Store #230)
743 Days (March 26, 2003 – April 15, 2005)
669.99
649.99
619.99
589.99
Price
559.99
529.99
499.99
469.99
439.99
409.99
379.99
349.99
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
Figure R8f. Price of a Digital Camera (Product #273, Store #108)
743 Days (March 26, 2003 – April 15, 2005)
549.00
519.00
479.00
Price
439.00
399.00
359.00
319.00
279.00
239.00
199.00
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
58
Figure R8g. Price of a PC Monitor (Product #189, Store #17)
743 Days (March 26, 2003 – April 15, 2005)
219.00
209.00
Price
199.00
189.00
179.00
169.00
159.00
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
Figure R8h. Price of a PDA (Product #490, Store #207)
743 Days (March 26, 2003 – April 15, 2005)
450.00
419.00
418.99
400.00
Price
377.99
359.00
350.00
300.00
298.99
282.99
250.00
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
59
Figure R8i. Price of a Software Product (Product #96, Store #292)
743 Days (March 26, 2003 – April 15, 2005)
400.00
399.95
369.95
350.00
Price
318.95
312.95
312.00
300.00
250.00
237.95
200.00
1
61
121
181
241
301
361
421
481
541
601
661
721
Days
Figure R8j. Price of a Video Game (Product #205, Store #68)
743 Days (March 26, 2003 – April 15, 2005)
60.00
56.95
50.00
48.95
Price
40.00
30.00
23.05
23.05
23.05
20.00
23.05
19.99
19.99
19.99
19.99
10.00
1
61
121
181
241
301
361
421
481
541
601
661
721
Days