Zero -Ending Prices Cognitive Convenience and Price Rigidity Avichai Snira Haipeng Allan Chenb Daniel Levyacdef

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Zero-Ending Prices, Cognitive Convenience,

and Price Rigidity*

Avichai Snira, Haipeng (Allan) Chenb, Daniel Levya,c,d,e,f **

a Department of Economics, Bar-Ilan University, Ramat-Gan 5290002, Israel

b Gatton College of Business and Economics, University of Kentucky, Lexington, KY 40506, USA

c Department of Economics, Emory University, Atlanta, GA 30322, USA

d International School of Economics at Tbilisi State University, Tbilisi, Georgia

e International Centre for Economic Analysis (ICEA)

f The Rimini Centre for Economic Analysis (RCEA)

Last Revision: October 2, 2022

Abstract: We assess the role of cognitive convenience in the popularity and rigidity of 0-

ending prices in convenience settings. Studies show that 0-ending prices are common at

convenience stores because of the transaction convenience that 0-ending prices offer.

Using a large store-level retail CPI data, we find that 0-ending prices are popular and rigid

at convenience stores even when they offer little transaction convenience. We corroborate

these findings with two large retail scanner price datasets from Dominick’s and Nielsen. In

the Dominick’s data, we find that there are more 0-endings in the prices of the items in the

front-end candies category than in any other category, even though these prices have no

effect on the convenience of the consumers’ check-out transaction. In addition, in both

Dominick’s and Nielsen’s datasets, we find that 0-ending prices have a positive effect on

demand. Ruling out consumer antagonism and retailers’ use of heuristics in pricing, we

conclude that 0-ending prices are popular and rigid, and that they increase demand at

convenience settings, not only for their transaction convenience, but also for the cognitive

convenience they offer.

JEL Classification: E31, L16, D90, E70, M30

Keywords: Cognitive Convenience, Transaction Convenience, Price Rigidity, Price

Stickiness, Sticky Prices, Rigid Prices, 0-Ending Prices, Round Prices,

Convenient Prices, 9-Ending Prices, Just Below Prices, Psychological Prices,

Price Points

*We are grateful to two anonymous reviewers for detailed and constructive comments, and to the associate editor for

comments, suggestions, and guidance, which helped improve the paper substantially. We thank the participants of the

2014 LABSI conference in Siena, the 2017 Pricing Research Workshop at the University of Illinois, and the 2016 Israeli

Economic Association annual conference, particularly Dhruv Grewal, Yishay Maoz, Kent Monroe, Robert Schindler,

and Michael Tsiros for thoughtful comments. We are grateful to Ed Knotek for useful conversations and suggestions,

and for answering our questions on measuring and quantifying the convenience of various denomination coins. We are

particularly grateful to Doron Sayag for providing us with the CPI price and the consumer expenditure distribution data

for Israel. An earlier version of this paper was written when the first author was a senior lecturer at Netanya Academic

College. All authors contributed equally. The usual disclaimer applies.

** Corresponding author at: Department of Economics, Bar-Ilan University, Ramat-Gan 5290002, Israel

E-mail address: Daniel.Levy@biu.ac.il (D. Levy)

Forthcoming

Journal of Economic Behavior and Organization

Bruno was still standing at the window…

“Don’t imperrupt!” he said as we came in. “I’m counting the Pigs in the field!”

“How many are there?” I enquired. “About a thousand and four,” said Bruno.

“You mean ‘about a thousand,’” Sylvie corrected him. “There’s no good saying ‘and four’: you can’t be sure about the four!”

“And you’re as wrong as ever!” Bruno exclaimed triumphantly. “It’s just the four I can be sure about; ‘cause they’re here, grubbling

under the window! It’s the thousand I isn’t pruffickly sure about!”

Lewis Carroll, Sylvie and Bruno Concluded, 1893, Chapter 5, pp. 77–78 (spelling as in the original)

At the museum of natural history, a visitor asks the curator: “How old is this dinosaur over here?”

“Seventy million and thirty-seven years” is the answer.

As the visitor marvels at the accuracy of the dating, the curator explains:

“I’ve been working here for 37 years, you know, and when I arrived, I was told that it was 70 million years old!”

Stanislas Dehaene, the Number Sense: How the Mind Creates Mathematics, 1997, p. 108

On January 3, 2012, [Starbucks] set the net price of a tall cup of coffee in Manhattan at precisely $2.01, including tax. “I didn’t have the

penny” … Ms. Schmais wasn’t especially irked by the price increase, which comes to 10 cents for a tall cup. But that orphaned penny

had her fuming. “It’s the stupidity of it,” she said, “It’s what I’d call ‘the annoyance factor.’…It’s ridiculous. Why the extra penny?

Who has pennies? Didn’t anyone think this through? Couldn’t they round down or even up? Why leave it at a penny?” … When David

Turnbull presented two $1 bills for coffee at the Starbucks on Astor Place, he met the same problem. He wasn’t carrying any pennies.

“I can’t believe it,” he said. “Now I need to walk around with pennies? Who could possibly think a price of $2.01 makes sense?”

Jeff Sommer, “Dear Starbucks: A Penny for Your Thoughts,” New York Times, January 15, 2012, p. BU3

1. Introduction

Many retail prices end with 9 because retailers believe that 9-ending prices lead to

higher demand. 9-ending prices are also more rigid than non 9-ending prices. At

convenience stores, however, the most common prices are round, i.e., ending with 0, such

as a newspaper for $1.00, a movie ticket for $6.00, etc. At convenience stores, round

prices also tend to be more rigid than other prices.

The popularity of round prices at convenience stores is often explained by transaction

convenience they offer (i.e., the ease of making the payment and the amount of time it

takes). Shoppers at convenience stores often purchase one or two items and tend to pay in

cash. In such settings, round prices minimize the number of coins needed. In other words,

round prices make the purchase process less time-consuming, and thus offer greater

transaction convenience.

In this paper, we argue that in addition to transaction convenience, cognitive

convenience (i.e., the mental and cognitive ease of making a transaction) plays an

important role in the popularity of 0-ending prices at convenience stores. 0-ending prices

are cognitively more accessible, and thus they offer greater cognitive convenience

because the mental and cognitive efforts needed to process information on 0-ending

Round numbers usually end in 0 (Bellos 2015). The greater the number of the right-hand side zeroes, the “rounder” a

number is (Johnson et al. 2009, Snir et al. 2021). Convenient prices usually coincide with existing denomination

coins/bills. Therefore, a 0-ending price is usually convenient, but not all convenient prices are round. For example, 25¢

is a convenient price as it can be paid with a single 25¢ coin. Sometimes 5-ending prices are also considered round, but

less so than 0-ending prices (Schindler and Kirby 1997). In this paper, our focus is on 0-ending prices.

prices are low.

To test our hypothesis, we employ three large datasets. First, we use a retail price

dataset from stores Israel. Following Knotek (2011), we classify a store as a convenience

store if Israel’s Central Bureau of Statistics (CBS) flags it as a convenience store, a small

grocery, a kiosk, an open market stall, or a specialty store. We find that at convenience

stores, 0-ending prices were common and rigid when non-round endings had little effect

on transaction convenience. During the study period, the smallest denomination coin in

Israel was 10 Agora (NIS 0.10), yet the use of non 0-ending prices, such as prices ending

with 5 or 9, was allowed. In cash transactions, when the final price was not a multiple of

NIS 0.10, the law required that the final price be rounded to the nearest 0-ending.

Therefore, because of the rounding, 0-ending prices were no more transaction-convenient

than nearby non 0-ending prices. And yet, we find that 0-ending prices were more

common and more rigid than other prices.

Second, we use data from a large US retailer Dominick’s, where most prices are 9-

ending, to show that in a category where cognitive convenience is likely to be particularly

beneficial, 0-ending prices are common and rigid, and have a positive effect on demand.

The US data thus provide convergent evidence that the popularity of 0-ending prices is

not driven only by transaction convenience. After all, supermarket shoppers typically buy

a basket of goods, and thus the end digit of a single good’s price (or a small number of

goods’ prices) should have little effect on the roundness of the final total price.

Third, we use retail price data from the Nielsen dataset, covering 30,803–47,136

retailers across the US. Despite some important shortcomings because of the way prices

are measured and reported in Nielsen dataset, we use it to test the robustness of the

results.

The work that is the closest to ours is Wieseke et al. (2016), who also suggest that 0-

ending prices facilitate purchases at convenience stores because of the high cognitive

accessibility of 0-ending prices. Their empirical evidence, however, is limited to a single

product at three university cafeterias, with a few hundred dollars of sales. More

In his 2017 autobiography One Buck at a Time, Macon Brock, the founder of Dollar Tree, a dollar store chain

operating about 8,000 stores across the US, explains the benefits that shoppers get form the chain’s round, $1.00 prices:

“When a customer walked into our store, she could shut off her brain. She didn't have to think, didn't have to calculate

how much she was spending” (our emphasis). See: https://abcnews.go.com/Business/wireStory/dollar-tree-makes-

official-items-now-cost-125-81361316, accessed February 22, 2022.

For example, no change was given if one used a NIS 10 coin to pay any price in the range NIS 9.95−NIS 10.04.

important, however, they cannot distinguish the cognitive convenience of 0-ending prices

from their transaction convenience. In contrast, we study three large retail price data sets

for hundreds of goods from two countries. In addition, the legal setting in place in Israel

during our study period creates an environment that helps us rule out transaction

convenience as a possible explanation of our results concerning the prevalence and

rigidity of 0-ending prices.

In addition, we explore a possible effect of the 2011 “cottage cheese protests” (Hendel

et al. 2017) on the use of 0-ending prices at Israeli stores. Cottage cheese is a staple food

in Israel and its price was regulated by the government until 2006. Once the regulation

was lifted, the price of cottage cheese increased quickly. In the summer of 2011, a group

of activists organized public protests, which escalated quickly.

In the peak, about 1

million Israelis (about 12.8% of the population at the time) went to the streets to

demonstrate against the high costs of living.

Among other things, the protests drew the

media’s attention to retailers’ practices that were deemed “unfair” (Hendel et al. 2017).

That could have led retailers to reduce the number of 9-ending prices and increase the

number of 0-ending prices, in an attempt to reduce consumer antagonism (Blinder et al.

1998). However, our analysis rules out consumer antagonism, as well as retailers’ use of

heuristics in setting the prices (DellaVigna and Gentzkow 2019, Strulov-Shlain 2021,

Huang et al. 2022), as possible explanations of our results.

Our empirical strategy is to use the three datasets, the Israeli CPI retail price data, the

US scanner price data, and the Nielsen data, and four types of analyses, as follows. First,

we demonstrate the popularity of 0-ending prices at convenience stores (Israel) and

supermarkets (US) by examining the prevalence of 0-ending prices. Second, to

demonstrate the rigidity of 0-ending prices, we estimate baseline linear probability

models, which are expanded to include various control variables. Third, we assess the

effect of 0-ending prices on demand. Fourth, we subject our findings to multiple

robustness tests and find that the results we report are robust.

Our finding that 0-ending prices are more rigid than other prices in settings where

cognitive convenience is beneficial adds to a growing literature on price rigidity. Price

rigidity (or price stickiness) is a phenomenon where prices do not respond to changes in

See, for example, https://www.ynet.co.il/articles/0,7340,L-4446809,00.html (in Hebrew), accessed February 22, 2022.

Source of the data on Israel’s population in 2011: Israel’s Central Bureau of Statistics.

market conditions, or when their response is sluggish and incomplete. In such situations,

monetary policy actions might not immediately translate into prices, and thus they can

have a real effect. Price rigidity, therefore, is a critical ingredient in modern New

Keynesian macroeconomic models because of its implications for monetary neutrality.

The finding that 0-ending prices enhance sales is also related to optimal price

information provision in retail settings. Some recent studies conclude that retailers often

use prices to conceal information (Gabaix and Laibson 2006, Chen et al 2008,

Chakraborty et al 2015, McShane et al 2016, Levy et al 2020, Snir and Levy 2021). Our

findings imply that in settings where shoppers make spontaneous decisions on a small

number of goods, reducing the cognitive load that is needed to make decisions can

increase the likelihood of a sale. In such settings, transparency of price information can

benefit both the sellers and the buyers.

For the remainder of the article, we proceed as follows. In section 2, we review the

relevant literature. In section 3, we state our formal hypotheses. In section 4, we study the

data from Israel. In section 5, we study the data from the US. In section 6, we briefly

summarize the results of the robustness tests. We conclude in section 7.

2. Literature review

2.1. Price rigidity in New Keynesian macroeconomics

“A central question in macroeconomics is whether nominal rigidities are important”

(Eichenbaum et al. 2011, p. 234). Therefore, a large stream of empirical literature on

price rigidity tries to assess the extent of price rigidity using a variety of micro-level data.

Examples of earlier studies include Carlton (1986) who studies the rigidity of wholesale

prices, Cecchetti (1986) who studies the rigidity of magazine prices, Kashyap (1995) who

studies mail-order catalog prices, Lach and Tsiddon (1992, 1996, 2007) who study data

from a high-inflation period, Levy et al. (1997) who study price rigidity using data from

five large US supermarket chains, Blinder et al. (1991, 1998) who survey price

adjustment practices at 200 large US firms, and Dutta et al. (2002) and Levy et al. (2002)

who study price rigidity using retail orange juice price data from a large US supermarket

chain and the corresponding commodity spot price data from the New York Cotton

Exchange.

More recent examples include Zbaracki et al. (2004) who employ an ethnographic

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Zero-EndingPrices,CognitiveConvenience,andPriceRigidity*AvichaiSnira,Haipeng(Allan)Chenb,DanielLevya,c,d,e,f**aDepartmentofEconomics,Bar-IlanUniversity,Ramat-Gan5290002,IsraelbGattonCollegeofBusinessandEconomics,UniversityofKentucky,Lexington,KY40506,USAcDepartmentofEconomics,EmoryUniversity,Atlanta...

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Zero -Ending Prices Cognitive Convenience and Price Rigidity Avichai Snira Haipeng Allan Chenb Daniel Levyacdef

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