Price Points and Price Rigidity Daniel Levy* Bar-Ilan University and RCEA [email protected]Dongwon Lee Korea University [email protected]Haipeng (Allan) Chen Texas A&M University [email protected]Robert J. Kauffman Arizona State University [email protected]Mark Bergen University of Minnesota [email protected]Last revision: November 26, 2010 JEL Codes: E31, L16, D80, M21, M30 Key Words: Price Point, 9-Ending Price, Price Rigidity Forthcoming : Review of Economics and Statistics
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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.
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Table 2. Descriptive Statistics for the Internet Price Data
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.)
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Table 3. Top 10 Highest Frequencies in the Internet Data
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 right-most 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.
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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
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.
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Table 5. Transition Probability Matrix Conditional on a Price Change
for a 10-State Markov Chain, Internet Data, for the Penny Digit
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.
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Table 6. Transition Probability Matrix Conditional on a Price Change
for a 10-State Markov Chain, Internet Data, for the Dollar Digit
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.
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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
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.
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Table 10. Results of the Logit Regression (Equation 1) Estimation
for the Dominick’s Data, Regular Prices, Stores #8, #12, #122 and #133
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.
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Table 11. Results of Logit Regression (Equation 1) Estimation for the Internet Dataset
Category 9¢-
Endings 99¢-
Endings $9-
Endings $99-
Endings $9.99-
Endings $99.99- Endings
Music CDs -0.0727*** (0.9299)
-0.5463*** (0.5791)
-0.0125*** (0.9876)
-0.4430*** (0.6421)
Movie DVDs -0.4716*** (0.6240)
-0.5827*** (0.5584)
-0.3551*** (0.7011)
-0.9068*** (0.4038)
Video Games 0.1630*** (1.1770)
0.0729*** (1.0756)
-0.3572*** (0.6996)
-0.2807*** (0.7553)
Software -0.3185*** (0.7272)
-0.4998*** (0.6067)
-0.5892*** (0.5548)
-1.0831*** (0.3385)
-0.8032*** (0.4479)
-1.4014*** (0.2463)
PDAs -0.1496*** (0.8611)
-0.2253*** (0.7983)
-0.4370*** (0.6460)
-0.5944*** (0.5519)
-0.4041*** (0.6676)
-0.8986*** (0.4071)
Hard Drives -0.2276*** (0.7964)
-0.2777*** (0.7575)
-0.3368*** (0.7141)
-0.3242*** (0.7231)
-0.5197*** (0.5947)
-0. 6072*** (0. 5449)
DVD Players -0.5161*** (0.5968)
-0.5808*** (0.5595)
-0.7455*** (0.4745)
-0.5246*** (0. 5918)
-0.6718*** (0.5108)
-0.6074*** (0.5448)
PC Monitors -0.1893*** (0.8275)
-0.3734*** (0.6884)
-0.5445*** (0.5801)
-0.7598*** (0.4678)
-0.7457*** (0.4744)
-1.3102*** (0.2698)
Digital Cameras
-0.3634*** (0.6953)
-0.4199*** (0.6571)
-0.4464*** (0.6339)
-0.9363*** (0.3921)
-0.5052*** (0.6034)
-1.1454*** (0.3181)
Notebook PCs
-0.3583*** (0.6989)
-0.5335*** (0.5865)
-0.7383*** (0. 4779)
-0.5533*** (0. 5750)
-0.7014*** (0.4959)
-0.7149*** (0.4892)
Total -0.2800*** (0.7558)
-0.4330*** (0.6486)
-0.4378*** (0.6455)
-0.7787*** (0.4590)
-0. 5841*** (0.5576)
-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.
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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
All Products
Low Quartile of Products in Terms of Popularity of 9-Ending Prices
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.
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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 9-dummy 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.
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.
9 Two categories, Music CDs and Video Games, contained no prices with a $99-and $99.00
endings.
10 There were no Music CDs, Music DVDs or Video Games with $99- or with $99.99-ending
prices.
11 See, for example, http://www.globes.co.il/news/article.aspx?did=1000403091 (in Hebrew).
12 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
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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 A recent New York Time report (Toy, 2010) lists numbers that have particular significance in
some cultures. 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. In the
Jewish culture the number 18 has a special significance because numerically it is equivalent to
chai which means life, and therefore, donations made by Jews are often in multiples of 18. In the
Indian society, the person's birth date is used to determine the person's lucky numbers based on
Vedic astrology.
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. According to Toy (2010), in many residential and commercial
buildings the 13th floor is missing, skipping from the 12th floor to the 14th floor.
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12‐01 Network Topology and the Efficiency of Equilibrium
Igal Milchtaich, June 2001.
13‐01 General Equilibrium Pricing of Trading Strategy Risk
Abraham Lioui and Patrice Poncet, July 2001.
14‐01 Social Conformity and Child Labor
Shirit Katav‐Herz, July 2001.
15‐01 Determinants of Railroad Capital Structure, 1830–1885
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Daniel A. Schiffman, September 2001.
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Eliakim Katz and Hillel Rapoport, October 2001.
18‐01 Property Rights, Theft, and Efficiency: The Biblical Waiver of Fines in the Case of Confessed Theft
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19‐01 Ethnic Discrimination and the Migration of Skilled Labor
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1‐02 Can Vocational Education Improve the Wages of Minorities and Disadvantaged Groups? The Case of Israel
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2‐02 What Can the Price Gap between Branded and Private Label Products Tell Us about Markups?
Robert Barsky, Mark Bergen, Shantanu Dutta, and Daniel Levy, March 2002.
3‐02 Holiday Price Rigidity and Cost of Price Adjustment
Daniel Levy, Georg Müller, Shantanu Dutta, and Mark Bergen, March 2002.
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5‐02 Coordination and Critical Mass in a Network Market – An Experimental Evaluation
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Amir Etziony and Avi Weiss, April 2002.
8‐02 Brain Drain and LDCs’ Growth: Winners and Losers
Michel Beine, Fréderic Docquier, and Hillel Rapoport, April 2002.
9‐02 Heterogeneity in Price Rigidity: Evidence from a Case Study Using Micro‐Level Data
Daniel Levy, Shantanu Dutta, and Mark Bergen, April 2002.
10‐02 Price Flexibility in Channels of Distribution: Evidence from Scanner Data
Shantanu Dutta, Mark Bergen, and Daniel Levy, April 2002.
11‐02 Acquired Cooperation in Finite‐Horizon Dynamic Games
Igal Milchtaich and Avi Weiss, April 2002.
12‐02 Cointegration in Frequency Domain
Daniel Levy, May 2002.
13‐02 Which Voting Rules Elicit Informative Voting?
Ruth Ben‐Yashar and Igal Milchtaich, May 2002.
14‐02 Fertility, Non‐Altruism and Economic Growth: Industrialization in the Nineteenth Century
Elise S. Brezis, October 2002.
15‐02 Changes in the Recruitment and Education of the Power Elitesin Twentieth Century Western Democracies
Elise S. Brezis and François Crouzet, November 2002.
16‐02 On the Typical Spectral Shape of an Economic Variable
Daniel Levy and Hashem Dezhbakhsh, December 2002.
17‐02 International Evidence on Output Fluctuation and Shock Persistence
Daniel Levy and Hashem Dezhbakhsh, December 2002.
1‐03 Topological Conditions for Uniqueness of Equilibrium in Networks
Igal Milchtaich, March 2003.
2‐03 Is the Feldstein‐Horioka Puzzle Really a Puzzle?
Daniel Levy, June 2003.
3‐03 Growth and Convergence across the US: Evidence from County‐Level Data
Matthew Higgins, Daniel Levy, and Andrew Young, June 2003.
4‐03 Economic Growth and Endogenous Intergenerational Altruism
Hillel Rapoport and Jean‐Pierre Vidal, June 2003.
5‐03 Remittances and Inequality: A Dynamic Migration Model
Frédéric Docquier and Hillel Rapoport, June 2003.
6‐03 Sigma Convergence Versus Beta Convergence: Evidence from U.S. County‐Level Data
Andrew T. Young, Matthew J. Higgins, and Daniel Levy, September 2003.
7‐03 Managerial and Customer Costs of Price Adjustment: Direct Evidence from Industrial Markets
Mark J. Zbaracki, Mark Ritson, Daniel Levy, Shantanu Dutta, and Mark Bergen, September 2003.
8‐03 First and Second Best Voting Rules in Committees
Ruth Ben‐Yashar and Igal Milchtaich, October 2003.
9‐03 Shattering the Myth of Costless Price Changes: Emerging Perspectives on Dynamic Pricing
Mark Bergen, Shantanu Dutta, Daniel Levy, Mark Ritson, and Mark J. Zbaracki, November 2003.
1‐04 Heterogeneity in Convergence Rates and Income Determination across U.S. States: Evidence from County‐Level Data
Andrew T. Young, Matthew J. Higgins, and Daniel Levy, January 2004.
2‐04 “The Real Thing:” Nominal Price Rigidity of the Nickel Coke, 1886‐1959
Daniel Levy and Andrew T. Young, February 2004.
3‐04 Network Effects and the Dynamics of Migration and Inequality: Theory and Evidence from Mexico
David Mckenzie and Hillel Rapoport, March 2004.
4‐04 Migration Selectivity and the Evolution of Spatial Inequality
Ravi Kanbur and Hillel Rapoport, March 2004.
5‐04 Many Types of Human Capital and Many Roles in U.S. Growth: Evidence from County‐Level Educational Attainment Data
Andrew T. Young, Daniel Levy and Matthew J. Higgins, March 2004.
6‐04 When Little Things Mean a Lot: On the Inefficiency of Item Pricing Laws
Mark Bergen, Daniel Levy, Sourav Ray, Paul H. Rubin and Benjamin Zeliger, May 2004.
7‐04 Comparative Statics of Altruism and Spite
Igal Milchtaich, June 2004.
8‐04 Asymmetric Price Adjustment in the Small: An Implication of Rational Inattention
Daniel Levy, Haipeng (Allan) Chen, Sourav Ray and Mark Bergen, July 2004.
1‐05 Private Label Price Rigidity during Holiday Periods
Georg Müller, Mark Bergen, Shantanu Dutta and Daniel Levy, March 2005.
2‐05 Asymmetric Wholesale Pricing: Theory and Evidence
Sourav Ray, Haipeng (Allan) Chen, Mark Bergen and Daniel Levy, March 2005.
3‐05 Beyond the Cost of Price Adjustment: Investments in Pricing Capital
Mark Zbaracki, Mark Bergen, Shantanu Dutta, Daniel Levy and Mark Ritson, May 2005.
4‐05 Explicit Evidence on an Implicit Contract
Andrew T. Young and Daniel Levy, June 2005.
5‐05 Popular Perceptions and Political Economy in the Contrived World of Harry Potter
Avichai Snir and Daniel Levy, September 2005.
6‐05 Growth and Convergence across the US: Evidence from County‐Level Data (revised version)
Matthew J. Higgins, Daniel Levy, and Andrew T. Young , September 2005.
1‐06 Sigma Convergence Versus Beta Convergence: Evidence from U.S. County‐Level Data (revised version)
Andrew T. Young, Matthew J. Higgins, and Daniel Levy, June 2006.
2‐06 Price Rigidity and Flexibility: Recent Theoretical Developments
Daniel Levy, September 2006.
3‐06 The Anatomy of a Price Cut: Discovering Organizational Sources of the Costs of Price Adjustment
Mark J. Zbaracki, Mark Bergen, and Daniel Levy, September 2006.
4‐06 Holiday Non‐Price Rigidity and Cost of Adjustment
Georg Müller, Mark Bergen, Shantanu Dutta, and Daniel Levy. September 2006.
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Igal Milchtaich, October 2008.
2008‐02 Federal, State, and Local Governments: Evaluating their Separate Roles in US Growth
Andrew T. Young, Daniel Levy, and Matthew J. Higgins, December 2008.
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Igal Milchtaich, December 2008.
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Leonid V. Azarnert, December 2008.
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Leonid V. Azarnert, January 2009.
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Gil S. Epstein and Yosef Mealem, January 2009.
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Daniel Levy, Haipeng Chen, Georg Müller, Shantanu Dutta, and Mark Bergen, February 2009.
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Dror Goldberg, April 2009.
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Dror Goldberg, April 2009.
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Dror Goldberg, April 2009.
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Raphaël Franck, April 2009.
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Adi Schnytzer and Sara Westreich, April 2009.
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Leonid V. Azarnert, April 2009.
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Sarit Cohen‐Goldner, Chemi Gotlibovski and Nava Kahana, May 2009.
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Nava Kahanaa, Yosef Mealem and Shmuel Nitzan, May 2009.
2009‐15 Après nous le Déluge: Fertility and the Intensity of Struggle against Immigration
Leonid V. Azarnert, June 2009.
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Ruth Ben‐Yashar, Winston T.H. Koh and Shmuel Nitzan, June 2009.
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Kobi Kriesler and Shmuel Nitzan, June 2009.
2009‐18 Demystifying the ‘Metric Approach to Social Compromise with the Unanimity Criterion’
Shmuel Nitzan, June 2009.
2009‐19 On the Robustness of Brain Gain Estimates
Michel Beine, Frédéric Docquier and Hillel Rapoport, July 2009.
2009‐20 Wage Mobility in Israel: The Effect of Sectoral Concentration
Ana Rute Cardoso, Shoshana Neuman and Adrian Ziderman, July 2009.
2009‐21 Intermittent Employment: Work Histories of Israeli Men and Women, 1983–1995
Shoshana Neuman and Adrian Ziderman, July 2009.
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Pablo Brañas‐Garza, Teresa García‐Muñoz and Shoshana Neuman, July 2009.
2009‐23 The Big Carrot: High‐Stakes Incentives Revisited
Pablo Brañas‐Garza, Teresa García‐Muñoz and Shoshana Neuman, July 2009.
2009‐24 The Why, When and How of Immigration Amnesties
Gil S. Epstein and Avi Weiss, September 2009.
2009‐25 Documenting the Brain Drain of «la Crème de la Crème»: Three Case‐Studies on International Migration at the Upper Tail of the Education Distribution
Frédéric Docquier and Hillel Rapoport, October 2009.
2009‐26 Remittances and the Brain Drain Revisited: The Microdata Show That More Educated Migrants Remit More
Albert Bollard, David McKenzie, Melanie Morten and Hillel Rapoport, October 2009.
2009‐27 Implementability of Correlated and Communication Equilibrium Outcomes in Incomplete Information Games
Igal Milchtaich, November 2009.
2010‐01 The Ultimatum Game and Expected Utility Maximization – In View of Attachment Theory
Shaul Almakias and Avi Weiss, January 2010.
2010‐02 A Model of Fault Allocation in Contract Law – Moving From Dividing Liability to Dividing Costs
Osnat Jacobi and Avi Weiss, January 2010.
2010‐03 Coordination and Critical Mass in a Network Market: An Experimental Investigation
Bradley J. Ruffle, Avi Weiss and Amir Etziony, February 2010.
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Leonid V. Azarnert, April 2010.
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Leonid V. Azarnert, April 2010.
2010‐06 The Effect of Limited Search Ability on the Quality of Competitive Rent‐Seeking Clubs
Shmuel Nitzan and Kobi Kriesler, April 2010.
2010‐07 Condorcet vs. Borda in Light of a Dual Majoritarian Approach
Eyal Baharad and Shmuel Nitzan, April 2010.
2010‐08 Prize Sharing in Collective Contests
Shmuel Nitzan and Kaoru Ueda, April 2010.
2010‐09 Network Topology and Equilibrium Existence in Weighted Network Congestion Games
Igal Milchtaich, May 2010.
2010‐10 The Evolution of Secularization: Cultural Transmission, Religion and Fertility Theory, Simulations and Evidence
Ronen Bar‐El, Teresa García‐Muñoz, Shoshana Neuman and Yossef Tobol, June 2010.
2010‐11 The Economics of Collective Brands
Arthur Fishman, Israel Finkelstein, Avi Simhon and Nira Yacouel, July 2010.
2010‐12 Interactions Between Local and Migrant Workers at the Workplace
Gil S. Epstein and Yosef Mealem, August 2010.
2010‐13 A Political Economy of the Immigrant Assimilation: Internal Dynamics
Gil S. Epstein and Ira N. Gang, August 2010.
2010‐14 Attitudes to Risk and Roulette
Adi Schnytzer and Sara Westreich, August 2010.
2010‐15 Life Satisfaction and Income Inequality
Paolo Verme, August 2010.
2010‐16 The Poverty Reduction Capacity of Private and Public Transfers in Transition
Paolo Verme, August 2010.
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Gil S. Epstein and Ira N. Gang, August 2010.
2010‐18 Political Culture and Discrimination in Contests
Gil S. Epstein, Yosef Mealem and Shmuel Nitzan, October 2010.
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Gil S. Epstein and Yosef Mealem, November 2010.
2010‐20 Beyond Condorcet: Optimal Aggregation Rules Using Voting Records
Eyal Baharad, Jacob Goldberger, Moshe Koppel and Shmuel Nitzan, December 2010.
2010‐21 Price Points and Price Rigidity
Daniel Levy, Dongwon Lee, Haipeng (Allan) Chen, Robert J. Kauffman and Mark Bergen, December 2010.
2010‐22 Price Setting and Price Adjustment in Some European Union Countries: Introduction to the Special Issue