Article: the unrelated adage Benford's law of controversy
Benford's law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small. For example, in sets which obey the law, the number appears as the most significant digit about 30% of the time, while appears as the most significant digit less than 5% of the time. By contrast, if the digits were distributed uniformly, they would each occur about 11.1% of the time. Benford's law also makes (different) predictions about the distribution of second digits, third digits, digit combinations, and so on.
It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.
The graph here shows Benford's law for base 10. There is a generalization of the law to numbers expressed in other bases (for example, base 16), and also a generalization from leading 1 digit to leading n digits.
It is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881.
Benford's law is a special case of Zipf's law.
Mathematical statement
A set of numbers is said to satisfy Benford's law if the leading digit ( ∈ {1, ..., 9}) occurs with probability
Numerically, the leading digits have the following distribution in Benford's law, where is the leading digit and ( ) the probability:
d P (d ) Relative size of P (d ) 1 2 3 4 5 6 7 8 9
The quantity ( ) is proportional to the space between and + 1 on a logarithmic scale. Therefore, this is the distribution expected if the mantissae of the logarithms of the numbers (but not the numbers themselves) are uniformly and randomly distributed.
For example, a number , constrained to lie between 1 and 10, starts with the digit 1 if 1 ≤ < 2, and starts with the digit 9 if 9 ≤ < 10. Therefore, starts with the digit 1 if log 1 ≤ log < log 2, or starts with 9 if log 9 ≤ log x < log 10. The interval [log 1, log 2] is much wider than the interval [log 9, log 10] (0.30 and 0.05 respectively); therefore if log is uniformly and randomly distributed, it is much more likely to fall into the wider interval than the narrower interval, i.e. more likely to start with 1 than with 9. The probabilities are proportional to the interval widths, and this gives the equation above. (The above discussion assumed is between 1 and 10, but the result is the same no matter how many digits has before the decimal point.)
Benford's law in other bases
An extension of Benford's law predicts the distribution of first digits in other bases besides decimal; in fact, any base b ≥ 1. The general form is:
For b = 2 (the binary number system), Benford's law is true but trivial: All binary numbers (except for 0) start with the digit 1. (On the other hand, the generalization of Benford's law to second and later digits is not trivial, even for binary numbers.)
Example
Examining a list of the heights of the 60 tallest structures in the world by category shows that 1 is by far the most common leading digit, irrespective of the unit of measurement (cf. "scale invariance", below):
Leading digit meters feet In Benford's law Count % Count % 1 26 43.3% 18 30.0% 30.1% 2 7 11.7% 8 13.3% 17.6% 3 9 15.0% 8 13.3% 12.5% 4 6 10.0% 6 10.0% 9.7% 5 4 6.7% 10 16.7% 7.9% 6 1 1.7% 5 8.3% 6.7% 7 2 3.3% 2 3.3% 5.8% 8 5 8.3% 1 1.7% 5.1% 9 0 0.0% 2 3.3% 4.6%
Another example is the leading digit of :
1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, 2, 4, 8, 1, 3, 6, 1...
History
The discovery of Benford's law goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm tables the earlier pages (that started with 1) were much more worn than the other pages. Newcomb's published result is the first known instance of this observation and includes a distribution on the second digit, as well. Newcomb proposed a law that the probability of a single number N being the first digit of a number was equal to log(N + 1) − log(N).
The phenomenon was again noted in 1938 by the physicist Frank Benford, who tested it on data from 20 different domains and was credited for it. His data set included the surface areas of 335 rivers, the sizes of 3259 US populations, 104 physical constants, 1800 molecular weights, 5000 entries from a mathematical handbook, 308 numbers contained in an issue of Reader's Digest, the street addresses of the first 342 persons listed in American Men of Science and 418 death rates. The total number of observations used in the paper was 20,229. This discovery was later named after Benford (making it an example of Stigler's Law).
In 1995, Ted Hill proved the result about mixed distributions mentioned below.
Explanations
Arno Berger and Ted Hill have stated that, "The widely known phenomenon called Benford’s law continues to defy attempts at an easy derivation".
However, limited explanations of Benford's law have been offered, including the following.
Overview
Benford's law states that the fractional part of the logarithm of the data is uniformly distributed between 0 and 1. It tends to apply most accurately to data that are distributed uniformly across many orders of magnitude. As a rule, the more orders of magnitude that the data evenly covers, the more accurately Benford's law applies.
For instance, one can expect that Benford's law would apply to a list of numbers representing the populations of UK villages, or representing the values of small insurance claims. But if a "village" is defined as a settlement with population between 300 and 999, or a "small insurance claim" is defined as a claim between $50 and $99, then Benford's law will not apply.
Consider the probability distributions shown below, referenced to a log scale.
In each case, the total area in red is the relative probability that the first digit is 1, and the total area in blue is the relative probability that the first digit is 8.
For the left distribution, the size of the areas of red and blue are approximately proportional to the widths of each red and blue bar. Therefore, the numbers drawn from this distribution will approximately follow Benford's law. On the other hand, for the right distribution, the ratio of the areas of red and blue is very different from the ratio of the widths of each red and blue bar. Rather, the relative areas of red and blue are determined more by the height of the bars than the widths. Accordingly, the first digits in this distribution do not satisfy Benford's law at all.
Thus, real-world distributions that span several orders of magnitude rather uniformly (e.g. populations of villages / towns / cities, stock-market prices), are likely to satisfy Benford's law to a very high accuracy. On the other hand, a distribution that is mostly or entirely within one order of magnitude (e.g. heights of human adults, or IQ scores) is unlikely to satisfy Benford's law very accurately, or at all. However, it is not a sharp line: As the distribution gets narrower, the discrepancies from Benford's law typically increase gradually.
In terms of conventional probability density (referenced to a linear scale rather than log scale, i.e. P(x)dx rather than P(log x) d(log x)), the equivalent criterion is that Benford's law will be very accurately satisfied when P(x) is approximately proportional to 1/x over several orders-of-magnitude variation in x.
This discussion is not a full explanation of Benford's law, because we have not explained why we so often come across data-sets that, when plotted as a probability distribution of the logarithm of the variable, are relatively uniform over several orders of magnitude. The following sections give examples of how this might happen.
Outcomes of exponential growth processes
An example of where Benford's law would occur is in measuring the population of bacteria over a period. If 1000 cells of bacteria are introduced into a dish full of food, the number of bacteria grows exponentially, doubling each day. Every few hours for 30 days, the number of bacteria that are in the dish are recorded. By the end of 30 days, there will be a trillion bacteria. This list of numbers will follow Benford's law quite accurately.
As the number of bacteria is growing exponentially, doubling each day, on the first day, the number of bacteria is increasing from 1000 towards 2000: The first digit is 1 the whole day. On the second day, there are 2000 bacteria increasing towards 4000: The first digit is 2 for fourteen hours and 3 for six hours. On the third day, there are 4000 bacteria increasing towards 8000: The first digit will pass through 4, 5, 6, and 7, spending less and less time in each digit. The next day, there are 8000 bacteria increasing towards 16,000. The leading digit will pass rapidly through 8 and 9 in a few hours, but then once there are 10,000 bacteria, the first digit will be 1 for a whole 24 hours, until the number of bacteria gets to 20,000. Therefore, the first digit is 1 with the highest probability, and 9 with the lowest.
An exponentially growing quantity is moving rightward on a log-scale at a constant rate. Measuring the number of bacteria at a random time in the 30-day window, gives a random point on the log-scale, uniformly distributed in that corresponding window (about 6 orders of magnitude). As explained in the previous section, this kind of probability distribution satisfies Benford's law with high accuracy.
Multiplicative fluctuations
Many real-world examples of Benford's law arise from multiplicative fluctuations. For example, if a stock price starts at $100, and then each day it gets multiplied by a randomly chosen factor between 0.99 and 1.01, then over an extended period the probability distribution of its price satisfies Benford's law with higher and higher accuracy.
The reason is that the logarithm of the stock price is undergoing a random walk, so over time its probability distribution will get more and more broad and uniform (see above). (More technically, the central limit theorem says that multiplying more and more random variables will create a log-normal distribution with larger and larger variance, so eventually it covers many orders of magnitude almost uniformly.)
Unlike multiplicative fluctuations, additive fluctuations do not lead to Benford's law: They lead instead to normal probability distributions (again by the central limit theorem), which do not satisfy Benford's law. For example, the "number of heartbeats that I experience on a given day" can be written as the sum of many random variables (e.g. the sum of heartbeats per minute over all the minutes of the day), so this quantity is unlikely to follow Benford's law. By contrast, that hypothetical stock price described above can be written as the product of many random variables (i.e. the price change factor for each day), so is likely to follow Benford's law quite well.
Scale invariance
If there is a list of lengths, the distribution of first digits of numbers in the list may be generally similar regardless of whether all the lengths are expressed in metres, or yards, or feet, or inches, etc.
This is not always the case. For example, the height of adult humans almost always starts with a 1 or 2 when measured in meters, and almost always starts with 4, 5, 6, or 7 when measured in feet.
But consider a list of lengths that is spread evenly over many orders of magnitude. For example, a list of 1000 lengths mentioned in scientific papers will include the measurements of molecules, bacteria, plants, and galaxies. If one writes all those lengths in meters, or writes them all in feet, it is reasonable to expect that the distribution of first digits should be the same on the two lists.
In these situations, where the distribution of first digits of a data set is scale invariant (or independent of the units that the data are expressed in), the distribution of first digits is always given by Benford's Law. To be sure of approximate agreement with Benford's Law, the data has to be approximately invariant when scaled up by any factor up to 10. A lognormally distributed data set with wide dispersion has this approximate property.
For example, the first (non-zero) digit on this list of lengths should have the same distribution whether the unit of measurement is feet or yards. But there are three feet in a yard, so the probability that the first digit of a length in yards is 1 must be the same as the probability that the first digit of a length in feet is 3, 4, or 5. Applying this to all possible measurement scales gives the logarithmic distribution of Benford's law.
Multiple probability distributions
For numbers drawn from certain distributions (IQ scores, human heights) the Law fails to hold because these variates obey a normal distribution which is known not to satisfy Benford's law, since normal distributions can't span several orders of magnitude and the mantissae of their logarithms will not be (even approximately) uniformly distributed.
However, if one "mixes" numbers from those distributions, for example by taking numbers from newspaper articles, Benford's law reappears. This can also be proven mathematically: if one repeatedly "randomly" chooses a probability distribution (from an uncorrelated set) and then randomly chooses a number according to that distribution, the resulting list of numbers will obey Benford's Law. A similar probabilistic explanation for the appearance of Benford's Law in everyday-life numbers has been advanced by showing that it arises naturally when one considers mixtures of uniform distributions.
Applications Accounting fraud detection
In 1972, Hal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions. Based on the plausible assumption that people who make up figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's Law ought to show up any anomalous results. Following this idea, Mark Nigrini showed that Benford's Law could be used in forensic accounting and auditing as an indicator of accounting and expenses fraud. In practice, applications of Benford's Law for fraud detection routinely use more than the first digit.
Legal status
In the United States, evidence based on Benford's law has been admitted in criminal cases at the federal, state, and local levels.
Election data
Benford's Law has been invoked as evidence of fraud in the 2009 Iranian elections, and also used to analyze other election results. However, other experts consider Benford's Law essentially useless as a statistical indicator of election fraud in general.
Macroeconomic data
Similarly, the macroeconomic data the Greek government reported to the European Union before entering the eurozone was shown to be probably fraudulent using Benford's law, albeit years after the country joined.
Price Digit Analysis
Benford's Law as a benchmark for the investigation of price digits has been successfully introduced into the context of pricing research. The importance of this benchmark for detecting irregularities in prices was first demonstrated in a European wide study which investigated consumer price digits before and after the euro introduction for price adjustments. The euro introduction in 2002, with its various exchange rates, distorted existing nominal price patterns while at the same time retaining real prices. While the first digits of nominal prices distributed according to Benford's Law, the study showed a clear deviation from this benchmark for the second and third digits in nominal market prices with a clear trend towards psychological pricing after the nominal shock of the euro introduction.
Genome data
The number of open reading frames and their relationship to genome size differs between eukaryotes and prokaryotes with the former showing a log-linear relationship and the latter a linear relationship. Benford's law has been used to test this observation with an excellent fit to the data in both cases.
Scientific fraud detection
A test of regression coefficients in published papers showed agreement with Benford's law. As a comparison group subjects were asked to fabricate statistical estimates. The fabricated results failed to obey Benford's law.
Statistical tests
Although the chi squared test has been used to test for compliance with Benford's law it has low statistical power when used with small samples.
The Kolmogorov–Smirnov test and the Kuiper test are more powerful when the sample size is small particularly when Stephens's corrective factor is used. These tests may be overly conservative when applied to discrete distribution. Values for the Benford test have been generated by Morrow. The critical values of the test statistics are shown below:
0.10 0.05 0.01 Kuiper Test 1.191 1.321 1.579 Kolmogorov–Smirnov 1.012 1.148 1.420
Two alternative tests specific to this law have been published: first, the max (m) statistic is given by
and secondly, the distance (d) statistic is given by
where FSD is the First Significant Digit and is the sample size. Morrow has determined the critical values for both these statistics, which are shown below:
0.10 0.05 0.01 Leemis' m 0.851 0.967 1.212 Cho–Gaines' d 1.212 1.330 1.569
Nigrini has suggested the use of a z statistic
with
where |x| is the absolute value of x, n is the sample size, is a continuity correction factor, pe is the proportion expected from Benford's law and po is the observed proportion in the sample.
Morrow has also shown that for any random variable X (with a continuous pdf) divided by its standard deviation (σ), a value A can be found such that the probability of the distribution of the first significant digit of the random variable ()A will differ from Benford's Law by less than ε > 0. The value of A depends on the value of ε and the distribution of the random variable.
A method of accounting fraud detection based on bootstrapping and regression has been proposed.
Generalization to digits beyond the first
It is possible to extend the law to digits beyond the first. In particular, the probability of encountering a number starting with the string of digits n is given by:
(For example, the probability that a number starts with the digits 3, 1, 4 is log10(1 + 1/314) ≈ 0.0014.) This result can be used to find the probability that a particular digit occurs at a given position within a number. For instance, the probability that a "2" is encountered as the second digit is
And the probability that d (d = 0, 1, ..., 9) is encountered as the n-th (n > 1) digit is
The distribution of the n-th digit, as n increases, rapidly approaches a uniform distribution with 10% for each of the ten digits. Four digits is often enough to assume a uniform distribution of 10% as '0' appears 10.0176% of the time in the fourth digit while '9' appears 9.9824% of the time.
Tests with common distributions
Benford's law was empirically tested against the numbers (up to the 10th digit) generated by a number of important distributions, including the uniform distribution, the exponential distribution, the half-normal distribution, the right-truncated normal, the normal distribution, the chi square distribution and the log normal distribution. In addition to these the ratio distribution of two uniform distributions, the ratio distribution of two exponential distributions, the ratio distribution of two half-normal distributions, the ratio distribution of two right-truncated normal distributions, the ratio distribution of two chi-square distributions (the F distribution) and the log normal distribution were tested.
The uniform distribution as might be expected does not obey Benford's law. In contrast, the ratio distribution of two uniform distributions is well described by Benford's law. Benford's law also describes the exponential distribution and the ratio distribution of two exponential distributions well. Although the half-normal distribution does not obey Benford's law, the ratio distribution of two half-normal distributions does. Neither the right-truncated normal distribution nor the ratio distribution of two right-truncated normal distributions are well described by Benford's law. This is not surprising as this distribution is weighted towards larger numbers. Neither the normal distribution nor the ratio distribution of two normal distributions (the Cauchy distribution) obey Benford's law. The fit of chi square distribution depends on the degrees of freedom (df) with good agreement with df = 1 and decreasing agreement as the df increases. The F distribution is fitted well for low degrees of freedom. With increasing dfs the fit decreases but much more slowly than the chi square distribution. The fit of the log-normal distribution depends on the mean and the variance of the distribution. The variance has a much greater effect on the fit than does the mean. Larger values of both parameters result in better agreement with the law. The ratio of two log normal distributions is a log normal so this distribution was not examined.
Other distributions that have been examined include the Muth distribution, Gompertz distribution, Weibull distribution, gamma distribution, log-logistic distribution and the exponential power distribution all of which show reasonable agreement with the law. The Gumbel distribution – a density increases with increasing value of the random variable – does not show agreement with this law.
Distributions known to obey Benford's law
Some well-known infinite integer sequences satisfy Benford's Law exactly (in the asymptotic limit as more and more terms of the sequence are included). Among these are the Fibonacci numbers, the factorials,<ref>{{cite journal | last1 = Sarkar | first1 = P. B. | year = 1973 | title = An Observation on the Significant Digits of Binomial Coefficients and Factorials | url = | journal = Sankhya B | volume = 35 | issue = | pages = 363–364 }}</ref> the powers of 2, and the powers of almost any other number.
Likewise, some continuous processes satisfy Benford's Law exactly (in the asymptotic limit as the process continues through time). One is an exponential growth or decay process: If a quantity is exponentially increasing or decreasing in time, then the percentage of time that it has each first digit satisfies Benford's Law asymptotically (i.e. increasing accuracy as the process continues through time).
Distributions known to not obey Benford's law
Square roots and reciprocals do not obey this law. Also, Benford's law does not apply to unary systems such as tally marks. The 1974 Vancouver, Canada telephone book violates Benford's law because regulations require that telephone numbers have a fixed number of digits and do not begin with 1. Benford's law is violated by the populations of all places with population at least 2500 from five US states according to the 1960 and 1970 censuses, where only 19% began with digit 1 but 20% began with digit 2, for the simple reason that the truncation at 2500 introduces statistical bias. The terminal digits in pathology reports violate Benford's law due to rounding, and the fact that terminal digits are never expected to follow Benford's law in the first place.
Criteria for distributions expected and not expected to obey Benford's Law
A number of criteria—applicable particularly to accounting data—have been suggested where Benford's Law can be expected to apply and not to apply.
Distributions that can be expected to obey Benford's Law
When the mean is greater than the median and the skew is positive
Numbers that result from mathematical combination of numbers: e.g. quantity × price
Transaction level data: e.g. disbursements, sales
Numbers produced when doing any multiplicative calculations with an Oughtred slide rule, since the answers naturally fall into the right logarithmic distribution.
Distributions that would not be expected to obey Benford's Law
Where numbers are assigned sequentially: e.g. check numbers, invoice numbers
Where numbers are influenced by human thought: e.g. prices set by psychological thresholds ($1.99)
Accounts with a large number of firm-specific numbers: e.g. accounts set up to record $100 refunds
Accounts with a built-in minimum or maximum
Where no transaction is recorded
Moments
Moments of random variables for the digits 1 to 9 following this law have been calculated:
mean 3.440 variance 6.057 skewness 0.796 kurtosis −0.548
For the first and second digit distribution these values are also known:
mean 38.590 variance 621.832 skewness 0.772 kurtosis −0.547
A table of the exact probabilities for the joint occurrence of the first two digits according to Benford's law is available, as is the population correlation between the first and second digits: .
See also
Fraud detection in predictive analytics
Zipf's law References Further reading
An Introduction to Benford's Law
Alex Ely Kossovsky. Benford's Law: Theory, the General Law of Relative Quantities, and Forensic Fraud Detection Applications, 2014, World Scientific Publishing. ISBN 978-981-4583-68-8.
http://mathworld.wolfram.com/BenfordsLaw.html Benford's Law – from Wolfram MathWorld
Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection
Probability of digits by dividing random numbers: A ψ and ζ functions approach
Price developments after a nominal shock: Benford's Law and psychological pricing after the euro introduction
International Journal of Research in Marketing
Scatter and regularity implies Benford's Law...and more
Zenil: Randomness through computation: some answers, more questions
Bernhard Rauch1, Max Göttsche, Gernot Brähler, Stefan Engel
Fact and Fiction in EU-Governmental Economic Data
Breaking the (Benford) Law: statistical fraud detection in campaign finance
The Law of Harmony in Statistics: An Investigation of the Metrical Interdependence of Social Phenomena. by L. V. Furlan Journal of the American Statistical Association
External links General audience
Benford Online Bibliography, an online bibliographic database on Benford's Law.
Companion website for Benford's Law by Mark Nigrini Website includes 15 data sets, 10 Excel templates, photos, documents, and other miscellaneous items related to Benford's Law
Following Benford's Law, or Looking Out for No. 1, 1998 article from The New York Times.
A further five numbers: number 1 and Benford's law, BBC radio segment by Simon Singh
From Benford to Erdös, Radio segment from the Radiolab program
Looking out for number one by Jon Walthoe, Robert Hunt and Mike Pearson, Plus Magazine'', September 1999
Video showing Benford's Law applied to Web Data (incl. Minnesota Lakes, US Census Data and Digg Statistics)
An illustration of Benford's Law, showing first-digit distributions of various sequences evolve over time, interactive.
Generate your own Benford numbers A script for generating random numbers compliant with Benford's Law.
Testing Benford's Law An open source project showing Benford's Law in action against publicly available datasets.
Testing Benford’s Law in OLAP Cubes Implementation with Microsoft Analysis Services.
http://www.numberphile.com/videos/benfords_law.html
A third of property values begin with a 1 An example of Benford's Law appearing in house price data.
Benford's Very Strange Law - Professor John D. Barrow, lecture on Benford's Law.
More mathematical
Benford’s law, Zipf’s law, and the Pareto distribution by Terence Tao
Country Data and Benford's Law, Benford's Law from Ratios of Random Numbers at Wolfram Demonstrations Project.
Benford's Law Solved with Digital Signal Processing
Interactive graphic: Univariate Distribution Relationships |
Source: Home Economics Consumer Economics Pricing Article
Price Developments After a Nominal Shock: Benford's Law and Psychological Pricing After the Euro Introduction
September 2005
International Journal of Research in Marketing
DOI: 10.1016/j.ijresmar.2005.09.002 Authors:
Tarek Josef el Sehity
Sigmund Freud University Vienna
Erik Hoelzl Erik Hoelzl
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Erich Kirchler University of Vienna Request full-text PDF
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Citations (60) References (41) Abstract
Retail managers use psychological pricing to make the prices of goods appear to be just below a round number. The euro introduction in 2002, with its various exchange rates, distorted existing nominal price patterns while at the same time retaining real prices. We studied consumer prices before and after the introduction of the euro by using Benford's Law as a benchmark for price adjustments. Results indicate the usefulness of this benchmark for detecting irregularities in prices, and a clear trend towards psychological pricing after the nominal shock of the euro introduction. In addition, the tendency towards psychological prices results in different inflation rates in dependence of the price pattern.
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... The scope for application incorporated, among others, balances of payments (Michalski & Stoltz, 2011), budget deficit 59 On the basis of Eurostat's European Statistics Code of Practice (downloadable at http://tinyurl.com/p48vspd) statistics (Rauch, Göttsche, Brähler & Engel,2011;Rauch, Göttsche, Brähler& Krongeld, 2014), political campaign financing (Cho & Gaines, 2007), academic publications (Toedter, 2009;Diekmann, 2007), survey results (Schäfer, Schräpler, Müller & Wagner, 2004;Judge &Schechter, 2009), macroeconomic statistics (Holz,2014;Nye &Moul, 2007;Gonzalez-Garcia &Pastor, 2009) and price fixing
(El Sehity, Hoelzl & Kirchler, 2005)
. This chapter fits within this novel research stream and shows, for the first time, that Benford's law can successfully be applied to the debate on the efficiency of global AML efforts and that it can offer new insights into the political processes underlying and undermining the efficiency of these global efforts. ...
... A second group had a set of theoretical predictions about misreporting, and used Benford's law to test these hypotheses (e.g. Nye & Moul, 2007;
El Sehity et al., 2005)
. These researchers started from two assumptions: people do a poor job in replicating known data-generating processes (Camerer, 2003) and Benford's law is not widely known by those constructing the data under investigation. ...
... And as Cho and Gaines (2007, p.221) pointed out, "a preferable statistic would be less sensitive to sample size than the statistic". Two years later, Gonzalez-Garcia and Pastor (2009)
(El Sehity et al., 2005)
. Instead, they found strong evidence of 'psychological pricing' and showed that this has had a significant impact on real inflation for different products given their initial proximity to a psychological price immediately after conversion took place. ...
Anti-money laundering: failures, fixes and the future
Thesis Full-text available Oct 2015 Ioana Deleanu
In this PhD thesis I address important topics in the debate on and the organisation of the Anti-Money Laundering efforts, which are related to the legitimacy and the effectiveness of the Anti-Money Laundering policies. First of all, this thesis provides a reflection on the assessments of concern that trigger policy makers in the field of crime fighting. Secondly, it provides an assessment of the effectiveness of the agencies entrusted with fighting money laundering at a national level and, of the country blacklisting practices of the Financial Action Task Force.
This thesis adheres to the literature of law and economics, while trying to approach the analysis of money laundering from a concept of choice that reflects human behavior as real as possible. Essentially, this thesis builds on the premises that Anti-Money Laundering policies are socially embedded, that a money launderer’s sentiment is socially founded and psychologically bounded and that our understanding of the effectiveness of Anti-Money Laundering efforts will benefit from an explicit consideration of these premises.
Four independent studies compose this PhD thesis. The first study looks at one of the core methods to estimate the underground economy, and argues for a behavioral change in the theoretical micro-foundations of this method. The study contends that by recognizing the psychophysical limitations of tax payers we are in a better position to measure the cash based underground economy and explain why, in some cases, the seminal measurement method of Tanzi (1983) is not applicable. Subsequently, the second study explores how the value of information is modified when transmitted hierarchically among institutions that play a role in the fight against money laundering. The study argues that by recognizing the role of institutional distance in the framing of communication between law enforcement organizations, we can enhance our capacity to measure and address the issue of effective cooperation. The third study is built on the behavioral finding that individuals perform badly at generating random numbers and maintains that international evaluations on performance may trigger strategic tampering with national statistics on money laundering. The study reflects on the effectiveness and legitimacy of the naming and shaming strategy that countries are subject to, when statistics are not objective representations of the truth. Finally, the fourth study looks at what may be the future of money laundering in the age of anonymous digital currencies. This study argued that if we recognize that individuals address uncertainty by relying on the common pool of experiential knowledge, then, the dynamics of the wisdom of the crowds may help us better anticipate future social outcomes, among which the global usage of BITCOINs for criminal purposes.
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... A small number of studies have analyzed the effect of the Euro changeover on the distribution of prices or on the use of psychological prices. El Sehity, Hoelzl, and
Kirchler (2005)
investigate the distribution of prices and price endings (psychological price) before and after the Euro changeover for 10 different countries. "If prices simply follow market rules, develop naturally through a mixture of random influences such as changes in demand and supply, and are subject to inflation, one would expect them to follow Benford's Law" (el Sehity, Hoelzl, & Kirchler, 2005: 472). ...
... Also, prices immediately after the Euro changeover better fit Benford's Law than prices observed later. El Sehity,
Hoelzl & Kirchler (2005)
interpret this as evidence for an adjustment back towards price patterns observed before the Euro changeover. ...
... The objective of this study is to analyze the impact of the Euro changeover on the distribu- tion and the development of food retail prices in Germany with respect to different product categories, namely occasional goods and signpost items. In our study, we use a detailed data set for German food retail stores and apply benchmarks proposed by El Sehity,
Hoelzl & Kirchler (2005)
and Aalto-Setala (2005). We also employ an additional benchmark by converting DM prices before the Euro changeover using the official rate. ...
The Distribution of Food Retail Prices and the Euro Changeover: Signpost Items Versus Occasional Goods
Article Jul 2015 AGRIBUSINESS Karen J. Schroeder Angela Hoffmann Jens-Peter Loy
The Euro changeover distorted previously well-formed nominal price patterns. Food retailers may have reacted by adjusting prices to reintroduce psychological prices as before the Euro changeover. We employ a detailed data set of German food retail prices before and after the Euro changeover to test three different benchmarks indicating potential adjustments of prices. However, none of these benchmarks do adequately reflect the actual distribution of prices. We find that prices of signpost items follow best a conversion at the official rate. Also, signpost items show a slower price adjustment. Occasional goods’ prices indicate a reestablishment of psychological price patterns, in particular for the ending digits; price distributions are adjusted faster. Further, price inflation is about zero for both goods, but prices in particular for signpost items have been significantly raised just before the Euro changeover. These different pricing patterns may be explained by consumer behavior. Consumers react more sensitive to price changes of frequently purchased goods (signpost items), and thus, retailers convert prices at the official rate and postpone price adjustments for these items after the Euro changeover. [JEL Classifications: D40, L66, Q13].
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... The image effect refers to altering the consumer's perception so that the prices that end in a nine are considered more affordable than the prices that end in a zero. This pricing method can often be deceitful to the consumer
(Hoelzl and Kirchler 2005)
. ...
... Apart from the prices that end in a 0 and a 5, one can also often encounter the number 9. According to the research conducted by Schindler and Kirby, 27% of all prices in dollars end in the number 0, 19% end in the number 5 and 31% of all prices in dollars end in the number 9. Research results for the German market have been similar: 13% of all prices ended in the number 0, another 13% ended in the number 5, whereas 45% of all prices ended in the number 9. This pricing method is considered psychological pricing and can be conducted in 2 ways: by only altering the last digit in the price, or by altering all the digits in the price apart from the first one
(Hoelzl and Kirchler 2005)
. Given how much psychological prices are present in retail, it is to be expected that experts agree that psychological prices work and that there is solid evidence to show that such prices have a positive effect on increasing sales. ...
Consumer Responses to Selected Activities: Price Increases, Lack of Product Information and Numerical Way of Expressing Product Prices
Article Full-text available Jun 2022 Mirela Martinčić Dijana Vuković Anica Hunjet
The importance of constant consumer testing is emphasized in order for companies to deliver the highest value for the quality of products and services. To explain the psychological impact of price on product selection, and other factors that determine consumer behavior, a survey method was applied. When deciding to buy a product, the consumer’s perception of the value of selected re-search products (clothing, footwear, children’s equipment) is crucial and it can often differ from the value derived from the price set by the seller. The conducted research proved that sellers can really influence consumers’ decision to buy a product with their price, and that a large number of consumers perceive the price incorrectly and thus buy more than they planned. Having in mind the subject of this paper, the basic scientific goal was to define a consumer model that integrates factors (variables) influencing consumer behavior to answer the question of how and why con-sumers react to rising product prices, how much they use the importance of information about product quality as a parameter of the decision, and how much consumers when choosing a product notice the price ending in a different number from the number of zeros. As consumer behavior is strongly influenced by a number of factors, it can be defined that the consumer’s response to selected activities: price increases, lack of product information and numerical way of expressing product prices may not contain all factors and their relationships and simplifies the picture of the consumer model. In order to test hypotheses about the extent to which customers are sensitive and willing to replace a product with certain substitutes, i.e., how willing they are to conclude about a product they buy based on price if they do not have enough information about the product and how much zeros are favored by consumers when shopping, an empirical study was conducted on a sample of 214 respondents. The results of the research indicate that in moments when respondents do not have enough information about the product, they are not inclined to draw conclusions solely on the basis of price, and prices ending in odd numbers or non-zero are not more attractive than those ending in zero.
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... Psychological pricing has been widely discussed because of its managerial implications (Levy et al., 2004;
El Sehity et al., 2005)
. Some research explains the role of round prices (Aalto-Setälä and Halonen, 2004;Manning and Sprott, 2009), other research insists on prices ending with the number nine (Schindler, 2006;Levy et al., 2011;Macé, 2012) or more broadly with odd numbers (Bambauer-Sachse and Grewal, 2011;Kleinsasser and Wagner, 2011;Lewis, 2015). ...
... In offline retailing, convenience pricing plays a rational role because of cash payments. Convenient prices help make easier change through fewer pieces of money
(El Sehity et al., 2005)
, reducing the time of a transaction, which customers rationally infer. Conversely in online retailing, convenience pricing seems at first glance non-rational because it is not possible to pay cash. ...
Convenience pricing in online retailing: Evidence from Amazon.com
Article Dec 2017 ECON MODEL Régis Chenavaz Joeffrey Drouard Octavio R. Escobar Bruno Karoubi
To expedite payments, firms use convenience pricing strategies. A price is considered convenient if it can be paid with few coins. Convenient prices are well understood in offline retailing, but not online. This article fills the gap, examining an original panel dataset more than 2.5 million observations of book prices from Amazon.com. We provide empirical evidence supporting two claims. First in a static setup, more convenient prices are more likely to be set. Second in a dynamic setup, more convenient prices are more rigid. Emphasizing the role of convenience, this work sheds new light on price setting in online retailing.
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... First, whereas there is extensive evidence on the impact of the price ending digit for Western cultures and countries (e.g.,
El Sehity, Hoelzl, and Kirchler 2005;
Schindler and Kirby 1997), little empirical evidence is documented for Eastern regions, rendering (un)lucky price endings an underresearched topic in Eastern culture. More importantly, we analyze pricing practices in Singapore, an Eastern culture that has experienced strong influences from Western MNCs. ...
... The literature on price endings portrays a general tendency that Western pricing practices are not guided by superstitious beliefs, whereas Eastern practices are (Schindler 2009). In Western cultures, the price endings 0, 5, and 9 dominate for reasons apart from superstition
(El Sehity, Hoelzl, and Kirchler 2005;
Nguyen, Heeler, and Taran 2007;Schindler and Kirby 1997). The endings 0 and 5 are preferred in the decimal system because their high cognitive accessibility, while the 9 ending is favored because it causes an underestimation effect on the overall price (Schindler and Kirby 1997). ...
Eastern Versus Western Culture Pricing Strategy: Superstition, Lucky Numbers, and Localization
Article Mar 2017 Stanford A. Westjohn Holger Roschk Peter Magnusson
Eastern versus Western culture pricing practices differ with respect to price endings; however, Eastern cultures are increasingly influenced by Western multinational corporations. At the same time, increasing antiglobalization sentiment suggests the use of localization strategies in these markets. The authors investigate whether pricing practices still differ in this new environment, examine the role of superstition, and ask whether Western brands can benefit from localizing pricing practices. They explore the use of lucky number price endings and consumer responses to such pricing strategies in Singapore, an Eastern culture that is strongly exposed to Western multinational influence. Using a content analysis of newspaper advertisements and two experiments, the authors find that superstitious pricing practices continue, especially with high-priced items and brands of Eastern (vs. Western) origin. In the experimental studies, they find that superstitious pricing has a positive effect on price attractiveness and that foreign brands that localize their prices benefit from a more positive brand attitude.
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... Several studies in marketing (see e.g., Twedt, 1965; Holdershaw et al., 1997; Stiving & Winer, 1997; Brambach, 2002;
el Sehity et al., 2005
) document the prevalence of so-called psychological pricing in the retail market. Whereas no formal definition exists, psychological pricing refers to the factual observation that an abnormally large quantity of retail prices fall just below a round number. ...
... Whereas no formal definition exists, psychological pricing refers to the factual observation that an abnormally large quantity of retail prices fall just below a round number. As discussed in el
Sehity et al. (2005)
, the latter has typically been illustrated by the higher than expected incidence of nines as the ending digit (e.g., 1.99 or 2.19 where 9 is used as the ending digit) and/or as any digit except for the first digit (e.g., 1.95 or 2,900 where 9 is used in the second-from-the-left position 2 ) in prices. While it has been argued that psychological pricing was originally introduced as an aid to prevent theft by employees (Gendall et al., 1996), it is nowadays common belief that psychological prices boost sales. ...
Psychological Pricing. Private vs. Professional Vendors
Article Full-text available Jan 2008 Tom Van Caneghem
Prior research in marketing documents the prevalence of so-called psychological (or odd) pricing. Unlike earlier studies that focused on prices of professional vendors, we also consider prices of private vendors in our analyses. Relying on a sample of prices for second-hand cars and employing three alternative ways to bare the phenomenon, our results present unequivocal evidence of psychological pricing being significantly more common among prices of professional vendors. Moreover, whereas findings based on all three methods are consistent with odd pricing for the sub-sample of professional vendors, only one method yields significant indications of psychological pricing for the sub-sample of private vendors. Consistent with humans’ reliance upon cognitive reference points, zeroes are found to dominate prices of both professional and private vendors. Nevertheless, round prices are significantly more common among private vendors. Our findings also indicate that private vendors tend to round their posted number of kilometers significantly more often, whereas professional vendors seem to provide more accurate numbers of kilometers. Finally, we provide some evidence of professional vendors strategically setting their sales prices just below pre-defined price thresholds that can be used to narrow search results in the online database employed for the current study.
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... It was quickly admitted that numerous empirical data sets follow Benford's law: economic data
(Sehity et al. (2005)
), social data (Golbeck (2015)), demographic data (Nigrini and Wood (1995); Leemis et al. (2000)), physical data (Knuth (1969); Burke and Kincanon (1991); Nigrini and Miller (2007); Alexopoulos and Leontsinis (2014)) or biological data (Costasa et al. (2008); Friar et al. (2012)) for instance; to such an extent that this law was used to detect possible frauds in lists of socio-economic data (Varian (1972); Nigrini (1999); Durtschi et al. (2004); Saville (2006); Tödter (2009) ;Rauch et al. (2011)) or in scientific publications (Alves et al. (2014)). ...
Benford or not Benford: new results on digits beyond the first
Article Full-text available May 2022
Stéphane Blondeau Da Silva
In this paper, we will see that the proportion of d as pth digit, where p > 1 and d ∈ [[0, 9]], in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than the generalization of Benford’s law to digits beyond the first one. These probability distributions fluctuate around theoretical values of the distribution of the pth digit of Benford’s law. Knowing beforehand the value of the upper bound can be a way to find a better adjusted law than Benford’s one.
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... If prices were determined with a cost-plus markup method, then each price ending would be equally likely to occur and we would, therefore, observe each in approximately 1% of the cases, following a uniform distribution
(El Sehity et al., 2005)
. This is not what happens (Dholakia, 2018), including in a luxury context: as shown by literature (Aiello et al., 2018;Macé, 2014, 2020;Fraccaro et al., 2021) and our introductory study, luxury pricing managers make explicit choices. ...
Compromise pricing in luxury Parguel B., Fraccaro A., Macé S.
Article Sep 2021 Béatrice Parguel Annalisa Fraccaro Sandrine Macé Purpose
Going beyond odd and even prices, this paper aims to explore the rationale behind the widespread practice of setting prices ending in “50” or “80” in the luxury industry. The authors argue that when they set such prices, managers agree to reduce their profit margin to limit the anticipated guilt luxury consumers associate with luxury shopping while also protecting their brand luxury. The authors label these prices compromise prices and formally define compromise pricing as the practice of choosing a price’s ending so that the price falls below (but not just below) a round number to boost sales without damaging brand luxury.
Design/methodology/approach
Following the observation of the overrepresentation of prices ending in “50” and “80” in the luxury clothing category, an experiment explores the impact of compromise prices on anticipated guilt and brand luxury in the luxury watch category. Then, to identify when luxury pricing managers typically favor compromise prices, multinomial regressions investigate prices collected on two online luxury fashion retailers for the luxury clothing and handbag categories.
Findings
Compromise prices reduce the anticipated guilt luxury consumers associate with luxury shopping compared with even prices while enhancing brand luxury compared with odd prices and interestingly, with even prices also. This finding gives rationale to luxury managers’ preference for compromise prices in the ninth hundred (i.e. €X950, €X980), especially for higher-priced products, i.e. when the potential for price underestimation and/or the risk of damaging brand luxury are more important.
Originality/value
This research contributes to the field of luxury pricing by providing evidence to an original price-ending practice, coined compromise pricing, which consists in agreeing to a slight reduction in prices and unit margin to protect brand luxury.
View Show abstract
... It was quickly admitted that numerous empirical data sets follow Benford's law: economic data
[6]
, social data [7], demographic data [8], [9], physical data [10], [11] or biological data [12], [13] for instance; to such an extent that this law was used to detect possible frauds in lists of socio-economic data [14], [15] or in scientific publications [16]. ...
BeyondBenford R Package to compare Benford's and BDS's Distributions
Article Full-text available Sep 2021
Stéphane Blondeau Da Silva
The package BeyondBenford compares the goodness of fit of Benford's and Blondeau Da Silva's (BDS's) digit distributions in a given dataset. It first enables to check whether the data distribution is consistent with theoretical distributions highlighted by Blondeau Da Silva or not; indeed, this ideal theoretical distribution must be at least approximately followed by the data for the use of BDS's model to be well-founded. It also allows to draw histograms of digit frequencies or probabilities (and their confidence or prediction intervals), both observed in the dataset and given by the two theoretical approaches. Finally, it proposes to quantify the goodness of fit of these laws via Pearson's chi-squared tests.
View Show abstract
... If prices were determined with a cost-plus markup method, then each price ending would be equally likely to occur and we would therefore observe each in approximately 1% of the cases, following a uniform distribution
(El Sehity et al., 2005)
. This is not what happens (Dholakia, 2018), including in a luxury context: as shown by literature (i.e., Aiello et al., 2018;Macé, 2014, 2020;Fraccaro et al., 2019) and our introductory study, luxury pricing managers make explicit choices. ...
Compromise pricing in luxury
Article Full-text available Aug 2021 Béatrice Parguel Annalisa Fraccaro Sandrine Macé
Purpose: Going beyond odd and even prices, this article explores the rationale behind the widespread practice of setting prices ending in "50" or "80" in the luxury industry. We argue that when they set such prices, managers agree to reduce their profit margin to limit the anticipated guilt luxury consumers associate with luxury shopping, while also protecting their brand luxury. We label these prices compromise prices and formally define compromise pricing as the practice of choosing a price's ending so that the price falls below (but not just below) a round number to boost sales without damaging brand luxury.
Design/methodology/approach: Following the observation of the overrepresentation of prices ending in "50" and "80" in the luxury clothing category, an experiment explores the impact of compromise prices on anticipated guilt and brand luxury in the luxury watch category. Then, to identify when luxury pricing managers typically favor compromise prices, multinomial regressions investigate prices collected on two online luxury fashion retailers for the luxury clothing and handbag categories.
Findings: Compromise prices reduce the anticipated guilt luxury consumers associate with luxury shopping compared with even prices, while enhancing brand luxury compared with odd prices and interestingly, with even prices also. This finding gives rationale to luxury managers' preference for compromise prices in the ninth hundred (i.e., €X950, €X980), especially for higher-priced products, i.e., when the potential for price underestimation and/or the risk of damaging brand luxury are more important.
Originality: This research contributes to the field of luxury pricing by providing evidence to an original price-ending practice, coined compromise pricing, which consists in agreeing to a slight reduction in prices and unit margin to protect brand luxury.
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... A good mechanism for explaining the uneven distributions stipulated by Benford's law has been proposed in [41]. Benford's law has been used for evaluating possible fraud in accounting data [42], legal status [43], election data [44][45][46], macroeconomic data [47], price data
[48]
, etc. From Equation (4), we observe that beyond the small digits, the probability approximately approaches the Zipf distribution with α = 1, P(d) = log 10 ...
Complex Systems, Emergence, and Multiscale Analysis: A Tutorial and Brief Survey
Article Full-text available Jun 2021 Jianbo Gao Bo Xu
Mankind has long been fascinated by emergence in complex systems. With the rapidly accumulating big data in almost every branch of science, engineering, and society, a golden age for the study of complex systems and emergence has arisen. Among the many values of big data are to detect changes in system dynamics and to help science to extend its reach, and most desirably, to possibly uncover new fundamental laws. Unfortunately, these goals are hard to achieve using black-box machine-learning based approaches for big data analysis. Especially, when systems are not functioning properly, their dynamics must be highly nonlinear, and as long as abnormal behaviors occur rarely, relevant data for abnormal behaviors cannot be expected to be abundant enough to be adequately tackled by machine-learning based approaches. To better cope with these situations, we advocate to synergistically use mainstream machine learning based approaches and multiscale approaches from complexity science. The latter are very useful for finding key parameters characterizing the evolution of a dynamical system, including malfunctioning of the system. One of the many uses of such parameters is to design simpler but more accurate unsupervised machine learning schemes. To illustrate the ideas, we will first provide a tutorial introduction to complex systems and emergence, then we present two multiscale approaches. One is based on adaptive filtering, which is excellent at trend analysis, noise reduction, and (multi)fractal analysis. The other originates from chaos theory and can unify the major complexity measures that have been developed in recent decades. To make the ideas and methods better accessed by a wider audience, the paper is designed as a tutorial survey, emphasizing the connections among the different concepts from complexity science. Many original discussions, arguments, and results pertinent to real-world applications are also presented so that readers can be best stimulated to apply and further develop the ideas and methods covered in the article to solve their own problems. This article is purported both as a tutorial and a survey. It can be used as course material, including summer extensive training courses. When the material is used for teaching purposes, it will be beneficial to motivate students to have hands-on experiences with the many methods discussed in the paper. Instructors as well as readers interested in the computer analysis programs are welcome to contact the corresponding author.
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... Jošić and Žmuk (2018) used Benford's Law for psychological pricing detection. Seminal paper in this field was published by El
Sehity et al. (2005)
which analyses consumer price digits before and after the euro introduction. Another piece of empirical evidence on psychological pricing was related to Austrian retailers, Wagner and Jamsawang (2012). ...
ASSESSING THE QUALITY OF COVID-19 DATA: EVIDENCE FROM NEWCOMB-BENFORD LAW
Article Full-text available Jun 2021 Hrvoje Jošić Berislav Žmuk
The COVID-19 infection started in Wuhan, China, spreading all over the world, creating global healthcare and economic crisis. Countries all over the world are fighting hard against this pandemic; however, there are doubts on the reported number of cases. In this paper Newcomb-Benford Law is used for the detection of possible false number of reported COVID-19 cases. The analysis, when all countries have been observed together, showed that there is a doubt that countries potentially falsify their data of new COVID-19 cases of infection intentionally. When the analysis was lowered on the individual country level, it was shown that most countries do not diminish their numbers of new COVID-19 cases deliberately. It was found that distributions of COVID-19 data for 15% to 19% of countries for the first digit analysis and 30% to 39% of countries for the last digit analysis do not conform with the Newcomb-Benford Law distribution. Further investigation should be made in this field in order to validate the results of this research. The results obtained from this paper can be important for economic and health policy makers in order to guide COVID-19 surveillance and implement public health policy measures.
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... Numerous empirical data, as economic data (
[55,
16]), social data ( [31,42,28]), demographic data ( [48,39]), physical data ( [36,13,47,52,18,3,1]), biological data ( [17,26,37]), data in psychology ( [20,6,15]) or internet data ( [4]), for instance, conform to Benford's law ( [34,46]); to such an extent that this law was used to detect possible frauds in lists of socio-economic data ( [59,45,22,53,58,51,14,38]) or in scientific publications ( [2]). ...
Limits of Benford's law in experimental field
Article Full-text available Aug 2020
Stéphane Blondeau Da Silva
View
... In the past the social representations were collected during the introduction of the European currency to measure the societal receptivity of a novel currency
(el Sehity, Hoelzl & Kirchler, 2005)
. The social representations of experts on the global competency of the U.S. ...
Intergenerational Equity Chapter Full-text available Jun 2020 Julia M. Puaschunder
The idea of intergenerational equity is as old as humankind. Intergenerational equity arises from the elderly wanting their offspring to prosper in at least as favorable conditions as experienced. The natural behavioral law of intergenerational equity was lived for centuries and transpired in the social compound as practiced in ancient, traditional customs ever since. Intergenerational equality is grounded on a human-imbued wish for fairness as there is an ethical preference for fair welfare distribution among different generations. Acknowledging intergenerational equity as a natural behavioral law may serve as a legal basis for the codification of human rights of intergenerational equity. A pro-active overcompliance with contemporary sustainability legislation may stem from a broader social contract within society to incorporate novel responsibilities and embrace discretionary activities that contribute to societal welfare and the well-being of future generations. Globalization increasing internationalization of public and private concerns create a need for an international outlook of intergenerational equity in order to solve global common goods predicaments and draw inferences on the harmonization of intergenerational justice on a global scale in the age of climate change in the twenty-first century.
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... For instance,Deckert et al. (2011) used it to detect frauds in elections, El
Sehity et al. (2005)
investigated consumer price digits before and after the euro introduction for price adjustments, Müller (2011) found out possible frauds in the macroeconomic data the ...
Digit analysis for Covid-19 reported data
Preprint May 2020 Jean-François Coeurjolly
The coronavirus which appeared in December 2019 in Wuhan has spread out worldwide and caused the death of more than 280,000 people (as of May, 11 2020). Since February 2020, doubts were raised about the numbers of confirmed cases and deaths reported by the Chinese government. In this paper, we examine data available from China at the city and provincial levels and we compare them with Canadian provincial data, US state data and French regional data. We consider cumulative and daily numbers of confirmed cases and deaths and examine these numbers through the lens of their first two digits and in particular we measure departures of these first two digits to the Newcomb-Benford distribution, often used to detect frauds. Our finding is that there is no evidence that cumulative and daily numbers of confirmed cases and deaths for all these countries have different first or second digit distributions. We also show that the Newcomb-Benford distribution cannot be rejected for these data.
View Show abstract
... In the past the social representations were collected during the introduction of the European currency to measure the societal receptivity of a novel currency
(el Sehity, Hoelzl & Kirchler, 2005)
. The social representations of experts on the global competency of the U.S. ...
Intergenerational Equity Book Full-text available Oct 2019 Julia M. Puaschunder View
... It was quickly admitted that numerous empirical data sets follow Benford's law: economic data
[SHK05]
, social data [Gol15], demographic data [NW95,LSE00], physical data [Knu69,BK91,NM07,AL14] or biological data [CLRTFM08,FGPM12] for instance; to such an extent that this law was used to detect possible frauds in lists of socio-economic data [Var72,Nig99,DHP04,Sav06,Tö09,RGBE11] or in scientific publications [AYS14]. ...
BeyondBenford: An R Package to Determine Which of Benford’s or BDS’s Distributions is the Most Relevant
Preprint Oct 2019
Stéphane Blondeau Da Silva
The package BeyondBenford compares the goodness of fit of Benford's and Blondeau Da Silva's (BDS's) digit distributions in a dataset. The package is used to check whether the data distribution is consistent with theoretical distributions highlighted by Blondeau Da Silva or not: this ideal theoretical distribution must be at least approximately followed by the data for the use of BDS's model to be well-founded. It also allows to draw histograms of digit distributions, both observed in the dataset and given by the two theoretical approaches. Finally, it proposes to quantify the goodness of fit via Pearson's chi-squared test.
View Show abstract
... Even if there are distributions known to disobey Benford's Law ( [18,10,22,20,1,5] or also phone numbers in directories), most of the empirical data, as economic data (
[21]
), social data ( [9]), demographic data ( [16,13]), physical data ( [12,3,15]) or biological data ( [4,7]) follow approximately Benford's Law. To such an extent that this law is used to detect possible frauds in lists of socio-economic data ( [25,17,23,19]) or in scientific publications ( [6]). ...
Benford or Not Benford: A Systematic But Not Always Well-Founded Use of an Elegant Law in Experimental Fields
Article May 2019
Stéphane Blondeau Da Silva
In this paper, we will propose a way to accurately model certain naturally occurring collections of data. Through this proposed model, the proportion of d as leading digit, d in [[1,9]], in data is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than Benford’s Law, as one might have expected. These probability distributions fluctuate nevertheless around Benford’s values. These peculiar fluctuations have often been observed in the literature in such data sets (where the physical, biological or economical quantities considered are upper bounded). Knowing beforehand the value of this upper bound enables to find, through the developed model, a better adjusted law than Benford’s one.
View Show abstract
... It was quickly admitted that numerous empirical data sets follow Benford's law: economic data (
[41]
), social data ( [19]), demographic data ( [34,27]), physical data ( [26,8,33,2]) or biological data ( [11,16]) for instance; to such an extent that this law was used to detect possible frauds in lists of socio-economic data ( [46,32,14,39,44,38]) or in scientific publications ( [3]). ...
Benford or not Benford: new results on digits beyond the first
Preprint May 2018
Stéphane Blondeau Da Silva
In this paper, we will see that the proportion of d as p th digit, where p > 1 and d $\in$ 0, 9, in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than the generalization of Benford's Law to digits beyond the first one. These probability distributions fluctuate around theoretical values determined by Hill in 1995. Knowing beforehand the value of the upper bound can be a way to find a better adjusted law than Hill's one.
View Show abstract
... Even if there are distributions known to disobey Benford's Law ( [18,10,22,20,1,5] or also phone numbers in directories), most of the empirical data, as economic data (
[21]
), social data ( [9]), demographic data ( [16,13]), physical data ( [12,3,15]) or biological data ( [4,7]) follow approximately Benford's Law. To such an extent that this law is used to detect possible frauds in lists of socio-economic data ( [25,17,23,19]) or in scientific publications ( [6]). ...
Benford or not Benford: a systematic but not always well-founded use of an elegant law in experimental fields
Preprint Apr 2018
Stéphane Blondeau Da Silva
In this paper, we will see that the proportion of d as leading digit, d $\in$ 1, 9, in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than Benford's Law. These probability distributions fluctuate around Benford's value as can often be observed in the literature in many naturally occurring collections of data (where the physical , biological or economical quantities considered are upper bounded). Knowing beforehand the value of the upper bound can be a way to find a better adjusted law than Benford's one.
View Show abstract
... Yet, this phenomenological law holds for an extraordinary diversity of datasets. Benford's distribution has been observed in geophysical data 3 , such as distributions of lengths of rivers, areas of lakes, etc., in the distribution of auction prices on eBay 4 , or in the effects of introducing Euro currency in EU member states
5
. Recently, Benford's law has been used in fraud detection [6][7][8] , to indicate vote counting manipulation during elections in the US 9 , Ukraine and Russia 10 (although some researchers claim that Benford's law is not the right tool to assess the veracity of elections 11 ), and to disclose inconsistencies in census surveys 12 . ...
Benford’s Distribution in Complex Networks
Article Full-text available Oct 2016 Mikolaj Morzy Tomasz Kajdanowicz Boleslaw K. Szymanski
Many collections of numbers do not have a uniform distribution of the leading digit, but conform to a very particular pattern known as Benford’s distribution. This distribution has been found in numerous areas such as accounting data, voting registers, census data, and even in natural phenomena. Recently it has been reported that Benford’s law applies to online social networks. Here we introduce a set of rigorous tests for adherence to Benford’s law and apply it to verification of this claim, extending the scope of the experiment to various complex networks and to artificial networks created by several popular generative models. Our findings are that neither for real nor for artificial networks there is sufficient evidence for common conformity of network structural properties with Benford’s distribution. We find very weak evidence suggesting that three measures, degree centrality, betweenness centrality and local clustering coefficient, could adhere to Benford’s law for scalefree networks but only for very narrow range of their parameters.
View Show abstract
... The first digit law also extends to diverse other data sets, such as numbers reported on the front pages of newspapers, baseball statistics, river lengths, and molecular weights. It also has been used to investigate stock market prices (Pietronero et al. 2001), prices in eBay auctions (Giles 2007), and grocery prices before and after the EURO introduction
(Sehity/Hoelzl/Kirchler 2005)
. These authors also claim, that Benford's law might enable to disclose pricing interventions by price setters (Sehity/ Hoelzl/Kirchler 2005, p. 478). ...
Several Aspects of Psychological Pricing: Empirical Evidence from some Austrian Retailers
Article Full-text available Jan 2011 Udo Wagner Jutatip Jamsawang
This empirical study concentrates on several aspects of price perceptions, especially on price endings, the first (non-zero) digit in a price, symbolic meanings, eye-catching sequences, and price cuts framed in percentage or euro terms and uses a descriptive design to determine the extent to which retailers of grocery, furniture, clothes, hardware, consumer electronics, and food apply these psychological pricing methods in Austria. Odd and even pricing are common practices for a wide range of prices. Remarkably, a low number of price points generate more than half of the sales for groceries and clothing. Benford’s law regarding first digits applies for furniture shops. The unlucky digit 4 appears less frequently in price endings in Chinese restaurants. The lucky number 9 is more frequently used on Chinese menus. Few retailers employ prices made up of digits that form a striking pattern. Finally, the lower the price cut, the more likely the discount gets promoted in terms of percentages off.
View Show abstract
... Ley [26] Sehity et al.
[28]
considered the pricing of goods. They assumed that the pricing based on psychology cannot follow Benford´s law. ...
The Benford paradox Article Full-text available Jan 2014 Johan Fellman
We consider Benford´s law, also called the first-digit law. Benford (Proc. Amer. Phil. Soc., 78, 1938:551-572) presented the law in 1938, but 57 years earlier Newcomb (Amer. J. Math., 4, 1881:39-40) made the same observation. The problem was identified when they used logarithm tables in performing numerical calculations. They noted that the earlier pages of the tables were more worn than later pages. Consistent with this observation, they noted using numbers starting with low digits more often than numbers with high. Benford considered different data sets and noted that for some this rule is valid while for others it is not. When he combined all data sets, the rule was satisfied. Benford was not the first to observe this curiosity, but Benford´s results aroused more attention. Consequently, in the literature the law was named Benford´s law.
This paradox has subsequently been established by other scientists, and it has been confirmed to hold under different circumstances. Benford´s law is a statistical tool of great interest for scientists both when they perform theoretical analyses or when they try to apply the law in empirical connections. There is an extensive literature concerning the use of Benford´s law in order to check data quality.
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... 79 At the 10, 5, and 1% significance level, the three values for the Kuiper test are 1.191, 1.321, and 1.579; for the modified m test 0.851, 0.967, and 1.212; and for the modified d test 1.212, 1.330, and 1.569. 80 Benford's Law has also been used to detect or examine unusual patterns in firm reported earnings (Thomas, 1989), tax fraud (Nigrini, 1996) and accounting fraud (Durtschi, Hillison, & Pacini, 2004;Nigrini, 2012), psychological product pricing
(el Sehity, Hoelzl, & Kirchler, 2005)
, price manipulations in eBay auctions (Giles, 2007), in-kind campaign donations (Cho & Gaines, 2007), fraud in scientific data (Diekmann, 2007), the quality of survey data (Judge & Schechter, 2009), and election fraud (Deckert, Myagkov, & Ordeshook, 2011). Varian (1972) proposed to use it as a criterion to evaluate a model's performance: if the input data obey Benford's Law but the output data do not, that would raise questions about the model. ...
The quality of China's GDP statistics
Article Sep 2014 Carsten A. Holz View
... In the past the social representations were collected during the introduction of the European currency to measure the societal receptivity of a novel currency
(el Sehity, Hoelzl & Kirchler, 2005)
. The social representations of experts on the global competency of the U.S. ...
On the Social Representations of Intergenerational Equity
Article Full-text available Feb 2012 Julia M. Puaschunder
Social representations describe the genesis of collective ideas, social norms and general moods. By capturing social perceptions of socio-economic change in times of crises, social representations allow predictions about future behavior of social masses during economic upheaval. The social representations of intergenerational equity were retrieved from 110 speeches, interviews and conversations with leaders, practitioners, experts and students representing academia, business, economics, finance, international organizations, media, politics, public affairs and religion at a European future conference. During the late summer of 2011, the social representations on intergenerational equity comprised of unsustainable pension systems in the light of aging, shrinking Western populations, overindebtedness in the wake of governmental deficit spending and ecologic decline related to unsustainable consumption patterns and climate change. Stakeholder views of intergenerational equity included environmentalism on public officials’ and international organizations’ agendas. Politicians connected intergenerational justice to human rights. The 2008/09 World Financial Crisis impacted intergenerational equity by stressing overindebtedness and uncertainty. Nationalism and protectionism appeared to be growing in the finance and corporate worlds during the Eurozone Eurobond negotiations. Intergenerational environmentalism features associations on ecologic sustainability, climate change and sustainable consumption patterns. Global solutions for complex common goods dilemmas and international remedies back intergenerational justice. Promoting solidarity, ethicality and social responsibility but also innovations and future investment are intergenerational equity implementation prerequisites. Intergenerational equity is obtained by efficiency, humane values and behavioral changes regarding conscientious consumption. Long-term solutions hold institutional regulation and foresighted taxation but also open debates informing global leaders of complex intertemporal frictions.
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... Moreover, psychological prices (i.e. prices ending with 00, 50, 90 or 99) disappeared during the time of the euro cash changeover; about one year later psychological prices were back again
(el-Sehity, Hölzl and Kirchler, 2005)
. Such a situation of uncertainty, caution and a considerable degree of distrust may easily lead to price changes being perceived as price increases rather than as price reductions. ...
Comment on "Perceived Inflation and the Euro: Why High? Why Persistent?
Article Full-text available Jan 2005 Erich Kirchler View
Last Digit Tendency: Lucky Numbers and Psychological Rounding in Mobile Transactions
Article Dec 2023 Hai Wang Tian Lu Yingjie Zhang Wen Huang View
Follow the money: Techniques for pricing rewards in crowdfunding projects
Article Oct 2023
ELECTRON COMMER R A
Bar Keisar Omer Lev View
More than a Penny’s Worth: Left-Digit Bias and Firm Pricing
Article Dec 2022 Avner Strulov-Shlain
Firms arguably price at 99-ending prices because of left-digit bias—the tendency of consumers to perceive a $4.99 as much lower than a $5.00. Analysis of retail scanner data on 3500 products sold by 25 US chains provides robust support for this explanation. I structurally estimate the magnitude of left-digit bias and find that consumers respond to a 1-cent increase from a 99-ending price as if it were more than a 20-cent increase. Next, I solve a portable model of optimal pricing given left-digit biased demand. I use this model and other pricing procedures to estimate the level of left-digit bias retailers perceive when making their pricing decisions. While all retailers respond to left-digit bias by using 99-ending prices, their behavior is consistently at odds with the demand they face. Firms price as if the bias were much smaller than it is, and their pricing is more consistent with heuristics and rule-of-thumb than with optimization given the structure of demand. I calculate that retailers forgo 1 to 4 percent of potential gross profits due to this coarse response to left-digit bias.
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A Mathematical Model for the Origin of Name Brands and Generics
Preprint Full-text available Dec 2021 Joseph Davis Johnson Adam M. Redlich Daniel M. Abrams
Firms in the U.S. spend over 200 billion dollars each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a "generic" group) and one with significantly more advertising (a "name brand" group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.
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A review on competitive pricing in supply chain management problems: models, classification, and applications
Article Nov 2021 Matineh Ziari Morteza Ghomi-Avili Mir Saman Pishvaee Hamed Jahani
Supply chain management (SCM) deals with various strategic, tactical, and operational level decisions in which pricing is of utmost importance to decision makers. Most of the real-life supply chain pricing problems consider competition as a crucial factor in order to expand the market share and tackle emerging competitors. Accordingly, competitive pricing in SCM has attracted great attention by practitioners and academicians in the last four decades. Now after 40 years, it seems necessary to systematically review and classify the previous studies and present the most appealing future research directions. This paper provides a comprehensive review of the state-of-the-art published papers in scientific journals. Here, 166 papers published from 1983 to 2021 are reviewed and classified to introduce the major models and specific considerations in this field. After reviewing the selected competitive pricing models, some research insights and potential subjects for extending the literature are presented to illustrate the most appropriate and challenging future research directions.
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The Application of the Law of Anomalous Numbers on Global Food Prices in Examining Psychological Pricing Strategies
Article Jul 2020 Hrvoje Jošić Berislav Žmuk
The goal of this paper is to present a new approach to examining psychological pricing strategies using the law of anomalous numbers on the global food prices database. Benford’s Law distribution is used in order to see whether first price digits follow Benford’s Law. On top of that, the discrete uniform distribution is used to examine whether the last digit and the last two digits of a price have the same frequency of occurrence or whether there are indications that there are symbolic meanings to price endings. The results of the analysis showed that the global food price digits distribution does not follow the chosen distributions.
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THE APPLICATION OF BENFORD'S LAW IN PSYCHOLOGICAL PRICING DETECTION
Article Full-text available Dec 2018 Hrvoje Jošić Berislav Žmuk
This paper presents the application of Benford's law in psychological pricing detection. Benford's law is naturally occurring law which states that digits have predictable frequencies of appearance with digit one having the highest frequency. Psychological pricing is one of the marketing pricing strategies directed on price setting which have the psychological impact on certain consumers. In order to investigate the application of Benford's law in psychological pricing detection , Benford's law is observed in the case of first and last digits. In order to inspect if the first and last digits of the observed prices are distributed according to the Benford's law distribution or discrete uniform distribution respectively, mean absolute deviation measure, chi-square tests and Kolmogorov-Smirnov Z tests are used. Results of the analysis conducted on three price datasets have shown that the most dominating first digits are 1 and 2. On the other side, the most dominating last digits are 0, 5 and 9 respectively. The chi-square tests and Kolmogorov-Smirnov Z tests have showed that, at significance level of 5%, none of the three observed price datasets does have first digit distribution that fits to the Benford's law distribution. Likewise, mean absolute deviation values have shown that there are large differences between the last digit distributions and the discrete uniform distribution implying psychological pricing in all price datasets.
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More than a Penny's Worth: Left-Digit Bias and Firm Pricing
Article Jan 2019 Avner Strulov-Shlain View
Using Benford’s law on the seismic reflectivity analysis
Article Jun 2018 Isadora Macedo
Jose J S De Figueiredo
Benford’s law (BL) is a mathematical theory of leading digits. This law predicts that the distribution of first digits of real-world observations is not uniform and follows a trend in which measurements with a lower first digit (1, 2, …) occur more frequently than those with higher first digits (…, 8, 9). A data set from earth’s geomagnetic field, the estimated time in years between reversals of earth’s geomagnetic field, the seismic P-wave speed of earth’s mantle below the southwest Pacific, and other geophysical data obey the BL. Although there are other statistical methods for analyzing a data set, we test, for the first time, the analysis of the seismic reflectivity through the Benford distribution point of view. We applied the BL on real reflectivity data from two wells from the Penobscot field and another two from the Viking Graben field. In both data sets, the reflectivity was in conformity with the BL. Moreover, after analyzing the effect of sonic and density logs despiking on Benford’s distribution through the BL, we found an optimum coefficient for the despiking process, which was a common procedure used to edit the well-log data before its use on reservoir studies.
View Show abstract Publ308 Data Full-text available Feb 2018 Johan Fellman View
THE FOREIGN TOURISTS’ PERCEPTIONS ABOUT THE PSYCHOLOGICAL PRICING PRACTICES IN FOOD AND BEVERAGE ESTABLISHMENTS: A STUDY ON BRITISH TOURISTS
Thesis Full-text available Jan 2009 Fırat Biçici View International Business Strategies Chapter Jan 2017 Michael Wynn-Williams View
Numbers in the Internet Web and Benford's Law
Article Full-text available Jun 2009 Dae-Heung Jang
Using the information about the frequency of occurrence of numbers in WWW, we can find properties of the array of numbers and validate whether this array satisfies the several laws(Power law, Zipf's law, Benford's law).
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L'euro tra aspettative e processi di adattamento. [The Euro: The aspects and processes of the adaptation.]
Article Jan 2006 Erich Kirchler Eva Hofmann Bernadette Kamleitner View
Set Menus Effects on Foreign Tourist Perceptions as a Product-Bundling Practice in Restaurants
Article Full-text available Jan 2013 Fırat Biçici Çağrı Köroğlu
Number of seasonal food&beverage establishments, whose customers are mainly foreigners are increasing rapidly in touristic regions and severe competition occurs among them. Food&beverage establishments want to impress foreign tourists who came to the country for a week or two to protect and improve their positions in the market by carrying out various strategies towards marketing. Although enstruments except prices are demanded and used commonly, importance and priority of prices are always more effective within strategies towards marketing.
Price bundling, the selling of products or services more than one such as package for a single price, is becoming increasingly common in the food&beverage industry. Because there is a difference between consumer buying behaviour of food&beverage industry and retailer industry. A consumer in a food&beverage establishment might place and order for a drink with his/her meal or supplementing garnish beside his/her main course. Namely, multiple buying behaviour might come into question. On the other hand, possibility of an increase of buying behaviour in retail sector would not be as it is in food&beverage industry. For example, to meet need of a pair of trainers, only one pair is bougth except exceptional situtaions. Buying a second pair of trainers or a t-shirt would not happen if not truly necessary, but this may change according to the marketing strategy of the establishments. In other words possibility of buying behaviour of the consumer is likely to be higher in a food&beverage establishments than it might be in a retail establishment. This fact brings set menu pricing practices as a price-bundling strategy into forefront in food&beverage establishments.
Set menus, which involves combining two or more products have been practised by fast-food restaurants such as Mc Donalds, Burger King andKFC for years successfully by offering various products in a single package price Theese chain restaurants derive benefit to the establishments by making consumers spend more on combined products, procure benefit to the customers by providing a lower price than buying the products separately. It was aimed to put forward importance of set menus in terms of menu-price relations and consumer buying behaviours. Besides, perception of foreign tourists on set menus were studied from the point of value.
According to marketing which is different from economics pricing should be regulated to influence consumer buying behaviour at the end of a planned process. Consumers do not behave rationalistic as it is stated in economics. Consumers exhibit buying behaviours by getting influenced from prices and they act in market conditions with limited information, time and energy.
Because of the structure of industry, marketing strategies are used a lot in food&beverage establishments. Although enstruments except prices are demanded and used commonly, importance of pricing strategies are always more effective.
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Price Ending Strategies: A Qualitative Study Focusing on the Effects of Students' Perceptionsfor Cafe and Restaurant Menu Prices
Article Full-text available Jan 2007 Murat Hancer Fırat Biçici Abdullah Tanrisevdi
ABSTRACT The primary aim of this study is to explore price-ending strategies utilized in coffee shops and luxury restaurants. Customers' image and expectations of quality with respect to the utilization of price-ending strategies is also investigated in the study. The methodology of the study has divided into two phases. The first phase involves the collection of menus from coffee shops and luxury restaurants in Ankara. Seventy menus collected, then carefully inspected to see the differences among the usage of different price-endings. This phase reveals that menu prices-ending with .00 (i.e. 7.00) and ending with no digits (i.e. 7) are the most commonly used strategies in the luxury restaurants. The second phase of the study uses scenarios to find out the customers' image of restaurant and food quality. The sample was comprised of students. This phase reveals that students who read the scenario explaining a " high quality restaurant " are affected by the prices ending with .00 and ending with no digits. On the other hand, a scenario about a place that offers a low price by using digits .99 and .00 does not give the image of " bargain place " in the minds of customers.
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Price Promotions and Psychological Pricing in German Grocery Retailing
Article Jan 2013 Angela Hoffmann Kerstin Hackelbusch
Price promotions play a prominent role in German grocery retailing. Their purpose is to increase store traffic and strengthen customer loyalty. It is hypothesized that other marketing tools, like psychological pricing can add to the positive impact of price promotions on sales. Thus, we investigate the joint impact of price promotions and different pricing points on sales. Our empirical analysis shows that just-below prices tend neither to raise sales of regularly priced products nor of price promoted products. The only exception is significant price reductions combined with 99 ending prices (especially of private labels). While our results show no alternatives to regular 9 ending prices, price promotions should rather end in a 99 or be round. Moreover, repdigits (eye-catching price figures) can significantly increase sales of price promoted manufacturers' labels when other cues of price promotions exist. However, German retailers, particularly discount stores, do rarely make use of such combined marketing tools. The results indicate that consumers pay less attention to the size of price reductions than to other cues of price promotions or displays, whereby psychological pricing can intensify the impact of other marketing tools on sales.
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Tracking Exchange Rate Managementin Latin America
Article Mar 2015 César Carrera
The exchange rate is one of the most important prices in any open economy. Tracking deviations from its long-run value may provide important information for policymakers. One way to track such deviations is to examine numerical patterns in exchange rates to see if the patterns appear to have been subject to some degree of policy management. Following this approach, we use Benford’s Law as our base case for free-floating exchange rates. Benford’s Law argues that the frequence of the appearance of numerals finds 1’s more frequent, than 2’s, than 3’s, etc., and this established statistical patterns has been verified and used in research tests in many scientific fields. We apply our forensic approach to exchange rates, computing the distribution of exchange-rate observed values and comparing them with those of Benford’s Law. We document such cases for 15 Latin American countries. Latin American countries are small open economies that are characterized for having different degrees of dollarization and intervention in the forex market, primary based on US dollar transactions. This is an alternative view of how these characteristics play a role with respect to an implied equilibrium exchange rate.
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Lay representations of an economic global crisis among different Italian and Romanian social groups
Article Full-text available Dec 2014 Anna Liguori Roberto Fasanelli Ida Galli Luminita Iacob View
Methods for recommending and predicting Nobel Prize candidates: A case study of HIV/AIDS subject area
Article Apr 2014 PROGRAM-ELECTRON LIB Guo Gen-Ming Chen Hui-Shan Purpose
– In the twenty-first century, technology and information are continuously being changed and rapidly updated. Many new innovations and discoveries emerge daily. This study aims to identify significant pioneers and milestones in academic research through utilizing bibliometric methods and heterogeneous data, including textbook citations, citations of theses and dissertations, and journal citations.
Design/methodology/approach
– This study proposes several methods and formulas for recommending Nobel prizes candidates. Through utilizing bibliometric methods and heterogeneous data, including textbook citations, citations of theses and dissertations, and journal article citations, this research facilitates the collection of numerous significant research results. The authors propose several new, useful formulae, including a pioneer paper impact factor, a popular classical paper impact factor, a ranking factor of specific fields, a groundbreaking author impact factor, and a frequently cited author impact factor.
Findings
– This study utilizes historical information on the Nobel Prize to examine, revise, and verify existing methods for recommending and predicting candidates, in order to enhance the accuracy and availability of the approach presented by this study. The experimental results show that the approach designed in this study had a rate of successful prediction exceeding 50 percent. The major reason for producing reasonable results is that the milestone paper and pioneer paper are filtered first, and then the important candidate authors from the most pioneer paper are filtered. Therefore, the results indicated the feasibility of the methods developed by this study.
Originality/value
– The purpose of the Nobel Prize is to reward original research findings or inventions that significantly and positively influence human life. However, due to budget limitations, only five fields are included in the academic domains for which Nobel prizes are awarded. The authors develop one useful new way to identify milestone papers and authors. Young students can choose, read and learn from these milestone papers. The pioneer authors identified by this research could be the recommended candidate list for some academic awards.
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Does Online Information Drive Offline Revenues?: Only for Specific Products and Consumer Segments!
Article Full-text available Mar 2011 J RETAILING Koen Pauwels Peter S.H. Leeflang Marije Teerling
Eelko K. R. E. Huizingh
While many offline retailers have developed informational websites that offer information on products and prices, the key question for such informational websites is whether they can increase revenues via web-to-store shopping. The current paper draws on the information search literature to specify and test hypotheses regarding the offline revenue impact of adding an informational website. Explicitly considering marketing efforts, a latent class model distinguishes consumer segments with different short-term revenue effects, while a Vector Autoregressive model on these segments reveals different long-term marketing response.We find that the offline revenue impact of the informational website critically depends on the product category and customer segment. The lower online search costs are especially beneficial for sensory products and for customers distant from the store. Moreover, offline revenues increase most for customers with high web visit frequency. We find that customers in some segments buy more and more expensive products, suggesting that online search and offline purchases are complements. In contrast, customers in a particular segment reduce their shopping trips, suggesting their online activities partially substitute for experiential shopping in the physical store. Hence, offline retailers should use specific online activities to target specific product categories and customer segments.
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Patterns of price endings used in US and Japanese price advertising
Article Feb 2009 INT MARKET REV Robert M. Schindler Purpose
The purpose of this paper is to guide managers' choices of rightmost digits in retail prices by acquiring a better understanding of the psychological mechanisms by which price endings can influence sales.
Design/methodology/approach
The paper observes and compares the price endings used in large matched samples of advertised prices in two countries with considerable cultural differences, the USA and Japan.
Findings
Although the digit 9 predominates among the rightmost digits of advertised prices in the USA the digit 8 predominates in Japan. In contrast to this difference, the US and Japanese prices are similar in that both show greater use of 9 or 8 endings when this choice lowers the price's leftmost digit and when the advertised price is claimed to be a discount price.
Research limitations/implications
Future research should include a wider range of price advertising media and should examine usage patterns of less frequently occurring digits.
Practical implications
Setting a price that falls just below a round number can be helpful in creating a low‐price image. Setting this just‐below price with a 9‐ending would be appropriate in the USA and European countries, but in Japan and other Asian countries, it would be more appropriate to set this just‐below price with an 8‐ending.
Originality/value
These results provide guidance to the retail price setter and illustrate to the basic researcher how universal psychological processes and specific cultural meanings can interact to determine consumer perceptions of marketing stimuli.
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Perceived inflation and the euro: Why high? Why persistent?
Article Helmut Stix
This paper employs an Austrian micro-dataset to analyze why inflation perceptions became disconnected from official inflation measures in the course of the euro cash changeover. We find evidence that persons who are confronted with prices of frequently purchased goods, who expected price increases and who mentally convert euro prices into old currency prices when making price comparisons have a significantly higher perception of inflation. Furthermore, our results indicate that the latter two factors have a persistent impact. This contributes in explaining why price perceptions have not normalized for several years in some countries. The results suggest that policy measures in countries which are going to introduce the euro should address these issues in order to prevent a similar development as experienced in many euro area countries.
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Does competitive entry structurally change key marketing metrics?
Article Sep 2008
INT J RES MARK
M. Kornelis Marnik G. Dekimpe Peter S.H. Leeflang
To what extent does competitive entry create a structural change in key marketing metrics? New players may just be a temporal nuisance to incumbents, but could also fundamentally change the latter's performance evolution, or induce them to permanently alter their spending levels and/or pricing decisions. Similarly, the addition of a new marketing channel could permanently shift shopping preferences, or could just create a short-lived migration from existing channels. The steady-state impact of a given entry or channel addition on various marketing metrics is intrinsically an empirical issue for which we need an appropriate testing procedure.In this study, we introduce a testing sequence that allows for the endogenous determination of potential change (break) locations, thereby accounting for lead and/or lagged effects of the introduction of interest. By not restricting the number of potential breaks to one (as is commonly done in the marketing literature), we quantify the impact of the new entrant(s) while controlling for other events that may have taken place in the market. We illustrate the methodology in the context of the Dutch television advertising market, which was characterized by the entry of several late movers. We find that the steady-state growth of private incumbents' revenues was slowed by the quasi-simultaneous entry of three new players. Contrary to industry observers' expectations, such a slowdown was not experienced in the related markets of print and radio advertising.
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Consumer Psychology for Marketing
Book Full-text available Mar 1998 Gordon Foxall Ronald E. Goldsmith View
The Role of Selective Information Processing in Price-Quality Inference
Article Full-text available Sep 2004 Frank R. Kardes James J. Kellaris Maria L. Cronley Steven S. Posavac
[enter Abstract Body]This research investigates the effects of the amount of information presented, information organization, and concern about closure on selective information processing and on the degree to which consumers use price as a basis for inferring quality. Consumers are found to be less likely to neglect belief-inconsistent information and their quality inferences less influenced by price when concern about closure is low (vs. high) and information is presented randomly (vs. ordered) or asmall amount of information is presented. Results provide a picture of a resource-constrained consumer decision maker who processes belief-inconsistent information only when there is motivation and opportunity.
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Effects of $9 Price Endings on Retail Sales: Evidence from Field Experiments
Article Full-text available Mar 2003 Eric T. Anderson Duncan Simester
Although the use of 9 price endings is widespread amongst US retailers there is little evidence of their effectiveness. In this paper, we present a series of three field-studies in which price endings were experimentally manipulated. The data yield two conclusions. First, use of a9 price endings is widespread amongst US retailers there is little evidence of their effectiveness. In this paper, we present a series of three field-studies in which price endings were experimentally manipulated. The data yield two conclusions. First, use of a 9 price ending increased demand in all three experiments. Second, the increase in demand was stronger for new items than for items that the retailer had sold in previous years. There is also some evidence that 9 price endings are less effective when retailers use < img src="/content/G27943713N352N8W/xxlarge8220.gif" alt="ldquo" align="MIDDLE" border="0Sale < img src="/content/G27943713N352N8W/xxlarge8221.gif" alt="rdquo" align="MIDDLE" border="0 cues. Together, these results suggest that9 price endings are less effective when retailers use Sale cues. Together, these results suggest that 9-endings may be more effective when customers have limited information, which may in turn help to explain why retailers do not use $9 price endings on every item.
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Does Money Illusion Matter?
Article Full-text available Dec 2001 Ernst Fehr Jean-Robert Tyran JR Tyran
Money illusion means that people behave differently when the same objective situation is represented in nominal terms rather than in real terms. This paper shows that seemingly innocuous differences in payoff representation cause pronounced differences in nominal price inertia indicating the behavioral importance of money illusion. In particular, if the payoff information is presented to subjects in nominal terms, price expectations and actual price choices after a fully anticipated negative nominal shock are much stickier than when payoff information is presented in real terms. In addition we show that money illusion causes asymmetric effects of negative and positive nominal shocks. While nominal inertia is quite substantial and long-lasting after a negative shock, it is rather small after a positive shock. Keywords: Money illusion, nominal inertia, sticky prices, non-neutrality of money JEL: C92, E32, E52. 1 University of Zrich, Institute for Empirical Research in Economics, Blmlisalpstr. 10, CH-8006 Zrich. E-Mail address: efehr@iew.unizh.ch 2 University of St. Gallen, Department of Economics, Bodanstr. 1, CH-9000 St. Gallen. E-Mail address: JeanRobert. Tyran@vwa.unisg.ch We are particularly grateful for two excellent referee reports and for comments by George Akerlof, Linda Babcock, Jim Cox, Urs Fischbacher, Simon Gchter, Ed Glaeser, Lorenz Goette, Charles Goodhart, Reinhard Selten, Dick Thaler and Michael Waldman. In addition, we acknowledge helpful comments by the participants of seminars at the universities of Berlin, Bonn, Harvard, Mannheim, the NBER conference on behavioral macroeconomics, the CEPR summer workshop on financial economics, the ESA-meeting in New Orleans and the Amsterdam workshop for experimental economics. Ernst Fehr also gratefully acknowledg...
View Show abstract Mental accounting matters Article Sep 1999
J BEHAV DECIS MAKING
Richard H. Thaler
Mental accounting is the set of cognitive operations used by individuals and households to organize, evaluate, and keep track of financial activities. Making use of research on this topic over the past decade, this paper summarizes the current state of our knowledge about how people engage in mental accounting activities. Three components of mental accounting receive the most attention. This first captures how outcomes are perceived and experienced, and how decisions are made and subsequently evaluated. The accounting system provides the inputs to be both ex ante and ex post cost–benefit analyses. A second component of mental accounting involves the assignment of activities to specific accounts. Both the sources and uses of funds are labeled in real as well as in mental accounting systems. Expenditures are grouped into categories (housing, food, etc.) and spending is sometimes constrained by implicit or explicit budgets. The third component of mental accounting concerns the frequency with which accounts are evaluated and ‘choice bracketing’. Accounts can be balanced daily, weekly, yearly, and so on, and can be defined narrowly or broadly. Each of the components of mental accounting violates the economic principle of fungibility. As a result, mental accounting influences choice, that is, it matters. Copyright © 1999 John Wiley & Sons, Ltd.
View Show abstract Mental Accounting Matters Conference Paper Sep 1999 Richard H. Thaler
Mental accounting is the set of cognitive operations used by individuals and households to organize, evaluate, and keep track of financial activities. Making use of research on this topic over the past decade, this paper summarizes the current state of our knowledge about how people engage in mental accounting activities. Three components of mental accounting receive the most attention. This first captures how outcomes are perceived and experienced, and how decisions are made and subsequently evaluated. The accounting system provides the inputs to be both ex ante and ex post cost-benefit analyses. A second component of mental accounting involves the assignment of activities to specific accounts. Both the sources and uses of funds are labeled in real as well as in mental accounting systems. Expenditures are grouped into categories (housing, food, etc.) and spending is sometimes constrained by implicit or explicit budgets. The third component of mental accounting concerns the frequency with which accounts are evaluated and 'choice bracketing'. Accounts can be balanced daily, weekly, yearly, and so on, and can be defined narrowly or broadly. Each of the components of mental accounting violates the economic principle of fungibility. As a result, mental accounting influences choice, that is, it matters. Copyright (C) 1999 John Wiley & Sons, Ltd.
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Considerations in the setting of retail prices
Article J MARKETING O. Knauth View
I've got your number
Article Jan 1999 M.J. Nigrini View Benford's law Article Jan 1972 AM STAT H. Varian View
Anchoring Effects on Consumers’ Willingness‐to‐Pay and Willingness‐to‐Accept
Article Dec 2004 Itamar Simonson Aimee Drolet
We examine the susceptibility of consumers' willingness-to-pay (WTP) and willingness-to-accept (WTA) judgments to influence by arbitrary anchors. The results of four studies suggest that, although circumstantial differences between buying and selling decisions can lead to systematic differences in susceptibility to anchoring effects, the principles governing the impact of anchoring on WTP and WTA judgments are essentially the same. In particular, robust anchoring effects are observed when the anchor relates to the focal source of uncertainty. Further, WTP and WTA judgments are most susceptible to anchoring (and endowment) effects under uncertainty about the desire to trade. The implications of this research for our understanding of anchoring and endowment effects are discussed.
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Image Communicated by the Use of 99 Endings in Advertised Prices
Article Dec 2001 Robert M. Schindler Thomas M. Kibarian
In a controlled experiment, use of the 99 rather than the 00 price ending (e.g., using $49.99 rather than $50.00) affects the impression created by a price advertisement. The 99 ending increases the likelihood that viewers judge an advertised price as relatively low and as representing a discount. However, in addition to these price-image effects, the 99 ending has negative effects on quality image in the ads sponsored by higher quality retailers. These results suggest that the choice of rightmost digits is an important executional variable in price advertising.
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The First Digit Problem
Article Aug 1976 Ralph A. Raimi View
The Impact of Price Thresholds on Profit Contribution - Should Retailers Set 9-Ending Prices?
Article Mar 1999 J RETAILING Karen Gedenk Henrik Sattler
Retail prices typically end in 9 cents. This can be due to thresholds between odd and even prices where sales decrease sharply (e.g., $2.89 versus $2.90). However, empirical evidence is inconclusive as to whether such thresholds really exist. We show that observed retailer behavior is rational even when there is uncertainty about the existence of price thresholds. Our analysis is based on the losses in profit contribution that are incurred when a retailer makes the wrong assumptions about the presence of thresholds. By analyzing different response and cost functions, we find that a retailer should typically set 9-ending prices, unless he suspects strong quality-image effects of price endings.
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Increased Consumer Sales Response Though Use of 99-Ending Prices
Article Jun 1996 J RETAILING Robert M. Schindler Thomas M. Kibarian
Through the cooperation of a direct-mail women's clothing retailer, we were able to conduct a well-controlled experiment testing the sales effect of using retail prices that end in the digits 99 rather than 00 (e.g., $29.99 rather than $30.00). The results indicated that the use of 99 endings led to increased consumer purchasing. This finding demonstrates the importance of the manager's decision concerning a price 's rightmost digits. © 1996 New York University. All rights of reproduction in any form reserved.
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L'Euro Ha Creato Inflazione? Changeover E Arrotondamenti Dei Prezzi Al Consumo in Italia Nel 2002. (Has the Euro Caused Inflation? The Changeover and Consumer Price Rounding in Italy in 2002)
Article Jan 2003 Franco Mostacci Roberto Sabbatini
The purpose of this paper is to estimate the specific impact of the introduction of the euro on Italian consumer inflation that can be attributed solely to the rounding of prices to figures that are "attractive" in euro. The empirical analysis is based on a large sub-set of prices used by Istat to calculate the general consumer price index for Italy. Between January and October 2002 the general consumer price index rose 2.4%; the impact of rounding on the general consumer price index in Italy amounted to between 0.3 and 0.9 percentage points, depending on the method of estimation used. With reference to the average rise in the general consumer price index of 2.5% in 2002, the impact on average annual consumer price inflation in 2002 lies between 0.1 and 0.5 percentage points. The changeover apparently worked its effect mainly through products sold by traditional retail channels.
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Transaction Decoupling: How Price Bundling Affects the Decision to Consume
Article Feb 2001 Dilip Soman John T. Gourville
In today's marketplace, price bundling is widespread: Manufacturers and retailers routinely offer multiple products for a single, bundled price. Although the effects of price bundling on purchase behavior have been well researched, the effects of price bundling on postpurchase consumption behavior have received almost no attention. In this article, the authors build on the sunk cost literature (e.g., Thaler 1980, 1985) and predict that price bundling leads to a disassociation or "decoupling" of transaction costs and benefits, thereby reducing attention to sunk costs and decreasing a consumer's likelihood of consuming a paid-for service (e.g., a theater performance). Four studies show this to be the case. In two lab studies, the authors show that having a bundled four-day ski pass as opposed to four one-day ski tickets decreases a person's likelihood of skiing on the final day of a four-day ski vacation. They replicate this result in a field study, showing that multiperformance ticket holders are more likely to forgo a given theatrical performance than are single-performance ticket holders, all else held constant. In a final study, the authors show that the decreased attention to sunk costs brought about by price bundling can be either cognitively driven (i.e., it is difficult to allocate a single payment across multiple benefits) or motivationally driven (i.e., there is an underlying desire to avoid consumption). Their findings have practical implications for managers interested in predicting or influencing actual product consumption.
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Note on the Frequency of Use of the Different Digits in Natural Numbers
Article Jan 1881 AM J MATH Simon Newcomb View
Anomalies in Income Numbers: Evidence of Goal Oriented Behavior
Article Jan 1988 C.A.P.N. Carslaw View
A Note on Non-Parametric Tests for the Interaction in Two-Way Layouts
Article Jan 1986 BIOMETRICAL J Klaus D. Kubinger
A suggestion is given of how to prove main and interaction effects in two-way layouts independent of each other even if the data are just ordinally scaled. Starting from HILDEBRAND'S (1980a, b) non-parametric approach which presupposes interval-scaled data, transformations of ranks are settled before analysis per analogy to the H-test takes place. That is, the same formula of an asymptotically X2-distributed test-statistic results but mean ranks are used instead of mean scores in order to partialize, for instance, main effects while testing interaction effect. Finally an allusion is given of how to handle ties as well as unequal sample sizes.
View Show abstract Mental Accounting Matters Article Sep 1999
J BEHAV DECIS MAKING
Richard H. Thaler
Mental accounting is the set of cognitive operations used by individuals and households to organize, evaluate, and keep track of financial activities. Making use of research on this topic over the past decade, this paper summarizes the current state of our knowledge about how people engage in mental accounting activities. Three components of mental accounting receive the most attention. This first captures how outcomes are perceived and experienced, and how decisions are made and subsequently evaluated. The accounting system provides the inputs to be both ex ante and ex post cost-benefit analyses. A second component of mental accounting involves the assignment of activities to specific accounts. Both the sources and uses of funds are labeled in real as well as in mental accounting systems. Expenditures are grouped into categories (housing, food, etc.) and spending is sometimes constrained by implicit or explicit budgets. The third component of mental accounting concerns the frequency with which accounts are evaluated and 'choice bracketing'. Accounts can be balanced daily
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A Taxpayer Compliance Application of Benford's Law
Article Jan 1996
J Am Taxat Assoc
Mark J. Nigrini View
The Law of Anomalous Numbers
Article Nov 1937
Proc Am Phil Soc
F. Benford View
On the Peculiar Distribution of the U.S. Stock Indexes' Digits
Article Nov 1996 Eduardo Ley
Recent research has focused on studying the patterns in the digits of closely followed stock market indexes. In this paper we find that the series of 1-day returns on the Dow-Jones Industrial Average Index (DJIA) and the Standard and Poor's Index (S&P) reasonably agrees with Benford's law and therefore belongs to the family of anomalous or outlaw numbers.
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Asking About Prices: A New Approach to Understanding Price Stickiness
Book Oct 1998 Alan S. Blinder Elie Canetti David E. Lebow Jeremy B. Rudd View
Metacognitive Experiences in Consumer Judgment and Decision Making
Article Dec 2004 Norbert Schwarz
Human reasoning is accompanied by metacognitive experiences, most notably the ease or difficulty of recall and thought generation and the fluency with which new information can be processed. These experiences are informative in their own right. They can serve as a basis of judgment in addition to, or at the expense of, declarative information and can qualify the conclusions drawn from recalled content. What exactly people conclude from a given metacognitive experience depends on the naive theory of mental processes they bring to bear, rendering the outcomes highly variable. The obtained judgments cannot be predicted on the basis of accessible declarative information alone; we cannot understand human judgment without taking into account the interplay of declarative and experiential information.
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Relative Price Level of 99-Ending Prices: Image Versus Reality
Article Aug 2001 Robert M. Schindler
Consumer research has indicated that the use of the 99 ending in a retail price creates the impression of a price that is relatively low. A comparative price survey of a wide assortment of general merchandise products indicates that this impression does not match marketplace reality. On the contrary, the price survey showed that retail prices with 99 endings were less likely than prices with other endings to be among the lower prices for an item. The finding of this discrepancy has implications for consumers, public policy-makers, and our understanding of how consumers make inferences from price information.
View Show abstract The Significant-Digit Phenomenon Article Apr 1995 Theodore P. Hill View
Patterns of Rightmost Digits Used in Advertised Prices: Implications for Nine‐Ending Effects
Article Sep 1997 Robert M Schindler Patrick N Kirby
Analysis of the rightmost digits of selling prices in a sample of retail price advertisements confirmed past findings indicating the overrepresentation of the digits 0, 5, and 9. The high cognitive accessibility of round numbers can account for the overrepresentation of 0- and 5-ending prices and suggests the existence of two effects that could account for the overrepresentation of 9-ending prices: (1) a tendency of consumers to perceive a 9-ending price as a round-number price with a small amount given back and (2) a tendency of consumers to underestimate a 9-ending price by encoding it as the first round number evoked during incomplete left-to-right processing. Analysis of the patterns of rightmost digits observed in the sample provides supportive evidence particularly for the second of these two 9-ending effects. Copyright 1997 by the University of Chicago.
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An Empirical Analysis of Price Endings with Scanner Data
Article Jun 1997 Mark Stiving Russell S. Winer
Several consumer behavior theories have been offered to explain the preponderance of prices that end in the digit 9. This study attempts to incorporate these proposed behaviors into the implicit utility function of consumer choice models, resulting in both a more accurate tool for managerial decision making and additional insights into how consumers actually behave toward price endings. An attempt is made to compensate for both level effects (those effects in which consumers may underestimate the value of a price) and image effects (those effects in which consumers may infer meaning from the right-hand digits). The models are estimated using scanner panel data for two frequently purchased products, tuna and yogurt. The results support the importance of accounting for the digits in consumer choice models, providing evidence for both image effects and level effects. Copyright 1997 by the University of Chicago.
View Show abstract Money Illusion Article Feb 1997 Peter Diamond Eldar Shafir Amos Tversky
The term 'money illusion' refers to a tendency to think in terms of nominal rather than real monetary values. Money illusion has significant implications for economic theory, yet it implies a lack of rationality that is alien to economists. This paper reviews survey questions regarding people's reactions to variations in inflation and prices, designed to shed light on the psychology that underlies money illusion. The authors propose that people often think about economic transactions in both nominal and real terms, and that money illusion arises from an interaction between these representations, which results in a bias toward a nominal evaluation. Copyright 1997, the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
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On the Peculiar Distribution of the U.S. Stock Indeces' Digits
Article Apr 1995 Eduardo Ley
Recent research has focused on studying the patterns in the digits of closely followed stock market indeces (see, \eg, Ley and Varian (1994) and Koedijk and Stork (1994)). In this paper, we find that the series of one-day returns on the Dow-Jones Industrial Average Index (\djia) and the Standard and Poor's Index (\sp) reasonably agrees with Benford's law and, therefore, belongs to the family of {\it anomalous\/} or {\it outlaw\/} numbers.
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Are UK Companies' prices sticky?
Article Jul 2000 OXFORD ECON PAP Anthony Yates Simon Hall Mark Walsh
This paper reports results from a survey by the Bank of England in 1995 to assess the extent of price-stickiness in 654 UK companies. In the year before the survey, firms on average reviewed prices monthly but changed them only twice. Time-dependent pricing was far more prevalent than state-dependent pricing and there was also some evidence of asymmetries in price-responsiveness to shocks. Firms assessed the importance of particular (layman's descriptions of) theories of price stickiness. Few respondents rated menu costs as material to their price-setting decisions. But (explicit and implicit) contractual arrangements and costs were important factors in pricing behaviour. Copyright 2000 by Oxford University Press.
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Unusual Patterns in Reported Earnings
Article Feb 1988 J.K. THOMAS View
A model for the effects of psychological pricing in Gabor-Granger price studies
Article Feb 1998 J ECON PSYCHOL Michel Wedel
Peter S. H. Leeflang
We present a model of consumers' price sensitivity that explicitly deals with the existence of so-called psychological price levels or odd prices, i.e. prices ending in an odd number. The model is formulated in a latent class framework, in which splines are used to model utility as a function of prices in consumer segments. The knots in the splines represent psychological prices. Additionally, the model allows for inferences on price expectations and the role of price as an indicator of quality. The model is tailored to the analysis of so-called Gabor–Granger price experiments. We provide an empirical application to the analysis of a Gabor–Granger study, and investigate the performance of our model relative to a competing model.PsycINFO classification: 2240; 3920
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The Euro and Psychological Prices: Simulations of the Worst-Case Scenario
Article Feb 2001 C.K. Folkertsma
Currently, nearly 90% of all prices of consumer goods and services in the Netherlands are psychological, conveniently broken or round prices. After converting these `attractive' guilder prices into euro using the official conversion rate, the resulting euro prices are generally not attractive. The Dutch public is concerned that retailers will not round their euro prices symmetrically upwards and downwards to the next attractive pricing point but only upwards? This paper investigates the question `What would be the effect on the consumer price index (CPI) if prices were systematically rounded upwards'. Firstly, the attractive pricing points are determined empirically using the actual price sample underlying the Dutch CPI. Secondly, different rounding scenarios are investigated and the likelihood of the worst-case scenario is discussed. It turns out that the euro introduction may cause an increase of the CPI by 0.7% at most. However, due to competition in the retail sector, this scenario is very unlikely.
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Using Benford's Law for fraud detection
Jan 2004 4 Moore
Moore, G. B., & Benjamin, C. O. (2004). Using Benford's Law for fraud detection. Internal Auditing, 19(1), 4 – 9.
Does money illusion matter? Amer-ican Economic Review
Jan 2001 91-1239 E Fehr J R Tyran
Fehr, E., & Tyran, J. R. (2001). Does money illusion matter? Amer-ican Economic Review, 91(5), 1239 – 1262.
Preispolitik des Handels im Zuge der Euro- Einfü hrung [Retail pricing policy during introduction of the euro], Working paper Nr
Jan 2002 G Brambach
Brambach, G., (2002) Preispolitik des Handels im Zuge der Euro-
Einfü hrung [Retail pricing policy during introduction of the euro],
Working paper Nr. 96. Erlangen-Nü rnberg: Universität Erlangen-
Nü rnberg.
Benford's Law. The American Statistician
Jan 1972 65-66 H R Varian
Varian, H. R. (1972). Benford's Law. The American Statistician,
26(3), 65 – 66.
Are UK companies' prices sticky? Oxford Economic Papers
Jan 2000 425-446 S Hall M Walsh A Yates
Hall, S., Walsh, M., & Yates, A. (2000). Are UK companies' prices
sticky? Oxford Economic Papers, 52(3), 425 – 446.
Preispolitik des Handels im Zuge der Euro-Einführung
G Brambach Recommended publications Discover more about: Pricing Article Full-text available
Price Setting in Austria — Results from the Eurosystem Inflation Persistence Network
February 2005 Claudia Kwapil Fabio Rumler
This study examines price setting in Austria using micro observations of Consumer Price Index (CPI) data on the one hand and a one-time survey on firms' price-setting practices on the other hand. The analysis of the micro CPI data shows that consumer prices are adjusted roughly once a year averaged over all items in the CPI. However, there are enormous differences across sectors: The prices of
... [Show full abstract]
energy products and unprocessed food are adjusted most often whereas the prices of nonenergy industrial goods and of services are changed less frequently. Austria ranks roughly in the middle range among euro area countries in terms of the frequency of price changes; it does not stand out for either especially rigid or especially flexible prices. Judging from the data set analyzed, the euro cash changeover did not bring about a significant inflationary effect. The supplementary company survey revealed that (producer) prices are reviewed four times as often as they are actually adjusted — about once a year. Price rigidity evidently tends to arise more at the second level of price formation, namely at the actual price-setting level. Firms state implicit (long-term customer relationships) and explicit contracts as causes for delaying price adjustments. JEL classification: E31, L14
View full-text Article Full-text available
In The Middle of the Heat:The GCC countries Between Rising Oil Prices and the Sliding Greenback
January 2008 Weshah Razzak
The paper asks two questions. One, what is the size of the effect of the increase in real oil price on competitiveness of the Gulf Cooperation Council (GCC) countries –the real exchange rate is a measure of competitiveness – and two, given recent concerns about the sliding greenback and the consequent income and inflationary problems, would the GCC countries been “better off” had they pegged
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their currencies to the Euro dollar in 1991? To answer these questions we model and estimate the effect of oil prices on the competitiveness for the GCC then we provide a test statistic to test whether the conditional variance of the model has remained stable under the US dollar peg compared to a counterfactual scenario, where the GCC countries peg their currencies to the Euro dollar in 1991. We find the effect of the increase in the real price of oil on competitiveness of the GCC countries to be small, most of the domestic inflation is imported, and that there is a relatively large variation among the GCC economies with respect to the currency peg. The financial problems the GCC countries face today are not about which currency (or a basket of currencies) they should peg to, but rather about the choice of the monetary arrangement as a whole.
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Oil Price Shocks and Exchange Rate Management: The Implications of Consumer Durables for the Small O...
January 2008 · SSRN Electronic Journal Michael Plante
This paper examines exchange rate management issues when a small open economy is hit by an exogenous oil price shock. In this model consumer durables play an important role in the demand for oil and oil based products as opposed to the traditional role of oil as a factor of production. When prices are sticky, oil price shocks lead to reduced output, lower inflation, and real exchange rate
... [Show full abstract]
deprecation. These recessionary effects occur whether or not oil is in the production function because of the close relationship between consumer durables and oil. Tentative results suggest that flexible exchange rates produce smaller output losses and less volatile inflation in the non-tradables sector than fixed exchange rates but at the cost of front-loading real exchange rate movements.
Read more Article Full-text available
An Emprical Analysis of Price Setting Behaviour in the Netherlands in the Period 1998-2003 Using Mic...
January 2005 Nicole Jonker Carsten Folkertsma Harry Blijenberg
In this paper we examine pricing behaviour of retail firms in the Netherlands during 1998-2003 using alarge database with monthly price quotes of 49 articles, representing different product types. We have conducted this study in order to gain in sight in the degree of nominal rigidity of consumer prices in the Dutch economy. We find that energy prices and prices of unprocessed food are most
... [Show full abstract]
flexible, whereas prices of services are stickiest. Our sample contains not only ample evidence of upward but also of downward flexible prices. A multivariate analysis shows that firm size matters with prices being stickiest in small retail firms and most flexible in large retail firms and in the smallest retail firms consisting of the owners only. Furthermore, we investigate pass-through effects of VAT changes in product prices. We find that VAT increases are almost completely passed on to consumers. Finally, there is some evidence indicating that, after controlling for inflation, pricing behaviour of retail firms was different during the introduction of the euro than in the period directly preceding it.
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