REVIEW 3 major objections 4 minor 2 references
Price Setting Rules, Rounding Tax, and Inattention Penalty
T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read This paper argues that Israel's 2014 ban on non-zero-ending prices backfired: it eliminated a negligible rounding tax but let retailers shift to 90-ending prices, so shoppers pay more overall.
desk verdict The paper's clean descriptive accounting of Israel's price-rounding ban is undercut by a headline welfare cost that rests on a before-after comparison with no control group. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the left-digit bias parameter $\theta$ from the perceived-price model $\hat p = (1-\theta)p + \theta(\Delta + \lfloor p \rfloor)$, where $\lfloor p \rfloor$ is the price's integer part and $\Delta$ is the focal ending. The paper estimates $\theta$ from the natural experiment created by the regulation: for products whose 2013 modal price was 99-ending, the ban forced some prices to NIS 0.01 above that modal price (a 00-ending) and others NIS 0.09 below (a 90-ending); the demand gap between these two outcomes, beyond what the price elasticity predicts, identifies $\theta \approx 0.22$ in the main sample. This parameter carries the argument because it explains why retailers can raise penny digits without losing sales. The rounding-tax side is carried by Monte Carlo simulations that combine the store-level distribution of price endings with the basket-size distribution from the household survey, following the standard method of simulating 10,000 cash transactions per store type.
What would settle it
Compare the penny-digit trends of regulated FMCG items with exempt products in the same stores after 2014; if exempt items such as fresh produce sold by weight or price-capped goods show the same increase in average pennies, the attribution to the regulation is falsified.
Extended reading notes
Core claim
The paper's central claim is that Israel's 2014 price rounding regulation, which outlawed all non-zero-ending prices, achieved its first goal but failed its second and made shoppers worse off overall. Using consumer-price-index price data, retail scanner data, a household expenditure survey, and one large retailer's scanner data, the authors estimate that the pre-regulation rounding tax was negligible, about NIS 507,000 in 2013, or 0.001% to 0.002% of FMCG revenue. They then show that retailers responded to the ban by making 90-ending prices the dominant ending; by 2021, 90-ending prices made up 71.8% of prices in supermarkets and drugstores, 57.0% in small grocery stores, and 42.0% in convenience stores. Because shoppers process prices left-to-right and underweight the rightmost digits, these 90-ending prices act as just-below prices, allowing retailers to raise the average number of pennies per price by 3.3 to 8.6 agora depending on store type. The paper estimates the resulting inattention penalty at NIS 269 million in 2021 relative to 2013 (0.66% of FMCG revenue), or NIS 111 million relative to 2012 (0.27%), concluding that the regulation's cost to shoppers exceeds the rounding tax it eliminated.
Load-bearing premise
The calculation that shoppers pay more rests on the assumption that the 2013-to-2021 rise in the average number of pennies per price was caused by the rounding regulation, rather than by inflation, product mix changes, the pandemic, or payment trends.
Editorial extensions
If this is right
- The pre-2014 rounding tax was so small, 0.001% to 0.002% of FMCG revenue, that eliminating low-denomination coins was not, by itself, a meaningful consumer cost.
- Banning non-zero endings did not remove psychological price points: 90-ending prices became the new just-below price, with 2021 shares reaching 71.8%, 57.0%, and 42.0% across the three store types.
- The regulation raised the average number of pennies per price by 3.3 to 8.6 agora depending on store type, adding an estimated NIS 269 million (0.66%) to shoppers' annual FMCG spending relative to 2013.
- Because the penny-digit increase applies to every item and to both cash and card payments, while the rounding tax applied only to cash bills, the post-regulation cost far outweighs the eliminated tax.
- A coarser allowed price grid of only ten endings makes small price changes less likely, which may increase price rigidity and reduce market efficiency.
Reading between the lines
- A natural causal test would compare penny-digit trends in regulated products with exempt categories in the same stores, such as fresh produce sold by weight or price-capped goods; if exempt items show a similar rise in average pennies, the regulation is not the cause.
- The welfare verdict could still favor the regulation if shoppers' documented aversion to 9-ending prices translates into a real willingness to pay for their abolition, a quantity the paper leaves unmeasured.
- The same mechanism may apply wherever rounding rules are adopted: retailers may migrate to the highest permitted ending, converting an intended consumer protection into a price-level increase.
- Recomputing the cost with 2021 rather than 2013 sales weights, or separating the pandemic years, would show how much of the 0.27% to 0.66% range depends on the before-after design.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper evaluates Israel's 2014 price rounding regulation that outlawed non-0-ending prices, using four datasets: CPI price quotes, Nielsen retail scanner data, a 2013 household expenditure survey, and a large supermarket chain's scanner data. The authors first simulate the pre-regulation 'rounding tax' from cash rounding and estimate it at 0.001%–0.002% of FMCG revenue. They then document that following the ban the share of 90-ending prices rose sharply, increasing the average number of agora (pennies) per price by 3.3–8.6 between 2013 and 2021, which they multiply by 2013 sales volumes to obtain an 'inattention penalty' of NIS 111–269 million per year (0.27%–0.66% of FMCG revenue). The paper concludes that the regulation backfired: shoppers pay more, not less.
Significance. If the causal interpretation is correct, the paper provides a striking, policy-relevant unintended consequence of price-ending regulation, with a concrete monetary magnitude and a natural link to the left-digit bias literature. The paper is transparent about its data sources and simulation procedures, and it includes several robustness checks (2012 baseline, all prices, two-week price-duration restriction, and an appendix test of whether 90-endings arise from rounding up rather than down). The headline cost estimate is a direct accounting of observed price-ending changes rather than a prediction from an estimated model, which is a strength. However, the causal claim that the penny-digit increase is attributable to the regulation rests entirely on a before-after comparison with no control group; the paper's own institutional setting offers exempted product categories that could serve as a natural comparator but are not used. The left-digit bias estimates are unstable across specifications and are reported without standard errors.
major comments (3)
- [Section 6, Table 3] The central claim that the 3.3–8.6 agora increase in average penny digits between 2013 and 2021 is caused by the 2014 price rounding regulation is identified solely from a before-after difference with no control group; inflation, changes in product mix, payment-method trends, or a gradual industry shift in price-point conventions could move average penny digits over eight years absent any role for the ban. The paper itself notes in footnote 8 that the regulation exempts 21 price-capped basic goods and goods sold by weight such as fresh produce and meat, whose non-0-ending prices remained legal; a difference-in-differences comparison of penny-digit changes between exempt and non-exempt FMCG products would directly test the causal attribution, but the paper does not run this or any equivalent control comparison.
- [Section 6, Table 3 and Appendix C] The cost estimate multiplies the 2021-vs-2013 penny-digit difference by 2013 sales volumes, ignoring any demand response to higher prices, entry and exit of products, and changes in the composition of products sold over the eight-year horizon; this affects the magnitude of the NIS 111–269 million estimate, and the authors should at least report robustness to using 2021 sales volumes or contemporaneous quantities.
- [Section 6, Table 2] The left-digit bias estimates are not accompanied by standard errors and are highly specification-dependent: theta-hat is 0.22 in the main sample, 0.30 for prices below NIS 10, 0.69 in the alternative identification, and 0.11 when the sample ends in December 2019; these estimates do not support the text's conclusion that the authors have confirmed a left-digit bias of about 0.2, and the instability weakens the interpretation that the regulation encouraged retailers to exploit inattention to a greater extent.
minor comments (4)
- [Section 5, Table 1] The rounding tax simulation assumes that basket sizes and price endings are independent within store type, but the paper does not state this assumption explicitly; the household expenditure survey and CPI data could at least be used to assess the sensitivity of the rounding tax estimate to this independence assumption.
- [Section 6, Figure 2] The text and figure notes mix '90–99 ending prices' (pre-2014) with '90-ending prices' (post-2014); please clarify that the series after 2014 is the share of exactly 90-ending prices, and make the figure legend consistent.
- [Section 7, caveat] The paper acknowledges in the final caveat that if shoppers strongly oppose 9-ending prices, the regulation might still make them better off even if they pay a few pennies more; this caveat is important enough to be mentioned in the abstract, which currently states unambiguously that 'shoppers end up paying more, not less.'
- [Appendix A] There is a typo in the appendix: 'the likelihood that a “spurious” price change would last more than 1 week is mute' should read 'moot.'
Circularity Check
No significant circularity: the headline cost is a direct accounting of observed price-ending changes, and the left-digit bias estimate is interpretive rather than load-bearing.
full rationale
The central quantity—the extra NIS 269 million (0.66% of FMCG revenue)—is computed in Section 6, Table 3, as (average pennies per price in 2021 minus average pennies per price in 2013) multiplied by 2013 sales volumes. This is a direct arithmetic decomposition of the observed CPI and Nielsen price-ending distributions, not a prediction from a fitted model. The left-digit bias parameter theta estimated in Table 2 (about 0.22) is used to interpret why retailers moved to 90-endings and to benchmark against Strulov-Shlain's external estimates; it does not enter the cost calculation, so no fitted input is renamed as a prediction. The causal claim that the 2014 regulation caused the penny-digit increase rests on a before-after comparison with no control group (the exempt price-capped goods are not used as a comparator), and the paper itself acknowledges the rounding-up versus rounding-down ambiguity and the final welfare ambiguity. These are identification and interpretation limitations, not circularity: the observed difference is not defined as the treatment effect, and no equation reduces to its own inputs by construction. Self-citations (Snir et al. 2017; Levy et al. 2011; Snir et al. 2022; Knotek et al. 2023) support background facts and an interpretive mechanism, but the headline calculation does not rest on them. Therefore no circular step is established.
Assumptions & free parameters
free parameters (3)
- left-digit bias parameter theta =
0.22 (main), 0.30 (prices below NIS 10), 0.69 (broader sample), 0.11 (pre-2020)
- cash share of FMCG transactions =
25% baseline; scenario bounds use varying shares
- cash share allocation bounds across store types =
Max: 10.6% supermarkets, 100% small groceries/convenience; Min: 29.8% supermarkets, 0% small groceries/convenience
assumptions (5)
- domain assumption Shoppers' perceived price follows Strulov-Shlain's left-digit bias model, p_hat = (1-theta)p + theta(floor(p) + Delta), and theta can be recovered as (beta90 - beta00) / (-epsilon * pbar).
- domain assumption No time-varying confounders between 2013 and 2021 affect the average penny endings differently from the regulation.
- domain assumption 2013 Nielsen sales volumes are the correct quantity weights for 2021; demand does not respond to the price-ending changes.
- domain assumption Basket sizes and price endings are independent in the rounding tax simulation.
- domain assumption Cash rounding is to the nearest NIS 0.10 during 2008-2014, with ties rounded up.
Cite this review
Pith. "Pith review of Price Setting Rules, Rounding Tax, and Inattention Penalty." pith.science (2026). https://pith.science/paper/FO5K4IMT
@misc{pith2026241113427,
author = {Pith},
title = {Pith review of: Price Setting Rules, Rounding Tax, and Inattention Penalty},
year = {2026},
howpublished = {\url{https://pith.science/paper/FO5K4IMT}},
note = {Machine review of arXiv:2411.13427}
}
read the original abstract
We study the price rounding regulation in Israel, which outlawed non-0-ending prices, forcing retailers to round 9 ending prices, which in many stores, comprised more than 60 percent of all prices. The goal of the regulation was to eliminate the rounding tax, the extra amount consumers paid because of price rounding, which was necessitated by the abolition of low denomination coins, and the inattention tax, the extra amount consumers paid the retailers because of their inattention to the prices rightmost digits. Using 4 different datasets, we assess the success of the government in achieving these goals, focusing on fast moving consumer goods, a category of products strongly affected by the price rounding regulation. We focus on the response of the retailers to the price rounding regulation and find that although the government succeeded in eliminating the rounding tax, the bottom line is that shoppers end up paying more, not less, because of the regulation, underscoring, once again, the warning of Milton Friedman that policies should be judged by their results, not by their intentions.
Reference graph
Works this paper leans on
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[99]
We then set 𝐷𝑖,𝑠,𝑡 99 equal to 1 if in 2013 𝑃𝑖,𝑠,𝑡 was equal to 𝑀𝑜𝑑𝑒2013𝑖,𝑠 99, and 0 otherwise. We set 𝐷𝑖,𝑠,𝑡 00 equal to 1 if in 2014 𝑃𝑖,𝑠,𝑡 was NIS 0.01 higher than 𝑀𝑜𝑑𝑒2013𝑖,𝑠 99, and 0 otherwise. We set 𝐷𝑖,𝑠,𝑡 90 equal to 1 if in 2014 𝑃𝑖,𝑠,𝑡 was NIS 0.09 lower than 𝑀𝑜𝑑𝑒2013𝑖,𝑠 99, and 0 otherwise. For example, if the modal 99-ending price of a produc...
work page 2023
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[2021]
Data is based on the CPI sample. The vertical line marks January 1, 2014, when the price rounding regulation came into effect. The figure is drawn for prices less than NIS 20. 29 Table 1. Estimation of the rounding tax (1) Average rounding tax per transaction (NIS) (2) Revenue (%) (3) Transactions (thousands) (4) Rounding tax (NIS): Equal shares (5) Maxim...
work page 2023
Reviewed August 12, 2026 · model on record in the stance chip above.
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