 Rounding and the bill-size gradient in tippingToby Qin and Vrund Gurjar No xvfde_v1, SocArXiv from Center for Open Science Abstract: Restaurant tip percentages often decline as bills increase. Rounding is one proposed explanation because a fixed upward adjustment adds more to the tip percentage on a small bill. We examine how much of the observed decline can be explained by adjustments of up to one dollar. We analyzed 22,446 checks with positive recorded tips, no automatic gratuity and bills of $10–$200 from three North Carolina restaurant outlets. For checks with a whole-dollar tip or reconstructed final payment, we allowed the pre-rounding tip to fall anywhere from one dollar below the recorded amount to the recorded amount, with a minimum of zero. We calculated the smallest and largest bill-size coefficients across these possible amounts, controlling for outlet, month, guest count, opening hour and weekday. Bootstrap checks resampled dates, weeks and servers. Each scheme used 999 draws, with the rounding bounds recalculated for each resampled dataset. Tip percentages fell by 4.29 points per bill doubling. Even the adjustments that most reduce this decline leave a coefficient of −1.62 points, which remains negative across all three bootstrap checks. Five-dollar rounding or restricting bills to $30–$200 allows the fitted decline to disappear. Upward dollar rounding cannot fully explain the negative gradient in the primary sample. Larger rounding increments and the exclusion of small bills produce ranges containing zero. Date: 2026-09-25 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:osf:socarx:xvfde_v1 Access Statistics for this paper More papers in SocArXiv from Center for Open Science |
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