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Suspicious Discontinuities (2020)

danluu.com

11–20 of 109 posts

Re: Suspicious Discontinuities (2020)

#11
post #4

I cracked up when I got to the marathon example. When I ran a half marathon I realized about 80% of the way through that I was on track to finish under 2:30:00 and pushed myself to make it happen. I should have guessed that sort of behavior would show up in the statistics!

After this year's Paris marathon, I ran the same per-minute graphs, and they match perfectly the "overall study" graphs with more than 9 million finishes in the article. I also added graphing by age category and gender. I don't want to deduce too much but I think it showed that young men are the most "competitive" (what I mean by that is targeting a specific time) since there are the clearest "goal time" peaks in the graphs.

Re: Suspicious Discontinuities (2020)

#12

I never understood why taxes or similiar absolute points aren't gradients instead.

I think because the gradient is simply too confusing for laypeople to understand.

Even for a simple system like US social security that has a gradient. For every $2 you make over the limit, you lose $1 in benefits. I've heard countless times misconceptions of people thinking they'd be losing money (as in literally having less money net) by working.

Re: Suspicious Discontinuities (2020)

#13
post #12

I never understood why taxes or similiar absolute points aren't gradients instead.

I think because the gradient is simply too confusing for laypeople to understand. Even for a simple system like US social security that has a gradient. For every $2 you make over the limit, you lose $1 in benefits. I've heard countless times misconceptions of people thinking they'd be losing money (as in literally having less money net) by working.

This does happen in Finnish tax system. Your tax rate (percent with one decimal) is calculated based on your annual gross income. Rates are supposed to be calculated smoothly, and they are certainly calculated for each individual separately.

In reality they are step functions. It is surprisingly common to have people refuse promotions because if would put them above an income tax threshold, bump up their rate, and end up with less money after taxes in the end.

The UK tax system is far from fair but at least it has clear brackets: income above threshold X is taxed at rate Y.

Re: Suspicious Discontinuities (2020)

#14

[ EDIT: Since the undated article is actually from Feb 2020, predating the expansion of federal health insurance subsidies, I withdraw everything I said below. ] ---------------------------------- The opening story is fabricated and/or bullshit. Last year (2025) there was no limit on income for health insurance subsidies. That ended for this year, but last year there would have been no reason for anyone who knew what…

This might vary state-by-state, CA MediCal for instance did limit the subsidies based on income last year. I don't think it was an all-or-nothing cutoff, but I do think there were points around the 50k mark where the delta between your subsidy and the one for the lower bracket was higher than the loss you'd take by a few thousand dollars.

Re: Suspicious Discontinuities (2020)

#15

I never understood why taxes or similiar absolute points aren't gradients instead.

It's very well established internationally that income taxes are defined by gradients. I have no idea why politicians want to reinvent them so often in other kinds of taxes.

Re: Suspicious Discontinuities (2020)

#16

[ EDIT: Since the undated article is actually from Feb 2020, predating the expansion of federal health insurance subsidies, I withdraw everything I said below. ] ---------------------------------- The opening story is fabricated and/or bullshit. Last year (2025) there was no limit on income for health insurance subsidies. That ended for this year, but last year there would have been no reason for anyone who knew what…

This might vary state-by-state, CA MediCal for instance did limit the subsidies based on income last year. I don't think it was an all-or-nothing cutoff, but I do think there were points around the 50k mark where the delta between your subsidy and the one for the lower bracket was higher than the loss you'd take by a few thousand dollars.

The subsidies were from the federal government, managed as part of your federal income tax return. They had nothing to do with additional state subsidies.

The basic story was that until the end of 2025, nobody in the USA had any reason to pay more than (roughly) 8.3% of their AGI for health insurance.

Re: Suspicious Discontinuities (2020)

#17
post #6

Would test score problem be solved if teachers graded individual questions, not entire test?

The reddit explanation in the post addresses your question I believe. If someone is at a 28 or 29 a few "charity" points can be found in subjectively-graded tests.

If you grade individual questions, you don't know the total score.

Re: Suspicious Discontinuities (2020)

#18
post #3

The UK tax system also has a bunch of unfortunate cliffs, and tapers that create >60% marginal tax rates and worse. There's a calculator here that illustrates it well https://tax-cliffs.britishprogress.org/calculator The childcare cliff edge is probably the worst, but the personal allowance taper isn't ideal either as it's compressed over a relatively short income range And of course all the thresholds remain frozen,…

The Economist has this crazy graph of UK VAT thresholds and how they are causing companies to stay small, to keep their turnover under the threshold which avoids a lot of paperwork. It's the most infuriating thing, we are literally throttling our companies, the engines of growth, because of some accounting stupidity.

Graph: https://www.economist.com/cdn-cgi/image/width=600,quality=10... from this article: https://www.economist.com/britain/2024/04/22/how-to-fix-brit...

Re: Suspicious Discontinuities (2020)

#20
post #12

I never understood why taxes or similiar absolute points aren't gradients instead.

I think because the gradient is simply too confusing for laypeople to understand. Even for a simple system like US social security that has a gradient. For every $2 you make over the limit, you lose $1 in benefits. I've heard countless times misconceptions of people thinking they'd be losing money (as in literally having less money net) by working.

A single benefit usually has an appropriate incentive structure, but a lot of people get multiple benefits -- even from different levels of government (local, state, federal) -- and adding up phase-outs in different systems can result in marginal phase-outs rates above 100%. It's hard to avoid that entirely given that we want to have a lot of transfers to the bottom of the income distribution while phasing those out by roughly the median. It would be easier to avoid phase-outs above (say) 80% of marginal income is we only had federal and state aid as predictable money transfers, but for various reasons we provide a lot of transfers in-kind or with limited authorized uses. Those limitations aren't necessarily wrong, but they do mean that transfers aren't fungible, so there's an incentive to provide transfers for other "good" uses, and that diversity is what makes it hard to bound the marginal phase-outs for everyone.
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