Suspicious Discontinuities (2020)
danluu.com
danluu.com
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, creating plenty of fiscal drag on top.
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...
It put her pension above a max threshold for old age / low pension (cheaper phone bill, no tv taxes, ...) by, ... hold your hats... 2 Euro.
Father called the service ... "sorry, we can not do anything about that".
She lost over 100 Euro in benefits because technically... she was not low pension anymore but was financially WAY more poor then when my grandfather was alive.
So when my grandfather was alive, their combined pension was higher, they qualitied as having a low pension. When only *part* of my grandfather pension got combined into my grandmothers. Well, now your not poor...
I do not remember the exact pensions but it was a massive haircut, with the insulting on top, losing those benefits. The lost benefits made it from threading water, to drowning.
Without my dad financial help, she will have lost the house. Ironically, if she did not get my grandfathers pension part, she will have qualitied for more social assistance, and will have been better off.
Sometimes, those lines really screw people over.
Another angle is how they affect the living. Plenty of young adults delay moving out from their parents, or starting a career, because changes in combined household income would cross one of those magic threshold, and ending up screwing the parents and younger siblings for life.
Such delaying may not be as immediately critical to the person, but it alters the course of their lives in significant ways.
Passive income of any sort? Bribes from the lobbying groups? Absolutely not.
Oh I don't doubt it. In my native country of Belgium the tax rate can go to 69% and more: 50% income tax (used to be as high as 52.5% and maybe even 55%, don't remember) and then, on top of that, an addition 19% social wellfare tax. That's not mentioning stuff like, if you manage to buy stocks with what you have left, 30% state tax (+ crazy bank fees) on any dividends you receive from those stocks.
And then the brand new (1st jan 2026) 10% tax on any capital gain, once again: in addition to all the already existing taxes.
Add some arbitrary decisions on top of that, where if you happen to maybe have bought/sell a bit too many stocks or if you happen to have managed to put a too big part of your wealth into stocks, they may consider you're a "professional investor" and then your capital gains are taxed at your income rate.
Some are going to say: "Oh but create a company, get back the VAT, do this/do that".
I don't want to basically become a fiscal lawyer just to not be assraped by ever more taxes.
Instead of trying to "optimize", I just voted --before they'll introduce an exit tax (I'm sure that's coming)-- with my feet, my money and the future wealth I was going to create and left the country.
For what was I getting in return? According to a flemish university an estimated 55 000+ undocumented illegal migrants are now living in the capital city of Belgium, Brussels, alone. That's 5% of the population of the city that are undocumented migrants. They don't live in proper conditions. They're a drag on the economy. They're not happy, they're not thriving. Locals aren't happy either.
I didn't vote for this.
To me once politicians go too far, that's what they deserve: the middle class living the city in drones and being replaced by poor people. As I tell of my friends and family who also left the city: I just went a bit further and left the country altogether.
Following the example of my friend and ex-neighbor who did so decades ago: he left for SoCal (btw I didn't go to the US) and created two startups. Second one was a big hit. Belgium (and the EU) saw exactly zero return of his incredible drive and talent.
Another recent statistics: 40% of the people of Brussels are living close to the poverty line.
But at least socialists got the utopia they dreamed of: they're sure to never lose an election again. The middle class is dying in Brussels. The poor won't vote against socialism.
I just packed and left and advice anyone who can flee a sinking ship to do so. Many countries in Europe have decided to commit suicide and to turn themselves into slums.
I think this is just the beginning for may EU cities/countries: there's much more pain ahead --and although AI is going to be used as a scapegoat-- this has absolutely nothing to do with AI and all to do with political decisions.
It pains to see how my native city has been dragged into poverty... But good riddance.
As for the next gen: from day one I raised my kid in english. At 11 y/o she's totally fluent and our thinking was simple: english is at least understood mostly everywhere in the world. She'll have to move because I fear it's not just my native city that is toast.
Many (most?) marathons have pace runners who run the course, hewing to each 30 minute and 15 minute finish. So there’ll be a 3:30:00 pacer, a 3:45:00 pacer and so on. Your local pacer might even have their pace on their shirt and may even have a flag so they’re super hard to miss as you’re running.
One friend of mine runs with a speaker, to play music and keep everyone’s spirits up.
By the end of the race they’d acquired a small army of marathoners! You could see their smiles for miles, and when they all finished together they had a huge party in the recovery area with the speaker :)
I’m surprised the marathon time discontinuity isn’t bigger :)
Given how hilly the course is, this makes sense: running an even pace the whole distance is not a good plan.
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Had you tried to read the paper, you’d have noticed the dead link.
How’s the wind up on your high horse?
From "Reference-Dependent Preferences: Evidence from Marathon Runners" https://devingpope.com/assets/files/Website_Marathons.pdf
Not sure why you think not making any effort to find the article beyond clicking a link is a flex, but ok.
Extra taxes on the stupid should be illegal.
If your (taxable) income is less than 7L (inr), no tax is assessed. If your income is greater than 7L, but upto 12L, tax is assessed, but a tax _rebate_ (a discount on payable tax) is granted for the exact amount of tax owed. This means net tax paid till 12L is zero. But if your income is 12L + 1, this rebate no longer applies, so the entire tax assessed (on the 7L+ income) is now due. This means that a person who earns 12L+1 INR makes ~70K inr less, post-tax, than the person who earns 12L INR.
After complaints, to correct this, they added another layer: If your taxable income is >12L but less than 12L+~70K (the tax thats due), then the maximum tax due is just the amount your income exceeds 12L bye. So you stagnate at the same post-tax salary from 12L to 12L+70K.
Right, it's as if someone shot the heart with a defibrillator - because that's a good analogy of what is actually happening, given the "arbitrary negative effects for people" failing the exam are basically determining the course of one's future (or at least feel like this to the people and their parents at the time).
In particular, having passed "matura" is the lowest level kind of threshold used (both formally and informally) by employers considering job applicants; much like some higher-skill jobs still require a specific university degree, not having "matura" will cut you out of a large chunk of low-skill and entry-level jobs.
Couple failed "matura" with any kind of criminal record - and the two, I imagine, are probably correlated - and you can be screwed for life, economically speaking. It is a big deal, and teachers know it.
IDK what the current system is, but for my cohort, it was possible to repeat the exam in subsequent years - but like with any kind of degree, chances of someone doing that drop sharply with temporal distance; at some point, people just find a path for their lives and are more interested in present-day challenges than going back to finish some degree.
How about the even simpler fix of not having phase-outs? This generally works: the cost of a subsidy generally does not increase as the recipient pays more taxes, so the higher total tax paid by a higher-income person will easily pay for the cost of a subsidy. And giving higher-income/wealthier people the same subsidies as poor people may help them appreciate the ways in which the subsidies are helpful and the ways in which they suck, which can help the whole system improve.
[1] https://cleartax.in/s/marginal-relief-surcharge
Another place where thresholding is misplaced is minors (below the age of 18 years) being subject to different laws (this is for India at least), e.g., seriously different punishments for crimes like homicide or rape. I have heard that crime groups then purposefully involve minors, push the blames on them if caught, and effectively get away for much less.
The broader point is that being a couple days or months younger or older than eighteen years should not result in a drastically different outcomes to begin with.
The problem is that anytime you create a division there are always some cases just on the border, and if the outcome difference is sized to the difference between the centers of the classes the jump from on size of the border to another gets large.
But on the other hand if the jump isn't large you end up saying that 13 year olds and 30 year olds should be treated the same, which is clearly just worse.
You can try smoothing out the jump at the edges by adding more cuts and doing less changes from one step to the next, but I don't think you gain much in terms of recruitment of youths compared to just pushing the breakpoint fore lenient sentences to larger ages than 18.
This also used to be common in the US, but nowadays for (violent?) crimes minors can be charged as adults, so this kind of thing is only done for drugs and organized stealing rather than murders and violent crimes.
I think it more or less still is. (Memorialized in The Offspring's Come Out and Play: "If you're under 18, you won't be doing any time.")
> but nowadays for (violent?) crimes minors can be charged as adults, so this kind of thing is only done for drugs and organized stealing rather than murders and violent crimes.
Minors are very occasionally charged as adults, but still mostly get lesser sentences for all kinds of crimes. Gangs prefer to recruit minors, probably in part because minors are stupid/immature enough to join gang life.
The more interesting part of the talk is how using what he calls "fenceposts" naturally results in bunching up against the fenceposts because even small regressions that cross the fenceposts are blocked but regressions of any size that don't cross a fencepost go unnoticed.
A decent metric for testing against might consist of a target mean, the sigma specifying a gaussian about that mean, a minimum sample size, and a hard upper cutoff.
> That means if an individual buying ACA insurance was going to earn $55k, they'd be better off reducing their income by $6440 and getting under the $48,560 subsidy ceiling than they are earning $55k.
I am told by a CPA: In the US tax system, one is limited to deduct $3,000 of net capital loss against their otherwise taxable income. These put options would generate a capital loss. Therefore, this strategy would not accomplish the goal stated in the article.
Isn't donating to charity a lot easier than gambling on options? It's both legal and extremely easy to donate 5k to a tax-deductible charity of your choice...
I think it's likely that politicians and their funding sources have found ways to profit off of these discontinuities. The infamous Medicare "donut hole" [2] was arguably a "benefit discontinuity" of the sort mentioned by the author and pharmaceutical companies profited off of it (more than a hypothetical Medicare structure without a donut hole, not relative to the spending cap that replaced it—which profits them even more).
[1] https://www.pennstatelawreview.org/penn-statim/dont-be-silly... (2013) ...which argues that this is a good thing!
[2] https://www.medicalnewstoday.com/articles/what-is-the-medica...
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.
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.
Because that is a marginal system, (and unless they've messed up the calculations, which they haven't in this case) you should never end up with less from earning more. Can you give an example of two income amounts where the lower income ends up with more money after-taxes than the higher income?
Or is it the additional municipal, church, or health levies mentioned on that page which have the discontinuities?
Lacking those basic skills might be a reason not to promote someone though, so perhaps it all works out for the best
See graph here: https://www.veronmaksajat.fi/tutkimus-ja-tilastot/tuloverot/...
They don't have to understand how it works to do their own taxes.
Not to mention the amount of misinformation that can get passed around
If they are curious, they can type in three different incomes, even if they aren't planning on submitting the tax form with the wrong amounts. So if their income is $59,000 and their tax bracket is say, 15% for that, instead of say, 24% for 60,000-the next end of that bracket- e.g. $75k or $95k) they might get a much smaller tax return if they type $60,000. But then if they earned a little more, like $61,000, they could type in that and see what their return is, along with the rate.
If it is a gradient with smooth progression for each dollar increase, then they can immediately see how much more they are paying in taxes from 15% to 20%. But in reality, in a smooth/gradient-based progressive tax increase, those amounts would be centered in the middle of those brackets (like 15% would right in the the center between $35,000 and $59,999, or $48,500, and the $59,000 income would be closer to 19.9% and the $61,000 income might be $20.1%.
It wouldn't be considered fraud if they are just determining what they would pay if they earned a little bit more. In fact, if they just discovered an invoice check they received from self-employment, and forgot to report it, they might have to type in different amounts, if they didn't report the right amount the first time. Everyone would pay the same tax rates at each income level (with $1000 intervals, or even $1 intervals.
The system could still be transparent because it can show a chart of the tax rates for each $1,000 increase, even if the tax brackets only provides an estimate for each bracket. I do agree some people can't read charts very well, but if they included 100 thin bars for taxable rates under $100,000, people would be able to see the estimated percentage that they would be paying. It might be 15%, 15.5%, 16%, 16.5%, or 17%, and so on for $48,500. $49,000, $49500, $50,000, and so on, respectively.
The idea with this is that it would disincentivize people from misreporting because if they report earning $500 less, they aren't saving much more money (not to mention illegally)- their tax rate might be 0.1% less, and on a $49500 income that might only be $250 less in taxes over reporting $50000. The risk of getting caught is not to going worth it if this method is in place. (Actually not in any case, but at least they can see it's not going to be a huge decrease in taxable income by reporting a little less, so the only way they can attempt to pay less is by reporting a lot less, and the penalties for that would be larger)
I've heard the same thing -- if they take a job they will lose money. What they really mean is that if they take a job (trade time for money), they will lose some of the pension they have already earned. This is a real economic loss (even if they might have a few more bucks at the end of the week) to say nothing of their lost time.
The better alternative would be to assume that normies are, in fact, capable of understanding these tools, and in the process forcing them to understand them by setting an expectation. I mean, this is what people should be told as answer when they ask, "what will learning math be useful for me in my life?". No, multiplying polynomials will not be useful to 99% of the people. But having a feel for basic linear algebra and feedback loops would be, because they describe the behavior of the simple and interesting control systems in any and all areas of life - which includes the Social Security examples of yours, too.
The worst thing is, letting majority of people off the hook here doesn't just impact them individually; in democracies, it prevents systems require certain level of understanding from being created in the first place. As shown in plenty of examples brought up in the discussion thread here.
So I guess one answer to "how is any of that math going to be useful for me in the future?" is, "if you all learn it, it will allow you to stop keeping yourselves in poverty in stupid and entirely unintentional ways".
I don't know how many people I've heard express that they didn't want to move into the next tax bracket because they didn't want to pay that rate on their whole income, but it's a lot.
A very small minority are worried about hitting a ceiling that removes eligibility for important services, and some are worried about the weird phaseouts where marginal rates are very high, but most just don't understand.
Maybe that means having a more complicated system is fine because it's already incomprehensible to most, but I dunno.
The problem is that the intuitive understanding doesn't line up with that, so that's what people have by default - and then we don't teach how it actually works as a basic skill! Sure, there's no shortage of explainers, but you need to be actually looking for them in the first place.
And the best way to teach that in school? Give students a small allowance that grows with each year, but they have to "pay taxes" on it to continue receiving it, complete with different brackets etc. I bet you that all the "normie" kids will figure it out in no time.
The UK didn't have civics classes in school; I think this would have been much more useful than my mandatory RE lessons with an exam centred on one of the gospels.
For example, they can keep certain tax exemption thresholds low while overall incomes rise. That means more people gradually fall into higher tax brackets or lose exemptions, even though the money they earn is worth less over time.
The rigidity itself is not a bug but a feature. It is a sneaky way to raise the taxes without openly raising taxes. But it's just a theory.
I wonder why we don’t define these things in terms of logistic functions or something. That’s high school or at least first semester college math, right?
https://taxfoundation.org/research/all/federal/earned-income...
One way to reduce income may be to buy a bunch of stocks with high variance - for any that is in the red during the year, sell and rebuy them. Any that has a gain, leave them be.
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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 they were doing to try to lose money to drop their income (especially in the cited range of $48-55k/year).
That is the case this year, in most states (thankfully not where I live), but that's not what TFA is talking about.
Suspicious? It certainly makes me skeptical that the author has got the details of the other examples correct.
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.
I can't see a date on the post (on mobile) but the archives link has month and year.
At this point I treat lack of dating articles as being done intentionally, and as evidence of malicious intent - i.e. that the entity publishing it has a reason they don't want readers to know the creation date, and there's really no reason other than trying to get away with lies or otherwise screw the reader over.
(Above is a heuristic I apply by default; this post is an example of a case-by-case exception, because of the type of site, my impression of articles read in the past, and of the author themselves.)