Friday , June 5 2020

Suspicious Discontinuities, Hacker News

Suspicious discontinuities

If you read any personal finance forums late last year, there’s a decent chance you ran across a question from someone who was desperately trying to lose money before the end of the year. There are a number of ways someone could do this; one commonly suggested scheme was to buy put options that were expected to expire worthless , allowing the buyer to (probably) take a loss.

One reason people were looking for ways to lose money was that, in the US, there’s a hard income cutoff for a health insurance subsidy at $ , for individuals (higher for larger households; $ , for a family of four). There are a number of factors that can cause the details to vary (age, location, household size, type of plan), but across all circumstances, it wouldn’t have been uncommon for an individual going from one side of the cut-off to the other to have their health insurance cost increase by roughly $ / yr. That means if an individual buying ACA insurance was going to earn $ 97 k, they’d be better off reducing their income by $ and getting under the $ 90, subsidy ceiling than they are earning $ 97 k.

Although that’s an unusually severe example,

US tax policy is full of discontinuities that disincentivize increasing earnings and, in some cases, actually incentivize decreasing earnings . Some other discontinuities are the TANF income limit, the Medicaid income limit, the CHIP income limit for free coverage, and the CHIP income limit for reduced-cost coverage. These vary by location and circumstance; the TANF and Medicaid income limits fall into ranges generally considered to be “low income” and the CHIP limits fall into ranges generally considered to be “middle class”. These subsidy discontinuities have the same impact as the ACA subsidy discontinuity – at certain income levels, people are incentivized to lose money.

Anyone may arrange his affairs so that his taxes shall be as low as possible; he is not bound to choose that pattern which best pays the treasury. There is not even a patriotic duty to increase one’s taxes. Over and over again the Courts have said that there is nothing sinister in so arranging affairs as to keep taxes as low as possible. Everyone does it, rich and poor alike and all do right, for nobody owes any public duty to pay more than the law demands.

If you agree with the famous Learned Hand quote then losing money in order to reduce effective tax rate, increasing disposable income, is completely legitimate behavior at the individual level. However, a tax system that encourages people to lose money, perhaps by funneling it to (on average) much wealthier options traders by buying put options, seems sub-optimal.

A simple fix for the problems mentioned above would be to have slow phase-outs instead of sharp thresholds. Slow phase-outs are actually done for some subsidies and, while that can also have problems, they are typically less problematic than introducing a sharp discontinuity in tax / subsidy policy.

In this post, we’ll look at a variety of discontinuities.

Hardware or software queues

A naive queue has discontinuous behavior. If the queue is full, new entries are dropped. If the queue isn’t full, new entries are not dropped. Depending on your goals, this can often have impacts that are non-ideal. For example, in networking, a naive queue might be considered “unfair” to bursty workloads that have low overall bandwidth utilization because workloads that have low bandwidth utilization “shouldn’t” suffer more drops than workloads that are less bursty but use more bandwidth ( This is also arguably not unfair, depending on what your goals are).

A class of solutions to this problem are random early drop and its variants, which gives incoming items a probability of being dropped which can be determined by queue fullness (and possibly other factors), smoothing out the discontinuity and mitigating issues caused by having a discontinuous probability of queue drops.

This post on voting in link aggregators is fundamentally the same idea although, in some sense, the polarity is reversed. There’s a very sharp discontinuity in how much traffic something gets based on whether or not it’s on the front page. You could view this as a link getting dropped from a queue if it only receives N-1 votes and not getting dropped if it receives N votes.

College admissions and Pell Grant recipients Pell Grants started getting used as a proxy for how serious schools are about helping / admitting low-income students. The first order impact is that students above the Pell Grant threshold had a significantly reduced probability of being admitted while students below the Pell Grant threshold had a significantly higher chance of being admitted. Phrased that way, it sounds like things are working as intended.

However, when we look at what happens within each group, we see results that are the opposite of what if the goal is to benefit students from low income families. Among people who don’t qualify for a Pell Grant, it’s those with the lowest income who are the most severely impacted and have the most severely reduced probability of admission. Among people who do qualify, it’s those with the highest income who are mostly likely to benefit, again the opposite of what you’d probably want if your goal is to benefit students from low income families.

We can see these in the graphs below, which are histograms of parental income among students at two universities in ((first graph) and (second graph), where the red line indicates the Pell Grant threshold.

A second order effect of universities optimizing for Pell Grant recipients is that savvy parents can do the same thing that some people do to cut their taxable income at the last minute. Someone might put money into a traditional IRA instead of a Roth IRA and, if they’re at their IRA contribution limit, they can try to lose money on options, effectively transferring money to options traders who are likely to be wealthier than them, in order to bring their income below the Pell Grant threshold, increasing the probability that their children will be admitted to a selective school. p-values

Authors of psychology papers are incentivized to produce papers with (p values ​​ below some threshold, usually 0. , but sometimes 0.1 or 0. .

Masicampo et al. plotted p values ​​from papers published in three psychology journals and found a curiously high number of papers with p values ​​just below 0.

The spike at p=0. 19 Consistent with a number of hypothesis that aren’t great, such as:

(Authors are fudging results to get p=0. 20 Journals are much more likely to accept a paper with p=0. (than if 0.)

    Authors are much less likely to submit results if p=0. 400 than if p 0. 11

    Head et al. (2019)

surveys the evidence across a number of fields.

Andrew Gelman and others have been campaigning to get rid of the idea of ​​statistical significance and p-value thresholds for years, see this paper for a short summary of why . Not only would this reduce the incentive for authors to cheat on p values, there are other reasons to not want a bright-line rule to determine if something is “significant” or not.

Drug charges (

The top two graphs in this set of four show histograms of the amount of cocaine people were charged with possessing before and after the passing of the fair Sentencing Act in , which raised the amount of cocaine necessary to trigger the – year mandatory minimum prison sentence for possession from (g ​​to) g. There’s a relatively smooth distribution before and a sharp discontinuity after )

The bottom-left graph shows the sharp spike in prosecutions at grams followed by what might be a drop in 4013 after evidentiary standards were changed.

Birth month and sports

These are scatterplots of football (soccer) players in the UFEA Youth League

. The x-axis on both of these plots is how old players are modulo the year, ie, their birth month normalized from 0 to 1.

The graph on the left is a histogram, which shows that there is a very strong relationship between where a person’s birth falls within the year and their odds of making a club at the UFEA Youth League (U 29) level. The graph on the right purports to show that birth time is only weakly correlated with actual value provided on the field. The authors use playing time as a proxy for value, presumably because it’s easy to measure. That’s not a great measure, but the result they find (younger-within-the-year players have higher value, conditional on making the U

league) is consistent with other studies on sports and discrimination, which ind (for example) that black baseball players were significantly better than white baseball players for decades after desegregation in baseball, French-Canadian defensemen are also better than average (French-Canadians are stereotypically afraid to fight, don’t work hard enough, and are too focused on offense) .

The discontinuity isn’t directly shown in the graphs above because the graphs only show birth date for one year. If we were to plot birth date by cohort across multiple years, we’d expect to see a sawtooth pattern in the probability that a player makes it into the UFEA youth league.

This phenomenon. , that birth day or month is a good predictor of participation in higher-level youth sports as well as pro sports, has been studied across a variety of sports.

It’s generally believed that this is caused by a discontinuity in youth sports:

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