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2 questions about HUD eligibility rules for federal housing programs

Daniel McCracken writes:

At work, I came across a potentially serious flaw in how HUD uses statistics to determine eligibility for federal housing programs (and the amount of subsidy each household receives). It seemed like something you might be interested in or blog about, so I figured I’d pass it along.

For background, here’s the simplified version of how HUD’s programs work. To qualify for affordable housing, a household’s income is compared to their area’s median family income (AMI). If their income is lower than, say, 50% of the AMI (different programs use different percentages, but 50% is pretty common), they’re eligible for the program.

To account for the higher costs of living for larger families, the income limits are adjusted for household size. So in Boulder County, CO (where I live), families of 4 qualify for the program with income less than $47,400, the limit for 2-person households is $37,950, and the limit for 6-person households is $55,000.

The specifics of the household size adjustment are what have me confused. Here’s how it works (again, I’ll use the 50% AMI eligibility standard): HUD finds each county’s AMI in the American Community Survey (for Boulder in 2016, $94,800). It then uses 50% of this amount ($47,400) as its limit for 4-person households, and this is then used to generate the limits for other household sizes.

That’s the first confusing thing. The average family size for Boulder County in the relevant ACS is ~3.1. If HUD cares about adjusting for household size in determining program eligibility, why isn’t the initial AMI figure of $94,800 also adjusted upwards (by ~$1900, based on the income limit tables) to account for Boulder County’s smaller family size?

The other confusing thing happens after a family qualifies, when rent amounts are calculated. Every program is different, but the general rule is that families pay 30% of their income for rent.

But this part is *not* adjusted for household size. A 1-person household making $30,000 pays the same amount of rent as a 5-person household making $30,000. Shouldn’t HUD be using 30% of a family’s household-size-adjusted income, so that the 1-person household pays more rent (due to lower costs of living)?

Anyways. It seems like HUD is being totally inconsistent in its adjustments for household size, but I wanted to run the idea past someone who knows what they’re talking about. I actually emailed HUD asking them about my first question (re: adjusting for the area’s average household size), and this was their response:

“As for your question about average family sizes, while the current average number of people in a family is [around 3], the fact that people are not divisible means that HUD would never base income limits on a portion of a person. At the time the income limits calculations were being derived, the most common size family was 4 persons nationally, and since Median Family Incomes are irrespective of family size, HUD always equates the very low-income limits to a 4-person family.”

This doesn’t make any sense to me, and they ignored my follow-up email. So maybe you can tell me what I’m missing.

(Here’s the documentation from HUD, in case you’re curious:

Income limits:$State_Count$&areaname=Boulder%20County&wherefrom=mtsp&incpath=C:\HUDUser\wwwMain\datasets\il\il2011\&level=50

Rent calculation:

There is an implicit adjustment for household size when determining rents, because HUD deducts $480 for each dependent when calculating a household’s annual income.

So in effect they appear to be adjusting for household size *twice* at the eligibility stage, using 2 totally different formulas. But at the rent calculation stage they only use one formula (one that results in a much smaller adjustment than the other one in most cases).

I’ve not had a chance to look into this at all but it seems like the kind of issue we should all be aware of, so I’m sharing. Feel free to contribute in comments.


  1. Krzysztof Sakrejda says:

    That’s been my experience with any income-related calculation. Too complicated for a lay person to really understand well (and somewhat arbitrary as it varies by locality) and too rule-of-thumbs-y to be consistent across income levels. Same happens in healthcare subsidy calculations, child support calculations, taxes(!) etc… we could do something principled but you would have to convince so much bureaucracy to go along that I don’t think it’s changing anytime soon. Maybe for child support where circumstances of both parties are likely to change into the future and you (can) negotiate individually there’s a chance. It’s not even consistent, when I was a grad student with kids sometimes with health care subsidies it would be “yikes, how am I going to pay rent?” and sometimes I would feel sorry for the middle class. The other weird thing is that at lower income levels your financial well-being is much more affected by subtle flaws in the process (i.e.-$50 can really matter) whereas higher up it might be one more or less expensive evening out over a few months (who really cares?)

    Of course nationally the conversation is around “OMG poor people have refrigerators!!” so…. this is all too subtle.

  2. Look, people, you’ve gotta stop reading my mind!

    I’ve been working on related stuff, trying to figure out what constitutes an “effective poverty” scale as a function of location and family size, how people’s living situations depend on these things, what policies could change to promote economic growth for the population (as opposed to for the high flying tech stocks) etc.

    Here are some general thoughts I’ve had.

    First off, I think it’s right that benefits shouldn’t be based on fractional people. I’ve recently posted to my blog on the concept of “person” or “capita” as a dimension.

    The motivation there was exactly this kind of situation. The property that makes “length” a dimension with arbitrary units is precisely that you can convert equations in meter units to equations in feet or cm or furlongs or whatever by multiplying all the variables that are measured in meters by a constant conversion factor and the conversion is *exact*.

    A similar symmetry property exists in the asymptotic regime for large numbers of people. If you want to convert GDP/capita to GDP/household and you define a household as the observed average household size… lets say 3.212 people in a household on average, then it’s an exact conversion…

    On the other hand, at the asymptotic regime where “people” is a small integer, the noise dominates the signal and you should treat people as a dimensionless integer. Adding 1 child to a family of 2 puts them into a different kind of equation, it doesn’t just scale the family size input variables by 3/2.

    For this kind of thing, what’s needed is a formula that actually attempts to predict a poverty level of income for families of all sizes, and I’d say it should go farther, a single mother with 3 kids is not the same family as two parents with two kids. So it’s not just size but at least number of adults and number of children… possibly for extended families you should include number of people post retirement age (say 65 years old maybe).

    So, the proper way to go here would be to use nonlinear regression to predict costs at all the integer combinations of adults and children that are of interest (families larger than say 11 people are ultra-rare, so it’s not too combinatorially bad).

    But the bigger question is not how to adjust for family size, the biggest question is really how to allocate welfare and how much to allocate? My own personal preference is strongly in favor of the Universal Basic Income, and again I’ve put some stuff up on my blog about it

    But even if we confine ourselves to HUD, we have a serious problem using income to set the HUD subsidy. The problem is the creation of a Poverty Trap. the idea being that your Real income (the amount you consume per month) can go DOWN when you work harder to earn more wage income, and this prevents people from ever getting out of the quagmire of welfare programs.

    So, should we adjust HUD for family size? Absolutely. but, should we adjust HUD for income? No, definitely not (at least there are some kinds of adjustments we definitely shouldn’t do). But then, eventually you have to decide whether someone is or is not on HUD right? And shouldn’t that be decided based on income? Well, no you could go UBI and give something to everyone, adjusting not for income but for basically any other variable such as disability, age, location where you live, etc.

    Getting back to how you could actually do something like HUD, you really should subsidize people in a way that tapers off slowly as their income increases in such a way that their total consumption level never declines with increasing wage income. But, this requires cooperation between departments! Because if HUD takes away 50 cents when you earn an extra dollar, and food stamps/SNAP takes away 50 cents, and the earned income tax credit takes away 20 cents… then the government takes away $1.20 for every dollar extra you earn. Again, argument for UBI.

    The ability to keep some fraction of a marginal dollar earned is critical to stability of our society, otherwise we wind up with a two class system “the poor trapped in welfare by a crappy system who aren’t allowed to improve their lives through work” and “the rich well above the welfare line who are allowed to improve their lives through work”. The end result is rioting in the streets. The precursor to that is electing Donald Trump in hopes to shake up the system enough that it stops oppressing people by poorly administered misguided “helping”.

    • If HUD says that families pay 30% of their income to rent, then for every dollar extra they earn… HUD keeps $0.30 the same is probably true for say health care subsidy under ACA, and child care subsidy, and etc etc it rapidly adds up to more than 100%.

      Is a PDF where they look at these effects for different kinds of families. The results can be striking, look at page 26 for single parent and two children. If the parent makes less than $80,000 / yr they are better off in terms of total consumption making $25,000/yr ($12/hr) in wages and qualifying for the RTC+Cash+Food+Housing+Child Care + MA + ACA subsidy level.

      If they make on the other hand just $18/hr which sounds like a pretty good wage increase for someone making $12/hr, their consumption level drops almost in HALF.

      • One way to deal with this issue without moving to a UBI, is to impute an income potential… say given age, education level, health or disability level, etc. Then have them pay a fixed percent of this fixed imputed amount. (say 30%). Then, when a person gets a job that pays them $1/hr more… they keep the regular after-tax portion of this extra amount, no additional “HUD tax” where because you earn x+1 you pay 0.3*(x+1). One issue would be that if education level is included and you decide to go get yourself some job training… your imputed potential might increase. To combat this it makes sense to have the imputed potential change slowly in time like say exponentially weighted moving average with time-scale of 4 years or something. So a steady improvement in your conditions always results in a lag before they make you pay more.

    • Daniel McCracken says:

      Agree with a lot of this. I would definitely prefer UBI (or an expanded EITC with slow tapering as income increases) as a replacement for the current jumble of programs, for many of the same reasons you mentioned. And also for some you didn’t: the current system requires welfare recipients to spend an inordinate amount of time and energy every year providing separate documentation to every agency they receive services from, and every one of those agencies requires a large workforce to administer their programs. So much waste! But I don’t think substantial reforms like that are particularly likely.

      Those graphs in the Illinois Policy report are misleading, though. The model assumes that “when employed, the adult does not receive healthcare benefits from her or his employer”, but one of the obvious benefits of increasing your income is that it increases the likelihood that your employer will provide health (and other) benefits. The model also only includes housing choice vouchers when calculating “Housing Assistance”, which has lower income limits and stricter guidelines for continuing eligibility than other available housing assistance (ie LIHTC, Project-Based Section 8, etc.). So the drop-off in real income is exaggerated.

      The reason I focused on those HUD policies in particular is that they don’t effectively serve their stated purpose–adjusting benefits to account for the different costs of living for different household sizes– but could be easily fixed.

      • I think it’s pretty likely that you don’t get health care from your employer until you’re up in the 50-75k range these days. You might be able to buy it from a group plan, but actually having it subsidized by an employer? Not all that likely. I certainly know several people making more than 40k who are in that situation.

        Even if exaggerated, the basic take home message is… don’t make more money at work, you’ll lose. This even happened to my mother when I was young (early 80’s), she qualified for reduced cost child care, and when her boss told her she was going to get a raise she refused it. It would have wiped her out because she’d have lost eligibility for her child-care subsidy.

    • Krzysztof Sakrejda says:

      It would also be useful to think of money at the lower income levels as not infinitely divisible. Intuitively this comes up when you talk about being one dentist’s bill ($150 or so?) away from missing your rent payment. The risk that should really be getting managed by programs like these is the risk of not making ends meet (a discrete event) rather than having a proportion of your dismal paycheck left over.

  3. Soho says:

    Don’t assume this is a bug in the system. It might be, but it could just as easily be a way of keeping costs low while leaving the program sounding more generous.

    • Daniel McCracken says:

      I considered that, but I think it’s unlikely for a few reasons. One is because the current system is designed so that small households have smaller “adjusted” rent burdens than large households. But because the average household size of public housing residents is less than their “standard” of 4 (,the current system may actually increase costs. Two is because the change would be unnoticeable to the layperson (“tenants pay 30% of income” becomes “tenants pay 30% of hh-size-adjusted income”). Three, because the change could also potentially be made in a revenue-neutral way that appears to make the program *more* generous (“tenants pay 30% of income” becomes something like “tenants pay 28% of hh-size-adjusted income”).

      Consider three households with identical non-HH-size-adjusted incomes ($24,000/year, or $2000/month).
      – HH 1 has one adult living alone
      – HH 2 has one parent and 2 children
      – HH 3 has two parents and 3 children

      Under HUD’s current rules (in which income is adjusted down by $40/month for each dependent):
      – HH 1 will pay $600/month in rent ($2000*.3)
      – HH 2 will pay $588/month in rent ($1960*.3)
      – HH 3 will pay $564/month in rent ($1880*.3)

      But imagine that HUD instead used a similar HH size adjustment to the one they currently use to determine program eligibility. That formula would look something like this:
      – If HH size = 4, adj income = income
      – If HH size 4, adj income = income * (1 – (.08 * (HH size – 4)))

      Under these rules, because of the small average household size of public housing recipients, revenue would increase:
      – HH 1 will pay $744/month in rent ($2000 * 1.24 * .3)
      – HH 2 will pay $648/month in rent ($2000 * 1.08 * .3)
      – HH 3 will pay $552/month in rent ($2000 * .92 * .3)

      Or to make it more revenue-neutral, they could change “30% of income” to “28% of income”:
      – HH 1 will pay $694/month in rent ($2000 * 1.24 * .28)
      – HH 2 will pay $605/month in rent ($2000 * 1.08 * .28)
      – HH 3 will pay $515/month in rent ($2000 * .92 * .28)

      Obviously HUD would need to tweak it based on a more detailed analysis of their programs’ demographics/the projected revenue impact, but that final idea seems to a) make their household size adjustments more consistent and b) make their programs seem more generous.

      • Daniel McCracken says:

        (I think my HH size adjustment formula got mangled due to my less than/greater than symbols. It should say this:
        – If HH size = 4, adj income = income
        – If HH size is less than 4, adj income = income * (1 + (.08 * (HH size – 4)))
        – If HH size is greater than 4, adj income = income * (1 – (.08 * (HH size – 4)))

        If it can be fixed by a moderator, just fix it there and don’t publish this one)

  4. Lord says:

    Whether 3 or 4 matters little since the 50% is adjustable and probably is adjusted to control program cost and size. The average household size may also differ with income, so the size adjustment mostly just adjusts for larger numbers needing larger incomes. Being one less makes it less generous but the differential amount is more important since each is a mouth to feed which is likely the reason for the amount. Households/housing are in units of one and 30% of income for housing has long been a standdard though rather low these days; higher incomes often spend more in urban areas. Remember that a larger household will need a larger space costing more but this will cost marginally less per person, their subsidy will be higher in absolute terms while being less per person but it is the household/housing being subsidized, not the person. Two can live for not much more than one as the housing would be shared and the second would mostly need food. One will have more space since non sleeping areas are not shared but their standard of living will be similar. Larger households will spend more on food, but there are other programs for that. How much of this is administered and how much legislated, I can’t say.

  5. Elin says:

    I believe that just like with setting the poverty level, which is also family size and regionally adjusted, they are attempting to treat families of the same size but different numbers of people under 18 (or other dependents) differently. That is if it is a family of 4 but they are all adults, they are going to expect more of the payment to come from the family than if it is a family of 4 but two are children. This is because they assume that adults should be bringing in some income and it is punitive to families where this is not the case. At the same time, more people does require more space no matter what the breakdown of adults and children is. Hence there are adjustments for both concepts at different points in the process.

    Similarly with poverty level, a 4 person, 2 kid family with a given income might be considered in poverty while a 4 person, 4 adult family with the same income would not.

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