Number of babies born in the US by year from 1978-2020

I was playing around with birth number statistics.  (Note there’s a small change in 2006 about where the data came from– the numbers are really similar for the overlap between 1990 and 2006 but in general, the numbers from 2006+ are usually just a little bit lower than their counterparts from the other dataset, generally in the 1,000s place.  The numbers for 2005 in both datasets are very similar.)

Here’s what you get if you plot out raw numbers.  This doesn’t include immigration or mortality or anything like that.  Also no information about education or income or race or socioeconomic status.  Just raw numbers.

Many kids applying to elite colleges this year were born in or around 2004/5.

There will be some red-shirted and otherwise delayed kids who were born a year or two before then.  And, of course, the pandemic gap year kids (kids who deferred a year and then made the next accepted college class smaller at many elite schools, which caused kids who didn’t get in where they wanted to delay a year etc.) are still moving through.  And there’s kids who would never have applied to elite colleges before who are now encouraged to do so through QuestBridge (this is really great– work by Carolyn Hoxby and Susan Dynarski has been pushing for connecting these kids to elite schools and it’s fantastic that’s actually happening now).  And international students no longer have to prove that they are rich to attend US colleges like they did at the turn of the century.  So those are a few additional causes of competition for elite schools.

But still, the raw numbers are important.  (There’s something called the Easterlin Hypothesis that talks about the effects of cohort size on economic outcomes– this is part of that theoretical thread.)

And while the number of colleges has no doubt changed, what is defined as elite and how many schools are considered elite maybe hasn’t as much.

So… if your kids are applying to elite schools, is their college application experience going to be different than yours?  YES.  How much different?  Well.. what cohort did you apply to college with?  What cohort are your kids applying to college in?

A nice thing about this chart is the knowledge that if we hadn’t let DC1 skip a couple grades, there would be even more competition for slots.  Of course, zie would (probably) be more accomplished as well and wouldn’t be only 16, so that would help too.  DC2 has a bit more leeway as zie was born in the middle of kind of a flat fertility period, though zie may be facing more competition from red-shirted and gap year kids.

(Note that a lot of people making predictions about how hard it is to get into college are focusing on the *birth rate*, which will be dropping if what they say is correct.  The Birth Rate is calculated by dividing the number of live births in a year by the mid-year resident population.  The reason the birth number is going up but the birth rate is going down is because of the denominator, not the numerator.  Personally I think the numerator is more important to college admissions 17-18 years later.  Lots of other stuff goes into who is applying to college, as mentioned before the graph, but the mid-year resident population the year a kid was born probably isn’t a first order thing.)

Complaint about AP stats: one tail hypothesis testing

Apologies for people who don’t care…

But DC1 needed help on hypothesis testing, which is totally understandable since it’s non-intuitive for a lot of people (including me!), particularly the one-tailed tests.

So, most of us who use stats regularly are used to the idea of two-tail t-testing– that’s when we want to know if there is actually a relationship between two variables or if it’s just random chance making it look like two variables are related.  This is kind of the essence of regression analysis– we want to know if we can be 95% ok with the idea that the coefficient we are getting is different from zero.  Two-tailed t-tests are used for a lot of other things besides regression, like seeing if a variable is different from a mean or two means are different from each other, but the basic idea is we want to know if things are the same or different.  We don’t assign any direction to the difference– we don’t say which is bigger or smaller, just that the sample was drawn from a distribution with the same/different mean, or the two samples were drawn from one distribution or from two separate distributions.

Hypotheses then look like:

H1: μ1≠μ2

H0: μ1=μ2

With a one-tailed test you are applying a direction– you’re saying that it could be equal, but it could also be going the other direction.  Your alternative (H1) hypothesis is that μ1 is bigger than μ2.  (Or that μ1 is smaller than μ2, depending on what you’re trying to show.)

So the hypothesis should look like:

H1: μ1>μ2

H0: μ1≤μ2

There are a number of different ways to write out H0.  You could write > but then cross it out (I couldn’t find that character in word).  I tell my students they can write “We cannot say that μ1>μ2,” because that’s really the point.  We don’t know if μ1=μ2 or if μ1<μ2 or… even if μ1>μ2 and we just have too small of a sample size to say for sure.  (My students generally will be doing practical t-testing for non-academic employers rather than writing up fancy scientific papers that require formal hypotheses, so it’s more important for them to understand what they’re doing and what their outputs mean than it is for them to follow a specific jargon structure.)

Imagine my astonishment when the AP review sheet DC1 had showed this instead:

H1: μ1>μ2

H0: μ1=μ2

Surely the teacher made a mistake, I thought.  But no!  This is how all the AP stuff is.  This is genuinely what they’re teaching and testing for AP stats.

The problem is that when you formulate it like this, you’re not allowing for the possibility of μ1<μ2, and you’re making kids think that you’ve actually proven the null hypothesis, that you can really say that μ1=μ2 when really all you can do is say you’re not sure if μ1>μ2.

I took a picture and texted it to my friends without comment and got replies like, “What fresh hell is this?” and “!!, No!  less than or equal.” And they were astonished to find it was AP Stats and for real, not just a mistake in the notes.

No wonder some of my students who come in to my class after having taken AP Stats never really got hypothesis testing the first time around.

Ask the grumpies: Is all irrational behavior rational?

CG asks:

Is most/all economically “irrational” behavior actually rational for one reason or another from the individual’s viewpoint?

Nope!  This is why we have the field of behavioral economics!  Behavioral economics deals with ways that people are systematically irrational.  That is, they deviate from rational assumptions of economics, but in ways that we can model.  (Other social sciences sometimes talk about irrational behavior we can’t model.)  A really good example is present discount bias– basically why we procrastinate or eat too much etc.  We value now more than we value later, even though we would be willing to pay for a commitment device that forces us to work instead of play video games, eat healthy food instead of junk, save for retirement instead of spend, etc. etc. etc.  That’s not rational.  Another example is when you break transitivity… like if you value a>b>c you should value a>c, and it shouldn’t matter if there’s also a d option that you value less floating around.  And yet, menus, for example, are designed with expensive items almost nobody buys in order to encourage people to buy something pricier than they normally would.  Irrelevant options do affect people’s decision-making and not just through information channels.  Behavioral economics is fun and exciting!

That said, some seemingly irrational behavior actually is rational.  For decades if not centuries, the (white male) economist answer to why women and minorities make less in the market place was because they don’t behave enough like men.  Women and minorities were irrational– they didn’t get the education needed, they didn’t ask, they weren’t competitive enough.  It’s only been in the past 15 years or so that this idea that no, women and minorities are just as rational as white men, perhaps even more so, but they’re playing different games.  They don’t get the education needed because there are barriers in the way or it isn’t rewarded, they don’t ask because they’re punished for asking, they avoid competition because the games are rigged against them or they get punished whether they win or lose.  Their (Our) behavior is actually rational given their different constraints.

Ask the grumpies: What’s your take on Oster’s interview about gun violence?

OMDG asks:

What’s your take on the Emily Oster interview of the ED Dr at brown about gun violence? 

I am sorry to disappoint, but sadly the interview is only available to paid subscribers and Emily Oster really does not need my money.  (She and Jesse make waaaaay more than DH and I do.)

From what I can tell, the interview is with Megan Ranney, so I looked to see what else she’s been saying on media recently.  Here’s a Boston Globe article.

Ranney said she believes all of the actions being taken by the Biden Administration on gun violence are significant and important, all for different reasons. But the investment in community violence programs is key, she said.

Everything she says in the article seems to be sensible and to be following our best knowledge about preventing gun violence and gun deaths at this time.  She’s also got a Ted talk, and many other interviews online that aren’t pay to access.  I think she knows what she is talking about.  I assume she doesn’t say anything wild and crazy in the Emily Oster interview.

Grumpy Nation:  What do you all think?

Myths about the value of college

ARGH, I’m seeing so much misinformation going around in twitter because of student loan forgiveness.  It’s driving me crazy.

Myth:  The value of a college degree is not worth it.
Reality (based on recent work of David Autor, but also many many other people): Even with the high costs of a degree and student loans, the additional earnings make it worth it for most college graduates.
Sub-Reality (I don’t remember a big name on this one, but lots of people are studying it with mixed results): The benefit of going to college and not finishing– we’re not as sure about that. Depending on the loans that you take out, it may not be worth it to spend a couple years in college and then not have a degree (though 2 years at community college with a degree is worth it). And lots of people go to college, take out loans, and don’t finish. That is a problem that lots of people are studying.
Sub-Reality (David Denning and several other papers): Even a degree from a for-profit college usually does result in higher earnings, but you are no better off with a for-profit degree than you would have been with a community college degree (worse given student loans, though the worst offenders have thankfully been addressed in the new Biden thing). They provide the same benefits, it’s just the for-profit degree is stupidly expensive by comparison.

Myth: It is better to go to a low tuition regional school (or community college) than to the best school that you can get into.
Reality (Hoxby and Turner in an amazing RCT, and other papers that are not experiments but use clever regression discontinuity designs): Schools with better endowments 1. Give more and better financial aid, meaning that for poor kids who can get into them, a state flagship or a highly endowed private prestige school will cost less. And 2. More prestigious schools do a better job of retaining low income kids– this seems to be through a variety of methods– better financial aid means working fewer hours, but also they just have a lot more resources devoted to keeping low SES kids, offices, sometimes mentorship programs, short-term loans etc. That means for low income kids, the more prestigious school means that they’re more likely to actually *graduate.* And, we also know among graduates (through a lot of different papers, though no RCT to my knowledge), prestigious schools help low SES kids make more money as grownups than do less prestigious schools.
Sub-Reality: For middle/upper middle/rich class kids, it doesn’t matter. They just need a degree.  (And the rich probably don’t need a degree.)

Myth:  The skyrocketing cost of college is caused by financial aid accessibility.
Reality: The skyrocketing cost of college is caused by decreased federal and especially state investment in state schools. (And to a much smaller extent: better quality education, gambling on fancy sports programs that don’t pay out, fancy dorms at private schools, etc. But this is like nothing compared to the effect of how much the government has stopped subsidizing higher education.)

And some stupid Republican propaganda:

Myth:  Non-college training is free.
Reality: Truck driving requires CDL training. Hairdressing requires training. Nursing requires training. Plumbing requires a TON of training. So many professions that don’t require a college degree still require technical training which still costs money.

Myth: Working class people don’t have student loans
Reality: A lot of people drop out of college and have student loans. A lot of people get student loans to pay for technical training.  Plenty of working class people have student loans.

It still boggles my mind that only 30-35% of US adults have college degrees.  But a big percent start but then drop out without an additional degree.  (You can get exact numbers from

Making fun of people for (rationally) picking and choosing covid/monkeypox risks

There’s a lot of people who complain about how we have to mask at conferences, except during meals when we’re all eating at the same time.  Why mask at all?  Or why mask at the grocery store but not at a wedding?  Or why go to parties at all if you’re worried about covid?  Or why not go to parties if you’re not going to mask at work or if you have a child in daycare?  Why don’t people take the same level of caution at every moment of their lives?

Some of the argument is the same as when people make fun of people who order big macs and supersized fries along with a diet soda. From an economics standpoint that makes sense– they get utility from the fries and big mac that justify the extra calories but not from the soda. (Ignoring that from a health standpoint diet sodas may mess with how your body deals with sweet things.)

Going to Walmart because the cost/benefit ratio makes sense but not going to a wedding because it doesn’t *is* reasonable. There’s a lot more things besides risk that go into a cost/benefit ratio. I mean, I avoid amazon when it’s easy and I use it when it’s not easy to avoid. I boycott Nestle when it is easy but sometimes still buy Haagen dazs because it’s actually good and one of our grocery stores only has Ben and Jerry’s as an alternative, which we like, but sometimes you need something they don’t have. That is rational, not hypocritical. (And yes, I know my individual boycott means nothing to Nestle… but bigger boycotts do matter, and *I* care.  Just… not always enough.)

Maybe it is that people don’t understand risk, but maybe some of it is that risk is only part of the cost-benefit ratio but the most acceptable of the social excuses these days. Or that going to the gym is the only way to force yourself to exercise and you wear gloves to remind you not to touch your face after touching the equipment even if you know that the air is more likely to spread covid than surfaces. (And to be fair, I stopped touching doorknobs without sanitizing back when I was on the job market decades ago because I realized I no longer came back from travel sick! Covid isn’t the only bug out there.)

Are there rational choices that you make that seem wrong to people who don’t understand your cost-benefit calculus?

Data and bias

This tweet recently made the rounds of twitter:

Justin Wolfers has since deleted his defense.

But… here’s my 2 cents as someone who isn’t bringing in over half a million per year in salary from the University of Michigan (Justin Wolfers and Betsey Stevenson’s salary info is available online as state employees):

1.  100K is a lot, and if you don’t think it’s a lot, there’s a problem.  To speak in terms that the top 2% can understand, that’s a whole new personal assistant.

2.  The motivation of 100K is not really as big a deal as getting stunning data. Just the data by themselves are incentive to not bite the hand that feeds the researcher (in this case Uber).  And the Uber data are stunning.  They’ve helped us learn a lot about human behavior and contingent labor markets, and probably lots of other stuff that’s more industrial organization.

Does that mean that you can’t trust anything that comes out of the Uber data, or any other study where the company has generously provided data?


But it does mean that you need to think really hard about the studies that do come out of the data (and the studies that don’t come out as well).

Ask yourself:

Does the company (or in some cases, government agency) benefit from the study results?  If not, then it’s probably ok.

There are plenty of amazing studies using the Uber data that tell us about the type of employee who uses the contingent labor market and what their preferences are.  Uber has no reason to benefit from or to suppress this information.  The studies are orthogonal to influences that Uber might be giving (purposefully or not) to grateful researchers.  These results are probably trustworthy, that is, they can be evaluated on the merits of their own internal validity.

If the company would have cause to benefit from the results– then you might be more cautious.  Not that a good economist would purposefully fudge data or results.  They don’t need to.  With any research project there are a lot of decisions that need to be made about specifications and samples and data cleaning.  Researchers just have to unconsciously feel grateful to the company to bias themselves with these choices, particularly if they don’t have a pre-analysis plan.  (And even if they do have a pre-analysis plan, they might still choose what they unconsciously think will benefit, or at least not hurt, the company).

On top of that, there’s selection bias in the choice of research question.  Even excellent economists will choose to just not go places that might make the company look bad when said company has provided data.

Similarly, negative results can be suppressed by the data provider.  I know of a case where the US government suppressed one of my colleague’s research findings that made their agency look bad after providing him with data (though they did allow someone else to publish the same negative findings later under a new, less fascist, government regime).  Any time that clearance is required to share results, that can be a problem.

To sum:

Just data provision is enough to bias research results.  If a company provides data, then results that show the company in a positive light will be shown and results that show the company in a negative light will not be shown to the public.  Results that don’t affect the company one way or the other are probably fine and can be evaluated on their own merits.

There’s a lot to be said for data that come from legal requirements (ex. FOIA), are available from third parties, or from internet leaks.

It is important to know who provided the data, not just who provided the funding, when doing disclosures.

Myths about TANF

This is an old post in the drafts from 2011.

Entitlement:  Not really sure what I meant by this one.

Cadillac mama:  The idea of the Welfare Queen was thought up and popularized by one of Ronald Reagan’s speech writers.  There’s little to no basis in reality, though some point to one woman who was perpetuating actual fraud (and was caught and went to jail for it).  There were no single mothers living large on Welfare back during Reagan’s time and TANF is even less generous, so that’s even less of a thing.

Encourages more babies:  TANF does not pay enough for an extra child to make it worthwhile to have an extra child.  The extra child will cost more than the additional benefit of TANF.  Anybody saying they want babies to get on welfare is delusional.

Encourages divorce/not getting married:  maybe.  Welfare (pre-TANF), potentially even more so, because it was targeted at single moms and even more difficult to get if married.  But even if TANF does encourage divorce/not getting married, that’s not necessarily a bad thing if it helps women not be trapped in dangerous marriages.

Discourages work:  yes and no.  Welfare pre-TANF did discourage work.  TANF is an improvement over that.  TANF is designed to try to keep it from discouraging work as much, though theoretically it still could.  Empirically it seems to not discourage work much.  One of the terrible things is that work doesn’t really provide a living wage for a lot of people on the margins of TANF.

People move to states with more generous benefits in order to receive benefits:  This just does not happen.  First:  People do not leave their families and support networks to chase benefits.  Second: even if they did, states have waiting periods where you have to live in said states for more time than most poor people can handle before benefits start up.

The CBT is awesome post

Disclaimer:  I did CBT 20 years ago at a research university that is/was known for CBT research, and this post had been sitting unfinished in drafts since 2016.  A lot of stuff may have changed since then!

Another one of those comments I’m always leaving.

CBT is amazeballs. It’s also what they use in Bradley class for natural childbirth. It takes practice but it totally changed my life even more than just the test anxiety I was getting it for. I’m so much of a calmer person now. Every time I start getting anxious my deep breathing automatically starts up. Personally I think everybody should get trained in it starting in high school!

It also has the benefit that it’s a set of specific techniques and once you’ve learned them, or learned even a set of them, you can stop going to therapy* for the specific anxiety. The one I did was a 6 week program, IIRC. (They graduated me a little early because I responded really well to the early techniques, which makes sense as they teach the most effective ones first.) I went to a university program, which was nice, though I had to wait a few months before they could see me. A private practitioner might not be as systematic, but may have less of a wait.  (DH tried it locally as a professor and it was not as focused or as good.)

The CBT place I went to recommended Mind Over Mood and Thoughts and Feelings while I waited to be seen. They were also helpful.

The main idea behind CBT is that anxiety causes a physical response that makes you more anxious.  If you can interrupt that physical response, you have a chance at letting your rational brain take over.  Ditto negative repeated thoughts (what my therapist called “ticker tape”).  It is NOT about getting to the root of your problems.  It’s only about getting tools to treat the symptoms of anxiety and anxiety-related disorders.

The first lesson for me was breathing.  When you’re in fight or flight your breathing changes and that gets you more anxious.  So we spent a lot of time practicing breathing in through the nose two three four, out through the mouth two three four.  I had to practice this at home too in a relaxed state, so I started identifying the breathing with being relaxed.  Eventually taking a deep breath became an immediate unconscious response every time I got anxious.

Cognitive restructuring was another important lesson.  With my anxiety I had these negative repeated thoughts, “you’re so stupid, you’re going to flunk out of graduate school, you’re a failure etc.”  In this step, the therapist folded a piece of paper in half length-wise and on the left wrote each negative thought down.  On the right we came up with something that was *true*.  It’s really important here for it not to be aspirational or unbelievable, but for the response to be completely believable and true.  Stuart Smalley-style affirmations don’t work.  But replacing incorrect negative thoughts with neutral or positive true things does work (on average, in RCT).  (And I decided what was true, not the therapist.)  So “You’re so stupid” would be replaced with “I’m not stupid.”  “You’re going to flunk out of graduate school” with “[Grad School] doesn’t flunk anybody out, they just give people consolation PhDs and make sure they work in industry instead of academia where they make more money.”  “Even if I leave graduate school I’m not a failure, I can still get a real job making money.” and so on.  I kept that original list on our refrigerator through several moves and really only didn’t put it back after our last sabbatical.

Progressive muscle relaxation was another interesting one.  With this one, you start at your toes and clench them super hard and focus on how they feel while clenched.  Then you unclench them and ponder how different they feel when unclenched.  Then you go up your feet and legs and so on.  I fell asleep in the therapist’s chair doing this and we decided maybe it was a bit overkill for test anxiety.  But it does help me get to sleep sometimes.

There were more lessons after this, I think positive visualization for which the science wasn’t really there yet was one.  I don’t remember what else.  Breathing and cognitive restructuring really helped me.  If they hadn’t worked so well, we might have done some aversion therapy which is NOT just throwing someone into a pit of their fears without support.

Anyhow, that’s my CBT post and now maybe instead of typing this all out each time it comes up in a chat I can just refer to this post.

*YOUR MILEAGE MAY HEAVILY VARY.  CBT didn’t do jack squat for #2, although she recommends it to most people.  Please don’t feel bad if 8 sessions of manualized CBT doesn’t fix your decade-long problems.  It’s not designed for that.  It works well for, say, test anxiety, or a first-time depressive episode.  It works less well for relational trauma and complex interactions of problems.

Have you done CBT?  What were your experiences with it?

Cognitive Restructuring

This is a post from 2011!  Or rather, there was an outline in 2011 and I turned it into sentences last weekend, 10 years later.  I was militantly happy back in 2011, and without a pandemic or incipient fascism and with Obama etc. things were looking up for the better, yet I was on a mommy forum local to a paradise where some highly privileged people seemed determined to be unhappy.


I like being happy.

Sometimes there’s no choice about how to take things because some things are genuinely bad.  For us, that kind of thing leads to grumpy rumbling.

And sometimes you know you *could* fight being unhappy but you also know that the occasional sulk is good for the soul so you indulge.

But for the many things, there’s a choice on how to view what’s going on, especially if your basic needs and then some are being met.

Happy people aren’t necessarily the luckiest, but they’re good at taking things as they are.

For example:  Rejection sucks and often it is unfair.  But, as they say in LA, when a door closes, open a window.  Take what you can from the rejection to learn, using your growth Mindset (all amazon links are affiliate), make your paper better, and submit it someplace else.

How to cognitively restructure:

  1. Fold a piece of paper in half length-wise.
  2. On the left, write down the negative thing that you keep telling yourself.  On the right, write down the thing that is actually true.  (Not Stuart Smalley, but what is actually true.)  So when I was in graduate school, on the left I had, “I’m going to flunk out of graduate school” and on the right I had “Nobody flunks out of this program, they just graduate you and make sure you don’t get an academic job so you make more money as a consultant.”  This is a technique from Cognitive Behavioral Therapy.  Two good books on CBT are Mind over Mood and The Thoughts and Feelings Workbook.
  3. If you don’t know what is actually true, you can tell yourself the best possible story.  For example, I have massive social anxiety and it is important to remind myself that no, actually, most people are too caught up in themselves to be concerned about or even notice my own awkwardness.  Often what can be attributed to malice can also be attributed to incompetence.  Sometimes you can convince the other person of your story by coming up with a face-saving (for them) story if you repeat it often enough.  There’s a lot more about these techniques in the book Crucial Conversations.

Do you ever cognitively restructure?