Taking Our Chances

This one's for the academy, I guess

“That mortal is a fool who takes joy in his prosperity,

thinking that it will last forever. The highs and lows of our life

are a lunatic, who lurches from place to place.

No man can control his own fortune.”

— Hecuba, Euripides’ The Trojan Women, L.1200-1205

*

Man, I’m in the fucking trenches these days. I don’t even know what to tell you. I was ill, I was well, I was ill. I was thinking about how we lost Frank Ramsey to illness at the tender little age of 26. Of course overall 26 is an adult, and he was married with children. But in scholarly terms, 26 is a child. I say “we” lost him, as though he hadn’t been lost almost 100 years ago. I say it imagining some immortal kind of stats community, though of course he was also an economist. There are surprisingly few of us working at the intersection now.

It’s not that there is not a lot of overlap; there is. But there is surprisingly little interest in the customs and thinking or traditions of the others, somehow, on the side of each group. It feels a little obvious that we in econ should care a lot more about stats. Why does it not happen — or why does it happen only among theorists? Why is it that the only people in economics functionally capable or trained to be capable of following an argument about subjective probability are the theorists? Everyone else, even many econometricians, sort of just takes the limit theorems as gospel. People for the most part don’t think of them as what they are; tools and thought experiments, designed just to create approximations. They believe too much in what is essentially a kind of quant heuristic. They don’t even know, by and large, what they don’t see.

I was lucky. I was lucky because when I was in graduate school, Jerry Hausman and Whitney Newey turned down my petition to replace my econometrics courses with statistics courses (up the road, at Harvard, since MIT did not and still does not have a statistics department per se). I think they would not mind me telling this story since they gave me, with this huge burden, as is often the way, a gift. Hausman told me he thought that the economics part of econometrics was important; he was right. (This insight would go on to help me finish my job market paper.) I asked if they or he would at least consider awarding me a statistics minor if I went up the road and took those stats classes in addition to what was shaping up to be taking an econometrics major field. They said yes.¹

It is only because of this, and the enormous suffering I endured trying to cram all of this knowledge into my head (but good suffering! Beautiful, valiant suffering, etc) that I ended up being able to open a kind of third eye that can rove at least to some extent quite freely over both of these disciplines together. Please do not mistake this for any kind of claim of mastery: like most ordinary people, I have sacrificed something to get breadth, and compared to most real theorists I know I have negative gifts. (To this day I do not easily “read” sentences written in mathematics, even if I am familiar with it. I have to translate and run almost all of this on verbal.) I am talking here more about having access to a much broader context. This alone will change the way you think.

But surely many in econ can see some of this, can perceive the value of what is happening in the realm of statistics, I think. With the rise of adjacent field achievments in machine learning and data science, many colleagues even want to use it. The problem is that trying to really learn something new is humbling, especially if you come at it from a position of apparent success. The ego gets built up so, so easily, when things are going well, unless you work hard for it not to. It is not just online writers and clout-chasing posters who mistake numbers or success for importance, or for virtue. It is also real for tenured academics.

And it is hard to replace the experience of having a graduate sequence of courses pounded forcibly into your head. I know we are supposed to be against this; I am for it. It changes you in ways too profound and complex to be able to render into words (this is a challenge later also, when your colleagues want you to do just that). I remain very indebted to Jun Liu, Thirthankar Dasgupta, and Joe Blitzstein, the latter of which changed my life forever by insisting that when you see the word “minimax” you should really be thinking “infisup”. Joe also set a midterm so profoundly challenging that I think we all failed it and I pretty much blocked it out; something to do with sprinklers on the roof in the sunshine? (Actually Jun also set delightfully challenging assessment and made many hilarious asides. The final for Stat 220 was an 8 hour take-home exam consisting of only 3 questions, one I almost still remember, about stick-breaking representations. I could not finish any of them and I received an A.)

Where was I? Yeah, the curse of knowledge. No, that’s something else. The curse of unusual perspective? Seeing things differently is a blessing as well as a curse. It is a blessing because you can contribute something. It is a curse because typically the others will not listen. (We will shortly speak some more about Kassandra, but this will be ugly.) Early on in my work I had to contend with people who thought quantitative evidence aggregation was unnecessary or useless in economics; later on some of these same people thought, well, look at the Cochrane handbook, this problem has already been solved. That’s sort of like looking at a stack of bibles and thinking we know everything about god. Actually people wrote the bible, and a lot of those people were fools.

It scares people to think about this. Nobody wants to admit it. But it scares them to think how flimsily constructed everything is that we know; how full of holes. That construction is still a great achievement, but it can be overstated, and indeed it often is, and so misused.

I remember when we were working through the Van Der Vaart blue book in our reading group in grad school. One of the math phd students got very upset at section 3.3, that shows that the appropriate use of the conventional asymptotic Chi squared test when applied to sample variances relies on a relatively thin (in fact, exactly Gaussian) true underlying tail index; this is because once the square of the underlying variable is your main statistic of interest, its variance is affected by the underlying variable's kurtosis (ie the kurtosis sort of "moves up" the roster in importance) and the higher order moments are not neutered by the usual asymptotics.

Therefore, though it is easy to feel that the delta method always allows you to squeeze more juice for free out of the central limit theorem, in the case of these sample variance tests, it doesn’t. All of us were upset by this; especially this other phd student, one of few other people I have known who took all this stuff super serious, like I do; BUT MEDICAL PEOPLE USE THE CHI SQUARED TEST he moaned. It’s true. If we were right then, in our interpretation, it does seem bad that only a handful of people even knows that there should be either some check, or some adjustment. Nobody seems to care that there are probably many cases where this test is not functioning at all.²

Van Der Vaart, in his customary mildness, just says, “Thus it is not always a good idea to apply general theorems.” After all, he has given us worse news before, in section 1.3: that we should not feel happy or lucky even if the logic seems to work. “In fact, strictly speaking, most asymptotic results that are currently available are logically useless. This is because most asymptotic results are limit results, rather than approximation consisting of an approximating formula plus an accurate error bound.”³ So: “This is why there is good asymptotics and bad asymptotics and why two types of asymptotics sometimes lead to conflicting claims.” We do know of this in certain situations, like for the case of weak instruments. The thing is that this failure is general, exactly as Van der Vaart says.

In principle, of course, there are ways to test or at least investigate the quality of these approximations. We, like our colleagues in medicine, pretty much do not use them.

*

People claim to care a lot about rigour, and exactitude, and chance. But people claim to care about a lot of things.

With chance, in practice, people usually disrespect it. A lot of the time when people say they care about something, they just like the idea of the thing. To respect and to accept something is real is to accept that at times, like all things, it brings challenges. But that is not the way that we normally treat chance.

The majority of respected academics in stats-adjacent fields like it only for what they think it may do for them; the way it could augment all the things that they already have. Perhaps you will all think me cynical; just call it a sign of the times. And every econometrician, statistician, etc, has stories about applied researchers asking them to p-hack. Psychology, economics, biology, medicine, genetics, I have heard it all. It seems that these applied researchers do this because they think they know the answer. They see the methods section as a kind of scientific theatre, or circus, where inference and tests are really nothing but a series of elaborate hoops for trained RAs to jump through.

I think most people do not really believe in inference, for inference means things are hidden. They only believe their own eyes. If something happens they think it obliterates all alternatives. It never could have been a different way. I think that lots of people think the whole world is completely deterministic. And maybe it is! Maybe there is no such thing as chance. (I do not intend for us to speak about quantum mechanics. Do not talk to me about quantum mechanics.) But even if you believe this, you still need to reason with statistics, because in many situations what you believe about this issue actually doesn’t change anything at all. If you’d like to know how we know that, you can consult De Finetti, or do yourself a favour and pick up the Persi Diaconis and Brian Skyrms book, “Ten Great Ideas About Chance”. This is the subject of chapter 7; they call the chapter “unification”; the great idea is “exchangeability”. A thing you can go your entire applied phd without ever hearing about once.

Ironically, the same people who think they really already know the answer when they collect or approach the data for their questions are often first in line to defend the “objectivity” of “science”. I find this combination very weird, because anyone interested in rigour in statistics should already know that objective probability is only really minimally possible, only possible as a set of axioms, nothing more and nothing else. Again, okay, you do not have to think that this matters. But some people evidently do. They do not see that the “long run frequency” interpretation cannot be made rigorous, though that is even sketched out in Chapter 1 of DeGroot and Schervish, an introductory textbook in statistics. But Ramsey noted that also, much earlier, in 1926, when he wrote Truth and Probability. He demolished that idea, in his time, in its then-incarnation: in Keynes.

Ramsey also noticed that this issue of a lack of exact objectivity — and thus the central importance of probability as rather a degree of belief — does not just arise in soft and squishy disciplines like econ, anthro, history, psych; it also arises in physics:

“The degree of a belief is in this respect like the time interval between two events; before Einstein it was supposed that all the ordinary ways of measuring a time interval would lead to the same result if properly performed. Einstein showed that this was not the case; and time interval can no longer be regarded as an exact notion, but must be discarded in all precise investigations. Nevertheless, time interval and the Newtonian system are sufficiently accurate for many purposes and easier to apply.”

A little while later he says:

“I do not want to discuss the metaphysics or epistemology of this process, but merely to remark that if it is allowable in physics it is allowable in psychology also”.

If you don’t want to read all of Truth and Probability, you could instead consult the summary in Diaconis and Skyrms Chapter 2. But first you would have to get through Chapter 1. And in there, there’s something else which you could go your whole econ phd without knowing: the fact that coin flips are deterministic.

Once you think a bit, it’s readily apparent, a simple case of classical mechanics. But the idea feels so ungodly, so counter-intuitive, that even as I write this, and I know it’s true, I doubt it. And this is not even new or advanced knowledge — De Groot and Schervish notes it in section 1.2. The trouble is that other books are not so clear on this: the Chernoff and Moses "Elementary Decision Theory" text, for example, is very confusing.

Diaconis and Skyrms go much further: they go into the mechanics of the coin. They show a picture of a coin tossing machine. They confess that this machine is disturbing. They confess this even though one of them has the very same ability. (It has to be the magician.) The perceived randomness in the coin toss comes from unknown and unpredictable variation in the starting conditions; ie, you.

It feels strange to me that this feels strange to us, when it’s been known for centuries. Ramsey was apparently influenced by Charles Pierce’s 1891 essay “Love and Chance”, (I link to it as repackaged in 1923 as a volume [see comments] called “Chance, Love and Logic”). There is a dialogue with an imaginary opponent that would suit any of our purposes today, in which Pierce ends with this banger line: “The chance lies in the diversity of throws.” (He in a later essay goes long into discussion of the Gospels.)

In fact apparently this was all also known to Bernoulli in 1713, or at least, was so conjectured. He is quoted in Chapter 1 of Diaconis and Scryms:

“What mortal, I ask, may determine, for example the number of diseases, as if they were just as many cases, which may invade at any age the innumerable parts of the human body and which imply our death? … In these and similar situations, they may depend on causes that are entirely hidden, and that would forever mock our diligence by an innumerable variety of combinations, it would clearly be mad to want to learn anything in this way.”

What determines all that throwing diversity? We still don’t really have any sure answers. We have made so much progess in some spheres, and yet so very little in others. We ought to feel the sting of our own ignorance; beset and bested on all sides by the things we do not know. Why then do so many academics — and applied, business, whatever, “sciency” people — want to act as a colossus, act as if astride the world? I must say this is particularly the case with applied frequentists, who spend all their time smug in their bunkers, convinced that they can do and explain it all with the tools they have, that they do not need to listen to new theories, learn new things.

It’s easy to feel this way in econ, now, when things are going well, or else they have been; especially compared to the rest of the academy. And unlike what we have done to much of these other disciplines — I do not say rightly or wrongly — so far no other field has come to consume and overtake us, claiming to deliver incredible things, eating our undergraduate enrolments and our prizes and our grant money.

Yet.

*

I mean, I wouldn’t really like that, would I? After all, have I not made my home here?

I have, I guess, though surely it would have to be said that I’ve prioritised security and stability, and that’s not unrelated to my forecast, nor is it unrelated to my sense that there can be a real tradeoff between shooting for (mortal, fleeting) glory and carving out the time and space for good and deep and satisfying work of any kind. I don’t know. Who knows what’s going to happen? This is a volatile time. And yet I feel okay about offering up that hint of a prediction. It’s a little bit weasely, I know.

Part of why that feels okay is that in general, being cynical or doom-foresaying is somehow rhetorically protected. We don’t hold each other to our predictions in this society. It’s considered rude, even in the academy, to point out people’s incorrect predictions. After so many people incorrectly, overconfidently, over-interpreted the polls in the run up to the last US election, it is still now considered rude to say this. It’s rude to point out that it’s stupid for these vacuous posts to have got thousands of retweets and likes.

Gelman used to talk about this on his blog all the time back in the day, but more about the ordinary news media. It just drove and maybe still drives him crazy how nobody ever punished any pundit for their garbage, bad predictions, wrong and wrong and wrong again, just time after time after time. It doesn’t matter. People want to hear what they want to hear. They don’t give a shit if it’s wrong. That’s what a pundit is for. (There are lots of them, now, in street clothing.)

It’s actually more frequent to be punished for being right, because people are confused about chance and causality; because prediction acts much like a threat.

The time has come to talk about Kassandra. Her incarnation as a line in popular culture does not do her any kind of justice. We think of her as a purely tragic figure, when we think of her at all. We do not think of her as aggressive, or menacing, or crazy. And yet, at least in the world of Euripides, that is what the people around her think of her, for that is exactly what she is.

In Diskin Clay’s translation of The Trojan Women he has Talthybios describe her as “god-frenzied”; Hecuba, her mother, scolds her for being unrestrained. But I think they both come off looking stupid. This is The Trojan Women, not the Iliad, or Agamemnon. This is Kassandra’s stage. She spends half the play walking around dunking on everybody. She would have killed on twitter.

In his introduction to his translation, Clay describes Kassandra as using “the threatening language of prophecy.” This is a powerful remark. I had never noticed it before, but my God it’s true, and it works; I just did it, earlier, and this is an ordinary thing that people do. It’s much easier to say I’ve merely noticed that you’ll get what’s coming to you than to own the fact that I’d like that, and that in fact I think you probably should.

Somehow, prophecy is also insulating. Like the god-frenzy of knowledge sets the physical body apart. Kassandra in Euripides does not show pain, she does not show fear. Married off to the invader, Agamemnon, here is her prediction, so rendered by Clay, arguably the hardest lines in fiction, L356-8:

“If Apollo Loxias is true to his name,

glorious Agamemnon, great Lord of the Achaeans,

will marry in me a bride more disastrous than Helen.”

She explicitly conceives of herself as a weapon, in fact as a suicide bomb (L405).

For this reason she tells her mother to rejoice. The chorus rebukes her; “The burden of this prophetic song will not be as compelling as you would have it.” Ugh. Women can’t have anything. (I still don’t really understand the rebuke, for she is right: she will have her way, if we can take Agamemnon as the sequel.)

Seeing her behave like a clout-drunken poster, it now feels very natural to join Kassandra up to Dionysus, though it surprised me when I read the introduction. Still, Clay’s note to L308 adds that her true marriage is not to Agamemnon but to Hades, as with all the dying maids. Apollo, Dionysis and Hades make a good trifecta. The sun god is slippery anyway; you cannot blindly trust what seems illuminated by his rays. Clay’s note to line 365: “One of Apollo’s epithets is Loxias. It is often associated with Apollo as a prophet. It means crooked or oblique and describes the ambiguous character of his prophecies”.

The history of the greeks, in as much as we know it, is littered with little lessons of this kind. If you read any story of the Oracle of Delphi then you’ll learn what troubles statisticians: just how specific you have to be when you are making your little requests.

It is dangerous to apply general theories. I do not mean to say we ought to have no general theories, but we should be handling them carefully. It is dangerous to learn a little of things and then overstate what you know. We, who for the most part live relatively happy (I mean lucky) coddled lives, still get shocked at regular intervals. We should know, but of course we refuse to know and don’t know, how open our lives are to new knowledge, and all of the resulting pain.

Most questions, like most things, are fragile. Shouldn’t we know that? Our misfortunes have little improved us. When we ride high we think: How could we lose? God is on our side! The long arc of history! It bends towards my idea of justice, my thoughts, ME. AND MY PREFERRED POLICY POSITION.

And then as soon as there is a setback or a wavering in this long magnificent elastic arc — which we are so small and close to that to us it looks like nothing, dust particles, a blue ribbon, the sky — then God hates us, and has forsaken us, and God was on my enemies’ side and now I am a nihilist — “So, so … The gods never really cared, or, if they cared, they cared / for my sufferings” (Hecuba L1240).

We don’t seem able to put these things together: our progress is fragile. Our setbacks are fragile also. Victory and defeat are not absorbing states. Very few things are robust. If you want to make them so, you usually sacrifice something. At certain times this price is very high.

The Trojan war is interesting and the Iliad is excruciating becuase the gods are on both sides of it; the same thing, and for almost the same reasons, is true of Odysseus alone. And in The Trojan Women, as one of her many dunks, Kassandra prophecies that Odysseus faces a journey home so harrowing that it will make him yearn for the horrors of war.

And she’s right! But no-one cares. Not even her own mother, who scolds her frequently, thus:

“Give me the torch. You are not holding is straight,

but dart about like a maenad possessed. Child, your misfortunes

have not taught you any restraint. You have not changed.”

— Hecuba to Kassandra, 345-350

Well, but she was young. Not as young as her brother, when Odysseus has him thrown from the rampart. It’s galling that he does this and still retains the protection of Athena, at least in the world of Euripides; he has a keen eye for the galling nature of things, as well as for the vagaries of nature.

To me the most striking scene is when Hecuba and Menelaus, who are enemies, discuss what should happen to Helen. They make for unlikely allies, but then, they both would like someone to blame. Perhaps especially because, as Helen points out, it was Hecuba and Priam who, in trying to avoid the prophecy of the very doom that has just come to pass, turfed out their infant son Paris — which is the only reason he grew up to be a shepherd, and was ever lying idle in a field, or known as fair.

Actually what Helen says is worse than this. She says they should have killed the infant child. And so when Helen also argues that she didn’t really have a choice: Aphrodite gave her as a prize — is it much of a surprise that Hecuba responds that she, Helen, should have killed herself instead? And yet somehow it does not seem possible, in 415 BC, for Helen to point out that Hecuba could have killed herself as well, to avert the prophecy, instead of casting off her helpless infant. And that the death of Astyanax at the hands of the enemy seems less atrocious when we remember Hecuba tried to kill her children too.

But Helen has already strayed too far from a typical Athenian script; she, just like Kassandra, speaks too much. The chorus of to-be slave girls acts fearful: “She is a bad woman who speaks well, and this alarms me.” (L967)

I think part of the reason we care about the deterministic-versus-random question is because it kind of touches (okay it exactly touches) on free will. Hecuba conceives of her own life as a ship, or a prow, though for all her power, she cannot steer it:

“Some god steers us.

In this disaster I cannot even direct the prow

of my life against the wave.”

( L100-105 )

She has this in common with Helen. But that much she is not inclined to see.

*

Here is another reason people do not get serious about chance: because they do not want to.

It’s not just that this reasoning is difficult. It is painful. Does anyone really want to know that there is no such rigorous thing as a “long run frequency”?⁴ That the randomness in gambling comes from you, not some apparently- or seemingly- or feelingly-inscrutable mechanics of the coin flip or the dice roll? Who wants to be left with subjective guesses, judgments, and weights? Nobody. Not even Bayesians! Even Bayesians go to sleep at night soothed with the complete class theorems, under the fluffy quilt of the Bernstein-von Mises theorem.

It’s better than Bernoulli’s swindle (Diaconis and Skyrms, P67 and again P195). Tedious, repeated frequentist attempts to prepare the Bayesian omelette without breaking Bayesian eggs. They do love their repeated attempts.

I do not mean to say all glory to statistics and no glory at all to economics. I am not saying what we’ve done does not have any value. (It’s also not necessarily the case that having value will save us; nor the case that becoming more inclusive, or better at statistics, will make us well remunerated or safe. Probably it does not do nothing. But this, all of this, too, is more than amply subject to the vagaries of chance.)

Those people inclined to dismiss econ might think that statisticians have little to learn from us; that is wrong. Economics is part of the foundations of probability, just as so much of what matters in our discipline is so deeply mired in chance. I don’t mean anything so narrow as betting — one of many ideas dispatched in a couple paragraphs by Ramsey — “fundamentally sound but insufficiently general”. (And this is not even close to the crowning glory of his campaign, his biggest kill aside from frequency itself: the principle of indifference, which, as far as I can see, he turfed out of formal logic altogether.)

No — Ramsey, like Savage who came after and formalised a lot of this mess, uncovered the truth that chance springs from and is bound indeed to something much deeper, the heart of economics, the fire in the breast: decision theory, or as laymen might say it, decision-making under uncertainty. You know, the thing that touches almost all of everything, not just in games and forecasting, or business, but in warfare, politics, research; family planning, disaster preparedness, and all of relational life.

It almost feels like Ramsey himself was a myth, or else a god-touched body, all aflame. The highest of all the Apostles, who vanished off the face of the earth at age 26 in the midst of his triumph, surrounded by his new family and friends, leaving behind to us in some sense everything, and all of our disciplines’ future, and in another sense like almost nothing, only 4-5 of the most seminal and excellent papers of all time and the immortal phrasing: “Margaret will you fuck with me?”.

Sometimes you have to write “Truth and Probability” just because Margaret won’t fuck with you. (Ramsey also went to therapy.) Don’t forget the sirens offer knowledge, past and future; they, also, do not offer sex.

Apparently Margaret said to him, in response: “Do you think once would make any difference?” Of course it makes a difference Margaret! God!!!

*

At least we have all of the Ramsey. 100 years is nothing, all his things survive intact.

Euripides almost surely wrote much more than what we have. It is not a given, then, which of all things survive. Of his work we have little, but this is not entirely due to a lack of popularity. He apparently submitted The Trojan Women to a contest. It came second. The play that came first has been lost.

At times it seems like in his play he even sees this coming. He has Talthybios put it:

“So it is: What is exalted and wise in people’s esteem,

collapses into ashes.” —(to Kassandra, L411)

We now know that it was prescient to stage this play, in 415, on the eve of the Sicilian Expedition. But this cannot have made him much loved.

Euripides lived for quite a long time, but he died separated from his polis. I kind of like to think of him as a Christopher Hitchens type of figure. As I’ve been ill, I’ve been thinking a lot about Hitch. Not the rambling impenetrable God Is Not Great but the essays, many of which are still good. My admiration for him was that of a teenage atheist, but I do think we miss having something, somebody so at war with himself and the world. In “On the limits of self improvement part 2” he has this great quote: “I am more than ever sure that it’s enough to be born once, and to take one’s chances, and to grow old disgracefully.”

The greeks of Euripides’ time, though very far in time from the Acheans, purportedly still really believed in the Gods of these legends. We are supposed to be much wiser than that now. Yet still I think prophecy works on us as a threat because we do not really believe in chance. We treat any real prediction more as if it’s something of a death sentence. But, at the same time I think, and, yet again, perhaps you will think me cynical, it is only for this reason that most people care about prediction.

*

What now is on top of the acropolis; picture my own, from 2023.

1. Actually I asked to take course 6, I don’t remember at what point I ended up re-fashioning the strategy to going up the road and getting approval for it, but somehow this happened. That is part of how I ended up being able to graduate with the joint econ and stats phd.

2. Having reread the relevant sections now, I think our interpretation indeed holds up. I also think that this error — assuming one can use a naive Chi squared test based on a loose but it turns out erroneous argument from the first-order asymptotics — shows up in economists’ use of the F test in most cases, but I have not fully checked this, so I am not sure.

3. I would like to point out than in our AMIP / data dropping paper we provided the second thing, including exact calculable error bounds in common cases. Nobody cared about our provision of bounds, perhaps because nobody thinks about what it means that we usually lack them.

4. Other than followers of Hume… I suppose? Maybe?