Mathematicians and the Prevention of Recessions

Note: I com­pleted a PhD in Math­e­mat­ics from Univer­sity of Illinois un­der the di­rec­tion of Nathan Dun­field in 2011. I worked as a re­search an­a­lyst at GiveWell from April 2012 to May 2013. All views ex­pressed here are my own.

About this post: I’ve long been in­ter­ested in ways in which math­e­mat­i­ci­ans can con­tribute high so­cial value. In this post, I dis­cuss a ten­ta­tive idea along these lines. My thoughts are very pre­limi­nary in na­ture, and my in­tent in mak­ing this post is to provide a launch­ing point for fur­ther ex­plo­ra­tion of the sub­ject, rather than to per­suade.

Re­ces­sions as a se­ri­ous threat to global welfare

In 2008, the US hous­ing bub­ble popped, pre­cip­i­tat­ing the Great Re­ces­sion. The costs of this were stag­ger­ing:

  • It’s been claimed that the cost to US tax­pay­ers in bank bailouts was $9 trillion.

  • The Dow Jones In­dus­trial Aver­age dropped by al­most 50% and took over 4 years to re­cover.

  • US un­em­ploy­ment jumped from ~5% to ~10%, and has only grad­u­ally been de­clin­ing.

  • Bud­get cuts were es­pe­cially great for gov­ern­ment sup­port of ac­tivi­ties with un­usu­ally high hu­man­i­tar­ian value to those with­out poli­ti­cal con­stituency, such as in­vest­ment in global health.

  • It’s been claimed that re­ces­sions cause a drop in proso­cial be­hav­ior.

All told, the Great Re­ces­sion had mas­sive nega­tive hu­man­i­tar­ian dis­value, and pre­vent­ing an­other such re­ces­sion would have mas­sive hu­man­i­tar­ian value.

Trans­par­ent fi­nan­cial anal­y­sis as a pos­si­ble solution

There are ac­tors in fi­nance who ac­cu­rately pre­dicted that there was a hous­ing bub­ble that was on the brink of pop­ping, and who bet heav­ily against sub­prime mort­gages, reap­ing enor­mous prof­its as a re­sult. The most promi­nent ex­am­ple is John Paul­son, who made $3.7 billion in a 2007 alone, start­ing from a base of less than $1 billion. There are less ex­treme ex­am­ples that are nev­er­the­less very strik­ing.

It’s difficult to de­ter­mine the rel­a­tive roles that skill and luck played in these peo­ples’ suc­cess, and the situ­a­tion is fur­ther ob­scured by hind­sight bias. Nev­er­the­less, it seems pos­si­ble that the fi­nan­cial suc­cess of Paul­son and oth­ers was a con­se­quence of care­ful anal­y­sis and shrewd­ness, and that other peo­ple of suffi­ciently high in­tel­lec­tual cal­iber and ra­tio­nal­ity would have been able to pre­dict it as well.

As is always the case in fi­nance, those who rec­og­nized the im­pend­ing pop of the hous­ing bub­ble kept their anal­y­sis se­cret, be­cause shar­ing it would have al­lowed oth­ers to par­tially close the ar­bi­trage op­por­tu­nity, re­duc­ing the po­ten­tial to profit. If these peo­ple had made their think­ing pub­lic, it could have re­sulted in other peo­ple bet­ting against the hous­ing bub­ble ear­lier on, popped the hous­ing bub­ble when it was smaller, pos­si­bly sub­stan­tially less­en­ing the sever­ity of the en­su­ing re­ces­sion. While there were peo­ple who pub­li­cly voiced con­cern, a large num­ber of peo­ple would have had a big­ger impact

This sug­gests that trans­par­ent fi­nan­cial anal­y­sis by in­tel­lec­tual elites could carry mas­sive hu­man­i­tar­ian value.

Math­e­mat­i­ci­ans as un­usu­ally well po­si­tioned to perform such analysis

In the course of my grad­u­ate school days, I be­came fa­mil­iar with math­e­mat­i­cal com­mu­nity. There’s a wide cul­tural gulf be­tween pure math and fi­nance. My ex­pe­rience was that math­e­mat­i­ci­ans gen­er­ally view fi­nance as “dirty busi­ness,” on ac­count of:

  • Often hav­ing left-wing poli­ti­cal beliefs

  • Dis­com­fort with the zero-sum and/​or nega­tive-sum na­ture of finance

  • Not iden­ti­fy­ing with materialism

  • Dis­lik­ing messy prob­lems that are less in­trin­si­cally in­ter­est­ing than prob­lems in pure math.

I be­lieve that this gulf has led to a po­ten­tial op­por­tu­nity be­ing over­looked: math­e­mat­i­ci­ans may be ideally suited to perform trans­par­ent fi­nan­cial anal­y­sis that re­duces dam­age from fi­nan­cial bub­bles.

This idea oc­curred to me a few weeks ago. Ideas for philan­thropic in­ter­ven­tions gen­er­ally fall apart upon closer ex­am­i­na­tion, and so I wasn’t too op­ti­mistic about it hold­ing up. So I was sur­prised when Neal Koblitz (co-cre­ator of el­lip­tic curve cryp­tog­ra­phy) raised the same idea in un­re­lated cor­re­spon­dence:

If math­e­mat­i­ci­ans had been notic­ing the du­bi­ous ways that peo­ple in the fi­nan­cial world were claiming to be ap­ply­ing math­e­mat­ics, and if they had pub­li­cly and loudly crit­i­cized the mi­suse of math­e­mat­ics, then the world might have been spared the col­lapse of 2008 (or, rather, it wouldn’t have been as bad). If math­e­mat­i­ci­ans could have played a role stop­ping the credit-deriva­tives bub­ble be­fore it got out of hand, the eco­nomic value of do­ing that would have been in the trillions of dol­lars.

When an idea oc­curs to two peo­ple in­de­pen­dently, the case for it be­ing a good idea is strength­ened. More­over, Koblitz has a long his­tory of in­volve­ment with hu­man­i­tar­ian efforts and so can be ex­pected to have per­spec­tive on them.

Some rea­sons why math­e­mat­i­ci­ans seem un­usu­ally well suited to the task are:

Trans­fer­able Skills — Most math­e­mat­i­ci­ans are un­fa­mil­iar with some of most im­por­tant tools used in fi­nance: statis­tics, data anal­y­sis & pro­gram­ming. But there’s a his­tor­i­cal track record of math­e­mat­i­ci­ans be­ing able to pick up these skills and use them to pow­er­ful effect. James Si­mons tran­si­tioned from differ­en­tial ge­om­e­try to quan­ti­ta­tive fi­nance, and be­came one of the most suc­cess­ful hedge fund man­agers ever. Cathy O’Neil did a PhD in alge­braic num­ber the­ory un­der Barry Mazur’s di­rec­tion, and got a job at DE Shaw, which is one of the most pres­ti­gious hedge funds. Math­e­mat­i­ci­ans who are mo­ti­vated to learn these skills are well po­si­tioned to do so.

There are other skills that are very im­por­tant for suc­cess­ful fi­nan­cial anal­y­sis – in par­tic­u­lar, one has to have a good eye for em­piri­cal data. This is a skill that’s not di­rectly trans­fer­able, but it still seems likely that a non­triv­ial frac­tion of math­e­mat­i­ci­ans could de­velop high fa­cil­ity with it.

In­tel­lec­tual Cal­iber — The math­e­mat­ics com­mu­nity has a very dense con­cen­tra­tion of in­tel­lec­tual power. James Si­mons offers a di­rect point of com­par­i­son be­tween math and fi­nance:

Si­mons won the Oswald Ve­blan Prize in Geom­e­try be­fore leav­ing academia to start Re­nais­sance Tech­nolo­gies. There are 25 liv­ing math­e­mat­i­ci­ans who have won this prize. The prize is awarded ex­clu­sively for work in ge­om­e­try/​topol­ogy, and if one looks more broadly at all math­e­mat­i­cal fields, one can gen­er­ate a list of about 100 liv­ing math­e­mat­i­ci­ans who were at least as ac­com­plished as Si­mons at the same age.

After leav­ing academia, Si­mons made $10 billion in quan­ti­ta­tive fi­nance. What I find most in­ter­est­ing about this is that the situ­a­tion is not that Si­mons suc­ceeded where other math­e­mat­i­ci­ans of the same cal­iber had failed – rather, Si­mons is vir­tu­ally the only pure math­e­mat­i­cian of his cal­iber to have left academia. This raises the pos­si­bil­ity that there are a hand­ful of elite math­e­mat­i­ci­ans who could make much bet­ter fi­nan­cial pre­dic­tions than most pre­sent day ac­tors in fi­nance. Less ac­com­plished but ca­pa­ble math­e­mat­i­ci­ans may also do very well.

Cau­tious­ness — Math­e­mat­i­ci­ans are nat­u­rally in­tel­lec­tu­ally con­ser­va­tive, as they spend much of their time rigor­ously ex­am­in­ing ar­gu­ments for flaws. Thus, they’re un­usu­ally un­likely to suc­cumb to greed and fear, which are fac­tors that are thought to play a large role in the be­hav­ior of fi­nan­cial mar­kets, and which lead to spec­u­la­tive bub­bles. This is cor­rob­o­rated by some of Cathy O’Neil’s re­marks on fi­nance.

Implications

The above con­sid­er­a­tions sug­gest that math­e­mat­i­ci­ans could con­tribute enor­mous so­cial value by en­gag­ing in trans­par­ent fi­nan­cial anal­y­sis.

Many math­e­mat­i­ci­ans who I know wish that they could con­tribute more so­cial value. In the es­say Is there beauty in math­e­mat­i­cal the­o­ries?, the great math­e­mat­i­cian Robert Langlands wrote:

In a let­ter to A.-M.Le­gen­dre of 1830, which I came across while prepar­ing this lec­ture, Ja­cobi fa­mously wrote

It is true that Mr. Fourier thought that the prin­ci­pal goal of math­e­mat­ics was their pub­lic util­ity and their use in ex­plain­ing nat­u­ral phe­nom­ena. A philoso­pher like him should have known that the only goal of Science is the honor of the hu­man spirit, and that as such, a ques­tion in num­ber the­ory is worth a ques­tion con­cern­ing the sys­tem of the world.

I am not sure it is so easy. I have given a great deal of my life to mat­ters closely re­lated to the the­ory of num­bers, but the honor of the hu­man spirit is, per­haps, too doubt­ful and too sus­pect a no­tion to serve as vin­di­ca­tion. […] More­over, the ap­peal to the com­mon welfare as a goal of math­e­mat­ics is, if not then at least now, of­ten abu­sive. So it is not easy to find an apol­ogy for a life in math­e­mat­ics.

A fair num­ber of math­e­mat­i­ci­ans don’t have any choice but to do pure math. Gro­mov wrote:

You be­come a math­e­mat­i­cian, a slave of this in­sa­tiable hunger of your brain, of ev­ery­body’s brain, for mak­ing struc­tures of ev­ery­thing that goes into it.

I’m very sym­pa­thetic to Gro­mov’s re­mark, and I think that for peo­ple who con­sti­tuted in this way, it’s prob­a­bly best not to try to sup­press these urges, as such at­tempts tend to be un­sus­tain­able and re­sult in lower con­tri­bu­tions to global welfare rather than higher ones.

But for math­e­mat­i­ci­ans who are:

  • Tenured pro­fes­sors who don’t have to worry about ca­reer con­sid­er­a­tions

  • Able to en­joy fi­nan­cial analysis

  • Strongly mo­ti­vated to do an ex­cel­lent job

there may be a ma­jor op­por­tu­nity to con­tribute enor­mous so­cial value by con­duct­ing trans­par­ent high qual­ity fi­nan­cial anal­y­sis.

This ques­tion war­rants fur­ther in­ves­ti­ga­tion.