Positivism

31 July, 2013 at 16:59 | Posted in Theory of Science & Methodology | Comments Off on Positivism

9789144014340_largeI min artikel häromdagen om ekonometrins felande ontologiska grundfundament — Econometrics – still lacking a valid ontological foundation — förde jag fram kritiska synpunkter på den förhärskande nominalistisk-positivistiska vetenskapssynen inom ekonometrin. Några läsare har hört av sig och undrat om jag skulle kunna elaborera lite kring vad denna vetenskapsuppfattning står för och varför den utifrån mina kritisk-realistiska utgångspunkter är ohållbar.

Som vetenskapsteoretiker är det intressant att konstatera att många ekonomer och andra samhällsvetare appellerar till ett krav på att förklaringar för att kunna sägas vara vetenskapliga kräver att ett enskilt fall ska kunna ”föras tillbaka på en allmän lag”.  Som grundläggande princip åberopas ofta en allmän lag i form av ”om A så B” och att om man i de enskilda fallen kan påvisa att om ”A och B är förhanden så har man ’förklarat’ B”.

Denna positivistisk-induktiva vetenskapssyn är dock i grunden ohållbar. Låt mig förklara varför.

sdEnligt en positivistisk-induktivistisk syn på vetenskapen utgör den kunskap som vetenskapen besitter bevisad kunskap. Genom att börja med helt förutsättningslösa observationer kan en ”fördomsfri vetenskaplig observatör” formulera observationspåståenden utifrån vilka man kan härleda vetenskapliga teorier och lagar. Med hjälp av induktionsprincipen blir det möjligt att utifrån de singulära observationspåståendena formulera universella påståenden i form av lagar och teorier som refererar till förekomster av egenskaper som gäller alltid och överallt. Utifrån dessa lagar och teorier kan vetenskapen härleda olika konsekvenser med vars hjälp man kan förklara och förutsäga vad som sker. Genom logisk deduktion kan påståenden härledas ur andra påståenden. Forskningslogiken följer schemat observation – induktion – deduktion.

I mer okomplicerade fall måste vetenskapsmannen genomföra experiment för att kunna rättfärdiga de induktioner med vars hjälp han upprättar sina vetenskapliga teorier och lagar. Experiment innebär – som Francis Bacon så måleriskt uttryckte det – att lägga naturen på sträckbänk och tvinga den att svara på våra frågor. Med hjälp av en uppsättning utsagor som noggrant beskriver omständigheterna kring experimentet – initialvillkor – och de vetenskapliga lagarna kan vetenskapsmannen deducera påståenden som kan förklara eller förutsäga den undersökta företeelsen.

Den hypotetisk-deduktiva metoden för vetenskapens förklaringar och förutsägelser kan beskrivas i allmänna termer på följande vis:

1 Lagar och teorier

2 Initialvillkor

——————

3 Förklaringar och förutsägelser

Enligt en av den hypotetisk-deduktiva metodens främsta förespråkare – Carl Hempel – har alla vetenskapliga förklaringar denna form, som också kan uttryckas enligt schemat nedan:

Alla A är B                    Premiss 1

a är A                     Premiss 2

——————————

a är B                     Konklusion

Som exempel kan vi ta följande vardagsnära företeelse:

Vatten som värms upp till 100 grader Celsius kokar

Denna kastrull med vatten värms till 100 grader Celsius

———————————————————————–

Denna kastrull med vatten kokar

Problemet med den hypotetisk-deduktiva metoden ligger inte så mycket i premiss 2 eller konklusionen, utan i själva hypotesen, premiss 1. Det är denna som måste bevisas vara riktig och det är här induktionsförfarandet kommer in.

Den mest uppenbara svagheten i den hypotetisk-deduktiva metoden är själva induktionsprincipen. Det vanligaste rättfärdigandet av den ser ut som följer:

Induktionsprincipen fungerade vid tillfälle 1

Induktionsprincipen fungerade vid tillfälle 2

Induktionsprincipen fungerade vid tillfälle n

—————————————————–

Induktionsprincipen fungerar alltid

Detta är dock tveksamt eftersom ”beviset” använder induktion för att rättfärdiga induktion. Man kan inte använda singulära påståenden om induktionsprincipens giltighet för att härleda ett universellt påstående om induktionsprincipens giltighet.

Induktion är tänkt att spela två roller. Dels ska den göra det möjligt att generalisera och dels antas den utgöra bevis för slutsatsernas riktighet. Som induktionsproblemet visar klarar induktionen inte av båda dessa uppgifter. Den kan stärka sannolikheten av slutsatserna (under förutsättning att induktionsprincipen är riktig, vilket man dock inte kan bevisa utan att hamna i ett cirkelresonemang) men säger inte att dessa nödvändigtvis är sanna.

En annan ofta påpekad svaghet hos den hypotetisk-deduktiva metoden är att teorier alltid föregår observationspåståenden och experiment och att det därför är fel att hävda att vetenskapen börjar med observationer och experiment. Till detta kommer att observationspåståenden och experiment inte kan antas vara okomplicerat tillförlitliga och att de för sin giltighetsprövning kräver att man hänvisar till teori. Att även teorierna i sin tur kan vara otillförlitliga löser man inte främst med fler observationer och experiment, utan med andra och bättre teorier. Man kan också invända att induktionen inte på något sätt gör det möjligt för oss att få kunskap om verklighetens djupareliggande strukturer och mekanismer, utan endast om empiriska generaliseringar och lagbundenheter. Inom vetenskapen är det oftast så att förklaringen av händelser på en nivå står att finna i orsaker på en annan, djupare, nivå. Induktivismens syn på vetenskap leder till att vetenskapens huvuduppgift beskrivs som att ange hur något äger rum, medan andra vetenskapsteorier menar att vetenskapens kardinaluppgift måste vara att förklara varför det äger rum.

Till följd av de ovan anförda problemen har mer moderata empirister resonerat som att kommit att eftersom det i regel inte existerar något logiskt tillvägagångssätt för hur man upptäcker en lag eller teori startar man helt enkelt med lagar och teorier utifrån vilka man deducerar fram en rad påståenden som fungerar som förklaringar eller prediktioner. I stället för att undersöka hur man kommit fram till vetenskapens lagar och teorier försöker man att förklara vad en vetenskaplig förklaring och prediktion är, vilken roll teorier och modeller spelar i dessa, och hur man ska kunna värdera dem.

I den positivistiska (hypotetisk-deduktiva, deduktiv-nomologiska) förklarings-modellen avser man med förklaring en underordning eller härledning av specifika fenomen ur universella lagbundenheter. Att förklara en företeelse (explanandum) är detsamma som att deducera fram en beskrivning av den från en uppsättning premisser och universella lagar av typen ”Om A, så B” (explanans). Att förklara innebär helt enkelt att kunna inordna något under en bestämd lagmässighet och ansatsen kallas därför också ibland ”covering law-modellen”. Men teorierna ska inte användas till att förklara specifika enskilda fenomen utan för att förklara de universella lagbundenheterna som ingår i en hypotetisk-deduktiv förklaring. [Men det finns problem med denna uppfattning t. o. m. inom naturvetenskapen. Många av naturvetenskapens lagar säger egentligen inte något om vad saker gör, utan om vad de tenderar att göra. Detta beror till stor del på att lagarna beskriver olika delars beteende, snarare än hela fenomenet som sådant (utom möjligen i experimentsituationer). Och många av naturvetenskapens lagar gäller egentligen inte verkliga entiteter, utan bara fiktiva entiteter. Ofta är detta en följd av matematikens användande inom den enskilda vetenskapen och leder till att dess lagar bara kan exemplifieras i modeller (och inte i verkligheten).]  Den positivistiska förklaringsmodellen finns också i en svagare variant. Det är den probabilistiska förklaringsvarianten, enligt vilken att förklara i princip innebär att visa att sannolikheten för en händelse B är mycket stor om händelse A inträffar. I samhällsvetenskaper dominerar denna variant. Ur metodologisk synpunkt gör denna probabilistiska relativisering av den positivistiska förklaringsansatsen ingen större skillnad. 

En följd av att man accepterar den hypotetisk-deduktiva förklaringsmodellen är oftast att man också accepterar den s. k. symmetritesen. Enligt denna är den enda skillnaden mellan förutsägelse och förklaring att man i den förstnämnda antar explanansen vara känd och försöker göra en prediktion, medan man i den senare antar explanandum vara känd och försöker finna initialvillkor och lagar ur vilka det undersökta fenomenet kan härledas.

Ett problem med symmetritesen äer dock att den inte tar hänsyn till att orsaker kan förväxlas med korrelationer. Att storken dyker upp samtidigt med människobarnen utgör inte någon förklaring till barns tillkomst.

Symmetritesen tar inte heller hänsyn till att orsaker kan vara tillräckliga men inte nödvändiga. Att en cancersjuk individ blir överkörd gör inte cancern till dödsorsak. Cancern skulle kunna ha varit den riktiga förklaringen till individens död. Men även om vi t. o. m. skulle kunna konstruera en medicinsk lag – i överensstämmelse med den deduktivistiska modellen – som säger att individer med den aktuella typen av cancer kommer att dö av denna cancer, förklarar likväl inte lagen denna individs död. Därför är tesen helt enkelt inte riktig.

Att finna ett mönster är inte detsamma som att förklara något. Att på frågan varför bussen är försenad få till svar att den brukar vara det, utgör inte någon acceptabel förklaring. Ontologi och naturlig nödvändighet måste ingå i ett relevant svar, åtminstone om man i en förklaring söker något mer än ”constant conjunctions of events”.

Den ursprungliga tanken bakom den positivistiska förklaringsmodellen var att den skulle ge ett fullständigt klargörande av vad en förklaring är och visa att en förklaring som inte uppfyllde dess krav i själva verket var en pseudoförklaring, ge en metod för testning av förklaringar, och visa att förklaringar i enlighet med modellen var vetenskapens mål. Man kan uppenbarligen på goda grunder ifrågasätta alla anspråken.

En viktig anledning till att denna modell fått sånt genomslag i vetenskapen är att den gav sken av att kunna förklara saker utan att behöva använda ”metafysiska” kausalbegrepp. Många vetenskapsmän ser kausalitet som ett problematiskt begrepp, som man helst ska undvika att använda. Det ska räcka med enkla, observerbara storheter. Problemet är bara att angivandet av dessa storheter och deras eventuella korrelationer inte förklarar något alls. Att fackföreningsrepresentanter ofta uppträder i grå kavajer och arbetsgivarrepresentanter i kritstrecksrandiga kostymer förklarar inte varför ungdomsarbetslösheten i Sverige är så hög idag. Vad som saknas i dessa ”förklaringar” är den nödvändiga adekvans, relevans och det kausala djup varförutan vetenskap riskerar att bli tom science fiction och modellek för lekens egen skull.

Många samhällsvetare tycks vara övertygade om att forskning för att räknas som vetenskap måste tillämpa någon variant av hypotetisk-deduktiv metod. Ur verklighetens komplicerade vimmel av fakta och händelser ska man vaska fram några gemensamma lagbundna korrelationer som kan fungera som förklaringar. Inom delar av samhällsvetenskapen har denna strävan att kunna reducera förklaringar av de samhälleliga fenomen till några få generella principer eller lagar varit en viktig drivkraft. Med hjälp av några få generella antaganden vill man förklara vad hela det makrofenomen som vi kallar ett samhälle utgör. Tyvärr ger man inga riktigt hållbara argument för varför det faktum att en teori kan förklara olika fenomen på ett enhetligt sätt skulle vara ett avgörande skäl för att acceptera eller föredra den. Enhetlighet och adekvans är inte liktydigt.

Advertisements

On the history of potential outcome models (wonkish)

31 July, 2013 at 10:24 | Posted in Statistics & Econometrics | 1 Comment

1-s2.0-S1053811911012997-gr2

My understanding of the history is as follows. The potential outcome framework became popular in the econometrics literature on causality around 1990. See Heckman (1990, American Economic Review, Papers and Proceedings, “Varieties of Selection Bias,” 313-318, and Manski (1990 American Economic Review, Papers and Proceedings, “Nonparametric Bounds on Treatment Effects,” 319-323.) Both those papers read very differently from the classic paper in the econometric literature on program evaluation and causality, published five years earlier, (Heckman, and Robb, 1985, “Alternative Methods for Evaluating the Impact of Interventions,” in Heckman and Singer (eds.), Longitudinal Analysis of Labor Market Data, Cambridge, Cambridge University Press) which did not use the potential outcome framework. When the potential outcome framework became popular, there was little credit given to Rubin’s work, but there were also no references to Neyman (1923), Roy (1951) or Quandt (1958) in the Heckman and Manski papers. It appears that at the time the notational shift was not viewed as sufficiently important to attribute to anyone.

Heckman’s later work has attempted to place the potential outcome framework in a historical perspective. Here are two quotes somewhat clarifying his views on the relation to Rubin’s work. In 1996 he wrote:

“The “Rubin Model” is a version of the widely used econometric switching regression model (Maddalla 1983; Quandt, 1958, 1972, 1988). The Rubin model shares many features in common with the Roy model (Heckman and Honore, 1990, Roy 1951) and the model of competing risks (Cox, 1962). It is a tribute to the value of the framework that it has been independently invented by different disciplines and subfields within statistics at different times.” p. 459
(Heckman, (1996) Comment on “identification of causal effects using instrumental variables”,
journal of the american statistical association.)

More recently, in 2008, he wrote:

“4.3 The Econometric Model vs. the Neyman-Rubin Model
Many statisticians and social scientists use a model of counterfactuals and causality attributed to Donald Rubin by Paul Holland (1986). The framework was developed in statistics by Neyman (1923), Cox (1958) and others. Parallel frameworks were independently developed in psychometrics (Thurstone, 1927) and economics (Haavelmo, 1943; Quandt, 1958, 1972; Roy, 1951). The statistical treatment effect literature originates in the statistical literature on the design of experiments. It draws on hypothetical experiments to define causality and thereby creates the impression in the minds of many of its users that random assignment is the most convincing way to identify causal models.” p. 19
(“Econometric Causality”, Heckman, International economic review, 2008, 1-27.)

(I include the last sentence of the quote mainly because it is an interesting thought, although it is not really germane to the current discussion.)

In the end I agree with Andrew’s blog post that the attribution to Roy or Quandt is tenuous, and I would caution the readers of this blog not to interpret Heckman’s views on this as reflecting a consensus in the economics profession. The Haavelmo reference is interesting. Haavelmo is certainly thinking of potential outcomes in his 1943 paper, and I view Haavelmo’s paper (and a related paper by Tinbergen) as the closest to a precursor of the Rubin Causal Model in economics. However, Haavelmo’s notation did not catch on, and soon econometricians wrote their models in terms of realized, not potential, outcomes, not returning to the explicit potential outcome notation till 1990.

Relatedly, I recently met Paul Holland at a conference, and I asked him about the reasons for attaching the label “Rubin Causal Model” to the potential outcome framework in 1986. (now you often see phrase, “called the Rubin Causal Model by Paul Holland”). Paul responded that he felt that Don’s work on this went so far beyond what was done before by, among others, Neyman (1923), by putting the potential outcomes front and center in a discussion on causality, as in the 1974 paper, that his contributions merited this label. Personally I agree with that.

Guido Imbens

Spirited debate on Fox News? I’ll be dipped!

30 July, 2013 at 22:26 | Posted in Politics & Society | Comments Off on Spirited debate on Fox News? I’ll be dipped!


(h/t barnilsson)

Some Other Time

29 July, 2013 at 10:37 | Posted in Varia | Comments Off on Some Other Time

 

Why average assumptions on average are wrong in finance and economics

28 July, 2013 at 12:40 | Posted in Statistics & Econometrics | 1 Comment

Notes7
 
In The Flaw of Averages Sam Savage explains more on why average assumptions on average are wrong …

Spurious statistical significance – when science gets it all wrong

28 July, 2013 at 11:20 | Posted in Statistics & Econometrics | 2 Comments

A non-trivial part of teaching statistics is made up of teaching students to perform significance testing. A problem I have noticed repeatedly over the years, however, is that no matter how careful you try to be in explicating what the probabilities generated by these statistical tests – p values – really are, still most students misinterpret them. And a lot of researchers obviously also fall pray to the same mistakes:

Are women three times more likely to wear red or pink when they are most fertile? No, probably not. But here’s how hardworking researchers, prestigious scientific journals, and gullible journalists have been fooled into believing so.

The paper I’ll be talking about appeared online this month in Psychological Science, the flagship journal of the Association for Psychological Science, which represents the serious, research-focused (as opposed to therapeutic) end of the psychology profession.

images-11“Women Are More Likely to Wear Red or Pink at Peak Fertility,” by Alec Beall and Jessica Tracy, is based on two samples: a self-selected sample of 100 women from the Internet, and 24 undergraduates at the University of British Columbia. Here’s the claim: “Building on evidence that men are sexually attracted to women wearing or surrounded by red, we tested whether women show a behavioral tendency toward wearing reddish clothing when at peak fertility. … Women at high conception risk were more than three times more likely to wear a red or pink shirt than were women at low conception risk. … Our results thus suggest that red and pink adornment in women is reliably associated with fertility and that female ovulation, long assumed to be hidden, is associated with a salient visual cue.”

Pretty exciting, huh? It’s (literally) sexy as well as being statistically significant. And the difference is by a factor of three—that seems like a big deal.

Really, though, this paper provides essentially no evidence about the researchers’ hypotheses …

The way these studies fool people is that they are reduced to sound bites: Fertile women are three times more likely to wear red! But when you look more closely, you see that there were many, many possible comparisons in the study that could have been reported, with each of these having a plausible-sounding scientific explanation had it appeared as statistically significant in the data.

The standard in research practice is to report a result as “statistically significant” if its p-value is less than 0.05; that is, if there is less than a 1-in-20 chance that the observed pattern in the data would have occurred if there were really nothing going on in the population. But of course if you are running 20 or more comparisons (perhaps implicitly, via choices involved in including or excluding data, setting thresholds, and so on), it is not a surprise at all if some of them happen to reach this threshold.

The headline result, that women were three times as likely to be wearing red or pink during peak fertility, occurred in two different samples, which looks impressive. But it’s not really impressive at all! Rather, it’s exactly the sort of thing you should expect to see if you have a small data set and virtually unlimited freedom to play around with the data, and with the additional selection effect that you submit your results to the journal only if you see some catchy pattern. …

Statistics textbooks do warn against multiple comparisons, but there is a tendency for researchers to consider any given comparison alone without considering it as one of an ensemble of potentially relevant responses to a research question. And then it is natural for sympathetic journal editors to publish a striking result without getting hung up on what might be viewed as nitpicking technicalities. Each person in this research chain is making a decision that seems scientifically reasonable, but the result is a sort of machine for producing and publicizing random patterns.

There’s a larger statistical point to be made here, which is that as long as studies are conducted as fishing expeditions, with a willingness to look hard for patterns and report any comparisons that happen to be statistically significant, we will see lots of dramatic claims based on data patterns that don’t represent anything real in the general population. Again, this fishing can be done implicitly, without the researchers even realizing that they are making a series of choices enabling them to over-interpret patterns in their data.

Andrew Gelman

Indeed. If anything, this underlines how important it is not to equate science with statistical calculation. All science entail human judgement, and using statistical models doesn’t relieve us of that necessity. Working with misspecified models, the scientific value of significance testing is actually zero –  even though you’re making valid statistical inferences! Statistical models and concomitant significance tests are no substitutes for doing real science. Or as a noted German philosopher once famously wrote:

There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.

Statistical significance doesn’t say that something is important or true. Since there already are far better and more relevant testing that can be done (see e. g. here and  here)- it is high time to consider what should be the proper function of what has now really become a statistical fetish. Given that it anyway is very unlikely than any population parameter is exactly zero, and that contrary to assumption most samples in social science and economics are not random or having the right distributional shape – why continue to press students and researchers to do null hypothesis significance testing, testing that relies on weird backward logic that students and researchers usually don’t understand?

Added 31/7: Beall and Tracy has a commnent on the critique here.

What’s the use of economics?

28 July, 2013 at 09:23 | Posted in Economics | 1 Comment

The simple question that was raised during a recent conference … was to what extent has – or should – the teaching of economics be modified in the light of the current economic crisis? The simple answer is that the economics profession is unlikely to change. Why would economists be willing to give up much of their human capital, painstakingly nurtured for over two centuries? For macroeconomists in particular, the reaction has been to suggest that modifications of existing models to take account of ‘frictions’ or ‘imperfections’ will be enough to account for the current evolution of the world economy. The idea is that once students have understood the basics, they can be introduced to these modifications.

However, other economists such as myself feel that we have finally reached the turning point in economics where we have to radically change the way we conceive of and model the economy. The crisis is an opportune occasion to carefully investigate new approaches. Paul Seabright hit the nail on the head; economists tend to inaccurately portray their work as a steady and relentless improvement of their models whereas, actually, economists tend to chase an empirical reality that is changing just as fast as their modelling. I would go further; rather than making steady progress towards explaining economic phenomena professional economists have been locked into a narrow vision of the economy. We constantly make more and more sophisticated models within that vision until, as Bob Solow put it, “the uninitiated peasant is left wondering what planet he or she is on” (Solow 2006) …

Entomologists (those who study insects) of old with more simple models came to the conclusion that bumble bees should not be able to fly. Their reaction was to later rethink their models in light of irrefutable evidence. Yet, the economist’s instinct is to attempt to modify reality in order to fit a model that has been built on longstanding theory. Unfortunately, that very theory is itself based on shaky foundations …

Every student in economics is faced with the model of the isolated optimising individual who makes his choices within the constraints imposed by the market. Somehow, the axioms of rationality imposed on this individual are not very convincing, particularly to first time students. But the student is told that the aim of the exercise is to show that there is an equilibrium, there can be prices that will clear all markets simultaneously. And, furthermore, the student is taught that such an equilibrium has desirable welfare properties. Importantly, the student is told that since the 1970s it has been known that whilst such a system of equilibrium prices may exist, we cannot show that the economy would ever reach an equilibrium nor that such an equilibrium is unique.

The student then moves on to macroeconomics and is told that the aggregate economy or market behaves just like the average individual she has just studied. She is not told that these general models in fact poorly reflect reality. For the macroeconomist, this is a boon since he can now analyse the aggregate allocations in an economy as though they were the result of the rational choices made by one individual. The student may find this even more difficult to swallow when she is aware that peoples’ preferences, choices and forecasts are often influenced by those of the other participants in the economy. Students take a long time to accept the idea that the economy’s choices can be assimilated to those of one individual.

Alan Kirman What’s the use of economics?

Simply the best – scientific realism and inference to the best explanation

27 July, 2013 at 15:42 | Posted in Theory of Science & Methodology | 1 Comment

In a time when scientific relativism is expanding, it is important to keep up the claim for not reducing science to a pure discursive level. We have to maintain the Enlightenment tradition of thinking of reality as principally independent of our views of it and of the main task of science as studying the structure of this reality. Perhaps the most important contribution a researcher can make is reveal what this reality that is the object of science actually looks like.

Science is made possible by the fact that there are structures that are durable and are independent of our knowledge or beliefs about them. There exists a reality beyond our theories and concepts of it. It is this independent reality that our theories in some way deal with. Contrary to positivism, I would as a critical realist argue that the main task of science is not to detect event-regularities between observed facts. Rather, that task must be conceived as identifying the underlying structure and forces that produce the observed events.

In a truly wonderful essay – chapter three of Error and Inference (Cambridge University Press, 2010, eds. Deborah Mayo and Aris Spanos) – Alan Musgrave gives strong arguments why scientific realism and inference to the best explanation are the best alternatives for explaining what’s going on in the world we live in:

For realists, the name of the scientific game is explaining phenomena, not just saving them. Realists typically invoke ‘inference to the best explanation’ or IBE …

IBE is a pattern of argument that is ubiquitous in science and in everyday life as well. van Fraassen has a homely example:
“I hear scratching in the wall, the patter of little feet at midnight, my cheese disappears – and I infer that a mouse has come to live with me. Not merely that these apparent signs of mousely presence will continue, not merely that all the observable phenomena will be as if there is a mouse, but that there really is a mouse.” (1980: 19-20)
Here, the mouse hypothesis is supposed to be the best explanation of the phenomena, the scratching in the wall, the patter of little feet, and the disappearing cheese.
alan musgraveWhat exactly is the inference in IBE, what are the premises, and what the conclusion? van Fraassen says “I infer that a mouse has come to live with me”. This suggests that the conclusion is “A mouse has come to live with me” and that the premises are statements about the scratching in the wall, etc. Generally, the premises are the things to be explained (the explanandum) and the conclusion is the thing that does the explaining (the explanans). But this suggestion is odd. Explanations are many and various, and it will be impossible to extract any general pattern of inference taking us from explanandum to explanans. Moreover, it is clear that inferences of this kind cannot be deductively valid ones, in which the truth of the premises guarantees the truth of the conclusion. For the conclusion, the explanans, goes beyond the premises, the explanandum. In the standard deductive model of explanation, we infer the explanandum from the explanans, not the other way around – we do not deduce the explanatory hypothesis from the phenomena, rather we deduce the phenomena from the explanatory hypothesis …

The intellectual ancestor of IBE is Peirce’s abduction, and here we find a different pattern:

The surprising fact, C, is observed.
But if A were true, C would be a matter of course.
Hence, … A is true.
(C. S. Peirce, 1931-58, Vol. 5: 189)

Here the second premise is a fancy way of saying “A explains C”. Notice that the explanatory hypothesis A figures in this second premise as well as in the conclusion. The argument as a whole does not generate the explanans out of the explanandum. Rather, it seeks to justify the explanatory hypothesis …

Abduction is deductively invalid … IBE attempts to improve upon abduction by requiring that the explanation is the best explanation that we have. It goes like this:

F is a fact.
Hypothesis H explains F.
No available competing hypothesis explains F as well as H does.
Therefore, H is true
(William Lycan, 1985: 138)

This is better than abduction, but not much better. It is also deductively invalid …

There is a way to rescue abduction and IBE. We can validate them without adding missing premises that are obviously false, so that we merely trade obvious invalidity for equally obvious unsoundness. Peirce provided the clue to this. Peirce’s original abductive scheme was not quite what we have considered so far. Peirce’s original scheme went like this:

The surprising fact, C, is observed.
But if A were true, C would be a matter of course.
Hence, there is reason to suspect that A is true.
(C. S. Peirce, 1931-58, Vol. 5: 189)

This is obviously invalid, but to repair it we need the missing premise “There is reason to suspect that any explanation of a surprising fact is true”. This missing premise is, I suggest, true. After all, the epistemic modifier “There is reason to suspect that …” weakens the claims considerably. In particular, “There is reason to suspect that A is true” can be true even though A is false. If the missing premise is true, then instances of the abductive scheme may be both deductively valid and sound.

IBE can be rescued in a similar way. I even suggest a stronger epistemic modifier, not “There is reason to suspect that …” but rather “There is reason to believe (tentatively) that …” or, equivalently, “It is reasonable to believe (tentatively) that …” What results, with the missing premise spelled out, is:

It is reasonable to believe that the best available explanation of any fact is true.
F is a fact.
Hypothesis H explains F.
No available competing hypothesis explains F as well as H does.
Therefore, it is reasonable to believe that H is true.

This scheme is valid and instances of it might well be sound. Inferences of this kind are employed in the common affairs of life, in detective stories, and in the sciences.

Of course, to establish that any such inference is sound, the ‘explanationist’ owes us an account of when a hypothesis explains a fact, and of when one hypothesis explains a fact better than another hypothesis does. If one hypothesis yields only a circular explanation and another does not, the latter is better than the former. If one hypothesis has been tested and refuted and another has not, the latter is better than the former. These are controversial issues, to which I shall return. But they are not the most controversial issue – that concerns the major premise. Most philosophers think that the scheme is unsound because this major premise is false, whatever account we can give of explanation and of when one explanation is better than another. So let me assume that the explanationist can deliver on the promises just mentioned, and focus on this major objection.

People object that the best available explanation might be false. Quite so – and so what? It goes without saying that any explanation might be false, in the sense that it is not necessarily true. It is absurd to suppose that the only things we can reasonably believe are necessary truths.

What if the best explanation not only might be false, but actually is false. Can it ever be reasonable to believe a falsehood? Of course it can. Suppose van Fraassen’s mouse explanation is false, that a mouse is not responsible for the scratching, the patter of little feet, and the disappearing cheese. Still, it is reasonable to believe it, given that it is our best explanation of those phenomena. Of course, if we find out that the mouse explanation is false, it is no longer reasonable to believe it. But what we find out is that what we believed was wrong, not that it was wrong or unreasonable for us to have believed it.

People object that being the best available explanation of a fact does not prove something to be true or even probable. Quite so – and again, so what? The explanationist principle – “It is reasonable to believe that the best available explanation of any fact is true” – means that it is reasonable to believe or think true things that have not been shown to be true or probable, more likely true than not.

Why economics needs economic history

27 July, 2013 at 14:15 | Posted in Economics | Comments Off on Why economics needs economic history

reality-checkKnowledge of economic and financial history is crucial in thinking about the economy in several ways.
Most obviously, it forces students to recognise that major discontinuities in economic performance and economic policy regimes have occurred many times in the past, and may therefore occur again in the future. These discontinuities have often coincided with economic and financial crises, which therefore cannot be assumed away as theoretically impossible. A historical training would immunise students from the complacency that characterised the “Great Moderation”. Zoom out, and that swan may not seem so black after all.

A second, related point is that economic history teaches students the importance of context …

Third, economic history is an unapologetically empirical field, exclusively dedicated to understanding the real world.
Doing economic history forces students to add to the technical rigor of their programs an extra dimension of rigor: asking whether their explanations for historical events actually fit the facts or not. Which emphatically does not mean cherry-picking selected facts that fit your thesis and ignoring all the ones that don’t: the world is a complicated place, and economists should be trained to recognise this. An exposure to economic history leads to an empirical frame of mind, and a willingness to admit that one’s particular theoretical framework may not always work in explaining the real world. These are essential mental habits for young economists wishing to apply their skills in the work environment, and, one hopes, in academia as well.

Fourth, economic history is a rich source of informal theorising about the real world, which can help motivate more formal theoretical work later on …

Fifth, even once the current economic and financial crisis has passed, the major long run challenges facing the world will still remain …
Apart from issues such as the rise of Asia and the relative decline of the West, other long run issues that would benefit from being framed in a long-term perspective include global warming, the future of globalisation, and the question of how rapidly we can expect the technological frontier to advance in the decades ahead.

Sixth, economic theory itself has been emphasising – for well over 20 years now – that path dependence is ubiquitous …

Finally, and perhaps most importantly from the perspective of an undergraduate economics instructor, economic history is a great way of convincing undergraduates that the theory they are learning in their micro and macro classes is useful in helping them make sense of the real world.

Far from being seen as a ‘soft’ alternative to theory, economic history should be seen as an essential pedagogical complement. There is nothing as satisfying as seeing undergraduates realise that a little bit of simple theory can help them understand complicated real world phenomena. Think of  … the Domar thesis, referred to in Temin (2013), which is a great way to talk to students about what drives diminishing returns to labour. Economic history is replete with such opportunities for instructors trying to motivate their students. Economic history is replete with such opportunities for instructors trying to motivate their students.

Kevin O’Rourke

[h/t Jan Milch]

Why hasn’t the crisis discredited neoclassical economics more?

26 July, 2013 at 22:32 | Posted in Economics | 3 Comments

There are probably many answers to the question. I suggested before that the best way to look at it is from a sociological standpoint. The same people hold the same positions at the key ‘respectable’ universities, go to the same ‘relevant’ meetings, and award the same ‘important’ prizes. And research does build on previous research. Let alone that the economics profession, like the others, is there to protect and reproduce the status quo.

At any rate, in his new book Philip Mirowski, from Notre Dame, and a member of Institute for New Economic Thinking (INET; which has funded I should say several heterodox authors) dedicates, in part, his first chapter to the topic. He says about the INET meetings, which were supposed to display some of the changes in the profession after the crisis:

“[…] the first INET meeting at Cambridge University in 2010 bore some small promise—for instance, when protestors disrupted the IMF platitudes of Dominique Strauss-Kahn in Kings great hall, or when Lord Adair Turner bravely suggested we needed a much smaller financial sector.weather 007But the sequel turned out to be a profoundly more unnerving and chilly affair, and not just due to the caliginous climate. The nightmare scenario began with a parade of figures whom one could not in good conscience admit to anyone’s definition of “New Economic Thinking”: Ken Rogoff, Larry Summers, Barry Eichengreen, Niall Ferguson and Gordon Brown … The range of economic positions proved much less varied than at the first meeting, and couldn’t help notice that the agenda seemed more pitched toward capturing the attention of journalists and bloggers [oh my, I’m included in this one], and those more interested in getting to see more star power up close than sampling complex thinking outside the box. It bespoke an unhealthy obsession with Guaranteed Legitimacy and Righteous Sound Thinking.”

I always thought naïve to think that the crisis would lead to the demise of neoclassical economics. In fact, in the US it was the Great Depression and the development of a certain type of Keynesianism (the Neoclassical Synthesis one) that led to the domination of neoclassical economics (before that the profession was more eclectic and if anything dominated, in the US, by institutionalists). But I had some hopes for INET to open dialogue with less crazy (sold out?) within the mainstream. The fact that Mirowski calls the second meeting a nightmare scenario does not bode well for the future of the profession.

Naked Keynesianism

What has Keynes got to do with New Keynesian Macroeconomics? Nothing!

24 July, 2013 at 17:39 | Posted in Economics | 1 Comment

Paul Krugman has a post on his blog discussing “New Keynesian” macroeconomics and the definition of neoclassical economics:

So, what is neoclassical economics? … I think we mean in practice economics based on maximization-with-equilibrium. We imagine an economy consisting of rational, self-interested players, and suppose that economic outcomes reflect a situation in which each player is doing the best he, she, or it can given the actions of all the other players …

Some economists really really believe that life is like this — and they have a significant impact on our discourse. But the rest of us are well aware that this is nothing but a metaphor; nonetheless, most of what I and many others do is sorta-kinda neoclassical because it takes the maximization-and-equilibrium world as a starting point or baseline, which is then modified — but not too much — in the direction of realism.

This is, not to put too fine a point on it, very much true of Keynesian economics as practiced … New Keynesian models are intertemporal maximization modified with sticky prices and a few other deviations …

Why do things this way? Simplicity and clarity. In the real world, people are fairly rational and more or less self-interested; the qualifiers are complicated to model, so it makes sense to see what you can learn by dropping them. And dynamics are hard, whereas looking at the presumed end state of a dynamic process — an equilibrium — may tell you much of what you want to know.

Being myself sorta-kinda Keynesian I  find this analysis utterly unconvincing. Why? Let me try to explain.

Macroeconomic models may be an informative tool for research. But if practitioners of “New Keynesian” macroeconomics do not investigate and make an effort of providing a justification for the credibility of the assumptions on which they erect their building, it will not fulfill its tasks. There is a gap between its aspirations and its accomplishments, and without more supportive evidence to substantiate its claims, critics will continue to consider its ultimate argument as a mixture of rather unhelpful metaphors and metaphysics. Maintaining that economics is a science in the “true knowledge” business, I remain a skeptic of the pretences and aspirations of “New Keynesian” macroeconomics. So far, I cannot really see that it has yielded very much in terms of realistic and relevant economic knowledge.

The marginal return on its ever higher technical sophistication in no way makes up for the lack of serious under-labouring of its deeper philosophical and methodological foundations. The rather one-sided emphasis of usefulness and its concomitant instrumentalist justification cannot hide that “New Keynesians” cannot give supportive evidence for their considering it fruitful to analyze macroeconomic structures and events as the aggregated result of optimizing representative actors. After having analyzed some of its ontological and epistemological foundations, I cannot but conclude that “New Keynesian” macroeconomics on the whole has not delivered anything else than “as if” unreal and irrelevant models.

If we are going to be able to show that the mechanisms or causes that we isolate and handle in our microfunded macromodels are stable in the sense that they do not change when we “export” them to our “target systems”, they do only hold under ceteris paribus conditions and are a fortiori of limited value to our understanding, explanations or predictions of real economic systems. Or as the always eminently quotable Keynes wrote in Treatise on Probability(1921):

The kind of fundamental assumption about the character of material laws, on which scientists appear commonly to act, seems to me to be [that] the system of the material universe must consist of bodies … such that each of them exercises its own separate, independent, and invariable effect, a change of the total state being compounded of a number of separate changes each of which is solely due to a separate portion of the preceding state … Yet there might well be quite different laws for wholes of different degrees of complexity, and laws of connection between complexes which could not be stated in terms of laws connecting individual parts … If different wholes were subject to different laws qua wholes and not simply on account of and in proportion to the differences of their parts, knowledge of a part could not lead, it would seem, even to presumptive or probable knowledge as to its association with other parts … These considerations do not show us a way by which we can justify induction … /427 No one supposes that a good induction can be arrived at merely by counting cases. The business of strengthening the argument chiefly consists in determining whether the alleged association is stable, when accompanying conditions are varied … /468 In my judgment, the practical usefulness of those modes of inference … on which the boasted knowledge of modern science depends, can only exist … if the universe of phenomena does in fact present those peculiar characteristics of atomism and limited variety which appears more and more clearly as the ultimate result to which material science is tending.

Science should help us penetrate to “the true process of causation lying behind current events” and disclose “the causal forces behind the apparent facts” [Keynes 1971-89 vol XVII:427]. We should look out for causal relations. But models can never be more than a starting point in that endeavour. There is always the possibility that there are other variables – of vital importance and although perhaps unobservable and non-additive not necessarily epistemologically inaccessible – that were not considered for the model.

This is a more fundamental and radical problem than the celebrated “Lucas critique” have suggested. This is not the question if deep parameters, absent on the macro-level, exist in “tastes” and “technology” on the micro-level. It goes deeper. Real world social systems are not governed by stable causal mechanisms or capacities. It is the criticism that Keynes first launched against the “atomistic fallacy” already in the 1920s:

The atomic hypothesis which has worked so splendidly in Physics breaks down in Psychics. We are faced at every turn with the problems of Organic Unity, of Discreteness, of Discontinuity – the whole is not equal to the sum of the parts, comparisons of quantity fails us, small changes produce large effects, the assumptions of a uniform and homogeneous continuum are not satisfied. Thus the results of Mathematical Psychics turn out to be derivative, not fundamental, indexes, not measurements, first approximations at the best; and fallible indexes, dubious approximations at that, with much doubt added as to what, if anything, they are indexes or approximations of.

The kinds of laws and relations that economics has established, are laws and relations about entities in models that presuppose causal mechanisms being atomistic and additive. When causal mechanisms operate in real world social target systems they only do it in ever-changing and unstable combinations where the whole is more than a mechanical sum of parts. If economic regularities obtain they do it (as a rule) only because we engineered them for that purpose. Outside man-made “nomological machines” they are rare, or even non-existant. Unfortunately that also makes most of the achievements of econometrics – as most of contemporary endeavours of economic theoretical modeling – rather useless.

Keynes basically argued that it was inadmissible to project history on the future. Consequently an economic policy cannot presuppose that what has worked before, will continue to do so in the future. That macroeconomic models could get hold of correlations between different “variables” was not enough. If they could not get at the causal structure that generated the data, they were not really “identified”. Dynamic stochastic general euilibrium (DSGE) macroeconomists – including “New Keynesians” – has drawn the conclusion that the problem with unstable relations is to construct models with clear microfoundations where forward-looking optimizing individuals and robust, deep, behavioural parameters are seen to be stable even to changes in economic policies. As yours truly has argued in a couple of post (e. g. here and here), this, however, is a dead end.

So here we are getting close to the heart of darkness in “New Keynesian” macroeconomics. Where “New Keynesian” economists think that they can rigorously deduce the aggregate effects of (representative) actors with their reductionist microfoundational methodology, they have to put a blind eye on the emergent properties that characterize all open social systems – including the economic system. The interaction between animal spirits, trust, confidence, institutions etc., cannot be deduced or reduced to a question answerable on the idividual level. Macroeconomic structures and phenomena have to be analyzed also on their own terms. And although one may easily agree with Krugman’s emphasis on simple models, the simplifications used may have to be simplifications adequate for macroeconomics and not those adequate for microeconomics.

“New Keynesian” macromodels describe imaginary worlds using a combination of formal sign systems such as mathematics and ordinary language. The descriptions made are extremely thin and to a large degree disconnected to the specific contexts of the targeted system than one (usually) wants to (partially) represent. This is not by chance. These closed formalistic-mathematical theories and models are constructed for the purpose of being able to deliver purportedly rigorous deductions that may somehow by be exportable to the target system. By analyzing a few causal factors in their “macroeconomic laboratories” they hope they can perform “thought experiments” and observe how these factors operate on their own and without impediments or confounders.

Unfortunately, this is not so. The reason for this is that economic causes never act in a socio-economic vacuum. Causes have to be set in a contextual structure to be able to operate. This structure has to take some form or other, but instead of incorporating structures that are true to the target system, the settings made in these macroeconomic models are rather based on formalistic mathematical tractability. In the models they appear as unrealistic assumptions, usually playing a decisive role in getting the deductive machinery deliver “precise” and “rigorous” results. This, of course, makes exporting to real world target systems problematic, since these models – as part of a deductivist covering-law tradition in economics – are thought to deliver general and far-reaching conclusions that are externally valid. But how can we be sure the lessons learned in these theories and models have external validity, when based on highly specific unrealistic assumptions? As a rule, the more specific and concrete the structures, the less generalizable the results. Admitting that we in principle can move from (partial) falsehoods in theories and models to truth in real world target systems does not take us very far, unless a thorough explication of the relation between theory, model and the real world target system is made. If models assume representative actors, rational expectations, market clearing and equilibrium, and we know that real people and markets cannot be expected to obey these assumptions, the warrants for supposing that conclusions or hypothesis of causally relevant mechanisms or regularities can be bridged, are obviously non-justifiable. To have a deductive warrant for things happening in a closed model is no guarantee for them being preserved when applied to an open real world target system.

In microeconomics we know that aggregation really presupposes homothetic an identical preferences, something that almost never exist in real economies. The results given by these assumptions are therefore not robust and do not capture the underlying mechanisms at work in any real economy. And models that are critically based on particular and odd assumptions – and are neither robust nor congruent to real world economies – are of questionable value.

Even if economies naturally presuppose individuals, it does not follow that we can infer or explain macroeconomic phenomena solely from knowledge of these individuals. Macroeconomics is to a large extent emergent and cannot be reduced to a simple summation of micro-phenomena. Moreover, as we have already argued, even these microfoundations aren’t immutable. The “deep parameters” of  “New Keynesian” DSGE models– “tastes” and “technology” – are not really the bedrock of constancy that they believe (pretend) them to be.

So I cannot concur with Krugman – and other sorta-kinda “New Keynesians” – when they try to reduce Keynesian economics to “intertemporal maximization modified with sticky prices and a few other deviations”. “New Keynesian” macroeconomics is a gross misnomer, since it has nothing to do with the fundamentals of Keynes’s economic thoughts. As John Quiggin so aptly writes:

If there is one thing that distinguished Keynes’ economic analysis from that of his predecessors, it was his rejection of the idea of a unique full employment equilibrium to which a market economy will automatically return when it experiences a shock. Keynes argued that an economy could shift from a full-employment equilibrium to a persistent slump as the result of the interaction between objective macroeconomic variables and the subjective ‘animal spirits’ of investors and other decision-makers. It  is this perspective that has been lost in the absorption of New Keynesian macro into the DSGE framework.

A critical realist re-thinking of Das Adam Smith Problem

23 July, 2013 at 15:58 | Posted in Economics | Comments Off on A critical realist re-thinking of Das Adam Smith Problem

Talk of a ‘natural harmony’ in human affairs, of a ‘concord’ produced by the now-celebrated ‘invisible hand’, runs like a leitmotif through Adam Smith’s work. A key question in Smith-scholarship is then: how does Smith suppose this harmony to be constituted? According to the Problem-theorists, Smith claims in Wealth of Nations (WN) that individuals motivated by self-interest, and in virtue of that motivation alone, are able to co-ordinate their activities, whereas in Theory of Moral Sentiments (TMS) he claims that benevolence alone is supposed to do the job. Of course, if Smith had claimed these things, he would stand guilty (of inconsistency) as charged. But these assertions play no role in Smith’s social theory; the Problem, for whatever reason(s), is a post-Smith fabrication.

images-10Smith did claim that self-interest is endemic to human behaviour. But this kind of self-interest — and this kind of interest pervades TMS just as much as WN — is more a matter of perspective than some crude (economic) impulse to self-gratification: of course, as human actor, I have to see the act as mine and so, in some sense, as in my interest, even when I act ‘benevolently’.

As for the other kind of self-interest, or ‘self-love’. Yes, this kind of act — behaviour motivated by self-interest — dominates the discourse of WN, but not because Smith (sometime between TMS and WN) has changed his opinion on how people are motivated. It is rather that WN (unlike TMS ) is not concerned with situations in which a ‘benevolent’ disposition is to be expected: that is why benevolence is not much discussed. There is no inconsistency … it is all a matter of the ‘spheres of intimacy’.

But, in any case, Smith does not claim in WN (or in anywhere else for that matter) that people are able to co-ordinate their activities because they are motivated by self-interest; for Smith, motivation of any kind does not enable or capacitate anything at all. And Smith has not changed his opinion sometime between TMS and WN as to how people are capacitated to act, as to the competencies that they draw on, whatever the motivation. In TMS Smith offers ‘sympathy’ or ‘fellow-feeling’ as that core capacity or competence, and there is no reason in WN to suggest that he has changed his mind. Whether we act out of concern for self or for other, we are only able to act as we do because we are sympathisers.

Apropos Das Adam Smith Problem: For Smith to say that the human actor sympathises does not mean that the Smith of TMS postulates a naturally altruistic, rather than a naturally egoistic, actor — a view that he is then supposed to have reversed in the Wealth of Nations. Of course it is true (to paraphrase Smith himself) that we should not expect our dinner from the benevolence of the (commercially oriented) butcher and baker. On the other hand, it would be surprising (and worrying, for all sorts of reasons) if the dependent child did not expect his dinner from the benevolence of his kith and kin (who, for some people at least, are also commercial butchers and bakers). Smith recognises that, depending on circumstance, we are capable of both behavioural dispositions. But Smith also recognises that to say that we are capable of acting and that this acting takes different forms — of course we are and of course it does — is not to say how we are capable. Smith’s position on these matters hardly came as a bolt from the blue. Rather it is all part of a wider current of eighteenth century thought that rejects the crude Hobbesian view of self-interested behaviour. Like others in the so-called British Moralist tradition Smith wants to re-think the question as to what a viable (and prosperous) social order presupposes. The spontaneous emergence of a (relatively) liberal political economy in Britain by the early eighteenth century had called into question many of the fundamental assumptions Hobbes makes in regard to human nature. In Hobbes, individual self-interest needs to be held in check by an all-seeing, all-powerful Sovereign. Evidently, though, in the light of events, self-interest needed to be re-thought as a constructive, rather than destructive, force. The human being as sympathiser became a key element in that recon- ceptualisation. For Hume, for example, ‘no quality of human nature is more remarkable, both in itself and its consequences, than that propensity we have to sympathize with others, and to receive by communication their inclinations and sentiments, however different from, or even contrary to our own’. Hume here seems to come very close to anticipating Smithian sympathy. Ultimately, however, Hume cannot get there, because for Hume to hold to a Smithian view of sympathy would render what he has to say about other things incoherent …

Fortunately Smith is not bound by Hume’s self-imposed methodological strictures: entities for Smith do not need to be conspicuous to be real. Smithian sympathy, presupposing a third-person perspective within the self, cannot be conspicuous because, by definition, it can only ever be the first person that is on view. But it can be retroductively inferred from that which is conspicuous: sympathy is real enough, according to Smith’s lights, or how else would any form of (harmonised) behaviour be possible? In the terminology of the critical realist, Smith’s talk of sympathy is not concerned with the actual, not concerned with our acts as such — whether self-interested or benevolent — nor with the significance that the moralist reads into those acts: a significance that is also actual. Rather his concern is with the real: the condition of possibility of our actings and, related to this, how we are able, on reflection, to pass ‘moral’ judgement on the actions of others. Again, we cannot see the third-person perspective, the sense of right, that we carry around inside ourselves and that enables those actualities, but we can infer the existence of this capacity from the otherwise inexplicable “concords” that it produces. What we do in fact sense as right is context-sensitive. But the key to human action (and a fortiori human interaction) for Smith is that, always and everywhere, we do expect.

David Wilson & William Dixon

When randomized controlled trials fail

23 July, 2013 at 09:57 | Posted in Statistics & Econometrics, Theory of Science & Methodology | 1 Comment

Using randomized controlled trials (RCTs) is not at all the “gold standard” that it has lately often been portrayed as. As yours truly has repeatedly argued on this blog (e.g. here and here), RCTs usually do not provide evidence that their results are exportable to other target systems. The almost religious belief with which its propagators portray it, cannot hide the fact that RCTs cannot be taken for granted to give generalizable results. That something works somewhere is no warranty for it to work for us or even that it works generally:

Disappointing though its outcome was, the study represented a victory for science over guesswork, of hard data over hunches. As far as clinical trials went, Dr. Gilbert’s study was the gold standard …

The centerpiece of the country’s drug-testing system — the randomized, controlled trial — had worked.

Except in one respect: doctors had no more clarity after the trial about how to treat patients than they had before. Some patients did do better on the drug … but the trial was unable to discover these “responders” along the way, much less examine what might have accounted for the difference …

control-group1-1Rigorous statistical tests are done to make sure that the drug’s demonstrated benefit is genuine, not the result of chance. But chance turns out to be a hard thing to rule out. When the measured effects are small — as they are in the vast majority of clinical trials — mere chance is often the difference between whether a drug is deemed to work or not, says John P. A. Ioannidis, a professor of medicine at Stanford.

In a famous 2005 paper published in The Journal of the American Medical Association, Dr. Ioannidis, an authority on statistical analysis, examined nearly four dozen high-profile trials that found a specific medical intervention to be effective. Of the 26 randomized, controlled studies that were followed up by larger trials (examining the same therapy in a bigger pool of patients), the initial finding was wholly contradicted in three cases (12 percent). And in another 6 cases (23 percent), the later trials found the benefit to be less than half of what was first reported.

It wasn’t the therapy that changed in each case, but rather the sample size. And Dr. Ioannidis believes that if more rigorous, follow-up studies were actually done, the refutation rate would be far higher …

The fact that the pharmaceutical companies sponsor and run the bulk of investigative drug trials brings what Dr. Ioannidis calls a “constellation of biases” to the process. Too often, he says, trials are against “a straw-man comparator” like a placebo rather than a competing drug. So the studies don’t really help us understand which treatments for a disease work best.

But a more fundamental challenge has to do with the nature of clinical trials themselves. “When you do any kind of trial, you’re really trying to answer a question about truth in the universe,” says Hal Barron, the chief medical officer and head of global development at Roche and Genentech. “And, of course, we can’t know that. So we try to design an experiment on a subpopulation of the world that we think is generalizable to the overall universe” — that is, to the patients who will use the drug.

That’s a very hard thing to pull off. The rules that govern study enrollment end up creating trial populations that invariably are much younger, have fewer health complications and have been exposed to far less medical treatment than those who are likely to use the drug … Even if clinical researchers could match the demographics of study populations to those of the likely users of these medicines, no group of trial volunteers could ever match the extraordinary biological diversity of the drugs’ eventual consumers.

Clifton Leaf/New York Times

Ergodic and stationary random processes (wonkish)

22 July, 2013 at 22:07 | Posted in Statistics & Econometrics | Comments Off on Ergodic and stationary random processes (wonkish)

 

The price of human liberty

22 July, 2013 at 10:18 | Posted in Politics & Society | Comments Off on The price of human liberty

BuryingtheDeadonOmahaBeachbyWilliam

So you want to run your millionth regression?

21 July, 2013 at 22:00 | Posted in Economics, Statistics & Econometrics | Comments Off on So you want to run your millionth regression?


The cost of computing has dropped exponentially, but the cost of thinking is what it always was. That is why we see so many articles with so many regressions and so little thought.

Zvi Griliches
 
 
 
 

Läs om!

21 July, 2013 at 14:16 | Posted in Varia | Comments Off on Läs om!

Hur ska man läsa? Det är nog en rätt vanlig fundering alla någon gång har haft kring vårt förhållningssätt till litteratur och läsande.

Själv får jag anledning fundera kring detta när min älskade – som oförtrutet slukar nya böcker i ett rasande tempo – åter igen försöker övertala mig att ställa tillbaka Röda rummet, Hemsöborna, Martin Bircks ungdom, Den allvarsamma leken, Jerusalem eller Gösta Berlings saga i biblioteket och “pröva någon ny bok” för en gångs skull. För henne är det obegripligt att någon ens kommer på tanken att läsa om en roman när det finns så mycket oupptäckt och nytt att kasta sig över i litteraturens underbara värld. För henne – och säkert många andra bokslukare – är det bara dårar som hängivet ägnar sig åt ständiga omläsningar.

Men låt mig trots det försöka försvara oss dårar! Till min hjälp tar jag en bok som jag – just det – läst om gång på gång under snart tre årtionden. Olof Lagercrantz skriver i sin underbara lilla bok:

lagercrantz-olof-om-konsten-att-lasa-och-skrivaNär vi läser andra gången är det som att läsa en döds biografi eller se vårt liv strax innan vi ska lämna det. Nu står det klart varför den där upplevelsen i första kapitlet gjorde så starkt intryck på hjältinnan. Den avgjorde i själva verket hennes liv. Ett mönster träder fram. Det som var oöverskådligt blir enkelt och begripligt.

Nu kan vi också, liksom vi gör när vi minns vårt eget liv, stanna upp vid särskilt vackra och meningsfulla avsnitt. Vi behöver inte skynda oss ty vi vet fortsättningen. Ingen oro för framtiden hindrar oss att njuta av nuet.
 
 

How to understand science

21 July, 2013 at 10:21 | Posted in Theory of Science & Methodology | Comments Off on How to understand science

The primary aim of this study is the development of a systematic realist account of science. In this way I hope to provide a comprehensive alternative to the positivism that has usurped the title of science. I think that only the position developed here can do full justice to the rationality of scientific practice or sustain the intelligibility of such scientific activities as theoryconstruction and experimentation. And that while recent developments in the philosophy of science mark a great advance on positivism they must eventually prove vulnerable to positivist counter-attack, unless carried to the limit worked out here.

My subsidiary aim is thus to show once-and-for-all why no return to positivism is possible. This of course depends upon my primary aim.9781844672042-frontcoverFor any adequate answer to the critical metaquestion ‘what are the conditions of the plausibility of an account of science ?’ presupposes an account which is capable of thinking of those conditions as special cases. That is to say, to adapt an image of Wittgenstein’s, one can only see the fly in the fly-bottle if one’s perspective is different from that of the fly. And the sting is only removed from a system of thought when the particular conditions under which it makes sense are described. In practice this task is simplified for us by the fact that the conditions under which positivism is plausible as an account of science are largely co-extensive with the conditions under which experience is significant in science. This is of course an important and substantive question which we could say, echoing Kant, no account of science can decline, but positivism cannot ask, because (it will be seen) the idea of insignificant experiences transcends the very bounds of its thought.

This book is written in the context of vigorous critical activity in the philosophy of science. In the course of this the twin templates of the positivist view of science, viz. the ideas that science has a certain base and a deductive structure, have been subjected to damaging attack. With a degree of arbitrariness one can separate this critical activity into two strands. The first, represented by writers such as Kuhn, Popper, Lakatos, Feyerabend, Toulmin, Polanyi and Ravetz, emphasises the social character of science and focusses particularly on the phenomena of scientific change and development. It is generally critical of any monistic interpretation of scientific development, of the kind characteristic of empiricist historiography and implicit in any doctrine of the foundations of knowledge. The second strand, represented by the work of Scriven, Hanson, Hesse and Harré among others, calls attention to the stratification of science. It stresses the difference between explanation and prediction and emphasises the role played by models in scientific thought. It is highly critical of the deductivist view of the structure of scientific theories, and more generally of any exclusively formal account of science. This study attempts to synthesise these two critical strands; and to show in particular why and how the realism presupposed by the first strand must be extended to cover the objects of scientific thought postulated by the second strand. In this way I will be describing the nature and the development of what has been hailed as the ‘Copernican Revolution’ in the philosophy of science.

To see science as a social activity, and as structured and discriminating in its thought, constitutes a significant step in our understanding of science. But, I shall argue, without the support of a revised ontology, and in particular a conception of the world as stratified and differentiated too, it is impossible to steer clear of the Scylla of holding the structure dispensable in the long run (back to empiricism) without being pulled into the Charybdis of justifying it exlusively in terms of the fixed or changing needs of the scientific community (a form of neoKantian pragmatism exemplified by e.g. Toulmin and Kuhn). In this study I attempt to show how such a revised ontology is in fact presupposed by the social activity of science. The basic principle of realist philosophy of science, viz. that perception gives us access to things and experimental activity access to structures that exist independently of us, is very simple. Yet the full working out of this principle implies a radical account of the nature of causal laws, viz. as expressing tendencies of things, not conjunctions of events. And it implies that a constant conjunction of events is no more a necessary than a sufficient condition for a causal law.

Greetings from Greg Mankiw

20 July, 2013 at 23:28 | Posted in Varia | Comments Off on Greetings from Greg Mankiw

Long tails and the attraction of geek-wonkish blogs

20 July, 2013 at 19:00 | Posted in Varia | 1 Comment

Tired of the idea of an infallible mainstream neoclassical economics and its perpetuation of spoon-fed orthodoxy,  yours truly launched this blog two years ago. The number of visitors has increased steadily, and with almost seventy thousand visits per month I have to admit of still being – given the rather “wonkish” character of the blog, with posts mostly on economic theory, statistics, econometrics, theory of science and methodology – rather gobsmacked that so many are interested and take their time to read this often rather geeky stuff.

images-4In the 21st century the blogosphere has without any doubts become the greatest channel for dispersing new knowledge and information. As a blogger I can specialize in those particular topics a critical realist professor of social science and economist happens to have both deep knowledge of and interest in. That, of course, also means – in the modern long tail world – being able to target a segment of readers much narrower than newspapers and magazines as a rule could aim for – and still attract quite a lot of readers:

Each individual listener, viewer, or reader is, and has always been, a unique mix of generic interests and specific interests. Although many of these individuals might share some generic interests, such as the weather, most, if not all of them, have very different specific interests. And each individual is a truly unique mix of generic and specific interests. Until about 30 years ago, the average American hadn’t access to any medium that could satisfy each of their specific interests. All they had was the mass medium, which could somewhat successfully satisfy many of their generic (i.e., “mass”) interests.

Then media technologies evolved in ways that started to satisfy their specific interests. During the 1970s, improvements in offset li-thography led to a bloom of specialty magazines; no longer were there a dozen or two magazines on newsstands, but hundreds, most about only specific topics. Proliferations of, first, analog cable television systems during the 1980s, then digital ones during the late 1990s, increased the average American’s number of accessible TV stations from four to hundreds, mostly specialty channels … Then the Internet became publicly accessible during the 1990s and the average individual quickly had access to millions of websites, most of those sites about very specific topics.

The result is that more and more individuals, who had been using only the (generic) mass medium because that’s all they had, have gravitated to these specialty publications, channels, or web- sites rather than continue to use only mass medium publications, channels, or websites. More and more use the mass medium less and less. And more and more will soon be most. The individuals haven’t changed; they’ve always been fragmented. What’s changing is their media habits. They’re now simply satisfying the fragmented interests that they’ve always had. There are as many fragments as there are individuals.

Vin Crosbie

A second best suggestion

20 July, 2013 at 10:15 | Posted in Economics | 1 Comment

For governments and central banks that do not understand the principle of effective demand, Keynes presents a second best alternative in The General Theory of Employment, Interest, and Money

If – for whatever reason – the rate of interest cannot fall as fast as the marginal efficiency of capital would fall with a rate of accumulation corresponding to what the community would choose to save at a rate of interest equal to the marginal efficiency of capital in conditions of full employment, then even a diversion of the desire to hold wealth towards assets, which will in fact yield no economic fruits whatever, will increase economic well-being.keynes-cartoonIn so far as millionaires find their satisfaction in building mighty mansions to contain their bodies when alive and pyramids to shelter them after death, or, repenting of their sins, erect cathedrals and endow monasteries or foreign missions, the day when abundance of capital will interfere with abundance of output may be postponed. “To dig holes in the ground,” paid for out of savings, will increase, not only employment, but the real national dividend of useful goods and services. It is not reasonable, however, that a sensible community should be content to remain dependent on such fortuitous and often wasteful mitigations when once we understand the influences upon which effective demand depends.

Or:

If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coalmines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well-tried principles of laissez-faire to dig the notes up again (the right to do so being obtained, of course, by tendering for leases of the note-bearing territory), there need be no more unemployment and, with the help of the repercussions, the real income of the community, and its capital wealth also, would probably become a good deal greater than it actually is. It would, indeed, be more sensible to build houses and the like; but if there are political and practical difficulties in the way of this, the above would be better than nothing.

Bernanke’s hubris

19 July, 2013 at 14:44 | Posted in Economics | 2 Comments

It is amazing that a lot of criticism of the Federal Reserve today focuses on what it clearly got right — the response to the debt crisis in 2008 and thereafter, a response that may well have prevented Great Depression II — and not on what it got wrong: policies that allowed the dangerous imbalances to grow and bring on the crisis …

At least Mr. Bernanke’s hubris was not as great as that of Robert E. Lucas Jr., the Nobel Prize-winning University of Chicago economist. In 2003, he began his presidential address to the American Economic Association by proclaiming that macroeconomics “has succeeded: Its central problem of depression prevention has been solved.”

In his speech last week, Mr. Bernanke cited several assessments of the Great Moderation, including the one by the Fed economists. None questioned that it was wonderful.

The Fed chairman conceded that “one cannot look back at the Great Moderation today without asking whether the sustained economic stability of the period somehow promoted the excessive risk-taking that followed. The idea that this long period of calm lulled investors, financial firms and financial regulators into paying insufficient attention to building risks must have some truth in it.”

One economist who would have expected that development was Hyman Minsky. In 1995, the year before Minsky died, Steve Keen, an Australian economist, used his ideas to set forth a possibility that now seems prescient. It was published in The Journal of Post Keynesian Economics.

He suggested that lending standards would be gradually reduced, and asset prices would rise, as confidence grew that “the future is assured, and therefore that most investments will succeed.” Eventually, the income-earning ability of an asset would seem less important than the expected capital gains. Buyers would pay high prices and finance their purchases with ever-rising amounts of debt.

When something went wrong, an immediate need for liquidity would cause financiers to try to sell assets immediately. “The asset market becomes flooded,” Mr. Keen wrote, “and the euphoria becomes a panic, the boom becomes a slump.” Minsky argued that could end without disaster, if inflation bailed everyone out. But if it happened in a period of low inflation, it could feed upon itself and lead to depression …

charles-p-kindleberger-manias-panics-and-cgrashes-2011When I talked to Mr. Keen this week, he called my attention to the fact that Mr. Bernanke, in his 2000 book “Essays on the Great Depression,” briefly mentioned, and dismissed, both Minsky and Charles Kindleberger, author of the classic “Manias, Panics and Crashes.”

They had, Mr. Bernanke wrote, “argued for the inherent instability of the financial system but in doing so have had to depart from the assumption of rational economic behavior.” In a footnote, he added, “I do not deny the possible importance of irrationality in economic life; however it seems that the best research strategy is to push the rationality postulate as far as it will go.”

It seems to me that he had both Minsky and Kindleberger wrong. Their insight was that behavior that seems perfectly rational at the time can turn out to be destructive. As Robert J. Barbera, now the co-director of the Center for Financial Economics at Johns Hopkins University, wrote in his 2009 book, “The Cost of Capitalism,” “One of Minsky’s great insights was his anticipation of the ‘Paradox of Goldilocks.’ Because rising conviction about a benign future, in turn, evokes rising commitment to risk, the system becomes increasingly vulnerable to retrenchment, notwithstanding the fact that consensus expectations remain reasonable relative to recent history.”

New York Times

Keynes on speculators taking advantage of mob psychology

19 July, 2013 at 12:14 | Posted in Economics | Comments Off on Keynes on speculators taking advantage of mob psychology

How far the motives which I have been attributing to the market are strictly rational, I leave it to others to judge. They are best regarded, I think, as an example of how sensitive – over-sensitive if you like – to the near future, about which we may think that we know a little, even the best-informed must be, because, in truth, we know almost nothing about the more remote future …

175976The ignorance of even the best-informed investor about the more remote future is much greater then his knowledge … But if this is true of the best-informed, the vast majority of those who are concerned with the buying and selling of securities know almost nothing whatever about what they are doing … This is one of the odd characteristics of the Capitalist System under which we live …

It may often profit the wisest to anticipate mob psychology rather than the real trend of events, and to ape unreason proleptically … (The object of speculators) is to re-sell to the mob after a few weeks or at most a few months. It is natural, therefore, that they should be influenced by the cost of borrowing, and still more by their expectations on the basis of past experience of the trend of mob psychology. Thus, so long as the crowd can be relied on to act in a certain way, even if it be misguided, it will be to the advantage of the better informed professional to act in the same way – a short period ahead.

Mistaking luck for skill

18 July, 2013 at 20:38 | Posted in Economics | Comments Off on Mistaking luck for skill

It’s often said that people misperceive skill and luck, for example by saying that a team is on form when it has merely had a run of good fortune. A new experimentat the Autonomous University of Barcelona shows that this error is even worse than we thought.

Jordi Brandts and colleagues got a group of students to predict a sequence of five coin tosses, and then selected the best and the worst predictor. They then asked other subjects to bet on whether the best and worst predictor could predict another five coin tosses. The subjects were told that they would bet on the worst predictor from the first round, unless they paid to switch to the best predictor.

82% of subjects paid to make the switch.images-3

But of course, there is no such thing as an ability to predict the toss of a coin. Most subjects, then, saw skill where there was only luck. And, what’s more, they were willing to spend good money to back this daft opinion.

These people weren’t just idiots plucked from the street. They were fourth year finance undergraduates at one of the best universities in Spain …

There is a vast industry which owes its existence to people believing there is skill where there is (for the most part) only luck. I refer of course to the fund management industry. There’s good evidence that actively managed funds generally do badly; for example, in the last five years most UK all company unit trusts have under-performed a decent tracker fund. Despite this, investors spend billions on fees for such managers. This is consistent with the experimental evidence showing that people see skill where none actually exists.

Now, you might object here that if people lose money by buying stupid they’ll eventually wise up. Such a view relies upon a silly Econ 101 misunderstanding of how markets work. We know from the work of people such as Andrei Shleifer (pdf), Bernard Dumas and Bjorn-Christopher Witte that financial markets do not necessarily select against the stupid and in favour of the smart.

Stumbling and Mumbling 

(h/t Ralph Musgrave)

That’s when tender sadness rolls in

18 July, 2013 at 10:30 | Posted in Varia | Comments Off on That’s when tender sadness rolls in


Absolutely fabulous video by Ted Ström.

Is libertarian freedom free of charge?

17 July, 2013 at 10:59 | Posted in Economics, Politics & Society | 5 Comments

As interpreted by the important Chicago school of economics, faith in human rationality is closely linked to an ideology in which it is unnecessary and even immoral to protect people against their choices. Ratonal people should be free, and they should be responsible for taking care of themselves …

The assumptin that agents are rational provides the intellectual foundation for the libertarian approach to public policy: do not interfere with the individual’s right to choose, unless the choices harm others … I once heard Gary Becker [argue] that we should consider the possibility of explaining the so-called obesity epidemic by people’s belief that a cure for diabetes will soon become available …

Much is therefore at stake in the debate between the Chicago school and the behavioral economists, who reject the extreme form of the rational-agent model. Freedom is not a contested value; all the participants in the debate are in favor of it. But life is more complex for behavioral economists than for true believers in human rationality. No behavioral economist favors a state that will force its citizens to eat a balanced diet and to watch only television programs that are good for the soul. For behavioral economists, however, freedom has a cost, which is borne by individuals who make bad choices, and by a society that feels obligated to help them. The decision of whether or not to protect individuals against their mistakes therefore presents a dilemma for behavioral economists. The economists of the Chicago school do not face that problem, because rational agents do not make mistakes. For adherents of this school, freedom is free of charge.

Daniel Kahneman

Keynes explained already in 1930 why austerity is a loser

16 July, 2013 at 18:15 | Posted in Economics | 1 Comment

jmkThe world has been slow to realize that we are living this year in the shadow of one of the greatest economic catastrophes of modern history. But now that the man in the street has become aware of what is happening, he, not knowing the why and wherefore, is as full to-day of what may prove excessive fears as, previously, when the trouble was first coming on, he was lacking in what would have been a reasonable anxiety. He begins to doubt the future …

In this quandary individual producers base illusory hopes on courses of action which would benefit an individual producer or class of producers so long as they were alone in pursuing them, but which benefit no one if everyone pursues them … If a particular producer or a particular country cuts wages, then, so long as others do not follow suit, that producer or that country is able to get more of what trade is going. But if wages are cut all round, the purchasing power of the community as a whole is reduced by the same amount as the reduction of costs; and, again, no one is further forward.

Thus neither the restriction of output nor the reduction of wages serves in itself to restore equilibrium.

Bei Mir Bistu Shein

16 July, 2013 at 10:13 | Posted in Varia | Comments Off on Bei Mir Bistu Shein

 

Time and time again

15 July, 2013 at 18:35 | Posted in Economics | 2 Comments

British astrophysicist Sir Arthur Eddington once  famously said:

If your theory is found to be against the second law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

In the same vein, mathematical statistician and ecological economist Nicholas Georgescu-Roegen again and again stressed that real historical time is irreversible. Is it overoptimistic to hope that not only physicists, but also neoclassical economists, soon will wake up from their modelling strategy comatose where real irreversible historical time is, over and over again, conscientiously neglected?

At an interdisciplinary gathering of academics discussing the concept of time, I once heard a scientist tell the assembled humanities scholars that physics can now replace all their woolly notions of time with one that is unique, precise and true. Such scientism is rightly undermined by theoretical physicist Lee Smolin in Time Reborn, which shows that the scientific view of time is up for grabs more than ever before.

The source of the disagreement could hardly be more fundamental: is time real or illusory? Until recently, physics has drifted toward the latter view, but Smolin insists that many of the deepest puzzles about the universe might be solved by realigning physics with our everyday intuition that the passage of time is very real indeed.

Clocks tick; seasons change; we get older. How could science have ever asserted this is all an illusion? It begins, Smolin says, with the idea that nature is governed by eternal laws, such as Newton’s law of gravity: governing principles that stand outside time. The dream of a “theory of everything”, which might explain all of history from the instant of the big bang, assumes a law that preceded time itself. And by making the clock’s tick relative – what happens simultaneously for one observer might seem sequential to another – Einstein’s theory of special relativity not only destroyed any notion of absolute time but made time equivalent to a dimension in space: the future is already out there waiting for us; we just can’t see it until we get there.

This view is a logical and metaphysical dead end, says Smolin. Even if there was a theory of everything (which looks unlikely), we’d be left asking: “Why this theory?” Or equivalently, why this universe, and not one of the infinite others that seem possible? Most of all, why one in which life can exist? …

In Farewell to Reality, Jim Baggott now castigates theoretical physicists for indulging a whole industry of “fairytale physics” – strings, supersymmetry, brane worlds, M-theory, the anthropic principle – that not only pile one unwarranted assumption on another but are beyond the reach of experimental tests for the foreseeable future …

Baggott has a point, and he makes it well, although his target is as much the way this science is marketed as what it contains … The basic problem – that the institutional, professional and social structures of science can inflate such dreams into entire faddish disciplines before asking if nature agrees with them – is one that Baggott doesn’t quite get to.

The Guardian

[h/t Lord Keynes]

Why expected utility theory is an ex-parrot (wonkish)

14 July, 2013 at 16:01 | Posted in Economics | 6 Comments

Although the expected utility theory is obviously both theoretically and descriptively inadequate, colleagues and microeconomics textbook writers all over the world gladly continue to use it, as though its deficiencies were unknown or unheard of.

That cannot be the right attitude when facing scientific anomalies. When models are plainly wrong, you’d better replace them! As Matthew Rabin and Richard Thaler have it in Risk Aversion:

ex-ParrotIt is time for economists to recognize that expected utility is an ex-hypothesis, so that we can concentrate our energies on the important task of developing better descriptive models of choice under uncertainty.
 
 
 

If a friend of yours offered you a gamble on the toss of a coin where you could lose €100 or win €200, would you accept it? Probably not. But if you were offered to make one hundred such bets, you would probably be willing to accept it, since most of us see that the aggregated gamble of one hundred 50–50 lose €100/gain €200 bets has an expected return of €5000 (and making our probabilistic calculations we find out that there is only a 0.04% risk of losing any money).

Unfortunately – at least if you want to adhere to the standard neoclassical expected utility maximization theory – you are then considered irrational! A neoclassical utility maximizer that rejects the single gamble should also reject the aggregate offer.

In his modern classic Risk Aversion and Expected-Utility Theory: A Calibration Theorem Matthew Rabin  writes:

Using expected-utility theory, economists model risk aversion as arising solely because the utility function over wealth is concave. This diminishing-marginal-utility-of-wealth theory of risk aversion is psychologically intuitive, and surely helps explain some of our aversion to large-scale risk: We dislike vast uncertainty in lifetime wealth because a dollar that helps us avoid poverty is more valuable than a dollar that helps us become very rich.

Yet this theory also implies that people are approximately risk neutral when stakes are small. Arrow (1971, p. 100) shows that an expected-utility maximizer with a differentiable utility function will always want to take a sufficiently small stake in any positive-expected-value bet. That is, expected-utility maximizers are (almost everywhere) arbitrarily close to risk neutral when stakes are arbitrarily small. While most economists understand this formal limit result, fewer appreciate that the approximate risk-neutrality prediction holds not just for negligible stakes, but for quite sizable and economically important stakes. Economists often invoke expected-utility theory to explain substantial (observed or posited) risk aversion over stakes where the theory actually predicts virtual risk neutrality.While not broadly appreciated, the inability of expected-utility theory to provide a plausible account of risk aversion over modest stakes has become oral tradition among some subsets of researchers, and has been illustrated in writing in a variety of different contexts using standard utility functions.

In this paper, I reinforce this previous research by presenting a theorem which calibrates a relationship between risk attitudes over small and large stakes. The theorem shows that, within the expected-utility model, anything but virtual risk neutrality over modest stakes implies manifestly unrealistic risk aversion over large stakes. The theorem is entirely ‘‘non-parametric’’, assuming nothing about the utility function except concavity. In the next section I illustrate implications of the theorem with examples of the form ‘‘If an expected-utility maximizer always turns down modest-stakes gamble X, she will always turn down large-stakes gamble Y.’’ Suppose that, from any initial wealth level, a person turns down gambles where she loses $100 or gains $110, each with 50% probability. Then she will turn down 50-50 bets of losing $1,000 or gaining any sum of money. A person who would always turn down 50-50 lose $1,000/gain $1,050 bets would always turn down 50-50 bets of losing $20,000 or gaining any sum. These are implausible degrees of risk aversion. The theorem not only yields implications if we know somebody will turn down a bet for all initial wealth levels. Suppose we knew a risk-averse person turns down 50-50 lose $100/gain $105 bets for any lifetime wealth level less than $350,000, but knew nothing about the degree of her risk aversion for wealth levels above $350,000. Then we know that from an initial wealth level of $340,000 the person will turn down a 50-50 bet of losing $4,000 and gaining $635,670.

The intuition for such examples, and for the theorem itself, is that within the expected-utility framework turning down a modest-stakes gamble means that the marginal utility of money must diminish very quickly for small changes in wealth. For instance, if you reject a 50-50 lose $10/gain $11 gamble because of diminishing marginal utility, it must be that you value the 11th dollar above your current wealth by at most 10/11 as much as you valued the 10th-to-last-dollar of your current wealth.

Iterating this observation, if you have the same aversion to the lose $10/gain $11 bet if you were $21 wealthier, you value the 32nd dollar above your current wealth by at most 10/11 x 10/11 ~ 5/6 as much as your 10th-to-last dollar. You will value your 220th dollar by at most 3/20 as much as your last dollar, and your 880 dollar by at most 1/2000 of your last dollar. This is an absurd rate for the value of money to deteriorate — and the theorem shows the rate of deterioration implied by expected-utility theory is actually quicker than this. Indeed, the theorem is really just an algebraic articulation of how implausible it is that the consumption value of a dollar changes significantly as a function of whether your lifetime wealth is $10, $100, or even $1,000 higher or lower. From such observations we should conclude that aversion to modest-stakes risk has nothing to do with the diminishing marginal utility of wealth.

Expected-utility theory seems to be a useful and adequate model of risk aversion for many purposes, and it is especially attractive in lieu of an equally tractable alternative model. ‘‘Extremelyconcave expected utility’’ may even be useful as a parsimonious tool for modeling aversion to modest-scale risk. But this and previous papers make clear that expected-utility theory is manifestly not close to the right explanation of risk attitudes over modest stakes. Moreover, when the specific structure of expected-utility theory is used to analyze situations involving modest stakes — such as in research that assumes that large-stake and modest-stake risk attitudes derive from the same utility-for-wealth function — it can be very misleading. In the concluding section, I discuss a few examples of such research where the expected-utility hypothesis is detrimentally maintained, and speculate very briefly on what set of ingredients may be needed to provide a better account of risk attitudes. In the next section, I discuss the theorem and illustrate its implications …

Expected-utility theory makes wrong predictions about the relationship between risk aversion over modest stakes and risk aversion over large stakes. Hence, when measuring risk attitudes maintaining the expected-utility hypothesis, differences in estimates of risk attitudes may come from differences in the scale of risk comprising data sets, rather than from differences in risk attitudes of the people being studied. Data sets dominated by modest-risk investment opportunities are likely to yield much higher estimates of risk aversion than data sets dominated by larger-scale investment opportunities. So not only are standard measures of risk aversion somewhat hard to interpret given that people are not expected-utility maximizers, but even attempts to compare risk attitudes so as to compare across groups will be misleading unless economists pay due attention to the theory’s calibrational problems …

Indeed, what is empirically the most firmly established feature of risk preferences, loss aversion, is a departure from expected-utility theory that provides a direct explanation for modest-scale risk aversion. Loss aversion says that people are significantly more averse to losses relative to the status quo than they are attracted by gains, and more generally that people’s utilities are determined by changes in wealth rather than absolute levels. Preferences incorporating loss aversion can reconcile significant small-scale risk aversion with reasonable degrees of large-scale risk aversion … Variants of this or other models of risk attitudes can provide useful alternatives to expected-utility theory that can reconcile plausible risk attitudes over large stakes with non-trivial risk aversion over modest stakes.

In a similar vein, Daniel Kahneman writes in his wonderful Thinking, Fast and Slow, that expected utility theory is seriously flawed since it doesn’t take into consideration the basic fact that people’s choices are influenced by changes in their wealth. Where standard microeconomic theory assumes that preferences are stable over time, Kahneman and other behavioural economists have forcefully again and again shown that preferences aren’t fixed, but vary with different reference points. How can a theory that doesn’t allow for people having different reference points from which they consider their options have an almost axiomatic status within economic theory?

The mystery is how a conception of the utility of outcomes that is vulnerable to such obvious counterexamples survived for so long. I can explain it only by a weakness of the scholarly mind … I call it theory-induced blindness: once you have accepted a theory and used it as a tool in your thinking it is extraordinarily difficult to notice its flaws … You give the theory the benefit of the doubt, trusting the community of experts who have accepted it … But they did not pursue the idea to the point of saying, “This theory is seriously wrong because it ignores the fact that utility depends on the history of one’s wealth, not only present wealth.”

On a more economic-theoretical level, information theory – and especially the so called the Kelly theorem – also highlights the problems concerning the neoclassical theory of expected utility.
Suppose I want to play a game. Let’s say we are tossing a coin. If heads comes up, I win a dollar, and if tails comes up, I lose a dollar. Suppose further that I believe I know that the coin is asymmetrical and that the probability of getting heads (p) is greater than 50% – say 60% (0.6) – while the bookmaker assumes that the coin is totally symmetric. How much of my bankroll (T), should I optimally invest in this game?

A strict neoclassical utility-maximizing economist would suggest that my goal should be to maximize the expected value of my bankroll (wealth), and according to this view, I ought to bet my entire bankroll.

Does that sound rational? Most people would answer no to that question. The risk of losing is so high, that I already after few games played – the expected time until my first loss arises is 1/(1-p), which in this case is equal to 2.5 – with a high likelihood would be losing and thereby become bankrupt. The expected-value maximizing economist does not seem to have a particularly attractive approach.

So what’s the alternative? One possibility is to apply the so-called Kelly-strategy – after the American physicist and information theorist John L. Kelly, who in the article A New Interpretation of Information Rate (1956) suggested this criterion for how to optimize the size of the bet – under which the optimum is to invest a specific fraction (x) of wealth (T) in each game. How do we arrive at this fraction?

When I win, I have (1 + x) times more than before, and when I lose (1 – x) times less. After n rounds, when I have won v times and lost n – v times, my new bankroll (W) is

The bankroll increases multiplicatively – “compound interest” – and the long-term average growth rate for my wealth can then be easily calculated by taking the logarithms of (1), which gives

(2) log (W/ T) = v log (1 + x) + (n – v) log (1 – x).

If we divide both sides by n we get

(3) [log (W / T)] / n = [v log (1 + x) + (n – v) log (1 – x)] / n

The left hand side now represents the average growth rate (g) in each game. On the right hand side the ratio v/n is equal to the percentage of bets that I won, and when n is large, this fraction will be close to p. Similarly, (n – v)/n is close to (1 – p). When the number of bets is large, the average growth rate is

(4) g = p log (1 + x) + (1 – p) log (1 – x).

Now we can easily determine the value of x that maximizes g:

(5) d [p log (1 + x) + (1 – p) log (1 – x)]/d x = p/(1 + x) – (1 – p)/(1 – x) =>
p/(1 + x) – (1 – p)/(1 – x) = 0 =>

(6) x = p – (1 – p)

Since p is the probability that I will win, and (1 – p) is the probability that I will lose, the Kelly strategy says that to optimize the growth rate of your bankroll (wealth) you should invest a fraction of the bankroll equal to the difference of the likelihood that you will win or lose. In our example, this means that I have in each game to bet the fraction of x = 0.6 – (1 – 0.6) ≈ 0.2 – that is, 20% of my bankroll. The optimal average growth rate becomes

(7) 0.6 log (1.2) + 0.4 log (0.8) ≈ 0.02.

If I bet 20% of my wealth in tossing the coin, I will after 10 games on average to be times more than when I started (≈ 1.22 times more).

This game strategy will give us an outcome in the long run that is better than if we use a strategy building on the neoclassical economic theory of choice under uncertainty (risk) – expected value maximization. If we bet all our wealth in each game we will most likely lose our fortune, but because with low probability we will have a very large fortune, the expected value is still high. For a real-life player – for whom there is very little to benefit from this type of ensemble-average – it is more relevant to look at time-average of what he may be expected to win (in our game the averages are the same only if we assume that the player has a logarithmic utility function). What good does it do me if my tossing the coin maximizes an expected value when I might have gone bankrupt after four games played? If I try to maximize the expected value, the probability of bankruptcy soon gets close to one. Better then to invest 20% of my wealth in each game and maximize my long-term average wealth growth!

When applied to the neoclassical theory of expected utility, one thinks in terms of “parallel universe” and asks what is the expected return of an investment, calculated as an average over the “parallel universe”? In our coin toss example, it is as if one supposes that various “I” are tossing a coin and that the loss of many of them will be offset by the huge profits one of these “I” does. But this ensemble-average does not work for an individual, for whom a time-average better reflects the experience made in the “non-parallel universe” in which we live.

The Kelly strategy gives a more realistic answer, where one thinks in terms of the only universe we actually live in, and ask what is the expected return of an investment, calculated as an average over time.

Since we cannot go back in time – entropy and the “arrow of time ” make this impossible – and the bankruptcy option is always at hand (extreme events and “black swans” are always possible) we have nothing to gain from thinking in terms of ensembles .

Actual events follow a fixed pattern of time, where events are often linked in a multiplicative process (as e. g. investment returns with “compound interest”) which is basically non-ergodic.

Instead of arbitrarily assuming that people have a certain type of utility function – as in the neoclassical theory – the Kelly criterion shows that we can obtain a less arbitrary and more accurate picture of real people’s decisions and actions by basically assuming that time is irreversible. When the bankroll is gone, it’s gone. The fact that in a parallel universe it could conceivably have been refilled, are of little comfort to those who live in the one and only possible world that we call the real world.

Our coin toss example can be applied to more traditional economic issues. If we think of an investor, we can basically describe his situation in terms of our coin toss. What fraction (x) of his assets (T) should an investor – who is about to make a large number of repeated investments – bet on his feeling that he can better evaluate an investment (p = 0.6) than the market (p = 0.5)? The greater the x, the greater is the leverage. But also – the greater is the risk. Since p is the probability that his investment valuation is correct and (1 – p) is the probability that the market’s valuation is correct, it means the Kelly strategy says he optimizes the rate of growth on his investments by investing a fraction of his assets that is equal to the difference in the probability that he will “win” or “lose”. In our example this means that he at each investment opportunity is to invest the fraction of x = 0.6 – (1 – 0.6), i.e. about 20% of his assets. The optimal average growth rate of investment is then about 11% (0.6 log (1.2) + 0.4 log (0.8)).

Kelly’s criterion shows that because we cannot go back in time, we should not take excessive risks. High leverage increases the risk of bankruptcy. This should also be a warning for the financial world, where the constant quest for greater and greater leverage – and risks – creates extensive and recurrent systemic crises. A more appropriate level of risk-taking is a necessary ingredient in a policy to come to curb excessive risk taking.

The works of people like Rabin, Thaler, Kelly, and Kahneman, show that expected utility theory is in deed an “ex-hypthesis.” Or as Monty Python has it:

This parrot is no more! He has ceased to be! ‘E’s expired and gone to meet ‘is maker! ‘E’s a stiff! Bereft of life, ‘e rests in peace! If you hadn’t nailed ‘im to the perch ‘e’d be pushing up the daisies! ‘Is metabolic processes are now ‘istory! ‘E’s off the twig! ‘E’s kicked the bucket, ‘e’s shuffled off ‘is mortal coil, run down the curtain and joined the bleedin’ choir invisible!! THIS IS AN EX-PARROT!!

Next Page »

Blog at WordPress.com.
Entries and comments feeds.