Deductivism — the original sin of ‘modern’ economics

30 September, 2015 at 12:57 | Posted in Economics | 3 Comments

For many people, deductive reasoning is the mark of science: induction – in which the argument is derived from the subject matter – is the characteristic method of history or literary criticism. But this is an artificial, exaggerated distinction. Scientific progress … is frequently the result of observation that something does work, which runs far ahead of any understanding of why it works.

aimageNot within the economics profession. There, deductive reasoning based on logical inference from a specific set of a priori deductions is “exactly the right way to do things”. What is absurd is not the use of the deductive method but the claim to exclusivity made for it. This debate is not simply about mathematics versus poetry. Deductive reasoning necessarily draws on mathematics and formal logic: inductive reasoning, based on experience and above all careful observation, will often make use of statistics and mathematics …

The belief that models are not just useful tools but are capable of yielding comprehensive and universal descriptions of the world blinded proponents to realities that had been staring them in the face. That blindness made a big contribution to our present crisis, and conditions our confused responses to it.

John Kay

Kay’s article is essential reading for all those who want to understand why mainstream – neoclassical – economics actively have contributed to causing todays’s economic crisis rather than to solving it.

Perhaps this becomes less perplexing to grasp when considering what one of its main proponents today – Robert Lucas – maintained already in 2003:

My thesis in this lecture is that macroeconomics in this original sense has succeeded: its central problem of depression-prevention has been solved, for all practical purposes, and has in fact been solved for many decades.

And this comes from an economist who has built his whole career on the assumption that people are hyper rational “robot imitations” with rational expectations and (stochastically) perfect ability to process information. Mirabile dictu!

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Limits of formalization in economics

30 September, 2015 at 10:16 | Posted in Economics | 4 Comments

A complete modeling system which yields definitive predictions (or at least multiple equilibria) requires the following conditions: given structures with fixed (or at least predictably random) interrelations between separable parts (e.g., economic agents) and predictable (or at least predictably random) outside influences. Such a system is … a‘closed’ system. Such a system, correctly applied, promotes internal consistency but risks inconsistency with the nature of the economic system unless that too is closed …

phelpsfrydmanAn open system is not the opposite of a closed system, since there is a range of possibilities for openness, depending on which conditions are not met and to what degree … Deviating from a closed system, and thus from certainty or certainty equivalence, does not mean abandoning theory or formal models. On the contrary, Keynes was concerned to identify the logical grounds on which we habitually form beliefs, make judgments and take decisions (both as economists and as economic agents) in spite of uncertainty. The question was what view on probability would be logically justified, in relation to the evidence, within an open system …

Any formal model is a closed system. Variables are specified and identified as endogenous or exogenous, and relations are specified between them. This is a mechanism for separating off some aspect of an open-system reality for analysis. But, for consistency with the subject matter, any analytical closure needs to be justified on the grounds that, for the purposes of the analysis, it is not unreasonable to treat the variables as having a stable identity, for them to have stable interrelations and not to be subject to unanticipated influences from outside … But in applying such an analysis it is important then to consider what has been assumed away …

Keynes’s argument is that any formal model is bound to be an incomplete representation of an open-system reality … Models are inevitably partial representations, invoking closures which are both porous and provisional. They can only be approximated in reality and even then cannot be presumed to persist …

This methodology explains why Keynes’s general theory did not take the form of a single large model, including formal microfoundations … It was not that Keynes lacked a microeconomic analysis, but rather that his study of individual behavior concluded that it was organic rather than atomistic.

Sheila Dow

Newspapers make you stupid

29 September, 2015 at 13:17 | Posted in Politics & Society | 1 Comment

Lydon: You say newspapers make us stupid, and I’m not quite clear why.

Taleb: Because they always give you an explanation to events so that you have the feeling that you know what’s going on. They tell you the stock market went down, because of fear of a recession, and that’s false causation with uncertainty there. They check their facts, but you can’t check their causes. So, you have the feeling of over-causation from newspapers. That’s number one, the first one.

The second one: newspapers aren’t going to tell you “we had 280 deaths on the roads today in America”. They’re going to tell you about the plane crash killing 14 people. So, you have misrepresentation of the math of risks. They are driven by the sensational. And the statistical and the sensational are not the same in our modern world.

sunThere’s a third thing about newspapers. Supplying someone with news reduces his understand-ing of the world. It’s more complicated than I can go into here, but let me tell you how I cope with it. I don’t mind knowing the news, but I go by a social filter. I eat lunch and dinner with other people. (I try to. I still have people who won’t eat lunch or dinner with me, even after writing the Black Swan). And I make sure. You can eavesdrop on conversations and stuff like that. I can tell if something is going on.

If there’s an event of significance, I know about it. And then I go to the web, or go buy a paper sometimes, or something like that.

Christopher Lydon interview with Nassim Nicholas Taleb

Är svenska nationalekonomers Törnrosasömn äntligen över?

29 September, 2015 at 11:01 | Posted in Economics | Comments Off on Är svenska nationalekonomers Törnrosasömn äntligen över?

SpisNär det brinner i köket är det dags att använda brandsläckaren. Det är ingen mening att spara pulvret tills det brinner i hela huset. I debatten om statsbudgeten tycks både regering och opposition ha glömt denna enkla insikt.

Vi föreslår att regeringen – allra helst i samförstånd med oppositionen – snarast möjligt gör betydande utbetalningar till alla invånare i Sverige … Årets budgetunderskott skulle öka i motsvarande grad. Regeringen bör dessutom signalera att den inte har för avsikt att i nära framtid återbetala denna skuld. Med andra ord, summan av statsobligationer, sedlar och mynt bör höjas permanent.

Förslaget kan tyckas radikalt och oseriöst. Under de tjugo år som passerat sedan nittiotalskrisen har ”sunda finanser” varit ett mantra bland svenska finansministrar. Att ta ansvar för Sverige har inneburit en stram budget – fulla lador, torrt krut! Men det finns lägen då det är skadligt att budgetera alltför stramt, och dagens läge är ett sådant. Anledningen är enkel. Penningpolitiken klarar bevisligen inte av att på egen hand att bekämpa lågkonjunkturen eller ens att någorlunda uppnå inflationsmålet. Hårdare begränsningar av hushållens lånemöjligheter medför en ytterligare press nedåt på konsumentpriserna. Finanspolitiken bör därför hjälpa till att ge konsumentprisindex en skjuts uppåt. Att i detta läge spara för framtiden framstår lika missriktat som att träna hårt med influensa i kroppen.

Vi är naturligtvis inte de första som förespråkar expansiv finanspolitik för att råda bot på de ekonomiska obalanserna i Sverige liksom i övriga världen. Men tills nyligen har vi, liksom många av våra kolleger, hoppats och trott att det skulle vara möjligt för Riksbanken att på egen hand sköta konjunkturpolitiken, om den bara helhjärtat ägnat sig åt uppgiften. Vi tog fel. Negativa räntor räcker inte för att nå inflationsmålet. Då finns ingen annan utväg än att trycka pengar, vilket alltså är vårt förslag. Med en större mängd pengar blir varje krona mindre värd, såvida det inte finns så mycket lediga resurser att produktionen går upp utan att priserna gör det. I båda fallen uppnås en önskad effekt.

David Domeij & Tore Ellingsen

Nej, de här herrarna är verkligen inte de första att förespråka expansiv finanspolitik …

Men bättre sent än aldrig! Denna föredömliga självkritik hoppas vi får se mer av från landets alla mainstream ekonomer som glatt traskat patrull och i årtionden salufört mantrat om “sunda statsfinanser” och penningpolitisk självtillräcklighet.

Economic models as knowledge-surrogates

28 September, 2015 at 16:29 | Posted in Economics | Comments Off on Economic models as knowledge-surrogates

The standard way in which time is introduced into economic theory is by having models with time lags in the equations. Shackle quickly disposes of this by pointing out that it poses a question rather than answers one …

One way out of these difficulties is simply to abandon time; to confine one’s attention to the ‘momentary world of perfect pre-reconciled choice’ … In the method of statics, one might expect, there is some hope of keeping things sufficiently watertight for the agent’s reason to have something definite to work on: the impoverishment of the framework of thought by the exclusion of time may be compensated for by the rigour with which one can formulate the now self-contained static theory …

Surrogate_reality-AugmentedThe second possibility is what I will call ‘the de-naturing of time’. Thus, one can consider agents choosing not a self-contained, momentary act of conduct, but rather a whole time-path or plan for future conduct. But this brings us immediately up against the … simultaneity problem. And this, in turn, means that the theory can only be made workable by supposing that these plans or time paths have somehow been pre-reconciledso that they are all mutually consistent and realisable. Accordingly, in such a situation, the expectations on which plans were based could all be fulfilled (or, more precisely, would be ‘self-generating’). This would then mean that the future produced no surprises: ‘time’ elapses but bears no novelty and no uncertainty. It is a future about which all agents have the perfect knowledge-surrogates for achieving the appearance of being ‘fully informed’. It will be no surprise to learn that in such a situation market prices (including now certain inter-temporal prices) are perfect knowledge-surrogates …

Alan Coddington

A Website Anniversary

28 September, 2015 at 10:52 | Posted in Economics | Comments Off on A Website Anniversary

Thomas-PalleyTen years ago (September 2005) I launched my website. To mark this anniversary, here are ten postings that I think got it right. Many of them are included in my book, The Economic Crisis: Notes From The Underground (2012).

1. Keynesianism: what it is and why it still matters (September 18, 2005). My first post. What was intellectually unfashionable back then is now in.

2. The Questionable Legacy of Alan Greenspan (October 16, 2005). Raining on the Maestro’s parade was not popular.

3. Winner’s curse: The Torment of Chairman-designate Bernanke (November 4, 2005). I suspect Mrs. Bernanke wishes Mr. Bernanke read this before accepting the job.

Thomas Palley

Robert Musil and yours truly in Berlin (private)

27 September, 2015 at 22:34 | Posted in Varia | Comments Off on Robert Musil and yours truly in Berlin (private)

20150925_164013Berlin has lately become a kind of second home to me, so it was time for a new sojourn there. Regular blogging is resumed tomorrow.

Relevance is not irrelevant

23 September, 2015 at 10:40 | Posted in Economics | 1 Comment

What is science? One brief definition runs: “A systematic knowledge of the physical or material world.” Most definitions emphasize the two elements in this definition: (1) “systematic knowledge” about (2) the real world. Without pushing this definitional question to its metaphysical limits, I merely want to suggest that if economics is to be a science, it must not only develop analytical tools but must also apply them to a world that is now observable or that can be made observable through improved methods of observation and measurement. Or in the words of the Hungarian mathematical economist Janos Kornai, “In the real sciences, the criterion is not whether the proposition is logically true and tautologically deducible from earlier assumptions. The criterion of ‘truth’ is, whether or not the proposition corresponds to reality” …

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One of our most distinguished historians of economic thought, George Stigler, has stated that: “The dominant influence upon the working range of economic theorists is the set of internal values and pressures of the discipline. The subjects of study are posed by the unfolding course of scientific developments.” He goes on to add: “This is not to say that the environment is without influence …” But, he continues, “whether a fact or development is significant depends primarily on its relevance to current economic theory.” What a curious relating of rigor to relevance! Whether the real world matters depends presumably on “its relevance to current economic theory.” Many if not most of today’s economic theorists seem to agree with this ordering of priorities …

Today, rigor competes with relevance in macroeconomic and monetary theory, and in some lines of development macro and monetary theorists, like many of their colleagues in micro theory, seem to consider relevance to be more or less irrelevant … The theoretical analysis in much of this literature rests on assumptions that also fly in the face of the facts … Another related recent development in which theory proceeds with impeccable logic from unrealistic assumptions to conclusions that contradict the historical record, is the recent work on rational expectations …

I have scolded economists for what I think are the sins that too many of them commit, and I have tried to point the way to at least partial redemption. This road to salvation will not be an easy one for those who have been seduced by the siren of mathematical elegance or those who all too often seek to test unrealistic models without much regard for the quality or relevance of the data they feed into their equations. But let us all continue to worship at the altar of science. I ask only that our credo be: “relevance with as much rigor as possible,” and not “rigor regardless of relevance.” And let us not be afraid to ask — and to try to answer the really big questions.

Robert A. Gordon

What went wrong with economics?

21 September, 2015 at 10:35 | Posted in Economics | 5 Comments

realty-check-aheadInternal coherence is one way of adjudicating among theories, but so is correspondence to everyday life. Too much realism may kill analysis, but too little realism is unscientific. If theoretical coherence alone were all that mattered, then the only constraint on theoretical exercises would be the human imagination. Interesting
puzzles would replace pragmatic solutions to problems encountered in the world — arguably, an accurate characterization of most contemporary economic theory. Economists must steer a course between (allegedly) pure description and the mere recording of events, on the one side, and self-indulgent mental gymnastics on the other …

Parsimony won out over thoroughness … By myopically pursuing only the formal aspects of the discipline, economics was reduced to its present state, in which we continually know more and more about less and less.

Peter Boettke

Mainstream economic theory today is in the story-telling business whereby economic theorists create make-believe analogue models of the target system – usually conceived as the real economic system. This modeling activity is considered useful and essential. To understand and explain relations between different entities in the real economy the predominant strategy is to build models and make things happen in these “analogue-economy models” rather than engineering things happening in real economies.

Formalistic deductive “Glasperlenspiel” can be very impressive and seductive. But in the realm of science it ought to be considered of little or no value to simply make claims about the model and lose sight of reality. Although the deductivist mathematical modeling method makes conclusions follow with certainty from given assumptions, that should be of little interest to scientists, since what happens with certainty in a model world is no warrant for the same to hold in real world economies.

Mainstream economics has since long given up on the real world and contents itself with proving things about thought up worlds. Empirical evidence only plays a minor role in economic theory, where models largely function as a substitute for empirical evidence. Hopefully humbled by the manifest failure of its theoretical pretences, the one-sided, almost religious, insistence on axiomatic-deductivist modeling as the only scientific activity worthy of pursuing in economics will give way to methodological pluralism based on ontological considerations rather than formalistic tractability.

To have valid evidence is not enough. What economics needs is sound evidence. Theories and models being “coherent” or “consistent with” data do not make the theories and models success stories.

No realism please. We’re Chicago economists!

20 September, 2015 at 16:52 | Posted in Economics | Comments Off on No realism please. We’re Chicago economists!

neoliberalism-meme-keanuSamuelson’s reconciliation of the micro-economic ideal type with involuntary unemployment was repudiated, along with Keynesian prescriptions, in favor of a view that there could be no involuntary unemployment , hence that government action was unnecessary. The result was a doctrinaire derivation of the laissez-faire conclusions that had been overturned by the formalist revolution; economics was now cleansed of Keynesian impurities that had been introduced in the interest of realism.

Peter Boettke

Efficient Market Hypothesis — an intellectually lazy ideology

20 September, 2015 at 10:21 | Posted in Economics | 1 Comment

Both Brad DeLong and Noah Smith have posts up on their blogs commenting on the status of the Efficient Market Hypothesis. As so often the really interesting questions however drown in the usual mumbo jumbo “the model is the message” pseudo science of four-factor models with two mispricing factors being better-performing than three-factor models …

Diane Coyle has a much more accurate view of what it’s all about:

I would defend using the assumption of rational choice as long as one realises that it is not a description of reality.

But there is one area where for 30 years economists – and others – have been making that mistake. That is unfortunately, of course, in the financial markets. Practitioners and policy makers acted as if the strong form of the Efficient Markets Hypothesis held true – in other words that prices instantly reflect all relevant information about the future – even though this evidently defies reality …

spock_in_2012_by_rabittooth-d4p2io9I think an honest conventionally-trained economist has to at least acknowledge that we grew intellectually lazy about this. Although we all knew at some level that the rational choice assumption was being made to bear too much weight, very few economists openly challenged its everyday use in justifying public policy decisions. Very few of us put this weight on it in our own work. But not all that many economists challenged its pervasive use in the public policy world …

The financial and economic crisis also spells a crisis for certain areas of economics, or approaches to economics. Financial economics and macroeconomics are particularly vulnerable. They are the subject areas where the consequences of the standard assumptions have been most damaging, because they are actually least valid. Financial market traders are not remotely like Star Trek’s Mr Spock, making rational calculations unaffected by emotion or by the decisions of other people. Macroeconomics – the study of how millions of individual decisions aggregate into economy-wide measures – is essentially ideological. How macroeconomists answer a question like ‘What will be the effect of cutting the budget deficit on growth next year?’ depends on their political views. This is not remotely a scientific area of the discipline. The consensus about macroeconomics during what’s been described as ‘the Great Moderation’ of the 1990s has entirely broken down.

Diane Coyle

Backfiring expectations

19 September, 2015 at 18:54 | Posted in Economics | Comments Off on Backfiring expectations

Economist Brian Arthur has made important contributions to our understanding of inductive versus deductive approaches to problem solving. Arthur notes that you can solve only the easiest problems deductively … But humans are superb at recognizing and matching patterns. We’re inductive machines.

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Arthur offers a model of inductive reasoning, effectively picking up where Lord Keynes left off. The model is based on the El Farol bar in Santa Fe, New Mexico … Attending the El Farol when it isn’t too crowded is fun … But the bar is a turn-off when it is packed.

To make the problem more concrete, Arthur suggests that the bar has a hundred-person capacity and that with sixty people or fewer it is not crowded and with more than sixty it is … This problem has two notable features. First, the problem is too complicated for a deductive solution. As individuals can only look at past attendance, there are a large number of legitimate expectational models. The potential bar goers must use an inductive approach. Second, common expectations backfire. If all believe most will go, nobody will go. And if all believe nobody will go, all will go. Like Keynes’s beauty contest, the issue is not just what you believe but rather what you believe others to believe.

Michael J. Mauboussin

Thank God Eric Schüldt is back!

19 September, 2015 at 10:12 | Posted in Varia | Comments Off on Thank God Eric Schüldt is back!

radioI dessa tider — när ljudrummet dränks i den kommersiella radions tyckmyckentrutade ordbajseri och fullständigt intetsägande melodifestivalskval — har man ju nästan gett upp.

Men det finns ljus i mörkret! I radions P2 går varje lördagmorgon ett vederkvickelsens och den seriösa musikens Lördagsmorgon i P2.

Så passa på och börja dagen med en musikalisk örontvätt och rensa hörselgångarna från kvarvarande musikslagg. Här kan man till exempel lyssna på musik av Jonathan Roberts, John Tavener, Arvo Pärt och Stefan Nilsson. Att i tre timmar få lyssna till sådan musik ger sinnet ro och får hoppet att återvända. Tack public-service-radio.

Och tack för Eric Schüldt! Äntligen är han tillbaka för att under höstmörkret vederkvicka våra utsvultna själar med gudomlig musik. En programledare som har något att säga och inte bara låter foderluckan glappa hela tiden — vilken lisa för själen!

Hallelujah

18 September, 2015 at 19:57 | Posted in Varia | Comments Off on Hallelujah

 

Applied econometrics — a messy business

18 September, 2015 at 11:14 | Posted in Statistics & Econometrics | 1 Comment

The applied econometrician is like a farmer who notices that the yield is
somewhat higher under the trees where birds roost, and he uses this for evidence
that bird droppings increase the yield. However, when he presents his findings … another farmer … objects that he used the same data but came up with the conclusion that moderate amounts of shade increase the yields … A bright chap … then observes that these two hypotheses are indistinguishable, given the available data …

51pDIwWiNLL__SX313_BO1,204,203,200_The obvious response of course, albeit one that econometricians occupied with
fitting a line to given sets of data rarely contemplate, is to add the ‘available
data.’ Specifically, the aim must be to draw consequences for, and seek out
observations on, actual phenomena which allow the causal factor responsible to
be identified. If, for example, bird droppings is a relevant causal factor then we
could expect higher yields wherever birds roost. Perhaps there is a telegraph
wire that crosses the field which is heavily populated with roosting birds, but
which provides only negligible shade … The fact that it is not possible to
state categorically at this abstract level the precise conditions under which
substantive theories can be selected amongst, i.e., without knowing the contents
of the theories themselves or the nature or context of the conditions upon which
they bear, is an unfortunate fact of all science …

Science is a messy business. It requires an abundance of ingenuity, as well as patience, along with skills that may need to be developed on the job.

Variable selection — not about having a ‘good fit’

17 September, 2015 at 11:08 | Posted in Statistics & Econometrics | Comments Off on Variable selection — not about having a ‘good fit’

cost-accounting-determining-how-cost-behaves-34-728Which independent variables should be included in the equation? The goal is a “good fit” … How can a good fit be recognized? A popular measure for the satisfactoriness of a regression is the coefficient of determination, R2. If this number is large, it is said, the regression gives a good fit …

Nothing about R2 supports these claims. This statistic is best regarded as characterizing the geometric shape of the regression points and not much more.

The central difficulty with R2 for social scientists is that the independent variables are not subject to experimental manipulation. In some samples, they vary widely, producing large variance; in other cases, the observations are more tightly grouped and there is Little dispersion. The variances are a function of the sample, not of the underlying relationship. Hence they cannot have any real connection to the “strength” of the relationship as social scientists ordinarily use the term, i. e., as a measure of how much effect a given change in independent variable has on the dependent variable …

Thus “maximizing R2” cannot be a reasonable procedure for arriving at a strong relationship. It neither measures causal power nor is comparable across samples … “Explaining variance” is not what social science is about.

Christopher Achen

Should we ‘control for’ everything when running regressions? No way!

16 September, 2015 at 12:55 | Posted in Statistics & Econometrics | 1 Comment

When I present this argument … one or more scholars say, “But shouldn’t I control for everything I can in my regressions? If not, aren’t my coefficients biased due to excluded variables?” This argument is not as persuasive as it may seem initially. First of all, if what you are doing is misspecified already, then adding or excluding other variables has no tendency to make things consistently better or worse … The excluded variable argument only works if you are sure your specification is precisely correct with all variables included. But no one can know that with more than a handful of explanatory variables.

piled-up-dishes-in-kitchen-sinkStill more importantly, big, mushy linear regression and probit equations seem to need a great many control variables precisely because they are jamming together all sorts of observations
that do not belong together. Countries, wars, racial categories, religious preferences, education levels, and other variables that change people’s coefficients are “controlled” with dummy variables that are completely inadequate to modeling their effects. The result is a long list of independent variables, a jumbled bag of nearly unrelated observations, and often a hopelessly bad specification with meaningless (but statistically significant with several
asterisks!) results.

A preferable approach is to separate the observations into meaningful subsets—internally compatible statistical regimes … If this can’t be done, then statistical analysis can’t be done. A researcher claiming that nothing else but the big, messy regression is possible because, after all, some results have to be produced, is like a jury that says, “Well, the evidence was weak, but somebody had to be convicted.”

Christopher H. Achen

How economists argue

15 September, 2015 at 17:17 | Posted in Economics | 2 Comments

Reality-Check-1024x682To a mainstream economist, theory means model, and model means ideas expressed in mathematical form. In learning how to “think like an economist,” students learn certain critical concepts and models, ideas which typically are taught initially through simple mathematical analyses. These models, students learn, are theory. In more advanced courses, economic theories are presented in more mathematically elaborate models. Mainstream economists believe proper models – good models – take a recognizable form: presentation in equations, with mathematically expressed definitions, assumptions, and theoretical developments clearly laid out. Students also learn how economists argue. They learn that the legitimate way to argue is with models and econometrically constructed forms of evidence …

Because all models are incomplete, students also learn that no model is perfect. Indeed, students learn that it is bad manners to engage in excessive questioning of simplifying assumptions. Claiming that a model is deficient is a minor feat – presumably anyone can do that. What is really valued is coming up with a better model, a better theory. And so, goes the accumulated wisdom of properly taught economists, those who criticize without coming up with better models are only pedestrian snipers.

Sherlock Holmes på besök i högskolevärlden

15 September, 2015 at 15:09 | Posted in Varia | Comments Off on Sherlock Holmes på besök i högskolevärlden

sherlock_holmesPå en av landets största högskolor

kunde man igår på dess hemsida läsa att

“Bra studiemiljö positivt för studieresultatet.”

Woah!

Vem hade kunnat ana det …

Simpson’s paradox and perspectival realism

15 September, 2015 at 13:23 | Posted in Economics | 1 Comment

Which causal relationships we see depend on which model we use and its conceptual/causal articulation; which model is bestdepends on our purposes and pragmatic interests.

simpsons_paradox_by_insecondsflat-d37lk7yTake the case of Simpson’s paradox, which can be described as the situation in which conditional probabilities (often related to causal relations) are opposite for subpopulations than for the whole population. Let academic salaries be higher for economists than for sociologists, and let salaries within each group be higher for women than for men. But let there be twice as many men than women in economics and twice as many women than men in sociology. By construction, the average salary of women is higher than that for men in each group; yet, for the right values of the different salaries, women are paid less on average, taking both groups together. [Example: Economics — 2 men earn 100$, 1 woman 101$; Sociology — 1 man earn 90$, 2 women 91$. Average female earning: (101 + 2×91)/3 = 94.3; Average male earning: (2×100 + 90)/3 = 96.6 — LPS]

An aggregate model leads to the conclusion that that being female causes a lower salary. We might feel an uneasiness with such a model, since I have already filled in the details that show more precisely why the result comes about. The temptation is to say that the aggregate model shows that being female apparently causes lower salaries; but the more refined description of a disaggregated model shows that really being female causes higher salaries. A true paradox, however, is not a contradiction, but a seeming contradiction. Another way to look at it is to say that the aggregate model is really true at that level of aggregation and is useful for policy and that equally true more disaggregated model gives an explanation of the mechanism behind the true aggregate model.

It is not wrong to take an aggregate perspective and to say that being female causes a lower salary. We may not have access to the refined description. Even if we do, we may as matter of policy think (a) that the choice of field is not susceptible to useful policy intervention, and (b) that our goal is to equalize income by sex and not to enforce equality of rates of pay. That we may not believe the factual claim of (a) nor subscribe to the normative end of (b) is immaterial. The point is that that they mark out a perspective in which the aggregate model suits both our purposes and the facts: it tells the truth as seen from a particular perspective.

Kevin Hoover

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