Thursday, November 3, 2011

Oh Jeez...

This is the open letter to Greg Mankiw from the Harvard students who walked out of his class in solidarity with OWS (HT - Tom Dowling). It's breath-taking in its ignorance (and I know a thing or two about breath-taking ignorance... interpret that how you will...):

"Wednesday November 2, 2011

Dear Professor Mankiw—

Today, we are walking out of your class, Economics 10, in order to express our discontent with the bias inherent in this introductory economics course. We are deeply concerned about the way that this bias affects students, the University, and our greater society.

As Harvard undergraduates, we enrolled in Economics 10 hoping to gain a broad and introductory foundation of economic theory that would assist us in our various intellectual pursuits and diverse disciplines, which range from Economics, to Government, to Environmental Sciences and Public Policy, and beyond. Instead, we found a course that espouses a specific—and limited—view of economics that we believe perpetuates problematic and inefficient systems of economic inequality in our society today.

A legitimate academic study of economics must include a critical discussion of both the benefits and flaws of different economic simplifying models. As your class does not include primary sources and rarely features articles from academic journals, we have very little access to alternative approaches to economics. There is no justification for presenting Adam Smith’s economic theories as more fundamental or basic than, for example, Keynesian theory.

Care in presenting an unbiased perspective on economics is particularly important for an introductory course of 700 students that nominally provides a sound foundation for further study in economics. Many Harvard students do not have the ability to opt out of Economics 10. This class is required for Economics and Environmental Science and Public Policy concentrators, while Social Studies concentrators must take an introductory economics course—and the only other eligible class, Professor Steven Margolin’s class Critical Perspectives on Economics, is only offered every other year (and not this year). Many other students simply desire an analytic understanding of economics as part of a quality liberal arts education. Furthermore, Economics 10 makes it difficult for subsequent economics courses to teach effectively as it offers only one heavily skewed perspective rather than a solid grounding on which other courses can expand. Students should not be expected to avoid this class—or the whole discipline of economics—as a method of expressing discontent.

Harvard graduates play major roles in the financial institutions and in shaping public policy around the world. If Harvard fails to equip its students with a broad and critical understanding of economics, their actions are likely to harm the global financial system. The last five years of economic turmoil have been proof enough of this.

We are walking out today to join a Boston-wide march protesting the corporatization of higher education as part of the global Occupy movement. Since the biased nature of Economics 10 contributes to and symbolizes the increasing economic inequality in America, we are walking out of your class today both to protest your inadequate discussion of basic economic theory and to lend our support to a movement that is changing American discourse on economic injustice. Professor Mankiw, we ask that you take our concerns and our walk-out seriously.


Concerned students of Economics 10"

I'm not sure what my favorite part is - where they accuse Mankiw of being unfriendly to Keynes, or when they try to juxtapose Keynesian economics with Smithian economics.

Also - I think Mankiw should assign his students to read, summarize, and critique a full-length article from the AER. The whole point of an intro course is to give you the tools to read the harder stuff. How the hell do they think this works? Maybe this requires taking my readers back to their first economics class. You probably only learned what "marginal cost" was in a vaguish sort of way. You did not do comparative statics. You saw no calculus. You struggled valiantly to calculate a price level index. Many of you succeeded in that. A lot failed and probably never took another economics class. "Economic profit" and "opportunity cost" were fairly straightforward concepts, but they still probably took much of the class to really sink in.

Here's a rule of thumb: if a freshman in college can comment intelligently on a journal article, it is probably not a high quality journal.


  1. Wrt the ability of a college freshman to comment intelligently on a journal article, I mostly agree but disagree in the shadows. There are some high quality journals (such as J. of Ec. Perspectives) that I believe intelligent college freshman could comment on intelligently. In fact, that journal is designed for that purpose.

    I think there are some papers that are laid out in such a way where a college freshman could understand them at a facial level. Prescott & Kydland's Rules v. Discretion paper comes to mind.

    Certainly, I wouldn't expect a college freshman to be able to pick up a issue of Econometrica or Journal of Economic Dynamics & Control and comment intelligently. Furthermore, I wouldn't expect a PhD economist to comment intelligently if it was outside his field.

    But, to expect review of economic literature is rather strange. I know college freshman are introduced to journals in certain disciplines (history, e,g.). But, never in technical disciplines.

  2. And even with Journal of Economic Perspectives, it has a very unique mandate to do just that.

  3. Daniel,

    As I am sure that you know, I have never actually sat in an economics course. I was just curious, how much bias can there really be in an introductory-level class? I mean, I understand that with certain things like "value" and "utility" there are different theories, but can you really say it is biased to teach subjective value or ordinal utility vs the LTV or cardinal utility? I mean, we're talking about the basics here.

    It's funny that they bring up Keynes, because I would be willing to bet that most of them haven't a clue about even the most basic of Keynesian theories; it's like going into calculus before you've learned to add and subtract. Mankiw should walk into the next class and tell them to draw up some IS-LM or AD-AS models. When they look at him blank-eyed, he should say "oh yeah, you don't know how to do that yet, so shut your pie holes and listen up."

    You know I am not a Keynesian (or, and economist for that matter), but these kids are just being stupid.

  4. What's the test of an intelligent comment, please, as I know several college freshman who could take a reasonable shot at it.

  5. Daniel, would you have supported them if they walked out because Mankiw doesn't know the difference between a labor glut and unemployment?

  6. Who do these kids think they are? Someone whose opinion matters?

    These kids had their parents shell out an ordinary person's retirement savings worth of money, in order to learn from the masters of knowledge.

    But then they decide, "You know what? They have nothing useful to say. I know better."

  7. Preteek,

    In all honesty, most kids that age think they know it all and have the whole world figured out. I didn't figure out how much I really didn't know until I was about 25 (and, that was after be in a war and traveling the world). While I wouldn't classify Mankiw as a "master of knowledge", I do think that he knows quite a bit more than the kids in his class (I would hope).

    I don't typically like to stereotype, but I would imagine that most kids that are going to an Ivy League school really have no concept of the costs because they probably grew up without want (i.e. they were spoiled).

  8. Weird post and weird comments. I think you are reading their demand for a broader introduction to economics as more than it is.

  9. You don't think they are being a tad bit naive and haughty here, Andrew?

    I don't know - I'm guessing Mankiw's introductory course is among the highest quality intro classes any freshman could ever hope to get. I would certainly say they are more naive than anything else. But I can't really endorse this. And they're clearly trying to paint Mankiw as some sort of shill too. They don't appear to have a very good idea of what they are criticizing.

  10. If you read the letter it is mostly from the perspective of non-economics majors who have to take the class. So while I'm sure Mankiw's class is excellent for people who want to go into finance or go to grad school for econ I imagine it is quite lacking for people not interested in being initiated into those religious orders. As well, I think it's at least good form for professors to cite where ideas come from so they at least appear to be a little less handed down from the mountain.

    I don't know how much this is targeted at Mankiw specifically and is a critique in general of how econ 101 is taught. Without a syllabus of the class though I can't say anything specific.

    Except I do want to say that even the 101 textbook from such leftist warriors as Krugman & Wells simply uncritically repeats the orthodoxy of all 101 textbooks.

    Also one thing I don't like about your post and the comments is the general dismissal of the students concerns by insisting they are ignorant becuase they haven't gone to grad school.
    I took my intro to econ with a marxist and he did a really good job of highlighting why the orthodoxy of the subject

  11. whoops I meant to erase that last sentence.

  12. Daniel, in agreement, I must say I envy anyone who gets to be in Mankiw's class.

    To dismiss such an opportunity like it is nothing is shocking.

    It reminds me of the story of a gypsy family in UK which bought a mansion, but tore off the doors to burn them as firewood.

  13. So is their an online copy of Mankiw's syllabus available? I'd be curious to see what they are reading and covering.

  14. This comment has been removed by the author.

  15. I'm really pleased to see that there are students in that class who are figuring this out sooner rather than later. I didn't shake off the bias of Intro Econ until I took a Post-Keynesianism course my junior year.

    A first-year econ student might not be able to read something from AER, but we were frequently given "pop econ" readings from accomplished mainstream economists. These same resources exist from its stalwart critics: it's not too much to read Amartya Sen's critiques of theories of value; nor is it too much to read Joan Robinson's economic philosophy; nor to read Keynes' political works, or Smith's moral philosophy, or even a Marx epistle.

    What I mean to say is that a typical neoliberal Intro Economics course leans too heavily on mathematics, and gives a tilted perspective on economics "as a science" without introducing students to the very real philosophical and political debates underlying the various models and shading their applications and interpretations.

    You shouldn't teach students to "maximize, maximize" without asking them to wonder what they should be maximizing; asking them to consider whether there is a tradeoff between profit and employment and inequality that is not captured by AS-AD; whether efficient micro decisions lead to broadly inefficient macro decisions.

    In terms of science, evolutionary/irrationality work like that from Paul Zak and Dan Ariely can help lead students to question the rationality assumption, and prevent so many students from wandering off into naive libertarianism. There are accessible and readable versions of all of these arguments, even for college freshmen; surely they don't surpass in difficulty what a freshman philosophy major is let to strech his mind upon.

    A freshman may not be able to offer a useful critique on any of these things, but that's not what reading above one's level is for - can a freshman really comment intelligently on Heidegger or Kant? - but they are made to read them nonetheless. Why shouldn't economics also admit its own internal disagreements, expose students to its intellectual evolution, and produce new economists who are aware of and engaged with the faultlines in the discipline, rather than pretending it is a "value-free science?"

  16. What anybody who reads Greg Mankiw's blog will realize is that Mankiw is extremely open to all forms of economic thought and has discussed alternative views on everything.

    What Post Keynesians do is simply read a quick online summary that Mankiw is a "New Keynesian" and thus decide that he must be the Devil. He probably preaches neoclassical economics only, and never talks about what other people think. Except Mankiw discusses marginal and fringe perspectives far more often than **anybody**.

    Post Keynesians have this slightly irritating siege mentality, where they label any opposing view as "neoliberal" or call any view different from theirs to be "bias". They are quick to find enemies where there had always been friends.

  17. Prateek, I'm not attacking Mankiw personally or intellectually, only arguing that the content of his course is in fact shaded by his personal ideology and the general ideology of the profession. In any other social science or liberal art this would be common sense, but the "economics as science" crowd has done quite a job convincing the world that economics is somehow different and can therefore be considered truly - scientifically - neutral.

    All I mean to say is that that is false, and that Intro Econ - no matter who teaches it - does its students a disservice by pretending otherwise. There are plenty of sources very near the mainstream of economics that would present this discussion in a fashion accessible to college freshmen, and it's a thread that I argue they ought to be exposed to.

  18. Excuse me, are you speaking specifically about Mankiw's textbooks? Even though he has his own preferences in policy, he outlines what every other group thinks and the logic of their disagreement.

    If you were hoping to colour him as a man bound by ideological orthodoxy and bias, and a man not showing any other point of view, I am afraid you have done the man some disservice. He's very close to the crowd of Daniel Kuehn or Brad deLong in his broad openness to ideas.

    In fact, what this proves about OWS and the Harvard students inspired by them is that while they claim to be a movement for new ideas and ways of thinking, they have shown themselves to be in opposition to forms of broad forms of thinking they do not like.

  19. Just because the textbook contains a typical discussion of policy disagreements does not mean that it addresses the fundamental issues I'm talking about. I give Mankiw a great deal of credit for engaging these viewpoints and for being open to legitimate policy discussion.

    But those are debates about specific preferences, and they are still presented in terms of the mainstream economic framework. They don't confront disagreements over the components of economic value or whether economics is a science.

    They don't discuss the basic value judgments that are implicit in supply and demand analysis, such as conceptions of utility (with which there is a huge mainstream debate, Amartya Sen still being the prime example).

    They don't discuss possibilities of implicit economic imbalances stemming from capitalism's tendency to accumulation; they don't discuss the meaning of ownership in theory and practice; they don't discuss economics as a cultural phenomenon (see of course Dani Rodrik for one approach to this).

    All these approaches are central to proper economic analysis in my opinion, and I'm not promoting one school of thought over the other. I'm saying that students should be shown that these disagreements exist and asked to read primary sources as examples of them.

    That's one argument. The other argument is that economics has far too much math and too little critical thinking anyway and this distorts the discipline away from proper thought, pushes away social discussion, and discourages students who would be excellent economists but terrible econometricians. Critical discussions within economics are therefore just as important as mathematical ones, and need to be given a lot more room in the into course.

  20. Andrew -
    re: "Also one thing I don't like about your post and the comments is the general dismissal of the students concerns by insisting they are ignorant becuase they haven't gone to grad school."

    I can't speak for the rest of the commenters, but my point was that they are ignorant because they are only halfway through an introductory course. Isn't this a reasonable claim to make? Usually people who take courses that introduce a subject are ignorant of that subject. It would seem to be a massive waste of Mankiw's time if they weren't ignorant of the material. I also don't think it's the outrageous for me to suggest that the sorts of primary material they're demanding is written assuming a grasp of the introductory material. I don't see what's so controversial about any of this.

    This isn't about pedagogy, Andrew. It's about the fact that freshman students regularly consider econ 101 to be right-wing. It's about the culture shock that comes along with realization that there are tradeoffs in the world. A good professor shows clearly that this is just a fact and he/she shows that there is no necessary ideological content to that fact. Based on my own familiarity with Mankiw's textbook, I'm guessing he makes that point in class.

  21. Ben -
    There will always be heterodoxies, and as any reader of this blog ought to know I take those heterodoxies - Austrian, Post-Keynesian, and anything else - quite seriously and that I think they have very real and very positive contributions to make. But you don't make those contributions by pretending we're referring to some up-in-the-air philosophy with broad, legitimate foundational disagreements. That I disagree with. These heterodoxies make contributions by contributing to the explanatory power of the science, not be deconstructing it or philosophizing it. We teach it like a science because it is a science. It's an old science, too - not as old as physics but its modern version is about as old as that of chemistry or biology. Of course more philosophical discussions have a place in any of these settings, but it's reasonable to teach it like we teach all sciences: textbooks for introductions and articles for initiates. There are a few interesting philosophical points to wrestle with, but they don't take on the significance that you're suggesting.

  22. Ben -
    On your last paragraph I'm not understanding why you're juxtaposing math and critical thinking. What's the logic behind that? It seems to me you can't do good econometrics, for example (since you mention that one) without being a good critical thinker. My econometrics professor (who Andrew knows and can attest to) made teaching critical thinking a major priority in the class. Anyone can run a regression and tell you what the math means. That's just a lot adding and subtracting and dividing. It may take a little time to learn, but that's not the hard part. The hard part is precisely the critical thinking, which for some unexplained reason you think is what's not being taught!!! Maybe you've just had bad experiences in the past.

  23. In other words - don't make this into a debate about "critical thinking". Neither I nor anyone else taking my side of this has ever suggested a good economics education can dispense with critical thinking skills. That's what people mean when they refer to the "economic way of thinking" or "thinking like an economist".

  24. Dan, you say, "There are a few interesting philosophical points to wrestle with, but they don't take on the significance that you're suggesting." I think they really do. To name one coarse point of divergence: When we look from a neoliberal perspective we can create models which emphasize aggregate output and consider distribution as a residual. When we look from a Marxian perspective we can create models which emphasize distribution and take aggregate output as a residual. Reading philosophical work like Rawls at least allows us to consider the trade-of between these two approaches. In a typical intro macro class however, we are mainly shown the former type of model without recognizing that there might be a reason to look at the latter.

    And I think I was not clear with respect to "critical thinking". I agree with you completely that critical thinking is essential for economic work and that it is well-taught in that respect. But I mean to say there is not enough critical thinking *about economics* - the sort that might lead you to question theories of value, or of distribution, or of economics as science. Economics can be a historical field, or a philosophical field, or a political field - it has ideas that can be expressed in words rather than numbers - and I suppose I mean more that the "liberal arts" facet has been shut out by the "econometrics" facet.

    To clarify a little (but not nearly enough): I think that econometrics is a 'real' explanatory science, but that economics is not; economics is by necessity too burdened with subjective values to be properly a science. Muddling the two branches (and putting so much weight on math as a result) is I think counterproductive - it presents as objective and scientific a set of descriptive models which require subjective valuation at every turn.

  25. I think this discussion between Daniel Kuehn and Ben can be resolved if we call economics what is properly is - a humanistic social science, or as the British would put it, a "moral science".

    That way, we can avoid the positive economics versus normative economics ddistinction. Of course economists realise that morals play a role in policy.

    I think you two might want to read this history of economic thought that was recently translated into English: "The Economics of Good and Evil". Here's a positive review to stimulate an interest.

  26. - I don't know what you mean by "from a neoliberal perspective". That sounds like a political disposition, not a scientific one. Anyway, I think it's fair to call me a neoliberal ideologically, and questions of distribution are not "residual" for me.

    - I don't know what you mean by "consider distribution as a residual". It seems to me distribution has been a central question of mainstream economics since Ricardo. Isn't discussion of distribution a central point in neoclassical economics? Isn't the innovation of game theory precisely an innovation about the way resources are distributed? I think all you mean here is "you guys don't talk about it how Marx talks about it and I wish you talked about it how Marx talks about it".

    - re: "Economics can be a historical field, or a philosophical field, or a political field - it has ideas that can be expressed in words rather than numbers - and I suppose I mean more that the "liberal arts" facet has been shut out by the "econometrics" facet.". OK... but those don't seem to be "economics". Deepak Chopra can philosophize all he wants about quantum mechanics, but I don't think they should teach him in a physics class. And that doesn't mean that these perhaps otherwise edifying perspectives aren't valuable. People should talk philosophically about value and distribution and equality and property. What I am concerned about is that philosophical predispositions displace the science of economics. We are understanding the social behavior of a highly evolve primate. If you want to discuss the implications of that, that's great. But if you want to understand the behavior itself, you do the science. There's certainly a lot of politics to be done and discussed once you get the answer from the science. I support welfare programs, for example, as a philosophical and political matter. But I don't pretend my philosophical justifications for these things represents a challenge to the science of the question.

  27. I remain indignant, Blue Aurora. I've always liked the positive/normative distinction. I certainly wouldn't deny that economics has moral significance, but it's precisely because of that that it's crucial to identify and continue to make the positive/normative distinction.

    If we studied resource allocation behavior for any other species on the face of the earth it would be done by a guy who was known broadly as a "biologist". Because we're doing the same damn thing for homo sapiens the history is muddied and the stakes are raised. But the moment we treat our work as anything other than primatology is the moment we start accepting the idea that our ideologies or our philosophies can lead us. My view is that on these positive questions they can't. And if anyone wants to tell me that they can or they should, you need to explain why that doesn't work when we're studying the social behavior of other primates.

  28. I definitely agree on keeping the positive/normative distinction. There is definitely a descriptive and scientific econometrics that is used to describe observable behavior of man as primate.

    But once you get into any sort of normative economics - once you start talking about "welfare" or "utility" especially - then this is gone. Here we are talking about a social animal that has observable individual preferences, but more importantly has a poorly-defined (in the mathematical sense) set of collective preferences.

    We want to objectively measure interpersonal utility comparisons; we want to talk about social gains and costs. These things are not possible without making value-laden assumptions about the equality or inequality of preferences, desires, and satisfactions between people; and worse, about collective entities which exist only metaphysically and are logically inconsistent.

    So I think root philosophical disputes are really very important in the way we think about economics as a social science, and why the liberal arts facets should be considered economics even though they exactly aren't the 'sciency' part.


    On the 'neoliberal perspective': it is a political position, and that's part of my point. I don't mean 'residual' in the sense of 'unimportant', but say you use a typical intro AS-AD model to observe distribution: it's not an immediate concern of the model. You can calculate it eventually, but why not look at, say, Kalecki's model that takes 'savers and spenders' and explicitly calculates the income distribution from their marginal propensity to save?

    This is no more difficult than the aggregate income model presented to freshmen but it gets at distribution directly and its first derivatives show you how to change distributional outcomes, rather than having its first derivatives show you how to change output. And I think distribution has been largely ignored by neoclassical economics, and especially by neoliberals. A model where 'efficiency' is a core concept silences questions of distribution because there is not an explicit metric for it.

    Take for example AS-AD in monopolistic competition (ie Card/Krueger). The immediate implication is that you can increase employment and wages by mandating minimum wages - which is seen as 'good' because it increases efficiency and moves closer to the marginal costs equilibrium. But when I look at the model I would say something like, well, we can redistribute income further from demanders of labor to suppliers of labor by pushing the minimum wage *above* the market equilibrium. But if we don't have a metric to describe that exchange, or a theory of what are the relative subjective valuations of these changes, then it's hard to describe that as a potentially desirable policy in terms of "maximization", and, more importantly, the model doesn't even suggest that possibility. That's really closely related to what I mean by 'distribution as residual', too.

    Likewise with inflation. There are clear theories of how inflation can decrease wealth in aggregate, but there is not really a discussion of why this might be a good thing if some people (debtors) gain while others (creditors) lose. The Kalecki model can begin to think about these changes from the impact on two separate class groups with different behavioral parameters (but we need something more Rawlsian to see the welfare impact), but a neoclassical model sees it as an unambiguous efficiency loss.

    Sorry this comment ran so long and ended so abruptly, but I have to get back to work, which, incidentally, is econometrics ;)

  29. Daniel Kuehn: Of course I wouldn't explain away the behaviour of other primates using philosophy. In fact, I did not say that objectivity was impossible in economics, but once again, I'm impressed. Nevertheless, virtue ethics is contained in the economics of Adam Smith, and to some extent, Amartya Sen today. Our moral underpinnings must always be recognised even when it comes to technicalities like say, the empirical findings of a macroeconomic stabilisation policy.

    Ben: As for neoclassical economists and normative economics Ben, I wouldn't totally agree on that. Arthur Cecil Pigou was responsible for the creation of welfare economics, and he was concerned about externalities. N. Gregory Mankiw also supports Pigouvian taxation.

  30. These kids are arrogant to even think themselves capable of determining whether the course is biased or not. A good sign that you're not qualified to discern what should and should not be taught in an introductory econ course is that you're taking an introductory econ course.

  31. I would be willing to bet that much of the content of the debate on this page never entered the minds of those students. Somehow, I believe that the motive was quite a bit simpler.

  32. Here's a rule of thumb: if a freshman in college can comment intelligently on a journal article, it is probably not a high quality journal.

    OR the field is lost, accumulating little knowledge, and thus producing little inferential distance from the layman

    OR the journal makes itself comprehensible and contains the pointers necessary to cover the inferential distance for any intelligent person.

    I'm generally troubled by the lauded correlation between incomprehensibility in a journal and quality.

  33. I can't speak for the rest of the commenters, but my point was that they are ignorant because they are only halfway through an introductory course. Isn't this a reasonable claim to make? Usually people who take courses that introduce a subject are ignorant of that subject. It would seem to be a massive waste of Mankiw's time if they weren't ignorant of the material. I also don't think it's the outrageous for me to suggest that the sorts of primary material they're demanding is written assuming a grasp of the introductory material. I don't see what's so controversial about any of this

    Then substitute "theology" for "economics" and see if you would make the same claim.

  34. After reading through several principles of microeconomics textbooks (including Mankiw's), I can't say that I am surprised at this incident.

    "We are walking out today to join a Boston-wide march protesting the corporatization of higher education as part of the global Occupy movement."

    These pro-interventionist brats have had their preconceived notions about the world challenged and now they think the economists are sycophants for corporations. I would bet they walked when he started talking about price controls.

  35. Anon, as I have said elsewhere, I doubt that they would have done the same if it was Stephen Marglin's class. Just sayin'

  36. (1) Introduction to economics is actually introduction to neoclassical economics.
    (2) Mankiw's books tell one side of the story. The 'kids' want to be taught the other sides.
    (3) The protest is an indicator of what the students want (their preferences). They need to be respected and addressed and not be labelled 'arrogant', 'childish' or 'ignorant'.

  37. "(1) Introduction to economics is actually introduction to neoclassical economics."

    Oh, do give it up.

    You are being no less frivolous than Pete Boettke, when he complains that introductory micro-economics courses are anti-market.

    It's time we admit that people who accuse others of ideological bias are often speaking from their own ideological bias. It says less about the ones criticised, and more about the critic.

  38. Prateek,
    I never said anything about the ideological bias of neoclassical economics. There is obviously no issue if a particular theory is biased, as long as they are not taught as "positive economics" which is supposedly unbiased.

    Also, in my comment, I did not accuse anybody. All I said is that the students' dissent need to be addressed.

  39. Here's my suggestion to the students: teach yourselves.

    Or to quote _Good Will Hunting_:

    " dropped 150 grand on a fuckin' education you could have got for a dollar fifty in late charges at the public library!"

  40. I prefer to buy my books (hardback is preferable). But, yup.

  41. ...unfortunately, all the public libraries are getting the ax these days. But yes, this is a good point that should be recognized more often. And for those who do drop the 150 grand, they should realize that the most valuable part of the university is its library.


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