Good Assumptions, Bad Assumptions, and Economists

It is a major bone of contention of mine that the word ‘assumption’ is used interchangeably when in many cases it should be replaced with ‘hypothesis’ in economics – for example, that firms equate MR=MC is a hypothesis that can be falsified in its own right, rather than an ‘assumption’ in the purely scientific sense of the word.

Economists enjoy demonstrating that they don’t understand the difference between a good and a bad assumption. For example, here are the SuperFreakonomics guys:

There are some 237 million Americans sixteen and older; all told, that’s 43 billion miles walked each year by people of driving age. If we assume that 1 out of every 140 of those miles are walked drunk — the same proportion of miles that are driven drunk — then 307 million miles are walked drunk each year.

Convenient if you can’t be bothered to do your research, but scientifically worthless. This is a hypothesis about how people behave, and the analysis follows directly from there. If the hypothesis is wrong, the analysis is simply wrong and we need to start over.

Now, here’s Scott Sumner on the Diamond and Saez ‘Marginal Tax rates’ paper:

 And S-D also seem to lean toward the “assume a can opener” school of policy analysis:

“In the current tax system with many tax avoidance opportunities at the higher end, as discussed above, the elasticity e is likely to be higher for top earners than for middle incomes, possibly leading to decreasing marginal tax rates at the top (Gruber and Saez, 2002). However, the natural policy response should be to close tax avoidance opportunities, in which case the assumption of constant elasticities might be a reasonable benchmark.”

So there you are.  It’s just too much to ask of our policymakers to actually make hedge fund managers pay labor taxes on their labor income, but S-D have no problem waving a magic wand and assuming away all tax loopholes.  

Of course, this is perfectly good assumption from a scientific point of view, as the presence of tax loopholes has a fairly simple (albeit hard to calculate empirically) impact on a variable, e. We can easily adjust the analysis to change this later on.

I feel it is important that, to progress, we need to differentiate between assumptions, for which a relaxation has a clear mathematical impact on the analysis, and hypotheses, which themselves need to be empirically verified, and for which a relaxation causes a model to collapse completely.


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  1. #1 by John77 on March 12, 2012 - 11:30 pm

    It is remarkable how many houses are still standing as nearly all of them were built using three-dimensional Euclidean geometry, i.e. a hypothesis that the surface of the Earth is a plane, instead of Riemannian geometry.
    It may be more relevant to your concerns that the tax avoidance through treating earnings as capital gains is mostly private equity rather than hedge funds.
    IMHO to say “If we assume that 1 out of every 140 of those miles are walked drunk” does not deserve to be dignified with the title “hypothesis”. The hypothesis is that the same proportion of miles are walked drunk as are driven drunk – but it is not readily falsifiable as no-one knows how many miles are walked or driven drunk.

    • #2 by Unlearningecon on March 13, 2012 - 1:38 am

      ‘IMHO to say “If we assume that 1 out of every 140 of those miles are walked drunk” does not deserve to be dignified with the title “hypothesis”.’

      True, hah. Glad we agree on something.

      Interesting info in that comment too.

  2. #3 by isomorphismes on March 13, 2012 - 12:38 pm

    No, there is a legitimate difference. It depends what kind of conclusion you are trying to draw.

  3. #4 by isomorphismes on March 13, 2012 - 12:42 pm

    an ‘assumption’ in the purely scientific sense of the word … scientifically worthless

    Physicists use plainly falsifiable assumptions as well, e.g. continuous fluids. And continuum fluid mechanics are not worthless.

    • #5 by Unlearningecon on March 13, 2012 - 4:50 pm

      Well, all assumptions are plainly falsifiable in sense, including operating in a vacuum. The question is:

      a) What is the impact of the assumption on the analysis? What happens when we relax it?

      b) Is there a practically/mathematically feasible alternative that better resembles real world mechanics?

      • #6 by isomorphismes on March 13, 2012 - 9:25 pm

        a) right

        b) hmm, maybe, depends what you mean by “resembles real world mechanics” … and maybe it should be “resembles counterfactual mechanics” since a lot of economics is speculative. (example not related to what i’ll say below: should we do policy X, Y, or Z? we model all of them but will only choose one so reality will only resemble one)

        Unless you’re building a gigantic computer sim and using a jillion real data, the point of a model is not to look exactly like reality.

        Famously these kinds of models (like a wickedly complicated excel model or something) predict what GDP next year with awful precision.

        Real traders do not fool themselves that their Excel models will price things accurately, although they will run some monte carlos to get an idea of the range / distribution, or run stress tests to get an idea of robustness.

        And bankers have much better data than academics.

        A purely mathematical model, not a computer sim / monte carlo, is just supposed to explain something — a point of view, a hypothetical, or a part of reality.

        I looked up James Mirrlees because I was going to use Mirrlees taxation as a obviously false model with a point, but the entry on the makes it sound like he was quite naive about the meaning of his own model. Of course the NMR inventors were also naive about the applications of their work, they thought it would be used to tune industrial magnets. The inventor is focussed on how to invent the thing not how it will be used. (Same deal with surgery theory. Try to understand what Bill Thurston is talking about in his clay lecture or “not knot”, it’s all in the theory development realm.)

        Anyway I believe the correct way to talk about mirrlees model is: it makes this argument.
        * If taxation creates a disincentive to work,
        * then you can’t make very much money from taxing the thin upper echelons,
        * and you would decrease the overall output

        and furthermore it investigates the magnitudes of these effects to make sure we are not talking out of our #rses.

        I would then say I hear you, however I believe the richest are motivated by internal drive, achievement, love of work so much that marginal rate hikes would not decrease their incentive to work very much. Perhaps also we need to talk about real hedons at that income level.

        However there is still the logic of the mirrlees argument: if you’re thinking about the public purse, even if you hike the marginal rates up very high on the top .001%, despite the fact that they have orders of magnitude more money than the 1%, it doesn’t add to much on a national scale. And how does this lesson about exp( exp( $ )) scaling apply comparing the .1% to the 5%? Go back to the model. In public purse terms, clearly the most effective thing you can do is take a quid from every member of the organisation, it won’t bother them a bit and it will add up to a lot.

        I have a draft ready to go up to some point in the next few weeks/months where I ballparked the gains to US from taxing the top .001% or the top .01% at the most usurious of rates, based on the pikkety saez estimates of the top 40,000 families etc, and it really does not add up to much. It was something like a few billion dollars a year for completely gouging the top earners in a purposeful unfair way. Which is not going to solve any social problems except income distribution problems per se, see below.

        That’s the Mirrlees story, it’s a very clear message without being the end-all final word on tax policy. Not even close to the final word but it is an informative viewpoint, a good thing to keep in mind (whether the back or the front of your mind, it depends on the issue at hand).

        I would argue also that envy effects constitute a good reason to raise marginal rates on the wealthiest. Of course. [Here is another place where some economists think illogically about their models. “Envy is bad” / by definition it’s not pareto optimal / so be like an ostrich and put your head in the sand. However envy is a real measurable phenomenon, it really causes pain to people / loses hedons, so it’s worth including in the policy discussion.] If seeing someone else’s wealth / monetary success causes hedonic loss then that’s its own reason to condense the wealth distribution. Furthermore if these people are workaholics and driven even more by the promise of greater lucre then reducing the amount attainable saves them from themselves.

        (Here again I think about envy as a separate model. mathematical model, not computer sim)

        Finally there are fairness reasons to institute progressive taxation. Here I am again thinking with a model but it’s not a mathematical or computer sim but a third kind, just the mental models we all carry around naively. (“Everyone uses models, even those who don’t admit it”) Most obviously it would be impossible to accumulate modern levels of wealth in an anarchical society, there have to be banks and legal guards and people believing that the institutional setup is fair, or else somebody would have beaten up bill gates and taken his lunch money, not to mention he couldn’t have organised such a large company. So even when extreme wealth is justly earned, the beneficiaries could only do so because of the way society is set up, therefore relative to a “natural state” (and here I get to pick any counterfactual fantasy I want, I will pick something like a society dominated by warlords / drug lords or even less extreme inequalities of wealth in a society with less expensive, less effective weapons) they “get more” from living in our peaceful, commercial OECD world so they rightly should “give back”. Also insert epsilons that get multiplied, another model. (either random transactions –> power law story or pick some anecdotes from your professional life and ask which positive epsilon draws, when, changed the phase space — for example the epsilon that gets you or someone else into Yale Law with the alternative being much less prestigious)

        So that’s a rather plump argument(s) about “the right” levels of taxation, and I think only loosely am I talking about “real world mechanics”. Mostly I am talking about the logic of how things “would work” or even less, using models as part of a larger argument — for example “insert Mirrlees story here” and using that bit of logic inside a fuller perspective.

      • #7 by Unlearningecon on March 13, 2012 - 10:07 pm

        Just briefly, on b)

        For example, it’s evident that most firms use cost plus pricing and very few accept economist’s characterisation of MC and MR. Regardless of anything else, I would argue this means we need to abandon MC=MR and similar analyses.

  4. #8 by isomorphismes on March 13, 2012 - 1:05 pm

    What you are talking about is not good & bad assumptions. If I have measured something to be correct it is in fact not an assumption at all.

    • #9 by Unlearningecon on March 13, 2012 - 2:26 pm

      Perhaps the thought needs to be developed, but I still stand by the overall thrust of my post.

      • #10 by John77 on March 13, 2012 - 4:08 pm

        The overall thrust is good, but if you want to develop it you would do well to distinguish between “necessary” and “sufficient” conditions. If you relax a “necessary” hypothesis, the model *will* fall over; if you relax a “sufficient” one, it *may* fall over.

      • #11 by isomorphismes on March 13, 2012 - 8:41 pm

        I disagree with John77. The right way to develop your critique, I think, is: reading the wrong thing into the model.

        Going back to the fluid mechanics example. If I want to model an actual fluid I would use a computer. Then I would try to get all the constants as close to real values, include everything I can think of, etc.

        However running simulations all day and looking at charts will get you a bunch of 100 page printouts, pretty graphs, and not necessarily understanding why or “what’s controlling”. If you don’t believe me, try it.

      • #12 by John77 on March 13, 2012 - 9:28 pm

        @ isomorphismes
        How on earth can you disagree with my recommending an elementary tool?
        Referencing an article that shows Krugman doesn’t understand cartography as a reason for not distinguishing between necessary and sufficient conditions is just weird.
        If you want to model fluid dynamics using a computer you need to write a computer programme (or several, depending on how complex a system you have) that involves a whole series of hypotheses and a range of parameters, not just constants.

      • #13 by isomorphismes on March 13, 2012 - 9:34 pm

        How on earth can you disagree with my recommending an elementary tool?

        I would have also disagreed if your advice to UL was to check his/her arithmetic. I just don’t think that is the root of the problem with assumptions in economics.

        Referencing an article that shows Krugman doesn’t understand cartography as a reason for not distinguishing between necessary and sufficient conditions is just weird.

        The relevant quote from the krugman article is where he talks about what you learn from a sim versus from a model.

        I did not mean to suggest that UL shouldn’t distinguish between necessary and sufficient conditions. (See above)

        If you want to model fluid dynamics using a computer you need to write a computer programme … that involves a whole series of hypotheses and a range of parameters, not just constants.

        What’s your point?

      • #14 by John77 on March 13, 2012 - 9:50 pm

        As I wasn’t suggesting that UL should *only* do that – and I fail to see how any rational reader would think I was – your comment was ill-advised.
        My point was that your analogy looked like playing around with a pre-existing computer programme which you seemed not to understand, as you ignored the need for parameters, until it gave the right answer as a contrast to economists not understanding causes and effects. That looks more like a parallel to me.

      • #15 by isomorphismes on March 14, 2012 - 2:29 am

        John77, you are being unnecessarily rude.

      • #16 by isomorphismes on March 13, 2012 - 8:48 pm

        But you’re right, for example economists on average think that people are more selfish / motivated by desire for consumption / etc than the typical human’s opinion.

        That would be economists confusing popular models with reality which is a huge mistake.

        You make assumption A, reason that B logically follows, and then get “A implies B”. But “assume A, therefore A” is, um, assinine.

        In other words: models have their uses. But doing continuum mechanics doesn’t mean you assume that fluids are actually continuous, that would just be stupid.

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