Noah Smith Picks Up the Theme

He writes,

In macro, most of the equations that went into the model seemed to just be assumed. In physics, each equation could be – and presumably had been – tested and verified as holding more-or-less true in the real world. In macro, no one knew if real-world budget constraints really were the things we wrote down. Or the production function. No one knew if this “utility” we assumed people maximized corresponded to what people really maximize in real life. We just assumed a bunch of equations and wrote them down. Then we threw them all together, got some kind of answer or result, and compared the result to some subset of real-world stuff that we had decided we were going to “explain”. Often, that comparison was desultory or token, as in the case of “moment matching”.

In other words, the math was no longer real. It was all made up. You could no longer trust the textbook. When the textbook told you that “Households maximize the expected value of their discounted lifetime utility of consumption”, that was not a Newton’s Law that had been proven approximately true with centuries of physics experiments. It was not even a game theory solution concept that had been proven approximately sometimes true with decades of economics experiments. Instead, it was just some random thing that someone made up and wrote down because A) it was tractable to work with, and B) it sounded plausible enough so that most other economists who looked at it tended not to make too much of a fuss.

I think that this is a well-expressed criticism, which Paul Krugman sidesteps in his response. I understand Krugman’s point to be that it is possible when expressing ideas verbally to say something that would be incoherent or self-contradictory if you were to try to express it in mathematical terms.

However, let us reflect on Smith’s point. Macroeconomic equations are not proven and tested. They are instead tentative and speculative. And macroeconomists have not been able to avoid allowing math to disguise this tentative, speculative quality of theory. Indeed, in the very same post in which Krugman defends math, he writes,

The basics of what happens at the zero lower bound aren’t complicated, but people who haven’t worked through small mathematical models — of both the IS-LM and New Keynesian type — generally get all tied up in verbal and conceptual knots.

In fact, it is pretty to easy to understand the liquidity-trap argument without mathematical models. However, the idea embedded in IS-LM models that there is only one interest rate is controversial (in fact, it is downright false). The idea that the Federal Reserve runs out of things to buy when the Fed Funds rate is zero is controversial. The idea that an interest rate that is “close to zero” is the same as an interest rate that is zero is controversial. Yet Krugman appears to be so persuaded by his math that he cannot seem to come to terms with anyone who disagrees with his view that the liquidity trap is an important characterization of the current U.S. economy.

I think that Noah Smith has expressed clearly and profoundly that macroeconomists who dress up like physicists are being tragically foolish. I think it is one of the best blog posts that I have ever read.

The idea of freeing macro from its pseudo-physics pretensions came up in Jag Bhalla’s post that I mentioned the other day. Perhaps it is something “in the air” right now. I hope so.

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24 Responses to Noah Smith Picks Up the Theme

  1. Ryan says:

    “Macroeconomic equations are not proven and tested. They are instead tentative and speculative.”

    And how is that different from narrative/heuristic theorizing? How is that different from your approach?

    While I agree that some researchers probably take the math too seriously and succumb to the illusion of precision, it also seems that those who prefer the narrative approach sometimes buy into the illusion that their own assumptions and mechanisms–sometimes unspoken–are something other than tentative and untested. Indeed, it sometimes seems that the math critics are deluded into thinking that they aren’t making any simplifying assumptions, since their method does not force them to be explicit!

    Math is just a tool. Of course it can be misused. But intellectual humility requires that we divulge as much of our thought process as possible so that we can all argue about it, and math is a disciplined way to do that (but not the only way, of course).

  2. Handle says:

    If you want a good example of the narrative approach prior to the popularization amongst economic intellectuals of tables, charts, and abstract mathematical expressions – try Adam Smith’s “The Wealth of Nations”. At times the writing is brilliant, but often it’s laborious and a trudge to get through. A contemporary individual trained to think with modern intellectual tools finds oneself thinking time and time again, “The last several hundred or thousand words could have been more efficiently expressed with a simple diagram and maybe a simple system of two or three relation equations.”

    Rigor, in general, is only productive when the noise to signal or dispersion of the data or assumptions is low. Otherwise errors propagate. The approach is best suited to situations heavy with accounting concepts (‘present value’) and when analyzing the behavior of medium-sized sophisticated forms who are trying to optimize their business.

    When dispersion is high, or assumptions strain credulity, or irrational human psychological factors are paramount – the mathematical approach merely gives the illusion of rigor. The easiest remedy is for the mathematician to include the ‘deltas’ of uncertainty and instead of pronouncing them ‘negligible’ carry them through the analysis, and then show us the ‘sensitivity’ of the final result to the magnitude of the uncertainty.

    It’s like artillery – if you’re off by an inch and you miss by a mile, and you can’t dial it in any better than an inch at a time, the gun’s no good. If a 0.001% change in one’s estimated discount rate means that the effect of climate change by 2100 is alternatively catastrophic impoverishment or untold riches, the answer is ‘We can’t know, we can’t even give an honest best guess.” If CAPM doesn’t line up with reality, maybe you can go back and find which assumptions hold up the least and why – there’s a decent research program.

    One of the problems of insisting upon this is that it makes it impossible to derive analytical expressions or solve differential equations. That’s disappointing to someone with an aesthetic preference for elegant expressions. Well, deal with it. Everyone has access to huge amounts of cheap computation these days – simulate the results and find some best-fit curve. As of yet – there seems to be some bias against this in the literature – perhaps because we can’t actually extract any strong, confident, elegant results.

    But if that’s so – what’s Macro for?

  3. peter dub says:

    Noah is making a point that about a kajillion blog commenters and an equal number of econ students have made over the years. In the absence of a new approach, the critics go off and do something else, leaving Krugman and his critics to argue over who is better at squeezing the same orange.

  4. Jack PQ says:

    Noah is great but, as usual, over-the-top. The problem is that having only one ”run” of data (no experiments), you have to relax your empirical approach and you end up with many models that could fit the data. Researchers are then tempted to choose a model that is most consistent with micro theory (because ”it should”), and empirical validation follows. But it is cherry-picking.

    I do not agree that ”the math is all made up” but rather it is just one among many equally plausible models. It is ”the truth”, but not ”the whole truth and nothing but the truth”.

  5. Ian says:

    As an econ layman, to me econ bloggers gain credibility when they make predictions that come true. I don’t really care which method they use. One good thing about Krugman is that he is very aggressive about reposting his old blog posts when something he described ends up occurring.

    Arnold, I don’t remember too many of your predictions, and when you’re right, I don’t think you advertise it as strongly as Krugman. Caplan and Henderson are constantly making bets (or trying to anyway), but again the results aren’t trumped up as much as Krugman’s. It may be that Krugman is better at trashing his competitors when his predictions come true so his wins are more memorable.

    • Arnold Kling says:

      In my view, Krugman is the master of the pseudo-prediction. He says 10 things that sound like predictions, but each has a “catch” that allows him to deny that it was a prediction. So even if 9 out of 10 of them go wrong, he uses his deniability catch on those 9 and then shouts the 10th from the rooftops. I feel sorry for anyone who falls for that.

      • Ian says:

        I agree with you. I don’t think I’m fooled by it. He’s much less explicit than Bryan about defining his bets. I think he typically ignores his failed predictions, or twists them into “victories”. But I think he’s very good at highlighting the importance of his wins. I can’t think of any PSST wins and I read your blog fairly closely. In fact I read other economists discussing structural unemployment more frequently than you do, which is surprising to me.

  6. Jeff R. says:

    I think of the whole debate in Hansonian terms: whose status is raised by dressing macroeconomics up like physics? People like Paul Krugman. In fact, it probably raises the status of all economists to dress untested theories up like Newtonian Laws. Making the entire field sound more authoritative gives everyone in the field more authority, so dressed up it shall be.

  7. David N says:

    Physics and economics have the same problem. A theory has a range of applicability, and there are scenarios outside the range where the assumptions or approximations don’t work.

    The difference between physics and economics is that in economics it is difficult to predict when and where your assumptions and approximations are invalid. Humans cannot be modeled like electrons.

    “Handle” above makes an important point. Many mathematical models in all kinds of science fail to adequately deal with uncertainty. In modeling human action it may be impossible even to quantify uncertainty.

  8. Mike Gibson says:

    Andrew Lo wrote a great paper on touching on these themes. It was called “Physics Envy is Hazardous to Your Wealth” He also gave a presentation on it that’s available as a video.

  9. Handle says:

    I’ll add one caveat – there is a lot of bogus, three-axes / politico-moralistic narrative-style economics that doesn’t actually, you know, crunch the numbers. Some of the best Social Science I see is basically economics-style ‘response to incentives’ that involves a large amount of big-data number crunching.

    It’s not ‘Physics Envy’ to have a preference in favor of empirical results over just-so storytelling intuition.

  10. Noah Smith says:

    Thank for the kind words!

    Really, I was talking about my personal lack of interest in economath, rather than its overall usefulness. Of course, the two are related. But my views on overall usefulness are a bit more nuanced:

    I get annoyed by economath, but I HATE the kind of “word salad” that certain people seem to consider a good substitute. I’d much rather have some equations than a bunch of terms whose definitions I won’t understand unless I’ve read 35 classic econ books (and which even then can be argued about ad infinitum).

    But anyway, in general, we seem to feel much the same…

    • Handle says:

      Sometimes it’s the lack of word salad that creates the trouble.

      People often use the expression “The Uses of X” to denote the political-influence exploitation of the products of a particular discipline. “The Uses of History”, and so on. The ability to place the imprimatur unquestionable objective ‘scientific’ authority on a result (and to ridicule critics as cooks) makes the assertion seem more fact-like.

      Economics is particularly vulnerable to being politicized in this manner because the court-like language of elite persuasion revolves around policy analysis and costs and benefits.

      Most commentators like to launder their personal ideological preferences under the guise of an objective evaluation of costs and benefits. But, of course, they don’t bother to explain their model of the dynamics of a particular question, why we should accept that model, or show how the calculations come out were one to actually accomplish the analysis.

      It’s a common pattern of discourse – I see it a lot from Yglesias, but he’s hardly alone. In my mind, when I read things like that, a little lie-detector voice screams, “Show me the model and the math and the numbers!”

      My worry about this particular conversation is that ‘economic math ain’t all it’s cracked up to be, and sometimes it’s a sham’ will itself be used by sly commentators and enable them to justify their insincere portrayals of mere preference (or judgments about agenda-furthering convenience) as instead being based in objective cost-benefit policy analysis, and abjure the need to be explicit about their implicit calculations by asserting (using this discussion as ‘basis’) that such explication has no genuine utility. It most certainly does.

  11. Ovidiu Racorean says:

    Math is indispensable in economics as in finance research. Just take a look , out of curiosity, of how far math goes into financial markets !!

  12. Rich Berger says:

    Karl Popper and F.A. Hopper both made the point that the aping of the physical science is a fundamental mistake, which they referred to as scientism. Here’s Hayek quoted in a letter by Burton Malkiel to the Wall Street Journal:
    As Hayek explained in his Nobel lecture, here alluding specifically to post-WWII macroeconomic modeling: “It seems to me that this failure of the economists to guide policy more successfully is closely connected with their propensity to imitate as closely as possible the procedures of the brilliantly successful physical sciences – an attempt which in our field may lead to outright error. It is an approach which has come to be described as the “scientistic” attitude – an attitude which, as I defined it some thirty years ago, ‘is decidedly unscientific in the true sense of the word, since it involves a mechanical and uncritical application of habits of thought to fields different from those in which they have been formed.’”

    These models are not derived from the bottom up and the individual elements cannot be effectively tested. As noted by Mr. Kling, the whole edifice is based on guesses about the individual parts which cannot be verified.

  13. Daniel Baker says:

    Thank you for the post. You do a good job of demonstrating that Krugman sidesteps many of the downsides of math in economics. It is not enough to show that there can be some benefits to showing something with math. Math in economics must also pass a cost-benefit test.

    Math has very real costs when its assumptions eventually prove to be misapplied. It convinces economists and the public that highly accurate analysis is possible where it is not. Even when this accuracy is disproven by events such as the global financial crisis, the models are not throw out and are instead used as a point of comparison for new models. Full argument of this position is in this article:

    Thank you for the interesting post.

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