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The role of institutions is largely invisible to models. One can interpret "institutions" as "technology" in Solowian growth, but insofar as access to better institutions is in part an ideological decision rather than a capital investment in innovation, then "better technology" is not merely a matter of investment. Advocates of prosperity must push back against anti-capitalist ideologies and advocate explicitly for property rights, rule of law, and economic freedom. Insofar as the Chinese SEZs were modeled on Hong Kong and Singapore, their models had been available for replication much earlier, but it took a decision by Chinese leaders to pilot the SEZs. Lee Kuan Yew to the rescue!

Of course, the SEZs then led to China's massive growth. What model would or could have predicted that growth (unless institutional changes such as SEZs were assumed in the models as exogenous factors, distinct from the mechanics of the model)?

Similarly, insofar as experiments with new jurisdictions and zones is an active field globally, growth models will be blind to the potential impact of such new jurisdictions.

Insofar moving from global poverty to prosperity necessarily involves institutional innovation, and insofar as mathematical models completely miss institutional innovation (at least at present, and please point me to any models that do incorporate institutional innovation), then mainstream economics based on mathematical modeling is missing the most important moral and practical issue pertaining to economics that matters for humanity.

Romer, of course, deserves considerably credit for advocating for charter cities. He basically saw this. It is a pity that his example has not been more widely followed among economists. Here is a piece he wrote which is much better than his well-known TED talk,

https://www.cgdev.org/publication/technologies-rules-and-progress-case-charter-cities

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"Using math can help you avoid making claims that are internally inconsistent. For example, you cannot claim that a perfectly competitive firm in long-run equilibrium is producing at a point where marginal cost is greater than the minimum of average cost. For a perfectly competitive firm, price equals marginal cost, and in the long run price equals average cost. A little calculus shows that marginal cost only equals average cost at the minimum of average cost."

I feel like you missed an opportunity here to point out how internal consistency is almost entirely besides the point, at best necessary for a good model, but nowhere near sufficient. One could start with how "a perfectly competitive firm" is something that does not exist, nor can exist, in the real world, and is in fact a construct to make the math easy. One could then step into how demonstrating that the model is correct, actually checking to see if all these firms that can't exist are charging the same price that also equals their lowest average cost, is also impossible as defining cost in the real world is terribly difficult. (Ask an accountant about activity based costing sometime.)

So we have a mathematical model about the behavior of firms that can't exist and how they price goods that we can't test. Yes, the model is internally consistent, but only because we have defined

'perfectly competitive firms' such that they behave the way the model suggests they should. In other words, the model is a mathematical tautology, telling us 2 +2 = 4 because 4 = 2 + 2.

What have we gained? A false sense of insight, and a false sense that we should be able to look at the world and say "aha! These firms are acting contrary to the model! We should do something!"

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This is a bit sophomoric, because the same argument can be made against any scientific theory or model. Euclidean geometry is an excellent example. It is internally consistent, but as we all know perfect straight lines, points and circumferences don't exist in the real world. So we have a mathematical model about figures that can't exist showing properties (such as an angle being right or points coinciding) that we can't test. The model is internally consistent only because we are working with theoretical entities. Nevertheless it would be tough to argue that we only gain a false sense of insight from Euclidean geometry.

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Except geometry does work, because we do have straight lines. They are not perfect, and the angles aren't perfect, but the model has lines and "lines" means the same thing between model and reality. Geometry is actually very useful because the ideals in the model can be approximated well enough in reality that you get consistent and predictable results. Machinists can actually make parts that fit together extremely closely, parts designed to do so using geometry.

In other words, we can test how close the model is to reality, and it is damned close even if we can't make reality match the theory exactly.

Perfectly competitive firms are as realistic as spherical cows in a vacuum, functionally speaking. Neither can exist in reality, and the model gives you false insight about how much milk they would produce. Both function in the model completely differently than their real life counter parts do for the purposes we are interested in.

Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.

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> the model has lines and "lines" means the same thing between model and reality

Not quite. That's why the editors of the text of Euclid (IV BC) which reached us prepended extracts from Theon's explanatory geometry handbook (V AD), including the pseudo-definitions 'a point is that which has no parts' and 'a line is length without width'. We have evidence that Euclid himself wished to disassociate his work from such statements, in that he used a different word for 'point', σημεῖον, which nobody before him used in the context of geometry, than the one Pythagoreans and the Platonic and Aristotelian philosophers had been using in the context of geometry, which was στίγμα. The model 'Euclidean geometry' abstracts some of the properties which real lines (drawn on paper, light rays, taut strings, edges of machined parts and so on) have, idealizes them, and this construct becomes the theoretical entity 'line' about which it is possible to make exact statements and prove theorems. This abstraction-idealization procedure also yields correspondence rules between 'lines' and lines.

> Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.

Okay, but then shouldn't this be your argument (preferably with details and examples) rather than a general attack on mathematical models?

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"> Lots of models work pretty well to help you understand and predict reality despite being abstractions, but perfect competition and perfectly competitive firms is not one of them.

Okay, but then shouldn't this be your argument (preferably with details and examples) rather than a general attack on mathematical models?"

That was my argument, with the examples. I also included the point that internal consistency is not enough.

Please, if you are going to respond to someone's comment, try to respond to their comment and not some half read and quarter understood version of it.

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Please to you. That wasn't your argument in the first comment. You wrote

> "a perfectly competitive firm" is something that does not exist, nor can exist, in the real world, and is in fact a construct to make the math easy

> we have a mathematical model about the behavior of firms that can't exist and how they price goods that we can't test

Call me pedantic if you wish, but nothing there says that models differ on how well they help one understand and predict reality despite being abstractions, and that the model of perfectly competitive firms just happens to be particularly bad at it.

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We are referring to different posts; I was referring to the post you immediately responded to, not the original in the thread. I didn't make a general attack on mathematical models in the original post, however.

The original post in the thread is about how internal consistency isn't so great, specifically in the example of perfect competition models as a class of mathematical models that achieve it by tautology. Apologies for not making it abundantly obvious, or going out of my way to point out that some mathematical models are not worthless even if that one in particular that I was talking about is. I also didn't feel it necessary to point out that murder is bad, or that one shouldn't steal.

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Yes, this.

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Application _theorems_ between models and reality are a contradiction in terms. Theorems belong to the world of models and apply to theoretical entities belonging to models. At best, when we reduce or otherwise map one model to another, there can be applicability theorems about applying conclusions made within one model to entities in the other. Reality, however, is infinitely richer than any intelligible model. Therefore correspondence rules which map between phainomena and theoretical entities cannot be entirely formalized. I'd even say that to the extent they _are_ formalized, they again map between models.

Lucio Russo calls this conscious delineation between models and reality the hallmark of the scientific method. He argues that it was developed by Hellenistic scientists such as Euclid, Archimedes, Eratosthenes, Ctesibius and Herophilus, but mostly lost after the Roman conquest of the kingdoms of the Diadochi. Later commentators who no longer understood this distinction considered the theoretical entities of Hellenistic science to be something as real as bricks and human beings and called them 'incorporeal'. Modern science mostly recovered it by late XIX century, but my impression is that it became obscure again in the XX century, since the tremendous success of science - first of all physics - blurred the distinction because the models became so successful as to be easily confused with reality itself.

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well, the fact that in September 2021 the FOMC median forecast for inflation for 2022 was 2.3% is a good indication that the current (?) econometric models are rubbish or informed by wishful thinking assumptions (Paul Romer wrote a wonderful essay on the trouble with macroeconomics). You can model rational economic agents behaviour but you capture a limited portion of the universe.

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Where is uncertainty? Policy makers, like people, have to make decisions under uncertainty - but most models minimize or eliminate the inevitable uncertainty. Of course, voters so often prefer false promises that are "certain" over honest discussions of the possible outcomes and the various probabilities of achieving those outcomes - such probabilities varying according to decisions taken.

And adding appropriate probabilities to already too-complex econ models will make them even more complex with a clearer range of outcomes, rather than a clear one that is more policy-deciding helpful.

Since economists agree that "money" is important - but can't agree on what money is, any and all equations that include money depend on the definitions used, as well as the assumptions and the measurements.

For instance, I don't like "CPI" (consumer price index) as a measure of inflation, because so much of what is bought in the economy is not included. Of course, if Apple shares are $1000, or $1500, or $2000, this doesn't much matter if you're not a stock investor -- but if the rich investors are getting the money printed by the gov't, and are using that money to buy shares, isn't that stock price inflation? Since the gov't bailed out irresponsible banks in 2008, the US economy has had increasing deficits and low CPI inflation but quite high asset price inflation.

Neither math nor stories will prove nor disprove MMT. See these posts from 2019 pre-Covid:

https://www.cnbc.com/2019/03/01/bernie-sanders-economic-advisor-stephanie-kelton-on-mmt-and-2020-race.html

https://econofact.org/what-is-modern-monetary-theory

How much national debt is "too much"? And why? At least Kelton's claim that inflation is the measure that there was too much spending seems a better answer than the non-MMT who don't have a theory about why Japan, with 240% (or more) is not having terrible problems.

Neither math nor politically corrected stories are sufficient for economists to achieve accurate predictions of the economy in future years, much less decades. The continued failure of economists to offer good predictions of future economic results means such macro economists should be lower status - but so far, this hasn't occured.

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I like how Kling thinks. Maybe it would be better if his views challenged my beliefs more rather than filling gaps but I learn a lot from his insights. He is a little more pessimistic than I'd prefer.

Two thoughts here:

1. Nevermind that Kling notes how mathematical models can be useful:

"But my guess is that the academic conversation in economics would be much improved without the math."

Do we want better conversations or more advancement? While some models and model result may be wrong or misleading, this is something that can eventually be identified. The harm can be overcome. But not all math is misused. I'm not at all confident what is lost by not having models can be overcome in their absence. It seems hard to believe adding tools and approaches to gaining insight is a net negative.

2 And now I go little in the opposite direction on models.

"Using math can help you avoid making claims that are internally inconsistent."

I suppose this has to be true but I'm not sure how often. It brings to mind a quote I don't know the source, "economist know the price of everything and the value of nothing." Models seem far more useful for prices than value. Making it even worse for models, Kahneman and Tversky made it pretty clear that framing changes our values and priorities. I don't see models catching any of this. At least not much and not well.

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Is math or English really the issue? Seems like it's the game itself. Economics as a professoin seems primarily oriented to producing esoteric knowledge. The purpose of esoteric knowledge isn't to understand things outside the profession, but to sort and rank economist within the profession--like Hesse's Glass Bead Game. A few talented and motivated economists try to produce exoteric knowledge of great insight. These latter few either rise quickly to the top of the profession or find more compatible vocations as essayists and authors outside academia as public intellectuals.

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A few points in favor of mathematical economics. The key point about math to me is what Arnold said, to wit, "Using math can help you avoid making claims that are internally inconsistent." And that core insight can go a long way. Math can show how inconsistent politicians are in their claims for helping the economy, prevent spending time on Modern Monetary Theory (which I like to say is neither modern nor a theory), and generate measurable models of economic events that can be tested empirically. Math isn't necessary for all of these benefits, but it can be useful in explicating hypotheses - and perhaps prescriptions - carefully, consistently and measurably.

Perhaps the academy leaned on overlapping generations models too much, but the basic model offers some important insights. Actually, particular insights can be gleaned from a simple, two dimensional, two-generation graph, which is a form of math. The graph can explain how and why money works and creates efficiencies, why it makes sense to discount future values to the present, how interest rates differentiate prices or the value of money in the present versus the future, and why social security can enhance efficiency by securing a retired generation's income using younger generations' income (as long as subsequent generations are larger or more productive). That's a lot of mileage from a simple graph.

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> But economists who question the wisdom of interventionist economic policies seem headed toward the fringes of the profession.

What I observed is that economists silo themselves into politically acceptable territory. For example, questioning the wisdom of interventionist economic policies puts you on the fringes if you are talking about domestic policy. But questioning the wisdom of non-interventionist economic policies puts you on the fringes when you you cross into discussing international trade.

But really, the same economic theory that suggests international free trade also suggests domestic free markets. Moreso really, because domestic trade more closely satisfies normal conditions of voluntary exchange (common property rights, etc).

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Being just a simple minded STEM nerd, I view mathematics as a language that allows you to "see" and "understand" the real world. Without this language, most views of the world must exclude dynamics and kinetics or any reasonable way to make decisions over time and space.

For an example, if you note that supply/demand market systems are feedback control systems where the control signal is the price. When the price goes above the marginal production cost, the production is increased. The mathematic of these systems is well known in control theory and the instabilities can also be fully described. Electrical engineers live in this world and that screech on a microphone is just a feedback loop going unstable .

The common view of this type of system would be your home thermostat that turns on or off according to the measured temperature being above or below the set point. If you put a pillow over the thermostat which puts a delay time in the measurement, the temperature in your home will go unstable and over heat then under heat then get too hot again and never get to a stable temperature. This is easily seen in complex phase space using complex numbers (a+bi) with i=√-1 type numbers.

When we get to economics as a feedback system we have regulators adding delay times slowing the response time of the supply function (can't build a new plant or housing without permissions). The mathematics of these systems says that delay times can create instabilities and will cause the price signal to oscillate unstably. A delay can make a stable supply/demand market system go unstable, independent of source of the delay.

Your statement: "But economists who question the wisdom of interventionist economic policies seem headed toward the fringes of the profession." hits a valid point. Most interventions create delays, but these delays themselves can shift a "working market system" into a "market failure". All the EE's I know understand the math of this problem, but economists can't seem to see that just adding another environmental or legal review will destroy the system.

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"each person can interpret Keynes or Minsky or Hayek to mean something a little closer to their desired conclusion. Mathematical modeling precludes that."

Do you think Noah Smith can't see the error here?

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"On the anti-math side, one argument is that the world is too complex to be reduced to equations. Equations “leave out” too much. Smith writes,"

Breaking news: Economists conclude the map is not the territory. Related: Water is wet.

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If more economists understood that the map is not the territory, it really would be a big deal. As it stands, most deeply believe the map is all that matters.

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If you think confusing the map with the territory is bad in economics, whatever you do, don't look at physics.

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"On the anti-math side, one argument is that the world is too complex to be reduced to equations. Equations “leave out” too much. Smith writes,"

Breaking news: Economists conclude the map is not the territory. Related: Water is wet.

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