Monday, February 8, 2016

Economics is not logic and therefore not true or false


Mark Thoma linked to an article by Edward Prescott (of RBC aka Kydland-Prescott and HP filter fame) which I haven't read. I made it through the abstract to this sentence:
Reality is complex, and any model economy used is necessarily an abstraction and therefore false.

This is a dumb sentence. It either has zero content or is wrong. Prescott is probably using it to defend his RBC theory against the fact that it doesn't really match up with empirical data, but even then it's still a dumb sentence. 

First: abstractions are not falsehoods (i.e. antonym of tautology). They are abstractions. All of mathematics is an abstraction, but 2 + 2 = 4 is not false. An abstraction may be an approximation of reality with varying degrees of usefulness. But usefulness is a continuum, not a Boolean.

Second: approximate theories are not false. This is the same sense of "false" that (apparently) Popper viewed Newtonian physics compared to Einstein. People who know the theories understand that one is an approximation to the other with a certain scope. How would calling an approximation "false" be helpful? What do we learn from the sentence (translating):
Reality is complex, and any approximation used is necessarily approximate and therefore approximate.
I hope you wrote that down in your copybooks. It's going to come in handy never. You can capture the same idea by saying "we haven't really figured economics out yet". Really? You don't say ...

This dumb sentence comes from a dumb view of economics; Brad DeLong gives us a quote from Keynes that encapsulates this dumb view:

It seems to me that economics is a branch of logic, a way of thinking ...

No it's not. It's an attempt to see if a real world system involving numerical quantities has regularities expressible in terms of mathematics [1]. You can use logic in economics, but economics is not a branch of logic. If it was a branch of logic, you could do economics without ever collecting data. This is something that is false in a useful sense of the word.

...

Footnotes

[1] I do always find it funny that people think economics has too much math. Are they ok with physics having that much math? Well physics doesn't even have any explicit numbers -- all of the numbers in physics are made up (human defined) quantities. Gravitational acceleration on Earth is 9.8 m/s/s. But we made up meters and seconds. Economics can actually have explicit numbers: e.g. two widgets for six tokens of money. You can count them.

15 comments:

  1. "Second: approximate theories are not false."

    For most of macroeconomics, I search in vain for an error term. :(

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    2. Thanks, Jason. :)

      Now if we can only get the Congressional Budget Office to include error estimates in their projections. ;)

      IMO, they do not include them because Congressmen do now want the graphs to reveal how useless they are.

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  2. "All of mathematics is an abstraction, but 2 + 2 = 4 is not false."

    If there were two apples in one box and two apples in another box - you would have four apples all together. This would be a precise description of reality.

    However, you are confusing mathematics with arithmetic. The operation to characterise the reality described above is arithmetical.

    A mathematical algorithm attempting to characterise the above reality would operate at a completely different level.


    "..approximate theories are not false.."

    You define approximate theories with your use of the comparison between the Newtonian and Einsteinian theories of gravity. This is not the way to define an "abstraction".

    And of course you take the Keynes quote out of its context.


    Henry




    e

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    1. There is no difference between "arithmetical" and "mathematical" -- nearly all of modern mathematics can be derived from the Peano axioms (or their set theory equivalent) which are basic arithmetic. There is no level at which mathematics becomes more abstract or less abstract (not sure what that even means). It is all a formal abstraction.

      I can write a DSGE model like Kydland-Prescott as a series of additions -- it actually is typically written as difference equations. It is no different than addition; it's just thousands of them.

      If it can be simulated on a computer, it can be written as a series of additions -- for that is all that computers do.

      And I have not taken the Keynes quote out of context; here is the context:

      But in [your manuscript], although I agree with nearly all your detail and your treatment within your own chosen terrain, I am not so clear that you have chosen or planned your terrain rightly.

      It seems to me that economics is a branch of logic, a way of thinking; and that you do not repel sufficiently firmly attempts à la Schultz to turn it into a pseudo-natural-science.


      Keynes argues that economics is logic and is telling Roy Harrod (the "you") that he not pushing back enough against the economics is natural science view (that I take above).

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    2. I just watched this video of Ed Prescott. I swear in here somewhere I heard him say "aggregate economics is a hard science." "Aggregate economics" is his terminology. He thinks macroeconomics is dead. It died in the 1960s he says.

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    3. "There is no difference between "arithmetical" and "mathematical""

      Of course there is. And I don't believe for a minute that you believe otherwise.


      "I can write a DSGE model like Kydland-Prescott as a series of additions"

      Again, of course. Any complex mathematical algorithm can be reduced to a series of arithmetical operations. The rules that govern those arithmetical operations, that is the mathematical algorithm, is what is in question here.

      The question here is whether the mathematical algorithm is an accurate representation of reality. This is of interest if you are seeking to draw conclusions about real world circumstances.

      Now you may not be interested in drawing conclusions around real world circumstances - you may be interested in examining the relationship between certain economic factors without resorting to experiment or testing data. In which case you will probably construct an abstract mathematical model of the relationship between the economic variables you intend to examine. Whether this bears any useful relationship to reality is unlikely but probably not intended anyhow.

      This is what Prescott is talking about. Abstract models are of minimal use in drawing conclusions about reality.


      Re the Keynes quote: the important part is the bit about economics being "a way of thinking", which it is. If you studied the GT, you would see the validity of this statement.

      Keynes was a realist. He wanted to solve real world problems. He was not primarily interested in penning mathematically clever papers which were exercises in pure abstract thought, although he was perfectly capable of so doing.

      Henry.

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    4. As for the Keynes quote, here is more context:

      Keynes: "It seems to me that economics is a branch of logic, a way of thinking; and that you [Roy Harrod] do not repel sufficiently firmly attempts à la Schultz to turn it into a pseudo-natural-science. One... cannot get very far except by devising new and improved models. This requires... 'a vigilant observation of the actual working of our system'. . . .

      "Economics is a science of thinking in terms of models joined to the art of choosing models which are relevant to the contemporary world. It is compelled to be this, because, unlike the typical natural science, the material to which it is applied is, in too many respects, not homogeneous through time."

      Quote from http://www.bradford-delong.com/2016/02/a-few-scattered-notes-observations-and-examples-of-graphs-and-diagrams-in-teaching-and-doing-economicsthe-honest-broker.html

      Keynes was not anti-empirical. Logic for him did not mean armchair or ivory tower thinking without regard to evidence. Keynes is arguing against context-free logic, because in real life the context is always changing. He is talking about the logic of Sherlock Holmes, not the logic of Aristotle or Russell.

      Now, it may be that he was mistaken, that there are universal laws of economics, just as there is a universal law of gravity that applies in both the celestial and sublunar contexts. But Keynes was not an economist who said that if reality differed from a model, so much the worse for reality.

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  3. Jason, I'm going to go out on a limb and guess you're not a fan of praxeology. ;D

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  5. Great post Jason, I struggle to understand why what you're saying is even controversial. I agree 100%.

    -Ken

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    1. Thanks Ken.

      To be fair, I don't think it's controversial among most economists ... just microfoundation-focused and Austrian economists ...

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