Arnold Kling  

You, Too, Could be Doing This

Good Question... Free Lunch!...

From the abstract of a recent NBER working paper:

we solve the stochastic neoclassical growth model with recursive preferences using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration.

These computations tell us how many angels can dance on the head of a pin about the properties of a class of macroeconomic models called Dynamic Stochastic General Equilibrium (DSGE).

If you want to get tenure, you too, should be doing this sort of research.

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COMMENTS (19 to date)
ed writes:

This paper is not about macro-economics per se, it's about numerical methods (which I actually find kind of interesting).

pushmedia1 writes:

Arnold, this is a methods paper written by people that specialize in methods. I'm happy, as a macroeconomist, that somebody is doing this work because then I can spend my time on real problems. Isn't specialization good?

Arnold Kriegbaum writes:

@ ED and Pushmedia1: Ok, maybe society has a place for this. I would hope that my tax dollars (few as they are) don't go toward funding this sort of thing. If not, then I have no problem with the market demanding such research.

hacs writes:

Perhaps, someone prefers to study about the angels gender, pleading exclusively to rhetoric arguments.

pushmedia1 writes:

"Founded in 1920, the National Bureau of Economic Research is a private, nonprofit, nonpartisan research organization dedicated to promoting a greater understanding of how the economy works. The NBER is committed to undertaking and disseminating unbiased economic research among public policymakers, business professionals, and the academic community."

Norman writes:

I take it you would prefer no taxpayer money go to mathematics departments' research as well? How practical does the research have to be to justify funding? Or would you prefer no public funds go to academic research at all?

mak writes:

I did do this. Fortunately I saw the light. As someone who spent countless hours writing MATLAB code to model physical systems yet now as a business analyst, I question why I, like so many ambitious economics undergraduates, spent so much time pursuing a second major in mathematics.

Leave the numerical analysis research for the mathematicians who can then apply their work to the unique engineering and physics problems that require it.

Lauren writes:

I want to put in a word in favor of economists who study or enjoy mathematics. This is not in any way a disagreement with Arnold about the sterility of claims that particular mathematical models (including stochastic models) are definitive, apt, or accurate representations of economic life. However, it is a plea for accepting different styles of thought and different styles of telling stories about economics with an open mind and without demeanment.

Mathematics is both beautiful and illuminating.

It is as beautiful and intriguing as a novel by James Joyce, poetry by T. S. Elliot, paintings by van Gogh, music by Beethoven, and the intricacy of an amaryllis.

It is as illuminating as the most perfectly encapsulated and poignantly pithy wonderment by Gertrude Stein on her deathbed, the simplicity of seeing a model of the planets revolving around the sun instead of vice versa, and the elegant wording of the greatest of thinkers in all kinds of fields, be they Isaac Newton or Milton Friedman, in their ability to say in a few dozen words or less what others spend lifetimes trying to express.

We sum up and are moved by phrases and circumstances when we repeat a momentary and timely phrase like Stein's "But what was the question?" or Smith's "he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention" or Friedman's "There is no such thing as a free lunch."

At its finest, mathematics offers exactly those stunner moments of clarity and understanding. For those who easily read not just the equations--the words--but the context and meaning, the layers of the onion reveal themselves with magnificence and satisfaction. Of course, for those who don't see or get the significance, it's a waste of time. That method of communication didn't work.

For some people--myself as one--mathematics offers a clarity and depth that instantly aids understanding. It has done so for me my whole life, from childhood through high school through college through grad school and beyond. For me, the quick language of mathematics--a few equations or a graph--is an immediate and relaxing window to understanding what sometimes takes others reams of paper or hours of words to communicate.

That doesn't mean I would force that particular window on others. What is a window for me is a murky veil for many others. The best analogy I know is that I cannot look at art, paintings, or drawings and understand a thing. Music--ah, beauty incarnate for me--but a painting might as well be code so encrypted that even the Pentagon can't crack it. Nice colors, nice scene, but you can't be serious that there is some other meaning or satisfying layer, can you? (My apologies to the artists and art historians in my family line, who may read this in shock at how I could possibly be from the same stock.)

Neither am I arguing that mathematics put to workaday use is not as beautiful or illuminating as elegantly expository or explanatory mathematics. The rooms in my house have walls that stand and paint that adheres. I appreciate that someone knows what paint to use and what kind of walls and boards will hold up my floors. There is beauty in that, too. I am in awe of the love that folks like Norm Abram and Rich Trethewey show for their art on This Old House. Watch them a bit and their math training and love of its illuminating powers is clear.

It is inappropriate to condemn the beauty and ability to illuminate inherent in mathematics because it is also used for workaday uses, because it is not clear or easy for any particular individuals who may themselves have other skills in art or writing or something else, or because it is used in extreme hypothesized ways by some for inappropriate applications without testing.

Theoretical models are what they are. Workaday mathematical models are what they are. Words written well and clearly are what they are. There is a healthy competition among these various ways to explain the world around us. Each has the potential to explain some things but not everything; and that some thing is usually pretty clear by reading the expositor's ideas with an open mind. Overreaching claims of solving or resolving more are puffery, but they are not how a whole class of models should be judged.

The only condemnation is of condemnation itself.

ajb writes:

We're waaayyy past the point when it's about tolerating different types of research. The top journals are filled with theory papers where the math involved outweighs the economic insights. Indeed, it's worse than that. Brilliant scholars like Coase, North, Olson, or Buchanan could not get tenure in most top 20 econ departments (note that Coase is in the Law school of Chicago) because they're not technical enough. There are almost no advances in economics which justify the increase in formalism of Econometrica today relative to the JPE in 1965, yet the Econometrica standard is in fact the standard for modern theory papers. Just try publishing a paper in JET using the notation and formalism of JET circa 1970 and see where it gets you. The greatest condemnation of all modern theory is that the superstar empirical work by Krueger, Levitt, Oster, Shapiro, Duflo, etc. would not be changed by one bit if ALL the formalism and formal theory of the last 30 years had been wiped out completely. This makes economics very much unlike physics.

Vasco writes:

Yea, I think I'll be doing my graduate work in micro now, thank you.

EclectEcon writes:

I laughed out loud with appreciation when I read the posting. I've done some math and some fancy tricks (with a co-author who knew what he was doing), and I know they have their place, but the way you phrased this in the posting was absolutely beautiful. Thanks for brightening my day!

fundamentalist writes:

I'm puzzled as to why economists are spending so much time on statistical methods. Neural networks and other data mining methods that combine traditional statistics with machine learning have proven far more accurate and robust. Shouldn't economists be looking at these techniques instead of refining traditional stats?

Nevertheless, Arnold's point is understood.

For Lauren, no one is condemning math. It is beautiful as you say and very useful. What Arnold criticizes is the excessive reliance on math models in economics and the refusal to question the assumptions underlying the models.

In addition, I would add that math modelling in economics has led most mainstream economists to the silly conclusion that economics is a subset of physics. They seem to believe that economic aggregates take on the nature of physical processes so that reducing the interest rate, for example, mechanically causes people to borrow. It doesn't. People decide how to respond to stimuli based on circumstances. Hydraulic fluid does not. Push a lever and hydraulic fluid responds immediately without much thought. People don't respond to levers that way. That's why math models in economics can be dangerous in the wrong hands.

nels writes:

Physicists seem to have the right approach. They use just enough math to explain the data. Economists should follow suit. Instead they force the data to the math. The irrelevance of macro economists has been made abundantly clear over the last year.

nels writes:

Physicists seem to have the right approach. They use just enough math to explain the data. Economists should follow suit. Instead they force the data to the math. The irrelevance of macro economists has been made abundantly clear over the last year.

fundamentalist writes:

nels: "The irrelevance of macro economists has been made abundantly clear over the last year."

That's very true of mainstream economics.

nels: "Economists should follow suit. Instead they force the data to the math."

I don't think that is the case. The problem is not how economists use math. It's in the theories supporting the math models. For example, a physics model of the path of a ship through space wouldn't be very accurate if the theory of gravity behind the model said that gravity repelled objects.

Natural sciences are held in high esteem because they involve a great deal of certainty. Compared to economics, creating math models in natural sciences is easy. The number of variables are few and the objects of study don't change their minds. In economics, we often don't even know what all of the variables are. What variables we know about we often don't have data for them and their importance and relationships change over short periods of time.

Because of the attempt to immitate physics, economists began to develop theory based on available data. Unfortunately, the available data was the wrong data, so the theories developed were wrong, too. As Hayek noted in his acceptance of the Nobel Prize, just because data for aggregate demand are widely available doesn't mean that economics should be built around aggregate demand. We know a lot about human behavior, and therefore economics, for which there is no data because in economics we are studying ourselves, not inanimate objects. Limiting our knowledge to the available data forces us to ignore vast amounts of knowledge for which no data is available.

Hayek brilliantly demonstrates the error of attempting to use the techniques of physics in economics in "The Counter-Revolution of Science" available in pdf at The attempt to duplicate the methods of physics in economics is responsible for macro-economics being so worthless.

fundamentalist writes:

nels, Can you imagine how different physics would be if it were based on random shocks? What if physics theory said that gravity, light and energy work the same most of the time, but occasionally you'll get gravity shocks in which gravity suddenly and without explanation reverses itself and repels objects. Or if the speed of light were a constant most of the time, but once in a while you would get a light "shock" in which light travelled twice as fast, or half as fast for no known reason?

That's how mainstream econ theory works. Most of the time we're in equilibrium. Everything is balanced. But random monetary or price shocks throw they system out of equilibrium once in a while.

nels writes:

Fundamentalist, I think we are in agreement. The math in economics is fairly straight forward as it should be (eg diminishing marginal utility, indifference curves etc). My point was that unlike physics which doesn’t feel the need to “be scientific” economists seem to have academic chips on their shoulders and feel the need to intellectually prove themselves but in doing so miss the nature of the subject.

fundamentalist writes:

nels, I agree. BTW, I just ran across an interesting comparison between physics and economics in Hayek's "The Counter-Revolution in Science":

"The physicist who wishes to understand the problems of the social
sciences with the help of an analogy from his own field would have
to imagine a world in which he knew by direct observation the inside
of the atoms and had neither the possibility of making experiments
with lumps of matter nor opportunity to observe more than the interactions
of a comparatively few atoms during a limited period.

From his knowledge of the different kinds of atoms he could build
up models of all the various ways in which they could combine into
larger units and make these models more and more closely reproduce
all the features of the few instances in which he was able to observe
more complex phenomena. But the laws of the macrocosm which he
could derive from his knowledge of the microcosm would always remain
"deductive"; they would, because of his limited knowledge of
the data of the complex situation, scarcely ever enable him to predict
the precise outcome of a particular situation; and he could never
confirm them by controlled experiment although they might be disproved
by the observation of events which according to his theory
are impossible.

In a sense some problems of theoretical astronomy are more similar
to those of the social sciences than those of any of the experimental
sciences. Yet there remain important differences. While the
astronomer aims at knowing all the elements of which his universe
is composed, the student of social phenomena cannot hope to know
more than the types of elements from which his universe is made up.
He will scarcely ever know even of all the elements of which it consists
and he will certainly never know all the relevant properties of
each of them. The inevitable imperfection of the human mind becomes
here not only a basic datum about the object of explanation
but, since it applies no less to the observer, also a limitation on what
he can hope to accomplish in his attempt to explain the observed
facts. The number of separate variables which in any particular
social phenomenon will determine the result of a given change will
as a rule be far too large for any human mind to master and manipulate
them effectively.

38 In consequence our knowledge of the principle
by which these phenomena are produced will rarely if ever enable
us to predict the precise result of any concrete situation. While
we can explain the principle on which certain phenomena are produced
and can from this knowledge exclude the possibility of certain
results, e.g. of certain events occurring together, our knowledge will
in a sense be only negative, i.e. it will merely enable us to preclude
certain results but not enable us to narrow the range of possibilities
sufficiently so that only one remains."

The Counter-Revolution in Science, Hayek p 41,42

valter writes:

I am puzzled by why this particular paper was picked on as an object of scorn.

If one wants to criticize DSGE models as divorced from reality, why not pick on a paper that uses a DSGE model to say something about reality?

Why pick on a paper on the application of numerical analysis tools to compute dynamic equilibria (which could be useful also in many other contexts, some of which may even have some connection to the real world)?

Unless one believes that (macro?) economics can (only) provide useful theories that are true in general independent of data, then one will have to construct quantitative models and compute the solutions of those models to see how they match (at least qualitatively) with the data. How can you be sure that the issues discussed in this paper won't help you choose a better way of doing those computations?

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