More on math and economic development

My previous post on this subject was not met with the warmest reception. Curiously those who liked it chose to send me a private e-mail, while the vast majority of the respondents on the blog itself were at best skeptical and at worst derisive.

Being the sucker for punishment that I am, I take this as an opportunity to expand on the original theme.

Let me do this by way of responding to some of the comments.

First let me agree with robertdfeinman, who writes:

It appears that many model makers aren't interested in validating their models with data. This is sort of like what happens in physics (my field) the theorists make up the theories and the experimentalists test them.

I'm afraid that I feel that much of the more abstruse mathematical models used in economics are just academic window dressing. Cloistered fields can become quite introspective, one only has to look at English literature criticism to see the effect.

"Academic window dressing" indeed. God knows there is enough of that going on. But I think one very encouraging trends in economics in the last 15 years or so is that the discipline has become much, much more empirical. I discussed this trend in an earlier post.

I also agree with gabriel who says

I am not supportive of economists who then forget that they have a "model", an abstraction of the world, and begin to believe that their model is the world. I find very few economists that are humble enough to admit that about their analysis.

and with peter who says

My experience is that high tech math carries a cachet in itself across much of the profession. This leads to a sort of baroque over-ornamentation at best and, even worse, potentially serious imbalances in the attention given to different types of information and concepts.

All I can say is that I hope I have never been that kind of an economist.

Meanwhile terence and inthemachine raise an interesting challenge for me:

All you need to do now is to provide me with some sound empirical evidence (consistency, consistency) that there have indeed been fewer erroneous development prescriptions produced by mathed up economists than by the rest of us development folk. (terence)

how about a single example of a development initiative where the presence or absence of "math" was the root of its failure? (inthemachine)

Let me give two examples, one from macro and one from micro, where a good grasp of a piece of mathematical machinery is indispensable to good policy.

• In macroeconomic policy, understanding and knowing how to work with the fundamental debt dynamics equation is critical to the conduct of fiscal and monetary policies. As with most of macro, a lot of this is based on accounting identities, but these identities plus a little bit of theory and empirics can go a long way to turn confusion into clarity about policy choices and tradeoffs. I know for example that Turkey's stabilization at the end of the 1990s came directly as a result of debt-dynamics analyses which showed the existing situation to be unsustainable. And call me naive, but I also think that Mugabe would not have pursued his policies for this long if he had a better grasp of debt dynamics.   
• In microeconomics, cost-benefit analysis and project evaluation have to be part of eery development economist's toolkit. How do we know otherwise whether the government is making appropriate policy and project selection choices? It is impossible to do this kind of analysis without using tools like consumer and producer surplus, shadow prices, distributional weights, and discounting--all of which are mathematical constructs.      

Jay complains:

What about the vast majority of people out there--the ones who are not smart enough to grasp the math? I guess they will never understand development. Every individual that hasn't had advanced level training in math should be automatically disqualified from having a strong opinion on poverty and underdevelopment. Well, that's just about most of the world, including nearly all political leaders in the developing world. Let's leave the strong opinions to the humble economists, the ones who realize that they're not smart enough.

I hate to be making an argument that may be construed as elitist, but yes, I do believe there is something valuable called "expertise."  Presumably Jay would not disagree that education is critical for those who are going to be in decision-making positions.  And if so, the question is what that education should entail and the role of math in it.

In any case, I disagree that you actually need to be very smart to do the kind of math that the practice of development policy requires.  Neither of the applications I mentioned above requires rocket science or even calculus beyond what is taught in a good high school. What matters most is a certain habit of mind--of being able and willing to break a complicated problem into its constituent parts and then put it back together. 

The last word goes to kinglear:

The maths - and the economic arguments - are all very well. But somewhere along the line,the man on the Clapham Omnibus needs to understand it - and that can ONLY be in a very short sentence of short words.The greatest writers hone their sentences by shortening them, giving the words more punch, and making the meaning crystal clear.

Well, I confess to not knowing the man on the Clapham Omnibus--or even the omnibus itself--but I certainly hope that I am clear in my own writing. As I tell my students, when you write your report, you do not have to regurgitate every twist and turn of the analysis that you undertook and every technique you have employed.   

But clarity better be based on sound analysis...

UPDATE:  Peter Boettke has some very thoughtful comments below and on his blog.

UPDATE2: The Randomizer has some really interesting comments below.

Comments

[Per Kurowski]

Re: And call me naive, but I also think that Mugabe would not have pursued his policies for this long if he had a better grasp of debt dynamics.

Sorry I cannot think of any debt dynamics model that could handle a swan as black as Mugabe.

[Ken Houghton]

I'm all for expertise, but when what we get as passing for Economics Expertise With Math is Dick Cheney's Napkin, I'm inclined to think that cactus's summary (http://angrybear.blogspot.com/2007/09/economics-is-bull.html) is correct:

In the end... the reason economics is bull$%!# is because the practitioners have allowed it to remain bull$%!#.

If Economics Professors are not Rational Actors, then we have to assume no one is. So let us assume they are RAs and construct a model that explains why data is eschewed and The Napkin is invoked.

The rest is a bit of algebra, some regression analysis, and a few touches of higher math--none of which will make phlogiston into gold.

[James]

As someone who wants to be an economist and is currently struggling with Calc III, I was very heartened by your comment, "Neither of the applications I mentioned above requires rocket science or even calculus beyond what is taught in a good high school." Great post and keep up the good work!

[robertdfeinman]

I haven't read too many theoretical economics papers, but those that I have read seem to be swatting a fly with a sledgehammer.

Perhaps someone can explain to me why anything more than normal statistical tools is required for any economic model which claims to based upon observable data?

Economics, after all, claims to be a social science and thus is trying to generalize human activity into a simplified model.

If the observed behaviors really have as many variables as, say, weather forecasting, then perhaps this is direction that the mathematics should go.

If that turns out to be the case, then the use of probabilistic models and stochastic techniques should be examined. Computers are now powerful enough to deal with thousands of inputs. If you have every seen the models of tornado dynamics you know what I mean.

The fundamental problem that remains, it seems to me, is sparse data. Just look at the debates over what the Fed should do next. Most of what it appears they are using as input is aggregate data such as changes in the GDP or employment rate, or the like.

In a multi-sector economy, like ours, this seems too abstract. We could be having a boom in one area while another is contracting. A single policy that would address both areas optimally would seem to be impossible.

[Bruce Wilder]

Let me quote without any further embellishment from a comment by "Matt" left on a Brad DeLong essay:

"The Solow growth model assumes labor devoted to consumption and labor devoted to capital stock are decorrelated. I know this because his exponentials are real valued, so the covariance matrix is not hermitian, not cyclic. The two eigen functions are orthogonal. But there is no valid real kernel approximation to such a long period of time. This also explains the Malthusian trap."

[inthemachine]

Just to clarify, I meant the original challenge for Terence, who seemed to suggest that math and development failure were somehow related. Of course math is necessary for economics - and for making sound economic decisions - how else are you going to consider and communicate about n-dimensional issues.

Apologies that my sarcasm clouded the point that when development programs or projects fail, it is never because "there was math" or because "there was not math," which seemed to be the direction some of the previous commets were going.

[krishna]

I also think math has tremendous utility and power in clarifying and making accurate a theory (like Robert Feinman, I am a physicist). But one problem I had when reading economic theory papers is that there is a tremendous amount of effort spent on making their mathematical models *rigorous*, i.e in proving them in a mathematically strong fashion (this is true even of the most famous economic theorists, like Lucas). It makes little sense to me to do this, because the models themselves are so imperfect, and often inconsistent with data. Would it not be more reasonable to spend this effort on fixing inconsistencies between the models and empirical data, rather than proving their mathematical exactness?I see very in my profession spend their time proving their models rigorously.

[Justin Rietz]

First, I think it is well known by readers of this blog and mine that I have a slight distaste for econometric modeling. Let me make it clear that I believe the use of math for teaching economic principals (calculus for marginal calculations), clarifying and explaining ideas, and doing sound statistical analysis of real world data is important and useful.

Some of my knocks against complex econometric models are:

1. Cleansing of data by removing outliers. While it is sometimes justified, it may just well be that these outliers are important data points that reflect an inconsistency in the theoretical assumptions underlying the model. I think there is a great danger that economists, unintentionally, shape data to fit preconceived notions of what they expect to find.

2. Similar to #1, the large role that assumptions play in determining what is useful and what is not. Again, unintentional biases by modelers may have a significant impact on such assumptions.

2. The inability to accurately capture critical human elements dependent upon politics, culture, and other social factors. There have been some interesting studies about this phenomena - I'll see if I can dig up some links.

3. The lack of attention given to correlation vs. causation found in many econometric-based research papers

4. The substituting of econometric models for on-the-ground research by economists who prefer to stay in their offices and theorize about people and events happening someplace thousands of miles away that they have never visited (just to be clear, I do not put Dani in this category).

I'm reading "Inventing Money" by Nicholas Dunbar, a book about the failure of Long Term Capital Management that focuses on the theory of LTCM's financial models (Black-Scholes, etc.) I have found some interesting correlations with our current topic. To put it a bit simplistically: theoretical, mathematical models can be quickly blown away by real world events.

[Peter]

"In macroeconomic policy, understanding and knowing how to work with the fundamental debt dynamics equation is critical to the conduct of fiscal and monetary policies."

Funny you should bring this up, since I just published a piece in Challenge that argues that most of the economics profession, despite its high-tech pretentions, is culpable of one of the most elementary mathematical errors, confusing identity and functional relations. The national accounting identities cannot be invoked to "explain" why causation supposedly runs from savings behavior to the current account.

When I reviewed the writings of prominent economists on this topic in preparation for the article, I was awestruck by the extent of the confusion.

Perhaps the right conclusion to draw is that math proficiency is, as you say, very important, but that real understanding is what matters most, rather than oodles of technique. (But, yes, there are some problems where technique is crucial.)

[hari]

Dani-

Economics is NOT rocket science, and must deal with social issues - more often than not - which cannot be readily quantified (without creating a static model!).

Of course, most economic texts become more redable with graphs,tables and whatnots.

The problem with model building in (global) political economy - unlike in physical sciences - one has to deal with macroeconomics of nations with indifferent statistical standards.

Let me take a real-life example to illustrate this issue:

When EU decided to expand and include (former) East European Communist States, EUROSTAT issued a red signal! Eurostat had to develop a statistical dossier for each applicant, and found it simply couldn't produce a standard document for EU negotiators. History will record EU (political) negotiations didn't begin until Eurostat had succeeded in developing a statistical standard for new applicants. Even then, it took a lot of time before the system was officially formalized.

Therefore, economists must always be aware that Chinese and Indian statisical data are not the same as official data issued by OECD for its member countries.

[Shampa]

Perhaps the question is not whether math should or shouldn't be used in development economics but how much of the development story it actually tells us? Development stories are generally complex, nuanced and case-specific and similarly figuring out what works and doesn't in development doesn't usually lend itself to just a pure mathematical interpretation. Balancing the information obtained from mathematical models with rigorous qualitative data assists in unpacking the black box. The danger is that once a model spits out a number, unenlightened policy-makers could in some cases latch onto it to make bad simplistic "magic bullet"-type decisions rather than delving into the shades of grey that qualitative data might reveal.

[Barkley Rosser]

There are really two different types of math going on here, and it is probably useful to keep them separate. One is the math used in pure theory and the other is the math used in econometric analysis of data. Of course, nobody likes to try to read a paper that uses math they do not understand, but sometimes such math is necessary for the task at hand.

The usual vice of the theorist is to make unrealistic assumptions and then take them too seriously as reflecting reality, irrespective of the level or type of math used in building the theoretical model and analysis. Clearly, Dani has lots of sympathy with this critique, and is more in favor of empirical analysis anyway.

Regarding empirics, well, problems with data can lead one to use more complicated econometric techniques to overcome these problems. That said, such techniques are more useful in disproving something that appears to be true from a simpler analysis (usually just good old OLS). However, I remain convinced that if it does not show up in the data pretty straightforwardly, indeed in the old eyeball test, it probably is not really there. And even if it is there via a fancy technique, if it does not pass the eyeball test, you are never going to convince a policymaker that it is there, especially one who is not convinced already that it is and wants it to be.

[Matt Nolan]

From what I understand, economists used to love doing economics with no maths.

Then someone discovered that maths was a neater way of illustrating some concepts. This discovery illustrated that some of arguments people were making were inconsequential, as mathematically they were saying the same thing.

The criticism of words at this point was that people used words to hide there inability to illustrate the phenomenon with a model.

In the last couple of decades the models have become extremely technical, and many economists will make assumptions based on the fact they are common in the literature. The small nuances that could so easily be described with words are shown through numerical models, and some of the economists that derive these models do not seem to understand the full extent of the environment they are describing. So in some sense, economists now use maths to hide the fact that they don't understand what they are doing.

Anyone that can describe there model clearly and succinctly without maths is a good economist.

[terence]

Oh - I feel obliged to say that I certainly didn't mean to sound derisive. Just light-hearted.

I do think there are two serious points that can be made in critique of the original post:

1. That math alone won't save you from bad economics (hence my jibe about the 1980s). (But I doubt this is news to anyone).

2. (More substantively) There is a lot to be said for mathematical rigor (and Dani's post makes an excellent case for this) but if you take this too far you run the risk of lapsing into the realms of extreme positivism, where things that can't be counted (or modeled) don't exist and where maths becomes the only means of understanding the world. Certainly without the formal logic of mathematics you do run the risk of woolly thinking but if you restrict yourself only to this means of understanding you seriously limit the things you may understand.

Anyhow, the most important point here is that I really enjoy reading this blog (it is my morning highlight) and certainly wouldn't ever want to deride its author.

[notsneaky]

"Perhaps someone can explain to me why anything more than normal statistical tools is required for any economic model which claims to based upon observable data?"

Perhaps I could if you make your question more precise. What are "normal" statistical tools? Are fancy econometric techniques - essentially extensions of the simple linear regression to particular data and statistical problems - "non normal"?

Or do you mean that economist should just use statistical techniques and forget about constructing mathematical theoretical models, which, uh, ultimately underlie those "normal" statistical techniques one is gonna use?

"As someone who wants to be an economist and is currently struggling with Calc III, I was very heartened by your comment, "Neither of the applications I mentioned above requires rocket science or even calculus beyond what is taught in a good high school.""

Unfortunately, in my experience it seems often to be the case that in order to truly understand a particular set of tools - to the point where one is able to use them and apply them outside the settings in which one learned them - one needs to study stuff that is two or three levels removed. So if you just wanna roughly understand what the papers in AER, JPE or QJE are talking about you can probably get on fine with Calc I. Well, Calc II. But if you wanna build your own models and *really* understand the stuff at the deeper level, you DO need the higher maths (but it's fine to get them from econ courses). Or have a lot of practice.

"The problem with model building in (global) political economy - unlike in physical sciences - one has to deal with macroeconomics of nations with indifferent statistical standards."

Yes and a lot of time and energy is expended by economists in trying to make the available data comparable (sometimes this is called "harmonization"). See for example Robert Feenstra's work with trade data or the Penn World Tables for that matter.

"the economics profession, despite its high-tech pretentions, is culpable of one of the most elementary mathematical errors, confusing identity and functional relations. The national accounting identities cannot be invoked to "explain" why causation supposedly runs from savings behavior to the current account."

Uhhh, this is well known. That's the difference between an identity and theory. Identity just tells you that when one variable changes another one's gotta give. The theory tries to tell you (perhaps unsuccessfully) which ones and maybe how much. So while S=I+X is an identity the statement that when there is an exogenous fall in savings X will fall by dX is a theory.

"When I reviewed the writings of prominent economists on this topic in preparation for the article, I was awestruck by the extent of the confusion."

You got examples or a link to your article? Somehow I'm suspicious of your claim.

"a comment by "Matt" left on a Brad DeLong essay"

Umm, I take this as an example of "too much math". It is a good example, since obviously the guy has no idea of what he's talking about. I'm willing to bet serious money he's not an economist. Maybe an over eager beginning student of economics.

Ok, I'll stop now.

[pat toche]

I have just read the two posts on mathematics, and I think this second post and the comments are well to the point. I just left a post there which attempts to answer what I think is the key problem to be addressed, as nicely put by Robert Feinman, why do so many economics papers "swat a fly with a sledgehammer."

The answer, I think, is that many economists seek to make their models as general as possible in the belief that if an idea is theoretically robust to the topology used to frame it, it will follow that the idea may be more relevant to the real world. But this need not be so, and the real test of an idea in economics is to put it to the data. As Dani correctly points out, this is increasingly being done. The smartest economists today do applied economics. The profession is changing dramatically, I think.

But it will take a few years before we can see the impact of this transformation. We are still under the declining influence of the 1960s and 1970s, where economists sought to check the theoretical validity of their ideas. We are now moving towards empirical economics. The most innovative economists these days do empirical stuff, the likes of Barro, Mankiw, Heckman, Card, Krueger, Levitt, etc.

So economics is changing, but it will take time for the change to be more clearly visible.

[pat toche]

To Terence,
"if you take this too far you run the risk of lapsing into the realms of extreme positivism, where things that can't be counted (or modeled) don't exist and where maths becomes the only means of understanding the world"

I have just learned that I am an "extreme positivist".

I also agree with the related idea articulated by Wittgenstein, "Whereof one cannot speak, thereof must one be silent"

[viking]

Whether in economics and other sciences, soft or hard, math is simply a tool to ensure that an argument or proposition is internally consistent, all assumptions and hypothesis are explicit, and therefore that a position opposed to another can be properly distinguished. Without elementary math and logic, tractable debates on how the world works or doesn't are impossible.

[robertdfeinman]

notsneaky:
"Normal statistical techniques" are those taught in courses on statistics.

There has been some interesting work recently in public health with meta studies. This is where the results of a large number of prior experiments or observations are then treated to further analysis. This is how it is possible to extract small effects from a large amount of uncorrelated data. It is what is frequently used to find side effects in drugs that weren't noticed during trials. Look up the Vioxx story if you want to see the technique at work. If enough people start to use these tools, they will also become "normal".

One of the dirty secrets of much economic and sociological work is that those conducting the studies have an ideological agenda. This throws their entire work into question, so they try to obscure things with fancy mathematics.

The day that a "study" comes out of Cato which proves that free-trade is a bad idea, let me know...

[Barkley Rosser]

I would also like to point out that having equations does not necessarily equal "math" and not having equations does not necessarily mean "not math." Math involves the ideas and their nature.

Thus, John Chipman has argued (sorry, no cite) that John Stuart Mill invented nonlinear programming in his chapter on exchange rates in one of the later editions of his Principles of Political Economy. He did so strictly using words in a verbal description. But, there is no question, he laid out a rigorous (and correct) mathematical argument. Also, while she generally said bad things about using math(s), Joan Robinson's growth theory models were generally mathematically rigorous, even if usually described strictly in words, although she would sometimes resort to figures or graphs, which is getting a bit more overtly mathy.

OTOH, there is a lot of fake or lousy math out there in econ that is not really math, that is really obfuscation and sometimes even wrong, irrelevant to what it is supposedly modeling or explaining, and so and so forth. There are equations, but the variables in them are meaningless, and there is no empirical content. They may even be made to look fancier and more complicated than they are with, unnecessary changes in variables, and so forth. Such things are not really math, even though they may look like it (and I am especially aware of this today, as I just finished writing a negative referee report on a paper of exactly this sort, with incoherent variables and even outright incorrect math).

[robertdfeinman]

I'll ask the professional economists, especially those who teach, if there is lots of shoddy work being done in economics papers as Barkley Rosser seems to think, then why?

Are students taught mathematical obfuscation explicitly? Are there schools of mathematical thought so that one technique is used by one school and another group does something else?

If the techniques are explicitly taught then they must be felt to be valid by those doing the teaching. Are there debates within the profession about this?

It reminds me of the fights at the beginning of the 20th Century between the Freudians and all the opposing camps. That wasn't science either.

[corvad]

"To Terence,
"if you take this too far you run the risk of lapsing into the realms of extreme positivism, where things that can't be counted (or modeled) don't exist and where maths becomes the only means of understanding the world"

I have just learned that I am an "extreme positivist".

I also agree with the related idea articulated by Wittgenstein, "Whereof one cannot speak, thereof must one be silent""

I believe Terence was making the point that quantification of the real is

a real narrow approach to describing reality and that Wittgenstein was making the point that (here, out of context pastiche style, surely but pastiched with Terence and pattoche) indeed, saying nothing is preferable to extreme positivism.

[The Randomizer]

Over the past decade or so, the math pre-reqs for getting into most leading programs in economics have ballooned, to the extent that it is (or at least was, until a couple of years) very difficult to get in without at least a math minor (incl. topology, real analysis etc.) As a result, the whole world of professional economics - founded on the concept of simplifying assumptions to describe generalities about social behavior - has been turned on its head and is now centered on complexifying assumptions and the manufacture of esoteric theoretical constructs of scant applicability to anything.

I've been asking economists for a long time to explain the necessity of the level of mathematization that now consumes the discipline and have found few coherent answers. The unfortunate conclusion I have come to is that math functions as a guild system for economists. Without the math, the discipline would be a lot more accessible to lay people (or at least those lay people armed with a desire to read books) and the perceived value of the professional economist (and thus the graduate program in economics) would thereby be a lot less.

This is not to say there is no justification for some math in economics. Of course, there is, but to standardize and simplify. The level of math that currently exists in the discipline renders what are simple concepts when described in textual language, more esoteric and complex. This adds negative value to the pursuit of scientific truth.

Until a few years ago, the state of economics was on a very grave trajectory. With the fall of barriers faced by international students wishing to pursue graduate in the U.S., graduate admissions became a lot more competitive during the 1990s. The response of economics departments, at least, was to select increasingly on the quality of mathematical training (as noted above). This result was pools of graduate students more interested in doing theoretical math than actual economics. That their work had little practical value was not of their concern, since their motivation was to construct mathematical beauty rather than to seek empirical truths.

Thankfully, the situation was saved somewhat by the exogenous shock that was the Poverty Action Lab (developments in matching techniques helped too), which reintroduced economics to science. How durable the impact of that shock will be against the incentives which produced the guild system of hyper-mathematization will be interesting to see . . .

[paine]

qunatitive thinking
may only require commercial arithmetic

give market prices are rational numbers

compare
facility
with a few
soft ware programs
with learning
to crack
a few diffy q
nuts for control theory target practice

( my old mentor vivian walsh
had a nice piece somewhere
on edgeworth math
as the glass slipper of economics )

rational speculation
has its appeal
and not just to logicians with a fondness for proper acting nymphets

and as noticed above
if tenure track research
makes it possible
it will bloom

( example
from an earlier era
too much time
spent on refining
altogether too abstract qualitative results
like unique equilibrium existence proofs
such runic gibberish
merely
mimics math
far more then
it applies it to economics
call it minor bird math
by math minors )

and not only
is it very often the wrong math
its also
a paotlatch contest
a serious time and tuition waster
too

analogy

the fashion
of
writing journal articles
in latin
especially after
say 1550

was it a lingua franca
or using a useless ornament of genteel education??
ie
a covert
gauntlet /barrier
to entering hoi- hois

some of both no doubt

but subsequent science
published in native tongues
shows it was primarily
a mandarin system

similarly( as pointed out
by ram above )
high math hurdles
exist as much for their own sake

topology ???

why even complex functions ???

either may well
winnow the field
to certain brain types
more or less useful
but the skills specifically acquired....

well
its as if
fencing lessons and horse riding
were required at west point

[notsneaky]

"This result was pools of graduate students more interested in doing theoretical math than actual economics. "

I really really think this is incorrect if you're talking about 1990's and after. As Dani notes the trend in economics has been towards empirical work and away from abstract theory (personally I actually think the pendulum has swung too far the other way).

Also, there really is a need to be more specific about which "fancy maths" people are talking about.
Is it the fancy econometric techniques? Or is it theoretical models which at this point may be too abstract to allow for empirical analysis?