tag:blogger.com,1999:blog-47992648112657599562024-03-05T01:11:26.859-05:00Quantitative Finance: Foundations and ApplicationsNews, comments and discussion forum following up the Fields Institute Thematic Program on Quantitative Finance: Foundations and Applications - January to June, 2010.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.comBlogger131125tag:blogger.com,1999:blog-4799264811265759956.post-14608304168329128292013-09-11T11:21:00.001-04:002013-09-11T11:21:15.706-04:00Objections to Bayesian Statistics: Lars Syll pulls a fast one on his readersSince my original post on <a href="http://fieldsfinance.blogspot.ca/2013/09/keynes-bayes-and-law.html">Keynes, Bayes, and the law</a>, Lars Syll has posted 5 subsequent entries on his blog about Bayesianism, so by frequency alone it's fair to infer that the subject is close to his heart. The general problem is that, when expressed in his own words his objections are baseless (e.g saying <a href="http://larspsyll.wordpress.com/2012/06/12/one-of-the-reasons-im-a-keynesian-and-not-a-bayesian/">here</a> that "The Bayesian rule of thumb is to simply assume that all outcomes are equally likely"), whereas when quoting from others it's impossible to know what is the argument he is trying to make. But apart from this, as I wrote in the comment section of his blog, <a href="http://larspsyll.wordpress.com/2013/09/11/objections-to-bayesian-statistics/">this last post of his</a> is, in my opinion, irredeemably misleading. <br />
<br />
Syll borrows the title for the blog post from a <a href="http://ba.stat.cmu.edu/journal/2008/vol03/issue03/gelman.pdf">2008 article</a> by Andrew Gelman and proceeds to quote very strong criticisms to Bayesian inference. The thing is, these are NOT Gelman's criticisms, but rather those of a hypothetical anti-Bayesian created by him to voice the objections. There are several passages in the article where this is clearly explained by Gelman, but all passages were purposefully omitted by Syll. Someone reading the blog post and not the article would rightly assume that these are criticisms that Gelman is raising himself (much like the <a href="http://andrewgelman.com/2008/04/01/problems_with_b/">April fool's joke</a> on which the article is based). Worse, Syll does not make any reference whatsoever to the <a href="http://www.stat.columbia.edu/~gelman/research/published/badbayesresponsemain.pdf">follow up article</a> where Gelman presents a spirited defence of Bayesian methods.<br />
<br />
Syll says that his purpose was to quote from an eminent statistician (Andrew Gelman) who "realized that these are strong arguments [against Bayesianism] to be taken seriously—and ultimately accepted in some settings and refuted in others." That is fine, but why do so in a way that implies that said statistician is trying to attack Bayesian inference, when in fact he is defending it?<br />
<br />
Finally, in response to my comment Syll says: "A quote is — yes — a quote. Nothing more, nothing less." Oh yeah? Well start with this quote:<br />
<br />
<blockquote class="tr_bq">
<blockquote class="tr_bq">
“Here follows the list of objections from a hypothetical or paradigmatic non-Bayesian:</blockquote>
<blockquote class="tr_bq">
Bayesian inference is a coherent mathematical theory but I don’t trust it in scientific applications.” Andrew Gelman</blockquote>
</blockquote>
and compare it with:<br />
<br />
<blockquote class="tr_bq">
<blockquote class="tr_bq">
“Bayesian inference is a coherent mathematical theory but I don’t trust it in scientific applications.” Andrew Gelman</blockquote>
</blockquote>
Same thing right? I don't think so.<br />
<blockquote class="tr_bq">
</blockquote>
Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com3tag:blogger.com,1999:blog-4799264811265759956.post-23913876425984877832013-09-08T19:02:00.000-04:002013-09-08T19:02:51.785-04:00Keynes, Bayes, and the law<br />
This is a combined response to a <a href="http://www.johnkay.com/2013/02/27/a-story-can-be-more-useful-than-maths">post by John Kay</a> on math and story telling, followed by <a href="http://larspsyll.wordpress.com/2013/09/08/probabilistic-reductionism/">another by Lars Syll</a> on probabilistic reductionism and a final one <a href="http://fixingtheeconomists.wordpress.com/2013/09/08/probabilities-keynesian-legal-versus-bayesian-mathematical/">by Philip Pilkington</a> on multiple versions of probabilities. Since I read the posts in reverse order, I'll structure my response in the same way.<br />
<br />
So starting with Pilkington, to say that there are alternative probabilities, one preferred by trained statisticians and another adopted by lawyers and judges is akin to say that there are alternative versions of chemistry, one suitable for the laboratory and another, more subtle and full of nuances, adopted by the refined minds of cooks and winemakers, honed in by hundreds or even thousands of years of experience. Clear nonsense, of course: the fact that a cook or winemaker uses tradition, taste, and rules of thumb, does not change the underlying chemistry. Same with probabilities and the court room.<br />
<br />
Before leaving Pilkington's post behind, let me just observe that he seems to be under the impression that confidence intervals and such are the domain of Bayesian statistics, whereas arguments based on the "degree of belief" are something else altogether. But anyone with a basic understanding of both confidence intervals and Bayesian statistics knows that nothing could be farther from the truth, as explained in this <a href="http://normaldeviate.wordpress.com/2012/11/17/what-is-bayesianfrequentist-inference/">very clear post by normaldeviate</a>, where one can find the statement that "Bayesian inference is the Analysis of Beliefs" - as simple as that.<br />
<br />
But Pilkington can be (partially) excused by the fact that he's getting his definitions from Lars Syll, who doesn't score any better in understanding or explaining Bayesianism. Syll gives the following example:<br />
<br />
<blockquote class="tr_bq">
<span style="background-color: white; color: #333333; font-family: 'Trebuchet MS', 'Bitstream Vera Serif', Utopia, 'Times New Roman', times, serif; font-size: 13px; line-height: 20px;">Say you have come to learn (based on own experience and tons of data) that the probability of you becoming unemployed in Sweden is 10%. Having moved to another country (where you have no own experience and no data) you have no information on unemployment and a fortiori nothing to help you construct any probability estimate on. A Bayesian would, however, argue that you would have to assign probabilities to the mutually exclusive alternative outcomes and that these have to add up to 1, if you are rational. That is, in this case – and based on symmetry – a rational individual would have to assign probability 10% to becoming unemployed and 90% of becoming employed.</span></blockquote>
<br />
While it is certainly true that a Bayesian would argue that you have to assign probabilities to the mutually exclusive events and that these have to add up to 1, no Bayesian would EVER say, based on symmetry or whatever, that a rational individual would have to assign probability 10% to becoming unemployed and 90% of becoming employed. A Bayesian could not care less how someone comes up with their priors. All a Bayesian says is that the priors need to add up to one and subsequently be revised in face of experience according to Bayes theorem. In this example, an assignment of 10% and 90% is just as rational as the exact opposite, namely 90% and 10%. What matters is that these priors eventually get corrected by new evidence. The only effect of a bad prior is that the correction takes slightly longer and requires a bit more evidence, that's all (for the technically minded, I should say that the only priors that don't get corrected by evidence are those of the form 0% to one event and 100% to another - no amount of new evidence can change these). Although trivial, this point is important to understand Syll's rejection of Bayesianism. For example, in <a href="http://larspsyll.wordpress.com/2012/06/12/one-of-the-reasons-im-a-keynesian-and-not-a-bayesian/">this other post</a> he explains why he's a Keynesian and not a Bayesian in terms of a "paradox" created by "the principle of insufficient reason", which is yet another way to select a prior and has precious little to do with Bayesianism.<br />
<br />
Next, moving on to Kay and his person-hit-by-a-bus example, evidently no court should find Company A liable simply because it has more buses than Company B, but absent any other information, this is a pretty decent way to form a prior. Another one is to come up with a narrative about the person and the bus. But in either case, the court should look at further evidence and recalculate its belief that a bus from Company A actually hit the person. For example they could hear testimony from eye witnesses or look at video footage and use Bayes theorem to find the posterior probabilities, which would then enter the "balance of probabilities" to lead to a decision. A court that finds Company A liable purely based on a story without looking at evidence is just as stupid as a one that bases its decision on the number of buses from each company.<br />
<br />
But the key passage in Kay's piece is:<br />
<br />
<br />
<blockquote class="tr_bq">
<span style="background-color: white; font-family: Georgia, Verdana, Helvetica; font-size: 14px; line-height: 19px; text-align: left;">Such narrative reasoning is the most effective means humans have developed of handling complex and ill-defined problems. A court can rarely establish a complete account of the probabilities of the events on which it is required to adjudicate. Similarly, an individual cannot know how career and relationships will evolve. A business must be steered into a future of unknown and unknowable dimensions.</span> </blockquote>
<blockquote class="tr_bq">
<span style="font-family: Georgia, Verdana, Helvetica;"><span style="font-size: 14px; line-height: 19px;">So while probabilistic thinking is indispensable when dealing with recurrent events or histories that repeat themselves, it often fails when we try to apply it to idiosyncratic events and open-ended problems. We cope with these situations by telling stories, and we base decisions on their persuasiveness. Not because we are stupid, but because experience has told us it is the best way to cope. That is why novels sell better than statistics texts.</span></span></blockquote>
<br />
so let me addressed this lest I receive hand-waving that I have not understood the criticism. There are two fundamental misunderstandings here. The first has to do with what it means to give a "complete account of the probabilities of the events" and the second is that probabilistic thinking involves some form of definite knowledge about the future, which has "unknown and unknowable dimensions".<br />
<br />
Now if by a "complete account of the probabilities of the events" one means "to assign probabilities to the mutually exclusive alternative outcomes and that these have to add up to 1", then as we have seen this is exactly what Bayes requires. But notice that "complete account" here simply means slicing up all mutually exclusive events that one is interested in (the technical term is a partition), and this can be as simple as two events (say hit by bus from Company A or from Company B, or being employed of unemployed in Norway). It does NOT mean a complete account of all the complex and ill-defined phenomena that led a person to be hit by a bus, or found in a cafe in Oslo with a diminishing amount of money in their pocket. Once the events of interest are identified, ANY method for assigning priors is fair game. This could be a narrative, or historical data, or an agent-based model for people, buses, and firms.<br />
<br />
Finally, about the notion that probabilistic thinking requires strong assumptions about the future, one hears often that because economics (or law, or politics, or baseball) is not ergodic, past experience is no guide to the future, and therefore there's no hope in using probability. As I said <a href="http://fieldsfinance.blogspot.ca/2013/08/small-brain-economics-pilkingtons.html">elsewhere</a>, Bayes theorem is a way to update beliefs (expressed as probabilities) in face of new information, and as such<br />
<br />
<blockquote class="tr_bq">
could not care less if the prior probabilities change because they are time-dependent, the world changed, or you were too stupid to assign them to begin with. It is only a narrow frequentist view of prediction that requires ergodicity (and a host of other assumptions like asymptotic normality of errors) to be applicable.</blockquote>
<br />
A few related exclamations to conclude:<br />
<br />
Mathematical models are stories like any other!<br />
<br />
Non-ergodicity is the friend of good modellers and story tellers alike!<br />
<br />
So is irreducible uncertainty!<br />
<br />
Think probabilistically! Estimate nothing!<br />
<br />
<blockquote class="tr_bq">
</blockquote>
Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com2tag:blogger.com,1999:blog-4799264811265759956.post-8375186506234815232013-08-28T16:16:00.002-04:002013-08-28T16:16:12.061-04:00Accounting identities for the Keen modelThis is long overdue, but now that Steve Keen is visiting the Fields Institute again I thought I should revisit the topic of aggregate demand, income, and debt in his models. Loyal readers will recall that this was the subject of a <a href="http://fieldsfinance.blogspot.ca/2012/10/of-course-its-model-duh-final-post-on.html">somewhat heated exchange</a> on this and other blogs last year. <div>
<br /></div>
<div>
So <a href="http://ms.mcmaster.ca/~grasselli/keen2011_table.pdf">here</a> is the full balance sheet/transaction/flow of funds table for one of Keen's models, together with the implied accounting relationships, as well as my take on the "demand = income + change in debt" statement and its variants. </div>
<div>
<br /></div>
<div>
As I had mentioned in <a href="http://fieldsfinance.blogspot.ca/2012/10/more-on-income-expenditure-and.html">one of the old posts</a>, the point it to disaggregate the firms and households from the banking sector, so that endogenous money creation can play a significant role in the story. </div>
<div>
<br /></div>
<div>
In my view, accounting identities that put the entire private sector together (i.e firms + houses + banks) somehow obfuscate the role of endogenous money and end up putting undue emphasis in the only other relevant observation, namely that private sector surplus should equal government deficit. </div>
Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com31tag:blogger.com,1999:blog-4799264811265759956.post-87654306140330802542013-08-21T11:47:00.000-04:002013-08-21T11:49:38.669-04:00Small-brain economics: Pilkington's strong prior against mathematics<!--[if gte mso 9]><xml>
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You know you have made it in heterodox economics when
someone claims that you have a plan to destroy post-Keynesianism as we know it
– muhahahaha. Hyperbole aside, this is essentially what one Philip Pilkington
thinks that I’m doing, as he explains in this <a href="http://fixingtheeconomists.wordpress.com/2013/08/20/brain-slug-economics-grassellis-project-to-turn-post-keynesian-economics-into-mathematical-formalism/">rant</a>, itself a spin-off of a
discussion that started at the INET YSI Facebook page and went somewhat astray
(the thread containing it has since been closed by the moderator of the page). </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Pilkington, a journalist-cum-research assistant currently
working on his dissertation at Kingston University, frames the discussion around two alleged sins
that I have committed,
namely, (i) not knowing what I’m talking about and (ii) mistake model for
reality and make grandiose claims. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As evidence of the first sin, he offers this comment of mine
from the facebook discussion (emphasis added here, you’ll see why in a second):</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>OK, this ergodicity
nonsense gets thrown around a lot, so I should comment on it. You only need a
process (time series, system, whatever) to be ergodic if you are trying to make
estimates of properties of a given probability distribution based on past data.
The idea is that enough observations through time (the so called time-averages)
give you information about properties of the probability distribution over the
sample space (so called ensemble averages). So for example you observe a stock
price long enough and get better and better estimates of its moments (mean,
variance, kurtosis, etc). Presumably you then use these estimates in whatever
formula you came up with (Black-Scholes or whatever) to compute something else
about the future (say the price of an option). The same story holds for almost
all mainstream econometric models: postulate some relationship, use historical
time series to estimate the parameters, plug the parameters into the
relationship and spill out a prediction/forecast.<o:p></o:p></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>Of course none of this
works if the process you are studying in non-ergodic, because the time averages
will NOT be reliable estimates of the probability distribution. So the whole
thing goes up in flames and people like Paul Davidson goes around repeating
“non-ergodic, non-ergodic” ad infinitum. The thing is, none of this is
necessary if you take a Bayes’s theorem view of prediction/forecast. You start
by assigning prior probabilities to models (even models that have nothing to do
with each other, like an IS/LM model and a DSGE model with their respective parameters),
<b>make predictions/forecasts based on
these prior probabilities, and then update them when new information becomes
available</b>. Voila, no need for ergodicity. Bayesian statistics could not
care less if the prior probabilities change because they are time-dependent,
the world changed, or you were too stupid to assign them to begin with. It is
only a narrow frequentist view of prediction that requires ergodicity (and a
host of other assumptions like asymptotic normality of errors) to be
applicable. Unfortunately, that’s what’s used by most econometricians. But it
doesn’t need to be like that. My friend Chris Rogers from Cambridge has a
t-shirt that illustrates this point. It says: “Estimate Nothing!”. I think I’ll
order a bunch and distribute to my students.<o:p></o:p></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Pilkington then goes on to say:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>It is not clear that
Grasselli’s approach here can be used in any meaningful way in empirical work.
What we are concerned with as economists is trying to make predictions about
the future. <o:p></o:p></i></div>
<div class="MsoNormal">
<i>These range from the
likely effects of policy, to the moves in markets worldwide. What Grasselli is
interested in here is the robustness of his model. He wants to engage in
schoolyard posturing saying “my model is better than your model because it made
better predictions”. <o:p></o:p></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Wait, what? Exactly which part of “make
predictions/forecasts based on these prior probabilities, and then update them
when new information becomes available” is not clear? Never mind that I’d give
a pound of my own flesh for this to be the Grasselli approach (it’s actually
the Bayesian approach), the sole purpose of it is to make precise predictions
and then update them based on new evidence, so it’s baffling that Pilkington
has difficulties understanding how it can be used in empirical work. Not to
mention the glaring contradiction of saying in one breath that </div>
<div class="MsoNormal">
“What we are concerned with as economists is trying to make
predictions about the future” and admonishing me in the next for allegedly
claiming that “my model is better than your model because it made better
predictions”. So you want to make predictions, but somehow don’t think that a
model that makes better predictions is better than one that made worse
predictions. Give me a minute to collect my brains from across the room…</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Back to my comment on the “ergodicity nonsense”, the key
point was that it is the frequentist approach to statistics that forces one to
make estimates of priors based on past time series, and this requires a lot of
assumptions, including ergodicity. In Bayesian statistics, the modeler is free
(in fact encouraged) to come up with her own priors, based on a combination of
past experience, theoretical understanding, and personal judgment. Fisher, the
father of the frequentist approach, wanted to ban any subjectivity from
statistics, advocating instead (I’m paraphrasing here) that one should
“Estimate everything!”. By contrasts, Bayesians will tell you that you should
estimate when you can, but supplement it with whatever else you like. To
illustrate how historical estimates are not only misleading (for example when
the underlying process is non-ergodic) but also unnecessary in Bayesian
statistics, Chris Rogers has the mantra “Estimate nothing!”. But nowhere does it
say “Predict nothing!”. On the contrary, once again, the nexus “make
predictions based on probabilities--compare with reality--change the
probabilities” is what the
approach is all about. So on the topic of advice for t-shirt making, Pilkington
should wear one that says “I ought to read the paragraphs I quote” in front,
followed by “and try to avoid self-contradictions” on the back. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Moving on, as evidence for the second sin, Pilkington quotes
another long comment of mine with the “clearest explanation” (his words, but I
agree!) of what I’m doing, namely: </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>I’m not comparing
models, I’m comparing systems within the same model. Say System 1 has only one
locally stable equilibrium, whereas System 2 has two (a good one and a bad
one). Which one has more systemic risk? There’s your first measure. Now say for
System 2 you have two sets of initial conditions: one well inside the basin of
attraction for the good equilibrium (say low debt) and another very close to
the boundary of the basin of attraction (say with high debt). Which set of
initial conditions pose higher systemic risk? There’s your second measure.
Finally, you are monitoring a parameter that is known to be associated with a
bifurcation, say the size of the government response when employment is low,
and the government needs to decide between two stimulus packages, one above and
one below the bifurcation threshold. Which policy lead to higher systemic risk?
There’s your third measure.<o:p></o:p></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
He then goes on to paraphrase it in a much more clumsy way
(question: if someone already gave you the clearest explanation about
something, why should you explain again? Just to make it worse?): </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>What Grasselli is
doing here is creating a model in which he can simulate various scenarios to
see which one produces high-risk and which will produce low-risk environments
within said model. But is this really “measuring systemic risk”? I don’t think
that it is. To say that it is a means to measure systemic risk would be like me
saying that I found a way to measure the size of God and then when incredulous
people came around to my house to see my technique they would find a computer
simulation I had created of what I think to be God in which I could measure
Him/Her/It.<o:p></o:p></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Now I don’t know what the God example is all about, but Pilkington seems to think that the only way
to measure something is to go out with an instrument (a ruler, for example) and
take a measurement. The problem is that risk, almost by definition, is a
property if future events, and you cannot take a measurement in the future. ALL
you can do is to create a model of the future and then “measure” the risk of
something within the model. As Lady Gaga would say “oh there ain’t no other
way”. For example, when you drive along the Pacific Coast Highway and read a
sign on the side of the road that says “the risk of forest fire today is high”,
all it means is that someone has a model (based on previous data, the theory of
fire propagation, simulations and judgment) that takes as inputs the
measurements of observed quantities (temperature, humidity, etc) and calculates
probabilities of scenarios in which a forest fire arises. As time goes by and
the future turns into the present you then observe the actual occurrence of
forest fires and see how well the model performs according to the accuracy of
the predictions, at which point you update the model (or a combination of
models) based on, you guessed it, Bayes’s theorem. <br />
<br />
So that’s it for the accusation of mistaken model for reality. But still on the
second fundamental sin according to Pilkington, recall that its second part consists
of making “grandiose claims about what they have achieved or will potentially
achieve that ring hollow when scrutinized”, against which his advice is to “tone
down the claims they are making lest they embarrass the Post-Keynesian
community at large”. This is all fine, but it sounds a bit rich coming from
someone who published a piece titled <a href="http://fixingtheeconomists.wordpress.com/2013/08/16/teleology-and-market-equilibrium-manifesto-for-a-general-theory-of-prices/">Teleology and Market Equilibrium:Manifesto for a General Theory of Prices</a>, which upon scrutiny contains some
common platitudes about neoclassical denials of empirical evidence, followed by
this claim:</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>My goal is to lay out
a general theory of prices in the same way Keynes laid out a general theory of
employment and output. This will provide a framework in which the neoclassical
case of downward-sloping demand curves and upward-sloping supply curves is a
highly unlikely special case. With such a framework we can then approach
particular cases as they arise in a properly empirical manner. In doing this I
hope to be able to introduce the Keynesian theory to pricing; and with that, I
think, the neoclassical doctrines will be utterly destroyed and a full,
coherent alternative will be available. Fingers crossed!<o:p></o:p></i></div>
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<br /></div>
<div class="MsoNormal">
So instead of an actual general theory of prices,
Pilkington’s “manifesto” states his goal to be as great as Keynes and utterly
destroy the neoclassical doctrines. Hear the low tone!<br />
<br />
Which brings me to Keynes’s advice on the use of mathematics that Pilkington
also quotes in his rant. Again, if you read the quote carefully you see that
Keynes warns against “symbolic pseudo-mathematical methods” and complains that
“Too large a proportion of recent ‘mathematical’ economics are mere concoctions”.
Notice the prefix pseudo and the inverted commas around the word mathematics in
the original quote, which suggests that Keynes’s peeve was not with mathematics
itself, but with the “imprecise…initial assumptions they rest on”. In
particular, Keynes singles out methods that “expressly assume strict
independence between the factors involved”, which is admittedly a very stupid assumption,
but in no way necessary for the application of (true, i.e not pseudo)
mathematical methods. For example, NONE of the models I work with assume
independence between factors, on the contrary, they highlight the complex and
surprisingly rich interdependencies, as well as their consequences. <br />
<br />
I conclude in meta fashion with a Bayesian framing of this discussion itself.
Pilkinton has a very strong prior that my mathematical methods are useless and
he’s honest enough to say so: “I heard about the work Grasselli and others were
doing at the Fields Institute some time ago and I was instantly skeptical”. He
bases this prior on a well-documented post-Keynesian intellectual tradition, as
well as a slightly misguided notion of what constitutes “giant formal models”
(my models are actually pretty easy low-dimensional dynamical systems, but if
you are Bart Simpsons then I guess anything looks like a giant formal model).
By contrast, I have a very strong prior that my models are useful, based on
similarly well-documented intellectual tradition of applications of mathematics
in other areas of study. Pilkington concedes that he might be wrong and
promises unreserved praise if that turns out to be true. Likewise, I might be
wrong, in which case I’ll abandon the models and do something else. In either
case, we’ll both be traveling the same Road to Wisdom, as in the exceptional
poem by Piet Hein:<br />
<i><br /></i>
<i>THE ROAD TO WISDOM?</i></div>
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<i>Well, it's plain<o:p></o:p></i></div>
<div class="MsoNormal">
<i>and simple to express.<o:p></o:p></i></div>
<div class="MsoNormal">
<i>Err and err and err
again,<o:p></o:p></i></div>
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<i>but less and less and less.</i>
</div>
<div class="MsoNormal">
<br /></div>
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Nate Silver uses this poem as inspiration for the title of
the chapter in his book explaining the Bayesian approach, which he ends with a meta
statement of his own: “Bayes’s theorem predicts that Bayesians will win”. <br />
<br />
Estimate nothing!</div>
<!--EndFragment-->Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com2tag:blogger.com,1999:blog-4799264811265759956.post-27537352705109077962013-04-17T18:06:00.001-04:002013-04-17T18:06:37.430-04:00My take on Reinhart-RogoffI have not blogged for a while, but <a href="http://www.nextnewdeal.net/rortybomb/researchers-finally-replicated-reinhart-rogoff-and-there-are-serious-problems">this</a> is too important to ignore, mostly because for the past two years or so I have been supervising different groups of undergraduate students on a <a href="http://www.fields.utoronto.ca/programs/scientific/12-13/summer-research12/index.html">data-driven project</a> based on reproducing and extending the results in the Reinhart-Rogoff book.<br />
<br />
So let me start with a few observations about the book:<br />
<br />
- the dataset used in the book is <i>not</i> readily available, despite what the authors say. What one can download from their website is secondary data prepared by the authors, for example the full set of crises dates for each country. On the other hand, the book does provide a more or less complete list of sources, from which we were able to download something like 95% of the primary data used by the authors (e.g from places like the IMF, World Bank, the Madison project, etc).<br />
<br />
- the books is full of small errors, like figures that do not quite match what their caption says, or numerical results that turned out to be slightly wrong when we tried to reproduced them based on the primary data, but overall we didn't find any major errors and agreed with almost all of their conclusions. Moreover, we were able to successfully implement the signals approach described towards the end of the book for currency, banking, and stock market crisis (not mentioned in the book!).<br />
<br />
- in other words, the book is both solid and a useful launchpad for further research, if only a little sloppy.<br />
<br />
Now, the story is very different (pun intended!) regarding their 2010 paper. Right from the beginning I thought that the possibility of reverse causation alone was enough reason not to take the results too seriously, so I didn't even bothered to try to reproduce the results.<br />
<br />
But alas, HAP have done the work and found that even the numerical results presented in the paper were significantly wrong, not to mention the conclusions. And the <a href="http://ineteconomics.org/blog/inet/reinhart-and-rogoff-respond-criticism">response</a> from Carmem Reinhart is even more appalling than the article itself. Basically she claims that HAP also find a negative correlation between debt and growth, so what's the big deal?<br />
<br />
Of course the big deal is that their original paper implied the existence of a hard threshold at 90% debt-to-GDP beyond which the slowdown in growth was very rapid, indicating some kind of nonlinear amplifying effects that would likely plunge the country into a state of crisis. But as it turns out, there's nothing special about the 90% mark, with the relationship being approximately linear all the way through, and therefore very manageable.<br />
<br />
In any case, I wish they had never written the 2010 paper (and perhaps by now they wish the same), if only because it's probably going to drag their good and useful book (along with their reputation in general) through the well-deserved mud where they find themselves at the moment.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-25533039574858811032012-10-15T16:48:00.002-04:002012-10-15T16:48:41.550-04:00And now for something completely different: Ngo Bau Chau at the Fields Institute I'm taking a break from all economics/finance/accounting-related activities (blogging included) tonight to attend the opening ceremony for the inaugural <a href="http://www.fields.utoronto.ca/programs/scientific/fieldsmedalsym/12-13/">Fields Medal Symposium</a>, which celebrates the work of a recent Fields medalist each year, right here at the Fields Institute.<br />
<br />
This year's symposium is dedicated to Ngo Bao Chau and you can watch his public lecture from 7:00pm onwards by following the link provided in the website above (his lecture will actually start a bit later, after the ceremonial speeches by a string of dignitaries, but if you tune in at 7:00 you can catch a glimpse of yours truly, sitting beside Ngo on the second row of the theatre and looking totally starstruck).Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com2tag:blogger.com,1999:blog-4799264811265759956.post-72195595174167473882012-10-13T16:50:00.000-04:002012-10-13T16:50:39.948-04:00Of course it's a model, duh! A final post on income, expenditure, and endogenous moneyMany comments on the <a href="http://fieldsfinance.blogspot.ca/2012/10/more-on-income-expenditure-and.html">different threads</a> related to Ramanan's critique of <a href="http://www.math.mcmaster.ca/~grasselli/KeenGrasselli2012EuropeanDisunionAndEndogenousMoneyFinal.pdf">my paper</a> with Steve Keen amount to saying that if we were trying to write down some kind of model for a perceived phenomenon (in this case the role of private debt in macroeconomics), then it would be ok, but because we violated an accounting identity (or more) in the process, oh boy, we have been very very naughty indeed.<br />
<br />
The thing is, we never claimed to be doing any accounting, let alone violating it. Accounting is about recording stuff during a given period (a year, a month, a day, but NOT an instant, since you need to wait for stuff to happen to record it) and in the only part in the paper where we mention any recording (Appendix, page 24, last paragraph of the paper) we say that "recorded expenditure and income over a finite period (t2 − t1 ), such as those found in NIPA tables, necessarily agree".<br />
<br />
So I'll say this again in a separate line and in capital for emphasis (with some superlatives in bracket, as commenters like):<br />
<br />
RECORDED EXPENDITURE AND INCOME OVER A FINITE PERIOD NECESSARILY AGREE (*always, toujour, siempre*) !!!<br />
<br />
Now suppose you read income statements for an economy months after months, year after year, and wonder why recorded spending (= recorded income !!) for the different periods happen to be different. You might think it has something to do with the Mayan calendar, or with the incidence of flu during that period, or maybe that it's completely random. If you are an economist you might want to explain it with a DSGE model that ignore private debt. Heck you might even write down a regression model that includes the change in private debt in one period as an explanatory variable for the spending (= income !!) to be recorded over the next period, as one commenter suggests. Or if you are Steve Keen you write down a model using differential equations, because they happen to be tractable and cool and predict many properties that sort of look like what goes on in real life. But none of that is accounting - all of it is modelling.<br />
<br />
Everything else we wrote in the paper was with the view of explaining why the heck recorded spending (= recorded income !!) changes from year to year. If along the way we wrote stuff down that looked like a violation of an accounting identity, then I profusely apologize for it (in fact I already bought a whip to punish myself) and pinky-promise never to do it again. So will the accounting police chill out and move on? Unless you actually care about the model, in which case please read on.<br />
<br />
As far as the model goes, what we are trying to capture is Minsky's assertion that "for real aggregate demand to be increasing, . . . it is necessary that current spending plans, summed over all sectors, be greater than current received income and that some market technique exist by which aggregate spending in excess of aggregate anticipated income can be financed."<br />
<br />
So our Y_E represent "current spending plans" (per unit of time) and our Y_I represent "current received income" (per unit of time). Equation 1.5 in the paper is the key behavioural assumption that links investment to change of debt, and is a schematic representation of the mechanism that both Steve and I have in the back of our minds, what I call the "Keen model" described in <a href="http://www.math.mcmaster.ca/~grasselli/GrasselliCostaLima_MAFE_published.pdf">this paper</a>, where investment (the rate of change in capital) is a function of current net profits, but can exceed profits in times of boom and therefore be financed by debt.<br />
<br />
All of this is pure modelling: in reality nobody looks at a differential equation before spending. The true test of the model is to see if it predicts the right behaviour for the key variables (employment rate, wage share, output, level of private debt, etc) over time, once the parameters of the several structural equations are calibrated using historical data (which includes income and flow of funds statements over many periods).<br />
<br />
As a final word, notice that neither Y_E nor Y_I are meant to represent recorded expenditure or income over a period anywhere in the paper (which again, are necessarily equal !!). Both are modelling abstractions of what goes on in the economy and could include stuff like the Mayan calendar and incidence of flu, but happen to depend on the level of private debt.<br />
<br />Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com30tag:blogger.com,1999:blog-4799264811265759956.post-34303553021607805072012-10-12T22:07:00.000-04:002012-10-12T22:07:13.012-04:00More on income, expenditure, and endogenous money - a non-vacuous response<br />
A reader of Mike Norman's very useful blog calls my last post a <a href="http://mikenormaneconomics.blogspot.ca/2012/10/matheus-responds-to-ramanan.html">vacuous response</a> to Ramanan. Of course it was not a response at all, merely a commentary. Notice how I said that "all the criticisms can be defended in two words: endogenous money!", not that they were defended... Plus I thought it implicit that whenever one says something like "I got n words for you: word_1 ... word_n", one's tongue is firmly in one's cheek. But I'm quickly learning that there is no such thing in the econo-blogosphere.<br />
<br />
In any event, after the avalanche of comments on Mike's re-posts (last count: 21 on the post above, 66 on Ramanan's <a href="http://mikenormaneconomics.blogspot.ca/2012/10/ramanan-income-expenditure.html">second take down</a>, and 124 on its <a href="http://mikenormaneconomics.blogspot.ca/2012/10/ramanan-steve-keen.html">predecessor</a>), perhaps it's time for a point-by-point reply (I originally called it a "point-by-pint" reply, which is perhaps a measure of what was on my mind while I was writing it).<br />
<br />
Let me start by saying that I'll refer mostly to <a href="http://www.math.mcmaster.ca/~grasselli/KeenGrasselli2012EuropeanDisunionAndEndogenousMoneyFinal.pdf">this paper</a>, since I had something to do with the notation and ideas presented in it, rather than to Steve's presentation at the UMKC conference, thought I might occasionally refer to it too. Let me also say that said paper (which is being refereed and therefore can sill improve quite a lot), could use a great deal of clarifications. Many of the ideas that were in the back of our minds as we were writing it clearly didn't make it to the printed page, so I welcome the opportunity to elaborate.<br />
<br />
With these in mind, here are the essential points:<br />
<br />
(1) Our "closed" economy does consist of firms, households, and banks, but we find it useful to <b>separate the banking sector from the rest of the private sector</b>. We do this explicitly on pages 18 to 23, but leave it implicit on page 15, which contains the passages that Ramanan has a beef with. So our "change in debt" is really change in debt of the non-bank private sector to the banking sector, which obviously does not need to cancel out in the aggregate (i.e excluding banks). This is in contrast with the view that "one person's asset is another person's liability", which underlines the view that firm's debt is mirrored by household's savings.<br />
<br />
(2) <b>Debt only matter after it has been spent</b>. This is the point of equation (1.5): we assume that investment is financed by retained earnings plus change in debt. If new debt is not spent, it doesn't finance anything, so we don't count it in the model.<br />
<br />
(3) <b>Accounting rules!</b> The whole point of the Appendix in the paper is to show that recorded income equals recorded expenditure at the end of a given period (say one year). We don't use continuous mathematics to upset accounting identities, but rather as "a simple way to represent the conceptual difference between spending plans and current received income".<br />
<br />
Observe that all 3 points are intimately connected with the idea of endogenous money, which is what I meant by my "two words" zinger. The effects of endogenous money only become apparent when banks are disaggregated from the rest of the private sector (1), capitalists finance new investment above and beyond savings by creating deposits through endogenous money (2), and spending plans exceed current received income for the same reason, even if this is not apparent when one measures recorded income and recorded expenditure (3).<br />
<br />
In the end, what we are tying to capture is the idea expressed on page 10, namely that "the essence of endogenous money hypothesis is that banks create spending power for borrowers without reducing the spending power of savers."<br />
<br />
Judging by the criticism, we haven't quite succeeded yet, but we'll keep on trying.<br />
<br />
<br />
<br />
<br />
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Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com6tag:blogger.com,1999:blog-4799264811265759956.post-47586630835441114042012-10-11T15:27:00.000-04:002012-10-11T15:27:00.718-04:00Income, expenditure, and endogenous money My supervisor <a href="http://en.wikipedia.org/wiki/Ray_Streater">Ray Streater</a> used to quote an example of a physicist's version of proof by <i>reductio ad absurdum </i>that goes more or less like this: "Assume that asymptotic completeness doesn't hold in quantum field theory. What an absurd!"<br />
<br />
I was reminded of that as I read this <a href="http://www.concertedaction.com/2012/10/09/income-expenditure/">take down</a> of my <a href="http://www.math.mcmaster.ca/~grasselli/KeenGrasselli2012EuropeanDisunionAndEndogenousMoneyFinal.pdf">paper</a> with Steve Keen, where we claim that expenditure is income plus change in debt. In an attempt to show that we are wrong, Ramanan shows that our model violates the "savings equals investment" identity. What an absurd!<br />
<br />
Hmm, actually, not only this is not an "inconsistency" of the model (we never claim that this was true, or rely on it to show anything else in the paper), but it is rather essential: in our model, investment is equal to savings plus change in debt. This is the essence of equation (1.5) in the paper, and we were always acutely aware of it.<br />
<br />
So much for the rather bombastic conclusion that we must be wrong because we violate the sacrosantity of "savings = investment" -- this is a feature of the model, not a bug!<br />
<br />
Having said that, it is nevertheless a feature that ought to be defended, together with the other criticisms raised in both the take down mentioned above and its <a href="http://www.concertedaction.com/2012/10/06/income-%E2%89%A0-expenditure/">predecessor</a>.<br />
<br />
As it turns out, without engaging in a point-by-pint reply (which would be a very boring read for anyone not called Grasselli, Keen, or Ramanan), it suffices to say that all the criticisms can be defended in two words: endogenous money!<br />
<br />
<br />
<br />
<br />
<br />Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com12tag:blogger.com,1999:blog-4799264811265759956.post-38007486615618179062012-10-02T21:59:00.000-04:002012-10-02T21:59:22.961-04:00Further thoughts on mathematics and economics<br />
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After almost 3 years of blogging to a reduced audience, I observed a sudden spike in my stats after my <a href="http://fieldsfinance.blogspot.ca/2012/09/having-fun-with-economics-and-lord.html">post about the UMKC conference</a> got re-blogged (or re--tweeted, who knows) in the legendarily active econo blogosphere. So I thought I should ride the wave and elaborate on my remarks. </div>
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First of all, as pointed out by a commenter, I only attended the last day of the conference, which according to the unwritten laws of scheduling was </div>
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bound to be the least exciting (especially on a Saturday!). I guess I should expect that - after all that was the spot on the schedule reserved for me... But still, </div>
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after being blown away by the vibrance and intellectual rigour of the likes of Stephanie Kelton and Scott Fulwiller when I <a href="http://www.fields.utoronto.ca/programs/scientific/11-12/nonlineareconomics/">met them at Fields a few months ago</a>, I had great </div>
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expectations about the event, and was disappointed to find out that most of the people I wanted to meet had already left (his lordship notwithstanding). </div>
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But on a more substantive note, I see from the comments (here and elsewhere), that the role of mathematics in economics is a bit of a raw nerve, hence the urge to elaborate.</div>
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Despite being a mathematician, I do not think that mathematical modelling is the most important part of economics, but I do think that it is somewhat essential. Here I'm reminded of the famous </div>
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saying that "logic is to mathematics what hygiene is to life: it's clearly essential, but not what it's all about". The same goes for mathematics and economics: historical awareness, acute observations, and empirical plausibility come first in economic reasoning, but I don't see how much progress can be made without mathematics. Notice that this is not about pedagogy, but about being able to even formulate crucial statements. </div>
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<br /></div>
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To borrow from other fields, it would be nearly impossible to even conceptualize something like the basic reproductive number in epidemiology without a mathematical model, and this means the difference between being able to handle a pandemic or not. For another example, no amount of analogy or logical thinking can pinpoint the phenomenon of bifurcations. The fact that smooth changes in some underlying parameter can cause a system to completely change its qualitative behaviour is not something that is predicated by logic and hard thinking alone - it needs mathematics. Needless to say, the list could go on and on.</div>
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Finally, just in case you associate mathematics too heavily with neoclassical economics, remember that the final blow to general equilibrium was dealt by a mathematical result: the SMD theorems essentially tell us that the whole framework (and much of neoclassical economics with it) is only guaranteed to work for the trivial case of one agent and one good. </div>
Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com16tag:blogger.com,1999:blog-4799264811265759956.post-67277516683761639092012-09-30T12:49:00.001-04:002012-09-30T12:49:41.133-04:00Having fun with economics and Lord Skidelsky I participated in the <a href="http://www.internationalpostkeynesianconference.org/">11th International Post Keynesian Conference</a> in Kansas City this weekend and presented a <a href="http://www.youtube.com/watch?v=_qcXR5P3rck&feature=plcp">paper</a> on the effect of government intervention in a macro model based on a system of ODE first developed by Steve Keen, who presented just before me.<br />
<br />
The conference itself was a bit of a sleepy affair, with most of the other talks I attended being more literary criticism (e.g several quotes from Keynes, Minsky, and others, strung together and compared with recent events) than actual modelling.<br />
<br />
My overall impression is that if this is all that heterodoxy has to offer as an alternative to mainstream economics, then the profession is in deeper trouble than I thought.<br />
<br />
But the highlight was the keynote after dinner speech by none other than Lord Robert Skidelsky (his business card actually says "Lord Skidelsky", no joking!)<br />
<br />
He started his speech with a joke saying that when John Kenneth Galbraith wrote an economic report to Lyndon Johnson, the president allegedly said "You know Ken, talking about economics is like peeing in you pants, it feels hot to you, but leaves everyone else in the cold", then proceeded to say that he was reminded of this story by listening to mathematicians earlier in the afternoon, who appeared to be having to much fun with his models (Steve and me!). Then at the Q&A session, his advice to an economics grad student included "don't use math". Finally when I asked him directly what his advice to mathematician trying to contribute to economics would be, he offered this gem: "well sometimes you just need to tell what hullaballoo is all about".<br />
<br />
So apart from all the fun to be had with economics (which I'll continue to do), I think that between the hyper mathematical (but incorrect!) DSGE guys on the mainstream and the math phobics in the fringes, this is going to be an uphill battle.<br />
<br />
<br />Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com4tag:blogger.com,1999:blog-4799264811265759956.post-21951435154120644422012-07-06T21:17:00.000-04:002012-07-06T21:17:08.763-04:00Steve Keen at Fields: a memorable monthSteve Keen left Toronto today after spending the last five weeks visiting the Fields Institute. As always happens when one is having so much fun, time went by very fast, but we collectively managed to get an awful lot done. Here are the highlights:<br />
<br />
- we had weekly <a href="http://www.fields.utoronto.ca/programs/scientific/11-12/nonlineareconomics/">seminars</a> where people with backgrounds in economics, financial mathematics, mathematical biology, history, and statistics gathered to present and discuss results related to a novel (nonlinear) dynamical systems approach to macroeconomics;<br />
<br />
- Steve gave a <a href="http://www.policyalternatives.ca/newsroom/updates/australian-economist-steve-keens-ccpa-lecture-video">public lecture</a> hosted by the Canadian Centre for Policy Alternatives, which was interesting in its own right, but also served to put Fields and CCPA on a path for future collaborations;<br />
<br />
- we held a very successful closed discussion session on a scorching hot Canada Day public holiday, with the purpose of reconciling Modern Monetary Theory (MMT) and Monetary Circuit Theory (MCT);<br />
<br />
- Steve gave <a href="http://www.fields.utoronto.ca/programs/scientific/12-13/public_lectures/">another public lecture</a> at Fields, which was not only streamed over the web using our FieldsLive system, but also recorded for an episode of TVO's show Big Ideas.<br />
<br />
<br />Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com1tag:blogger.com,1999:blog-4799264811265759956.post-85386972910377720342012-06-09T20:46:00.003-04:002012-06-09T20:46:47.383-04:00Steve Keen on endogenous moneyWe started our <a href="http://www.fields.utoronto.ca/programs/scientific/11-12/nonlineareconomics/">Sojourns in Nonlinear Economics</a> this week with Steve Keen giving a thorough introduction to his circuit theory for endogenous money creation in the banking system.<br />
<br />
Steve is visiting Fields this month and we organized these informal seminar to get the most out of his stay. Personally I'm anticipating that his highly original ideas and unorthodox models will provide research material for myself and other mathematicians for many years to come.<br />
<br />
Stay tuned!Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-34782243025889085462012-06-02T18:37:00.002-04:002012-06-02T18:37:35.198-04:00Myron Scholes at McMasterThe McMaster Alumni Association celebrated the 50 years of graduation for the class of 1962 by <a href="http://dailynews.mcmaster.ca/story.cfm?id=8959">inviting their most distinguished alumnus</a> back to campus.<br />
<br />
I attended the luncheon in his honour, where he treated us to personal recollections of his time as a student at McMaster and some insights on the future of economics. At question time I asked if he thought new techniques were necessary to deal with what I call mesoeconomic problems, such as banking regulation, which do not easily fit into either micro or macroeconomic toolboxes. He said "Yes, sure" and proceeded to explain an Ornestein-Uhlenbeck model for production, with a mean-reverting rate that had to be adjusted after each macroeconomic shock. Okay...<br />
<br />
At the public talk that followed, Myron accurately diagnosed the current economic woes of the world as a "debt-deflation" crisis, with all the symptoms associated with it. His prescription, however, was to get the government out of financial markets altogether. He used the analogy of putting out small forest fires for many decades only to discover that the practice created the perfect conditions for uncontrollable big fires.<br />
<br />
Now, apart from the obvious fact that this means that Greenspan should NOT have orchestrated the bailout of LTCM (something everyone in the room was too polite to point out), the prescribed medicine happens to be the opposite of what the doctor should call for given the correct diagnoses.<br />
<br />
But oh well, it was a day to celebrate, not to get bogged down in technical discussions.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-72541936558560717572012-05-20T23:05:00.001-04:002012-05-20T23:05:27.158-04:00Office of Financial ResearchJust after the crisis, a group of scholars associated with quantitative finance (mathematicians, finance professors, financial economists, etc) got together with practitioners and regulators and formed a committee to lobby for the creation of a <a href="http://www.ce-nif.org/">National Institute of Finance</a>. The idea was to gather data and expertise to monitor, analyze and potentially prevent future crises.<br />
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Against all odds, the idea was enshrined in the Dodd-Frank act and became the <a href="http://www.treasury.gov/initiatives/wsr/ofr/Pages/default.aspx">Office of Financial Research</a>. It has the potential to create an unprecedentedly useful database and spur paradigm shitting research with far reaching implications to the way finance is understood and practiced, and has already attracted some of the best minds in the field.<br />
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Naturally, the Republicans <a href="http://www.youtube.com/watch?v=F1YWtiWl3MM">want to kill it</a>.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-82891776064321538262012-05-20T10:54:00.002-04:002012-05-20T10:54:28.932-04:00Mathematics of New Financial SystemsThat was the theme of the recent <a href="http://www.ima.umn.edu/2011-2012/SW5.17-19.12/">Hot Topics Workshop</a> at the IMA in Minneapolis.<br />
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I was delighted to see many old friends doing some really interesting mathematics on relatively new topics, like systemic risk and stochastic portfolio theory.<br />
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My small contribution to the workshop was on the Keen-Minsky model for the dynamics of credit for the economy as a whole (see paper <a href="http://www.math.mcmaster.ca/~grasselli/GrasselliCostaLima_MAFE_final.pdf">here</a>). Because the workshop was open-minded by construction, many of the economists in attendance refrain from attacking the model too heavily, despite some of my provocative remarks (e.g "macroeconomics is too important to be left at the hands of macroeconomists").<br />
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All in all I came away encouraged and optimistic about the prospect of future contributions of mathematics to economics.<br />
<br />Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com1tag:blogger.com,1999:blog-4799264811265759956.post-25157661261820469832012-03-24T13:11:00.004-04:002012-03-24T13:14:51.638-04:00Last IJTAF special issueOver the past year the International Journal for Theoretical and Applied Finance published 3 special issues with papers presented during the <a href="http://www.fields.utoronto.ca/programs/scientific/09-10/finance/index.html">Thematic Program on Quantitative Finance: Foundations and Applications</a>, held at Fields in 2010.<br />
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The first issue was devoted to <a href="http://www.worldscinet.com/ijtaf/14/1401/S02190249111401.html">Foundations of Mathematical Finance</a>, the second to <a href="http://www.worldscinet.com/ijtaf/14/1403/S02190249111403.html">Computational Finance</a>, and the third and last, which has just appeared, to <a href="http://www.worldscinet.com/ijtaf/15/1501/S02190249121501.html">Financial Derivatives and Risk Management</a>. Each corresponds to one of the major workshops in the thematic program.<br />
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I had the privilege of being a guest editor for each of the issues and writing the prefaces together with my distinguished co-editors.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-18636744982852445652012-02-19T08:50:00.002-05:002012-02-19T08:50:42.979-05:00Summer school in Cape TownI'm writing these words while looking out the window of my temporary office at <a href="http://www.aims.ac.za/">AIMS</a> and gazing at a point not far from where two oceans meet.<br />
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I was here to give a series of lectures in the <a href="http://www.aims.ac.za/en/programmes/workshops-conferences/mathematical-finance-2012">5th Summer School in Financial Mathematics</a>.<br />
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It is hard to describe the striking beauty of Cape Town, the friendly atmosphere at the Institute, and the excitement surrounding the lectures and discussions that follow. In fact it's so hard that I'll resort to pictures instead:<br />
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<br />Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-43722333265958172162012-01-28T15:21:00.000-05:002012-01-28T15:21:43.104-05:00Dupire at FieldsThe first talk of 2012 in the <a href="http://www.fields.utoronto.ca/programs/cim/11-12/finance_seminar/index.html">Quantitative Finance Seminar series</a> was given this week by Bruno Dupire.<br />
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As I mentioned when I was introducing his talk, the <a href="http://en.wikipedia.org/wiki/Local_volatility">Dupire equation</a> is not the best known result in mathematical finance - that honour has to go to the Black-Scholes equation. But the Black-Scholes equation is an oversimplification of reality that most people try to stay away from as much as possible, whereas the Dupire equation, in the words of Alex Lipton who spoke at Fields in November, is the "most effective result in mathematical finance."<br />
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Bruno spoke about yet another remarkable innovation that he has produced in recent years, what he calls <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1435551">Functional Ito Calculus</a>, and its uses in the context of path dependent options. I think it's a fascinating result and have asked him to expand his paper into a short book format to be published as one of the first volumes of the soon to be launched <a href="http://www.springer.com/authors/book+authors/springerbriefs?SGWID=0-1720013-0-0-0">Springer Briefs</a> in Quantitative Finance.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-71078861988583727562011-12-04T07:25:00.001-05:002011-12-04T07:50:50.797-05:00RiO 2011Forget the Thanksgiving Parade. The real tradition this time of the year is to attend the <a href="http://www.impa.br/opencms/pt/eventos/store/evento_1107">Research in Options</a> conference in Rio. I already <a href="http://fieldsfinance.blogspot.com/2010/12/research-in-options-conference.html">wrote</a> about the origins and general features of this regular meeting, so it suffices to say that this year's event is a contender for the best one ever.<br />
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And I suspect that financial markets know that too, since the <a href="http://www.bloomberg.com/quote/IBOV:IND/chart">Bovespa index</a> was up all through the conference. At least this is as good an explanation as any other for how markets are moving these days.<br />
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I'll post a few more pictures from the conference when they become available, but here is a small taste of the kind of trouble we were getting ourselves into:<br />
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<span id="goog_1564592022"></span><span id="goog_1564592023"></span>Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-52416130545761463642011-11-23T20:14:00.001-05:002011-11-23T20:20:51.565-05:00Alex Lipton and Peter Carr in TorontoWe packed a lot of star power in the last instalment of the <a href="http://www.fields.utoronto.ca/programs/cim/11-12/finance_seminar/index.html">Quantitative Finance Seminars Series</a> at Fields last week with Alex Lipton and Peter Carr speaking back-to-back, fresh from their appearances at the <a href="http://www.informaglobalevents.com/event/derivates-USA-event-2011/dates-venue">Global Derivatives Conference</a> in Chicago.<br />
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As I always say, the only thing better than paying thousands of dollars to stay at fancy hotels and listen to some of the best quant minds worldwide is to bring them to your own city !Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-46465087488554222492011-11-04T23:00:00.001-04:002011-11-04T23:00:27.927-04:00A week to rememberIt took me an entire week to recover from the last one:<br />
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- from Tuesday to Friday we had Raghu Varadhan giving the <a href="http://www.math.mcmaster.ca/talks/britton_lectures.php">Britton Lectures</a> at McMaster. He spoke about large deviations, which sent me down memory lane, as this was the subject of the first research seminars I gave as a PhD student. One of these days I should read his notes on <a href="http://math.nyu.edu/faculty/varadhan/pdefin.html">PDE for Finance</a>.<br />
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- on Wednesday night I had the honour to speak at the <a href="http://www.fields.utoronto.ca/programs/cim/11-12/finance_seminar/">Quantitative Finance Seminar Series</a> at Fields alongside Bill Janeway, from whom I always learn a great deal.<br />
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- on Friday I attended the first day of a <a href="http://www.fields.utoronto.ca/programs/cim/11-12/3criskforum/index.html">Risk Forum</a> at Fields. Apart from the interesting talks and discussions I had a chance to meet the CEO of the new <a href="http://www.globalriskinstitute.com/">Global Risk Institute</a> in Toronto, which looks like a promising venue for exploring out-of-the-box research ideas in financial mathematics.<br />
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It was good to relax for the past few days after that.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-3390171125707520842011-10-15T10:56:00.003-04:002011-10-15T10:57:49.337-04:00Mathematics in Finance at Kruger ParkAcademics in general, but especially financial mathematicians, are known for holding conferences in exotic places, such as beach paradises or mountain tops, but nothing I have attended so far beats the sheer exuberance of the <a href="http://www.bachelierfinance.org/conferences/AdvertMIF2011.pdf">Mathematics in Finance conferences</a> at Kruger Park in South Africa.<br />
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Starting in 2002, these meetings happen every 3 years and bring a large number of international and local participants to the heart of the African wilderness. The high quality talks taking place at the Berg-en-Dal compound have to compete for attention with all sorts of impressive animals surrounding it. </div>
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And to cap it all, while most conferences have boring banquets with unbearable speeches over food of debatable quality, this one treated us to a bush brae - an African style barbecue in the middle of the bushes, complete with a ring of fire and armed rangers protecting us from the observing leopards.</div>
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Here is photographic evidence:</div>
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</div>Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-82895962891678826862011-10-14T16:36:00.002-04:002011-10-14T16:36:31.783-04:00Commodities and Energy Finance in RioEveryone knows that Brazil is a major player in the commodities and energy markets, mostly - but not exclusively - because of Petrobras, its giant oil company. It should, therefore, not come as a surprise that there is a very active academic community in Brazil dedicated to research in these areas, as demonstrated in the <a href="http://www.impa.br/opencms/pt/eventos/store_old/evento_1113">this small but highly informative workshop</a> that took place at IMPA last August. <br />
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Besides giving a mini-course on game theory and real options, I played a small role behind the scenes by strengthening the links between EDF and IMPA and by extension Petrobras. Having worked on consulting projects for both companies, I can vouch for the vibrancy of their R&D teams, which can only benefit from talking to each other.Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0tag:blogger.com,1999:blog-4799264811265759956.post-32468371073220399112011-10-10T14:22:00.001-04:002011-10-10T14:23:59.934-04:00Springer Briefs on Quantitative FinanceSpringer is launching a new series on quantitative finance as part of <a href="http://www.springer.com/authors/book+authors/springerbriefs?SGWID=0-1720013-0-0-0">Springer Briefs</a> - their new publishing paradigm for sweet and short books on current hot topics in several different areas.<br />
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The editorial board for the series, consisting of Nizar Touzi, Jaksa Cvitanic, Lorenzo Bergomi, Ralph Korn and yours truly, met for the first time in Paris in July to define the scope and guidelines for publication. Our strategy for now is to solicit titles from a wish list of authors that we think will help us set the tone and level for the series, with the hope that these will attract a steady stream of submissions in the future.<br />
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So if you have written or are thinking of writing a concise, high-quality, high-octane book on quantitative finance, do let us know !Matheushttp://www.blogger.com/profile/05386153701958504638noreply@blogger.com0