According to Prospect Theory, Gains feel good.  Really good.  And that’s great!  But losses suck.  I mean losses really suck.  More than gains feel good.  And that sucks.

Let’s say I double-parked at a gas station.  I go inside a buy a scratch-off ticket.  I scratch it off and win $500.  Looks like my lucky day!  Unfortunately, I also got a parking ticket while I was in there.  It costs me some amount of money, like $450.  But I’m up $250 bucks, right?  I should go home happy!  Nope, says prospect theory.  Odds are you’re way more pissed about losing the $450 than you are about winning the $500.  Even though you’re richer, you’re totally unhappier.

Enter the fourfold pattern of risk attitudes: People exhibit risk-averse behavior in situations involving moderate probability of gains and of small probability losses (e.g. .  Paradoxically, we also exhibit risk-seeking behavior in situations involving moderate probabilities losses and small probability of gains (e.g. buying a lotto ticket).

Let’s say I apply to Harvard.  I have a fairly low probability of getting in, and thus I could lose a non-trivial sum of money ($105) and time (~30 hours).  Because this is a situation in which I have a small probability of gain and large probability of loss, I should be happy to levy the risk.  Which sort of calls into question my prior assessment of my decision: it might have been rational, but was that just self-justification of my psychological disposition to have done it anyway?

Imagine a savvy un-PC second-year political science graduate musing about future specialization. With Commissars everywhere the best strategy is to choose sub-fields that are basically applied math–public choice, game theory, statistical modeling or any other of many quantitative methodologies. Or, if one still wants to do reality-based research, just minimize substantive content–never discuss any particular war (and thereby risk offending somebody); instead just talk about Country A attacking Country B and Country C using a game theoretic Prisoner’s Dilemma framework in choosing sides or deciding to remain neutral.

I cannot express how breathtakingly wrong this is.  Weissburg’s characterization of the field of Political Science is not so far off–it is very difficult for the layman to peruse the pages of the APSR and extract any useful knowledge.  However, his explanation as to why that is the case is unsupported, intellectually sloppy, and plainly incorrect.

Weissburg suggests that modern scholars pursue quantitative research because it insulates them from any danger of political incorrectness by creating a platonic form of the unit-of-analysis, which may then be subjected to mathematical scrutiny.  If this were truly so, why should scholars attempt triangulation?  Why should anyone be doing case studies at all?  Qualitative methods are far from dead to the social sciences.  And these do not provide the sort of protection that Weissburg credits to the quantitative approaches.  It thus becomes clear that Weissburg is not a scholar who is savvy on qualitative methods.

There is an even more fundamental flaw in Weissburg’s approach.  The core failure of Weissburg’s argument is that he dismisses the idea of the model because it requires math.  I may like math and you don’t, but that doesn’t mean my approach is incorrect.  It certainly doesn’t mean that my conclusions are automatically rendered invalid.  Statistics is hard; I get that.  Game theory can be very hard; I know that well.  But we use these tools because they provide us analytic leverage over the questions with which we grapple.

Weissburg opens with a pot-shot at a study on whether democratic electorates chose better educated leaders.  This question, he claims, “hardly requires mathematical complexity.”  OK, then–how would Weissburg go about it?  In this he fails to provide a direction.  My inclination is to believe that because he rejects the quantitative approaches outright, he might simply think through a handful of Presidents and their respective educations (Obama’s JD, W’s MBA, Clinton’s JD) and compare this to the educations of the first dictators to come to mind (Mao’s self-education, Stalin’s expulsion from seminary, Hitler’s failure to gain admission to art school).  There are two errors here: first is selection bias–he can only think of the leaders he knows, instead of the universe of leaders, so his conclusion only generalizes to leaders he would be able to think of.  The second is that this is a fundamentally quantitative approach.  He may not be calculating any means or running chi-squared tests, but he’s comparing two averages.

Now, I’m putting words in Weissburg’s brain on this, for which I apologize.  Let’s say he wasn’t using the method I suggested.  Let’s say he was doing something completely different, selecting only the first two leaders to come to mind.  Still a quantitative comparison by nature–after all, years of education is a number no matter how you present it.  Let’s say he just wanted to establish a theory–well, he’s shot himself in the foot there by extolling the dangers of the generalized unit-of-analysis.  So he can’t build a theory with a generic conception of a country, and he can’t compare leaders respective education levels.  I’m left scratching my head as to how he believes this is an easy problem to solve when he’s proclaimed the fundamental invalidity of the only methods by which the question may be addressed.  The fact that he doesn’t like the equation which was actually used to answer the question is his problem.

If Weissburg doesn’t like the quantitative approaches, and doesn’t admit the qualitative approaches still even exist, then it becomes clear that Weissburg’s problem isn’t with math.  It’s with the scientific method.  He dislikes modern political science because it actually makes an attempt at bringing intellectual rigor to a field which once, an era ago, lacked it.  The one point on which I think both he and I agree is that we wish he was back in that era.

The application to Harvard is a long shot for any student: “Approximately 9 percent of the applicant pool is offered admission to enroll in an incoming class of about 640.”  The Department of Government lists 175 Graduate Students.  If the attrition rate were zero (which it isn’t), and there were a uniform distribution of Students over years (which there isn’t), then approximately 35 students would be admitted each year.  If that, in turn, generalized to the entirety of the Graduate School (which it doesn’t), then Harvard would annually receive 315 applications to its department of Government.

So here’s a question: if attending Harvard is unlikely (p < .9), why should I expend $105 trying?  What’s the Payoff?  Well, the Expected Utility Function of any application can be given by the formula:

Where B is the benefit of applying and C is the application cost.  Since we know that the probability is low (say .09), we can determine the Benefit necessary to make this an even bargain (i.e. one in which the Utility is at least non-negative).

And B falls out to be… $1061.67.  Interesting–not actually a huge sum of money.  And the benefit is measured in a variety of ways.  For example, Harvard doesn’t guarantee placement after matriculation, but if you have a degree from Harvard, your placement is guaranteed.  A university with even a slightly lower placement rate will quickly absorb a cost like $1061.67 in the probability of not getting a job of any sort for six months/a year/the rest of your life.

Now, my grades aren’t stellar.  I don’t have any peer-reviewed publications.  I don’t speak five languages.  I’m a spoiled, poor, southern, white boy with little more going for him than a Master’s degree, a lot of drive, and a prayer.  How big a prayer?  Well, since I want to be a quantitative methodologist, I’ll guess that my odds are non-zero on that quality alone.  So, let’s say my probability of acceptance is .001.  One in a thousand.  In other words, they have 35 seats to fill, and the first 280 applications thought that Political Science means debating new policy measures all day and trying to figure out how the American Government works.  Not likely–OK, so my probability of acceptance is more like one in a hundred thousand (p < .00001).  What does that do to my calculations?

So the requisite benefit is now a hair north of $10 million.  Stated another way: if I were offered a choice between $10 million and admission for a Ph.D. at Harvard, which would I choose?  Definitely the money.  Which leads to the far more interesting question, how much would it cost to keep me out of Harvard, given this fanciful choice?  I estimate on the order of $1 million, though I would think it over extensively (and possibly come to a different conclusion under the circumstances).

If we plug $1 million into the benefit of our equation, we can reverse engineer a lower-bound probability on my acceptance:

So, in order to make my decision to apply for Harvard rational, I must have had a probability of p > .0001.  Interesting.  If p really is closer to .09, then applying to Harvard is like playing a lottery that strongly favors its players (to the tune of an expected win of $900 per ticket).  It was strictly rational for me to apply to Harvard.

The credit crisis in the Eurozone has sent tremors throughout the global economy, and the world is anxiously waiting to see if these tremors precede a coming earthquake.  Greece has come under particular scrutiny as the probability of a government default threatens the stability of the entire European Union and, by extension, the rest of the world.  However, common metrics of economic health and stability indicate many pivotal nations are in equally—if not more—dire straits.

These modern economic metrics have progressed far beyond the conception of the fathers of modern economics.  This does not, however, preclude these foundational ideas from furnishing potential insights into the origins and appropriate responses to the crises.  In particular, I claim that the works of Adam Smith, Karl Marx, and Max Weber each provide some substantive insights concerning the crisis, though each also carries stark limitations.

Strangled by the Invisible Hand

In his seminal work, The Wealth of Nations, Adam Smith espoused the belief that the maximally efficient economy was one in which the economy was permitted to effectively self-regulate.  The composite interests of all of the rational constituents of an economy yield the optimal economic outcomes.  For this fundamental tenet of Smithian economics, we can surmise some causal characteristics of the Greek credit crisis.  In particular, if we accept that the crisis is a suboptimal outcome, then we can conclude that the overbearing intervention of the government has caused the crisis.

There is some compelling support for this argument.  Since the Greek government adopted the Euro as its currency in 2002, it has expanded its deficit spending substantially.  The free exchange of a locally-universal currency streamlined the process of intergovernmental lending.  Greece took full advantage of this opportunity, rocketing its national debt to 10.5% of GDP in 2010.  The probability of a default has prompted the government to make significant cuts to its employment and services.  These cuts have lead to mass protests and riots in Greece in the recent months.

While the rule of free-market capitalism and rationality has become a mantra of modern economic liberalism, the world in which Smith first addressed his problem of explaining economic organization is far removed from the world today.  Smith conceived of the government as a distinct economic entity from individuals and other economic actors.  Smith viewed the world as a collection of discrete country-economies.  The world in which we live is far more complex.  Instead of an assortment of discrete markets which are solitary to the nation-state in which they exist, we experience single a global economy in which governments are better represented as firms with unique abilities, than institutions with absolute power and a moral obligation not to exercise such capabilities.  However, if we disregard the fundamental nationality of Smithian theory and conceive of an international market which mirrors Smith’s conception of a national market, then we can derive some small amount of substantive traction.  While Smith’s theory lacked the structural mechanisms to capture lending between governments, Smith did describe public debt and thereby foresee related crises:

The necessities of the state render government upon most occasions willing to borrow upon terms extremely advantageous to the lender. The security which it grants to the original creditor is made transferable to any other creditor, and, from the universal confidence in the justice of the state, generally sells in the market for more than was originally paid for it.

The government […] is very apt to repose itself upon this ability and willingness of its subjects to lend it their money on extraordinary occasions. It foresees the facility of borrowing, and therefore dispenses itself from the duty of saving. (V.3.7-8)

[…] The progress of the enormous debts which at present oppress, and will in the long-run probably ruin, all the great nations of Europe has been pretty uniform. Nations, like private men, have generally begun to borrow upon what may be called personal credit, without assigning or mortgaging any particular fund for the payment of the debt; and when this resource has failed them, they have gone on to borrow upon assignments or mortgages of particular funds. (V.3.10)

Smith fails to explain the means by which governments will be ruined by debt, but it’s only a small step beyond the content he did generate to assert that uncontrolled debt leads to probable default.  This is a sensible, tenable conclusion—one which we are seeing played out in Greece, and to a lesser extent in a variety of other European nations.  However, by failing to describe the mechanisms in any resolution, Smith denies us any ability to prescribe activity based on his theory.  In short, we know the causal factor, if not the mechanisms by which this mess emerged, but we do not know how to emerge from it in the short term.

A longer-term prescription to avoid this kind of crisis would be to more closely align to the functions of government Smith suggested.  Namely, the government should be responsible for functions which rationally self-interested actors cannot adequately generate profit: maintaining infrastructure and educating the populus.  A stripped-down government of this variety should be more capable of confining itself to the allocated budget, instead of spilling from revenues into defecit and thereby, debt.  In this, Smith betrays his thinking with a fundamental flaw.  For Smith, economic optimality is achieved by all actors behaving in rationally self-interested ways except for the governments.  The assumed rationality of governments has become a fundamental tenet of political science in the last 50 years (Levi 2007).  Ignoring this, Smith consigns his theory to dusty shelf of history to be revered as groundbreaking, but long since supplanted by superior approaches to the study of politics.

You Have Nothing to Lose but your Sovereign Debt

Karl Marx, being more an activist in his outlook, would likely take an entirely different tack.  The credit crisis emerged because the bourgeoisie has exploited the proletariat to the point that the current conditions are no longer sustainable.  Marxian theory is less descriptive in this regard than prescriptive. The credit crisis should alert the proletariat of Europe to his/her plight.  In this social dimension, Marx hits the mark much more closely than Smith.  Marx predicts that an aware, angry proletariat class should rise up against the institutions of bourgeoisie and install a more socialist system of governance in which wealth is distributed more equitably.  In short, this should mark the tipping point between the stages of economic development.

The current protests in Greece are indicative of this wealth disparity.  The bourgeoisie in the Greek government are maintaining their own income streams by cutting government spending, forcing thousands of proletariat government employees into unemployment.  The proletariat are actively responding with protests resulting in violence (Economic Times 10-19-2011).  Having nothing to lose but the government which embroiled them in this crisis, the Greek working class should resort to violence to attain their socialist utopia.  This closely reflects Marx’s observation that the revolts in France during his lifetime indicated the same sort of social change.

This approach, however, is a gross oversimplification.  As can be seen in Table 1, Greece’s income inequality is on par with the rest of the Eurozone (CIA 2011).  If Marx’s theory held uniformly, all the nations of Europe should be experiencing the kinds of protests that Greece is seeing presently.  Moreover, if the crisis were precipitated purely by the debt and its secondary effects on the working masses, then there should be a correlation between the probability of default and the relative size of the public debt.  In 2010, Greek debt constituted 10.5% of the nation’s GDP.  While this is admittedly a very bad valuation (199 worst in the world), Greece is in good company: The UK’s debt is estimated at 10.2%, and Ireland’s is a staggering 32.4% (CIA 2011).  And yet there is little credible talk of revolt in the British Isles.  Perhaps more surprisingly, Intrade predicts (as of October 25, 2011) that the probability of Greek default is 36%, where Ireland’s is a meager 4%.  So the probability of default is likely not proportional to the relative size of the debt, nor is it represented by the latent relative income inequality.

As we can see, there is no way to operationalize Marx’s predictions in a way which is both sensible and defensible.  Thus Marx’s calls for the working class to overthrow the stifling institution of bourgeois government seem less credible than Smith’s assessment that the debt crisis should emerge under the circumstances.

The Orthodox Ethic and the Spirit of Failure

Unlike Smith and Marx, Max Weber addressed the question of socio-economic organization by proposing a single variable instead of a grand theory.  Namely, Weber suggested that the protestant work ethic gave rise to economic competition and thereby modern capitalism.  He demonstrated his hypothesis by pitting majority protestant cultures (Germany, Britain) against Catholic ones (France, Spain).  He fails, however, to expand his worldview beyond these two categorizations.

For the purpose of argument, we can fixate (as Weber does) on the nature of Protestantism.  Unlike Weber, however, we can pit this spirit against the rest of the varieties of Christianity and other world religions to apply the theory to the Greek case, instead of assuming a diametrically opposed, Protestant versus Catholic, world. In other words, where Weber compared Protestant with Catholic, we will compare Protestant and non-Protestant so as to include Greek culture, which is predominantly Greek Orthodox.

With this assumption in mind, the Greek lack of Protestantism caused cultural non-competitiveness which stifled economic viability in the modern world.  We might even further look for support in the other countries suspected by prediction markets of facing default: Ireland, Spain, Italy, and Portugal (Intrade 2011), all of which are predominately Catholic nations.

While at first glance, this theory seems to hold water (and do so rather better, comparatively, than the others), Weber’s approach leads to some important self-contradictions.  Namely, Weber uses the relative success of individual Protestants in the fields of government and industry as indicators of the protestant work ethic.  However, no nation in Europe is exclusively non-protestant.  If Protestant leaders tend to emerge because of some inherent quality of Protestant worldview, Protestant leaders should emerge in non-Protestant societies.  As such the decision processes of government leaders should yield similar national trends, even in cases of religiously distinct societies.  Claims otherwise (namely, that Protestants shouldn’t be leaders in Catholic societies) hinge upon the assumption that culture affects decision processes in some conditions (for working individuals) but not for others (for state leaders).  This logical inconsistency is entirely unaddressed by Weber.

This approach of looking at the leader as the appropriate unit-of-analysis is emerging as a significant paradigm in the field of International Relations (Wolford 2007).  Whether the same should hold true in comparative studies is open for debate, but I contend that Weber fails equally as his forbears, both in predicting the crisis (largely because it is far out of the scope of his research intent) and in prescribing the solution.

Were we to take The Protestant Ethic at face value, we should conclude that the economic distortions which have embroiled Greece are caused by the non-Protestantism of the Greek people. Thus the Weberian solution to a crisis of this sort is to institute Protestantism world-wide.  Religious beliefs notwithstanding, this is an unbelievable pursuit.  Whether or not Weber would argue that this would be ideal is not imminently clear, as Weber does not advocate a convergence on a particular, uniform system of economic or social governance in the manner that both Marx and Smith advocate.

Too Big to Fail, Too Precarious to Sustain

The varied approaches to the comparative study of politics can each be traced back to one of the foundational thinkers of socio-economic theory.  Each can provide some insight to the causes of the current conditions in Greece.  Even so, devoid of newer approaches, none can provide a truly cohesive and comprehensive assessment of the crisis. More importantly, none can prescribe a viable route out of the impending disaster.  As such, we must venture outside the realms of classical economic theory in order to generate any adequate assessment of plausible solutions.

The global system has proven that Smith’s world outlook carries more weight than Marx’s, as grand theory goes.  This may be in no small part attributable to Smith’s far more accurate portrayal of humans as rationally self-interested, instead of Marx’s conception of the noble worker willing to sacrifice the well-being of the one for the benefit of the many.  It is interesting that Weberian theory can hold its own in this case, despite being far more limited in scope.

The most viable prescription comes from a modification of Smith’s approach to social theory.  It is in the best interest (i.e. rational) of the European Union to save the Greek government, thereby averting a cataclysmic economic downturn.  However, the gross costs thereof have made that process a halting one.  I would predict that the European leaders with enough financial capital to save this too-big-to-fail firm will pull through, though not without further painful concessions on the part of the Greek government.  This is not a clean solution: the Irish, Spanish, and Portugese governments are facing similar (though less developed) crises, and saving Greece will signal that a safety net exists for those governments.  This is, however, the state of things.  Whether or not this grim scenario will save us from the far grimmer scenario of a complete, unbridled collapse, only time may tell.

References

BBC. 2011. “Greece Timeline”. 10-25-11. http://news.bbc.co.uk/2/hi/europe/country_profiles/1014812.stm

CIA. 2011. “The World Factbook: Greece”. 10-18-2011. https://www.cia.gov/library/publications/the-world-factbook/geos/gr.html

Durkheim, Emile (Translated by George Simpson). 1947. The Division of Labor in Society, New York: The Free Press, 1947.

Economic Times. 2011. “Police Clash with Greek Protesters Outside Parliament”. 10-19-2011. http://articles.economictimes.indiatimes.com/2011-10-19/news/30297821_1_police-clash-greek-parliament-street-protest

Intrade. 2011. “Will Greece, Portugal, Spain, Ireland or Italy be declared in default? (as per S&P)”. 10-25-11. http://www.intrade.com/v4/markets/?eventClassId=23

Levi, Margaret. 2007. “Reconsiderations of Rational Choice in Comparative and Historical Analysis” from Comparative Politics: Rationalty, Culture, and Structure. Mark Irving Lichbach and Alan S. Zuckerman, ed. London: Cambridge University Press, 2007.

Smith, Adam. An Inquiry into the Nature and Causes of the Wealth of Nations. Edwin Cannan, ed. London: Methuen & Co., Ltd. 1904. Library of Economics and Liberty [Online] available from http://www.econlib.org/library/Smith/smWN22.html

Wolford, Scott. 2007. “The Turnover Trap: International Conflict and the Tenure of Leaders”. American Journal of Political Science, Volume 51, Issue 4, pp. 772–788

First, the global population is equal to last year’s population plus the births minus the deaths.  The quintessential gain-loss model.

Let’s start by unwrapping Births (actually births per capita), which should be the more complicated of the two:

So, if we cram these together:

Now, for death, if we remove the GlobalPop variable the way we did for births (since it was pre-factored out in the equation 1), deaths (again, deaths per capita) is simply equal to the deathrate.  So,

Thus, if we put this all together:

Since we can’t easily calculate GlobalPop into infinity this way (without some heavy-duty computation), let’s just think about the second half of the expression, and measure what happens as n approaches infinity.  If the output (which is basically a global population multiplier) hits 1, then an equilibrium state exists.  If not, then the global population should continue to fluctuate forever.  Let’s see:

Interesting.  Both Births and Deaths converge on 0, so the equilibrium state exists.  How big is it?  How long will it take?

Equilibrium is the point at which the global population no longer changes from year to year, or if it does, it begins to do so cyclically.  There aren’t any cyclical parameters in the model, and there aren’t enough independent variables for cyclicality to emerge organically, so my suspicion is that we should see a single point of convergence.  In other words, the global population will reach some number and stick to it.  Algebraically, we can represent this as:

or, since we’re solving for n*, the equilibrium condition, we know GlobalPop at n is equal to the GlobalPop at n-1.  Thus we can divide both sides of the equation by GlobalPop and voila!

We have now reached a substantively interesting and intuitively obvious point: equilibrium is the state of the population in which the number of annual births equals the number of deaths.  Moving on:

Ah, time to pull out the good ol’ fashioned calculator!

Yuck.  This is a sick variation on the old factoring polynomials problem.  Since my Algebra 2 is failing me right now, let’s just calculate this using the old guess ‘n check method a couple of hundred thousand times over.

Years	Global Population	Birthrate	Deathrate	Mean Female Lifespan
1960	3,027,185,898		0.089927	0.018907	54.6
1961	3,109,658,894		0.088470	0.016346	54.945
1962	3,197,918,219		0.087032	0.015012	55.29
1963	3,289,893,157		0.085612	0.014132	55.635
...
2009	7,906,471,643		0.035088	8.31E-03	71.505
2010	7,977,393,040		0.034238	8.28E-03	71.85
2011	8,045,839,833		0.033396	8.25E-03	72.195
...
3214	4,901,896,085		4.23E-03	4.23E-03	487.23
3215	4,891,491,260		4.22E-03	4.23E-03	487.575
3216	4,881,104,717		4.22E-03	4.22E-03	487.92

And we’re done!  The global population should converge sometime in the 33rd century.  But that can’t be right: the population continues to change after that year.  In fact, it changes in an very interesting way:

And it all comes together!  The “Equilibrium” I was talking about earlier wasn’t an equilibrium at all.  In order for that to be true, the two variables must be contingent upon each other.  Births and deaths are indifferent to one another (in this model), so being equal didn’t create an equilibrium–it created a maxima.  That’s the peak you see there: one day, birthrates will have slowed down more than deathrates, so that even though people live longer (and by longer I mean absurdly long–in excess of 1700 years by the end), they procreate so infrequently that the human species dies off, and not especially slowly in the grand scheme.

This brings that information we got from the limit approach into sharp relief: If no one is being born, and no one is dying, that’s either because we have a bunch of asexual immortals, or there aren’t any humans left.  The model says the latter, for posterity.  Of course, as they say, all models are wrong, and this one doubly so.  However, I’m most interested in the tipping point, and not the resolution: if current trends are maintained, the Global population shouldn’t exceed 17 Billion, which makes the UN’s high estimate seem very generous.  The whole world must be feeling very amorous to hit 35 Billion.

I cannot, however, based on this information, dismiss the low estimate.  In the absence of control or predictions for cataclysmic events, it seems to me that we should be braced for a world of bounded or diminishing population.

To start, we must find some data to compare against.  The U.N. publishes a biannual prediction of the global population trajectory.  The employ three creatively-named models: “high,” “medium,” and “low.”  High is a worst-case scenario.  It’s basically a prediction that Malthus was right, and populations grow exponentially.  Medium is a little sunnier–it’s really the world we want to live in.  The idea is that around 2050 we round out to about 9 Billion and we stay there, more or less.  High would be inconvenient–lots of starvation, bad sanitation, generally bad conditions with little to do to improve them, but Low is the real downer.  What if something went catastrophically wrong?  War, disease, disaster–take your pick.  Low is the image of the world picking up the pieces.

Against these models, I will compare two of my own: the system dynamic model I built, and the linear model that outperformed it.  By the way, that linear model is strikingly simple:

In which t is time (i.e. years since 2009) and the intercept is the approximate 2009 population.  So, let’s take a look at the next 90 years:

Interesting.  We have a uniform, fanning-out effect.  That means we all disagree pretty enthusiastically.  Only the low model begins to fall, while the medium converges on 9 Billion, and the top three forecasts (mine, the linear model, and the UN’s high, respectively in increasing order) continue to increase at varying speeds.  OK, what if we look a little farther forward?  Back in 2004 the UN published a projection to 2300.  Let’s see what the world looks like then:

Now this is interesting: Low and medium have both held their positions for a couple of centuries, and it looks like mine is getting to a point of convergence, but linear keeps growing (as linear models are wont to do) and high is skyrocketing.  We must have cured death or something at that point.

There are important sources of distinction between my model and the U.N.’s.  The UN possesses an immediate advantage in that its models may start projecting based on data which is empirically accurate for the current year.  Because my model was calibrated on the data from the prior 50 years, I must start with the year 1960 and project to 2010 and beyond.  This means the number I have for this year’s population is probably a little inflated, so the model on the whole is relatively high.  The other is that my model continues to project expectations into the realm of unlikelihood–by 2300, my model suggests the mean female lifespan should be over 100, and still rising.  Even so, it may accidentally prove to be the most accurate of them all, if for entirely spurious reasons.  As they say, “All models are wrong.”

The global population model is a bit simpler since we’re dealing with a single population (that is, humans).  We’ll call this a gain-loss model.  Gains are defined by births, and losses by deaths.  After all, when modeling the entirety of humanity, there are only these two ways to change the global population (i.e. humanity’s total population count is unaffected by migration, divine ascension, etc…).  Let’s take a look at that visually:

The Box at the center represents the entire human population.  The “flow” to the left of the box indicates births increasing the number of humans in the population, and the one to the right is deaths decreasing the total population.  The two “converters” (circles at the top left and right) define the rates at which births and deaths occur.  This is a cool setup because we can define any of these as numerical values or as functions.  For example:

and likewise with the deaths.  Thus,

Now, in order to define these numerical values, we must consult some statistics.  For this, there is the World Development Indicators.  I parsed the very same into separate datasets not so long ago, but this time it’ll be easier to just use the graphs.  For that, Google has set up a really nifty Public Data Explorer.  To start with, let’s look at Birthrate.  The graph looks pretty nonlinear, the take home point is that it’s trending downwards.  As such, we can represent it linearly with the knowledge that this may be something to revisit later on the the model construction.  Over the 49 year period from 1960-2009, the value drops from 4.91 to 2.52.  That’s a change of  2.39, or a mean change of .049 annually.  But what does this number actually mean?

“The average number of births per woman.”

Crap.  This creates two new problems.  The first is pretty clear: We will know how many people there are at any given time, but not how many women.  We’ll have to include another converter to capture this fact.  The second is much more subtle: this is evaluated over steps of time (in this case, years).  But the rate is measured over a woman’s lifespan.  So we also must include a variable which represents the mean female lifespan.  All told, here’s our model:

where:

Where the numerical values are derived from time series regressions on the data for female life expectancy and fertility rate.  As for the percent of the population which is female, it looks to be roughly stagnant around 49.7, so a fixed value should be good enough.

Now, all that remains is to define the Deathrate and test the model!  Deathrate presents a new problem–a truly nonlinear relationship.  As such, we’ll divide it by 1000 to give us a per capita probability of death per year, and fit the prediction curve using exponential regression, giving us this equation:

This curve actually gives a strikingly good fit to the data at hand:

With all of our values set and relationships defined, its high time we tested this puppy out!  We’ll set the initial population equal to the population in 1960, approximately 3 billion.  We should see population growth up to today’s estimate of 6.775 billion.  Let’s check it out, shall we?

Not too shabby.  Hardly perfect, but considering everything that can go wrong, I think we did pretty OK!  Two dangling observations: First, we started out modeling a phenomena which is strikingly linear.  Second, our prediction is slightly nonlinear.  Slightly, but conspicuously.  System Dynamic modeling is excellent at representing nonlinear phenomena, so it’s a little gratuitous to use it in a linear case.  Never the less, our model preforms very well:

We can see here the R-squared of .98, indicating a high degree of accuracy.  The Beta is pretty good as well–if it were perfect, we would see a beta of exactly 1.  However, if we compare this to a linear regression on the time series data, we look a little worse:

Not so good.  Oh well.  There are a few sources of this error:

1. The life expectancy is latent–it describes the life expectancy of people born in that year, not the life expectancy of people living in that year.
2. We didn’t describe the female percentage of the population with a function, which makes it entirely inflexible.
3. The pseudo-linear models we use to generate many of the coefficients are imperfect (though admittedly very good in this case).
4. The data are imperfect: the World Development Indicators are calculated using a completely different methodology, which one hopes would be fairly accurate.  Even so, it would be logistically impossible to count every single person on the planet at a fixed point in time–people are born and die every minute.  The WDIs are correct to the ballpark (as are the models we devise from them), but only so.

Even so, I claim we’ve accomplished something moderately cool.  We’ve set up a complex equation set which predicts the global population, controlling for life expectancy, fertility, proportion of the population which is female, and per capita deathrate.  Our model could survive an exogenous shock to any of these, while the linear model is left scratching its head.  System Dynamic modeling is cool because it is necessarily representative of the causal linkages between variables, thereby creating much more compelling forecasts.  This model hinges upon the irrefutable causality between births, deaths, and population size.  Maybe next time we can try something a little more debatable, and shed some light on something new.

Yawn.

I’m really sick of these sensational studies claiming that there are zillions of cyber bad guys out there stealing your money one penny at a time.  There’s a new one every month.  Speaking of which, according to the recently released Norton Cyber Crime Report for 2011 (via Franz Stefan Gady), 431 million adults in 24 nations were victims of cyber crime last year. The total cost of those crimes amounts to some $114 billion, with an additional $220 billion in lost productivity.

Let’s consider this rationally: Cybercrime cost 431,000,000 adults in a sample of 24 countries approximately $338,000,000,000.  So, on average, cybercrime victims lost:

$784.  Huh.  That’s not too terribly frightening.  Granted, if somebody took $784 from me, I’d be furious, but I’d certainly survive.  And I’m pretty poor, as denizens of one of these 24 fairly wealthy countries go.  So, what’s the probability that I (a random but regular user of the internet in one of these countries) will be a victim of such a crime?

Well, according to the Norton report, according to the CIA World Factbook, the 24 sampled countries (Australia, Brazil, Canada, China, France, Germany, India, Italy, Japan, New Zealand, Spain, Sweden, United Kingdom, United States, Belgium, Denmark, Holland, Hong Kong, Mexico, South Africa, Singapore, Poland, Switzerland and UAE) have a combined online population of 802,872,752.  That gives us an otherwise uninformed probability of suffering from an cyberassualt at approximately 1/2 (you know, 431 million/803 million).  So the expected cost of not changing my online habits is approximately:

OK, so what if I do as the Norton report suggests and purchase their software?  The annual license costs $69.99, so how much would the product need to lower the probability of a successful attack to merit purchase?  This calls for another Expected value calculation, this time of purchasing the software:

OK, so according to this, if the protection of Norton keeps just 20% more (or 9% total) of the bad stuff away, its totally worth it.

There are a few problems with this approach, however.  First, consider the data source: we’re taking statistics from a corporation which has every “incentive” in your wallet to make cybercrime look like a dire issue.  While they pointedly provide a page on their methodology, they also fail to provide the raw data for independent confirmation.  Welcome to the world of White Papers.

Secondly, their definitions belie a much more dangerous mislead on their definition page [colors added for coding purposes]:

Throughout the report cybercrime is defined as: Ever experienced 1+ of the following:

• Computer viruses or Malware appeared on my computer
• I responded to a Phishing message thinking it was a legitimate request
• Online Harrassment
• Someone has hacked into my social networking profile and pretended to be me
• I was approached online by sexual predators
• I responded to online scams
• I experienced online credit card fraud
• I experienced Identity theft
• I responded to a smishing message
• I experienced another type of cybercrime on my cell / mobile phone
• I experienced another type of cybercrime on my computer

Let’s break these down: I’ve coded green as a something which does not necessarily result in financial loss for the victim, yellow as something which creates potential for financial loss, and red as certain financial loss (black is ambiguous).  This basically takes any speculation about the distribution of losses over the population and ruins it.  My roommates occasionally “hack” my facebook (add erroneous information while I’m out of the room), and I’ve been viciously assaulted by spammers of several varieties.  And yet I have lost nothing financially to cybercriminals.  So I’m a victim, a card-carrying member of that 431 million, who contributed nothing to the $388 billion loss figure.

This suggests that the actual loss per crime ratio is much higher when it’s not zero.  Everyone gets spam.  Everyone gets harassed.  It’s the internet!  It’s like middle school all over again.  Coding recipients of these as victims of cybercrime artificially inflates the number of victims to sensational proportions, and decreases the mean amount lost by each victim.  So we know there’s a completely different world in which people who exercise a modicum of good judgement become “victims” at no cost to themselves, and that’s the world in which Norton advertises.  In reality, the best security suite in the world won’t save you from yourself.  The majority of successful attacks rely upon the user to make a critical fault, be it entering personal details in a man-in-the-middle page, or sending money to support a friend in need (should their e-mail be hacked), or enabling a virus to burrow in to your system.

Cybercrime isn’t all hype.  Just mostly.  There’s a fantastic array of effective, free software tools which greatly reduce a system’s vulnerability.  That said, if you are a corporation, run and hide.  If you are an individual, don’t ever give out any personal details (or money) over e-mail, use Firefox or Chrome instead of Internet Explorer and odds are you’ll be just fine.

For those who have no idea what I’m talking about, here’s a dataset in country-year format:

Every row has a country and a year (hence we say the unit of analysis is the “country-year”).  You can also use these to generate a unique identifier, in this case the first column.  That column is generated by appending the year to the ccode as a string (alternately, you can think of it as an evaluation of this expression: .

The World Development Indicators, however, are too big to play by these rules.  The combined dataset weighs in at a hefty 50+MBs.  Now, I know this impresses no one in the age of Big Data, but it’s pretty hard to come by anything you can measure in political science and come up with a 50meg country-year dataset.  The WDI comprise over 1100 variables measured over 50 years (1960-2009).  Problem is, they are in a hard-to-use format.  Here’s a peek:

 Notice how the years run across the x-axis, instead of the y (as seen above)?  That’s a problem.  Luckily, a few clever hacks turned the 50meg, uselessly formatted, massive dataset into a much more manageable collection of 1100+ datasets of 200-300kb each.

Each of these datasets is named for the variable it contains.  In other words, each dataset only contains the identifying variables (My version of a Unique IDentifier, CCode, Country, Year, Variable).  As such, these aren’t especially useful by themselves, but can easily be merged with other country-year data.  One other caveat: because of the way they were processed, the cells stop at the last year for which there was a measurement, meaning not all countries are represented for all variables over the complete timespan.  When you merge it, just don’t throw out unmatched entries, and everything will work fine.

In particular, I’m thinking of my classmates from my graduate Empirical Methods course.  None of them were actually especially interested in the mathematics of statistical analysis.  This is fair enough, but it didn’t help that our professor really wasn’t either.  To me, this represents a huge problem.  What kind of department gets away with sticking Empirical Methods to the newest assistant professor with a background in qualitative methods and utter disdain for quantitative methods?  DISCLAIMER: I have no grudge against qualitative analysis.  I have a grudge against the teaching of incorrect things, which the department invited by their selection of professor-course pairings.  For example, we were taught that if a linear regression did not yield a beta coeffecient which was “significantly” distinct from zero, then the two variables exhibited no correlation.

The problem with this approach is that it restricts said students to searching for fundamentally linear relationships.  Nassim Nicholas Taleb makes a damning argument against the linear model in The Black Swan.  The gist of it was that there is no such thing as a real linear correlation.  Consider the case of a person who is lost in the desert and thirsty.  Such a person will value a small quantity of water very highly.  However, as this person encounters more and more water, this person will value the water less and less.  Eventually, the wander stumbles into an  ocean and drowns.  The wanderer’s utility valuation of the water went from zero (how much she values water she doesn’t have) to some high amount, back down to zero (where the stuff is common and effectively free), and then below zero when it begins to harm her.  This is a fundamentally non-linear relationship.  Taleb then prompts the reader to try to think of a relationship which exhibits true, perfect linearity.  Of course, there is none.

I’m not a huge fan of Taleb’s.  His esoteric writing style rubs me the wrong way, and while I’ll be the first to call him a very smart guy with some excellent points, this one is off the deep end in the opposite direction.  Linear correlation exists in cases for which linear relationships exist.  However, linear modeling is perfectly appropriate for analyzing a wide array of non-linear relationships, given appropriate mathematical handling.

Take, for example, this graph I made a few weeks ago concerning the relationship between State Failure (Failed States Index) and Democracy (Polity Score).

There are two things I can tell you from a casual look at this plot: first, there exists some relationship between the polity score and the failed state score.  Second, there is not a very strong linear correlation between the two.  For those in my program, According to what I was taught, the presence of a linear relationship would constitute a publishable result.  In fact, these data happen to have just such a relationship:

Call:
lm(formula = Total ~ polity2)

Residuals:
    Min      1Q  Median      3Q     Max
-47.190 -13.393   3.519  16.036  35.625 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  78.6750     1.9792  39.750  < 2e-16 ***
polity2      -1.6577     0.2693  -6.155 6.23e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 21 on 154 degrees of freedom
  (2 observations deleted due to missingness)
Multiple R-squared: 0.1974,	Adjusted R-squared: 0.1922
F-statistic: 37.88 on 1 and 154 DF,  p-value: 6.228e-09

Following the instructions of my methods professor, because our p-value is below the .05 publication threshold, this is a result worth discussing.  But note the small R-squared value: This tells us that we need to get back to the drawing board on variables to incorporate.

This is the point at which I must call “Bullshit!”  The small R-squared tells us that a linear model doesn’t describe this relationship very well, but if we incorporate any other variable with a similarly curved relationship to state failure, it should go through the roof.  This approach tells us very little about what is actually going on, and reinforces the belief that poor showings of r-squared are a product of ill-selected variables.

Instead of going down this road, I tried to find some deeper relationship by looking at the component democracy and autocracy scores, which also yielded nonlinearities.  This was a better approach, but it overlooked a fundamental point about the data: there is a perfectly adequate mathematical description of this curve.  We can apply linear regression as a to use this variable as two variables: linearly (i.e., y = x) and quadratically (y = x^2).

Call:
lm(formula = Total ~ polity2 + I(polity2^2))

Residuals:
    Min      1Q  Median      3Q     Max
-62.759 -11.054   0.989  11.902  35.855 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  98.82394    2.39812  41.209   <2e-16 ***
polity2      -0.30748    0.23939  -1.284    0.201
I(polity2^2) -0.47004    0.04368 -10.760   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 15.89 on 153 degrees of freedom
  (2 observations deleted due to missingness)
Multiple R-squared: 0.5431,	Adjusted R-squared: 0.5372
F-statistic: 90.95 on 2 and 153 DF,  p-value: < 2.2e-16

This is a considerably better fit, don’t you think?  Using that same approach I’ve been using to plot this function, we get this plot:

Better, no?  Given a State’s Polity2 score, we can determine with reasonable confidence a range into which it likely falls in the Failed State Index, though we cannot do so with any degree of predictive accuracy using the simpler linear model.  If we simply must use a simple linear model, there is no reason we cannot still accomplish our goals by first applying the function to our polity2 variable, like so:

z <- (-.30748 * polity2) + (-.47004 * polity2^2) + 98.82394

We now have a variable, z, which is the polity2 score transformed using the second linear model I described.  We could graph this:

And determine that there is, indeed, a linear relationship to be seen.  Now, this is strictly an exercise in correlation demonstration: any correlation can be described as a linear model of the dependent variable over the independent variable using whatever mathematical transformation is appropriate.  However, if you already know that transformation, why bother displaying it linearly?

Depending upon Linear regression is not a crime.  However, believing that the absence of a linear relationship is the same thing as the absence of a relationship is preposterous.  As researchers, we must strive to remember that correlation is a simple concept with some very complex caveats, and that an understanding of correlation comes from spending a lot of time pondering correlation.  Normal people don’t invest that kind of time and effort into mathematical thinking.  It is thus incumbent upon us to recognize the linear relationship for its utility, and then promptly shelve it to begin examining the real world.  Relationships between directly causal variables need not be linear, and that must be clear.

EDIT: As Jimbo pointed out in the comments, this comes across as being unpleasantly hard on my classmates.  As a point of clarification, I overstated my confidence in my cohort’s general lack of interest in quantitative research methodology.  That said, because my program is very policy-oriented, the research methods course is by far one of the more hated points in our curriculum.  I don’t fault my fellow students for not being interested in statistics–this is solely a complaint against the poor teaching of a topic which is absolutely critical to having a solid grasp of a huge portion of the empirical research being done in international relations.

PS) Here’s my code:

FailedStateIndexPolity.Merge <- read.csv("http://nortalktoowise.com/wp-content/uploads/2011/07/FailedStateIndexPolity.Merge_1.csv")
attach(FailedStateIndexPolity.Merge)
plot(polity2, Total, main="Failed States Index over Polity2 Score")

model1 <- lm(Total ~ polity2)
summary(model1)
abline(model1)

model2 <- lm (Total ~ polity2 + I(polity2^2))
x <- seq(-10,10)
y <- model2$coef %*% rbind(1,x,I(x^2))
plot(polity2, Total, main="Failed States Index over Polity2 Score")
lines(x,y,lwd=2)

z <- (-.30748 * polity2) + (-.47004 * polity2^2) + 98.82394
model3 <- lm(Total ~ z)
plot(z, Total, main="Failed States Index over Polity2 Transformed")
abline(model3)