nhaliday + curvature   93

Social Animal House: The Economic and Academic Consequences of Fraternity Membership by Jack Mara, Lewis Davis, Stephen Schmidt :: SSRN
We exploit changes in the residential and social environment on campus to identify the economic and academic consequences of fraternity membership at a small Northeastern college. Our estimates suggest that these consequences are large, with fraternity membership lowering student GPA by approximately 0.25 points on the traditional four-point scale, but raising future income by approximately 36%, for those students whose decision about membership is affected by changes in the environment. These results suggest that fraternity membership causally produces large gains in social capital, which more than outweigh its negative effects on human capital for potential members. Alcohol-related behavior does not explain much of the effects of fraternity membership on either the human capital or social capital effects. These findings suggest that college administrators face significant trade-offs when crafting policies related to Greek life on campus.

- III. Methodology has details
- it's an instrumental variable method paper

Table 5: Fraternity Membership and Grades
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september 2017 by nhaliday
Subgradients - S. Boyd and L. Vandenberghe
If f is convex and x ∈ int dom f, then ∂f(x) is nonempty and bounded. To establish that ∂f(x) ≠ ∅, we apply the supporting hyperplane theorem to the convex set epi f at the boundary point (x, f(x)), ...
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august 2017 by nhaliday
The Determinants of Trust
Both individual experiences and community characteristics influence how much people trust each other. Using data drawn from US localities we find that the strongest factors that reduce trust are: i) a recent history of traumatic experiences, even though the passage of time reduces this effect fairly rapidly; ii) belonging to a group that historically felt discriminated against, such as minorities (black in particular) and, to a lesser extent, women; iii) being economically unsuccessful in terms of income and education; iv) living in a racially mixed community and/or in one with a high degree of income disparity. Religious beliefs and ethnic origins do not significantly affect trust. The latter result may be an indication that the American melting pot at least up to a point works, in terms of homogenizing attitudes of different cultures, even though racial cleavages leading to low trust are still quite high.

Understanding Trust: http://www.nber.org/papers/w13387
In this paper we resolve this puzzle by recognizing that trust has two components: a belief-based one and a preference based one. While the sender's behavior reflects both, we show that WVS-like measures capture mostly the belief-based component, while questions on past trusting behavior are better at capturing the preference component of trust.

MEASURING TRUST: http://scholar.harvard.edu/files/laibson/files/measuring_trust.pdf
We combine two experiments and a survey to measure trust and trustworthiness— two key components of social capital. Standard attitudinal survey questions about trust predict trustworthy behavior in our experiments much better than they predict trusting behavior. Trusting behavior in the experiments is predicted by past trusting behavior outside of the experiments. When individuals are closer socially, both trust and trustworthiness rise. Trustworthiness declines when partners are of different races or nationalities. High status individuals are able to elicit more trustworthiness in others.

What is Social Capital? The Determinants of Trust and Trustworthiness: http://www.nber.org/papers/w7216
Using a sample of Harvard undergraduates, we analyze trust and social capital in two experiments. Trusting behavior and trustworthiness rise with social connection; differences in race and nationality reduce the level of trustworthiness. Certain individuals appear to be persistently more trusting, but these people do not say they are more trusting in surveys. Survey questions about trust predict trustworthiness not trust. Only children are less trustworthy. People behave in a more trustworthy manner towards higher status individuals, and therefore status increases earnings in the experiment. As such, high status persons can be said to have more social capital.

Trust and Cheating: http://www.nber.org/papers/w18509
We find that: i) both parties to a trust exchange have implicit notions of what constitutes cheating even in a context without promises or messages; ii) these notions are not unique - the vast majority of senders would feel cheated by a negative return on their trust/investment, whereas a sizable minority defines cheating according to an equal split rule; iii) these implicit notions affect the behavior of both sides to the exchange in terms of whether to trust or cheat and to what extent. Finally, we show that individual's notions of what constitutes cheating can be traced back to two classes of values instilled by parents: cooperative and competitive. The first class of values tends to soften the notion while the other tightens it.

Nationalism and Ethnic-Based Trust: Evidence from an African Border Region: https://u.osu.edu/robinson.1012/files/2015/12/Robinson_NationalismTrust-1q3q9u1.pdf
These results offer microlevel evidence that a strong and salient national identity can diminish ethnic barriers to trust in diverse societies.

One Team, One Nation: Football, Ethnic Identity, and Conflict in Africa: http://conference.nber.org/confer//2017/SI2017/DEV/Durante_Depetris-Chauvin.pdf
Do collective experiences that prime sentiments of national unity reduce interethnic tensions and conflict? We examine this question by looking at the impact of national football teams’ victories in sub-Saharan Africa. Combining individual survey data with information on over 70 official matches played between 2000 and 2015, we find that individuals interviewed in the days after a victory of their country’s national team are less likely to report a strong sense of ethnic identity and more likely to trust people of other ethnicities than those interviewed just before. The effect is sizable and robust and is not explained by generic euphoria or optimism. Crucially, national victories do not only affect attitudes but also reduce violence. Indeed, using plausibly exogenous variation from close qualifications to the Africa Cup of Nations, we find that countries that (barely) qualified experience significantly less conflict in the following six months than countries that (barely) did not. Our findings indicate that, even where ethnic tensions have deep historical roots, patriotic shocks can reduce inter-ethnic tensions and have a tangible impact on conflict.

Why Does Ethnic Diversity Undermine Public Goods Provision?: http://www.columbia.edu/~mh2245/papers1/HHPW.pdf
We identify three families of mechanisms that link diversity to public goods provision—–what we term “preferences,” “technology,” and “strategy selection” mechanisms—–and run a series of experimental games that permit us to compare the explanatory power of distinct mechanisms within each of these three families. Results from games conducted with a random sample of 300 subjects from a slum neighborhood of Kampala, Uganda, suggest that successful public goods provision in homogenous ethnic communities can be attributed to a strategy selection mechanism: in similar settings, co-ethnics play cooperative equilibria, whereas non-co-ethnics do not. In addition, we find evidence for a technology mechanism: co-ethnics are more closely linked on social networks and thus plausibly better able to support cooperation through the threat of social sanction. We find no evidence for prominent preference mechanisms that emphasize the commonality of tastes within ethnic groups or a greater degree of altruism toward co-ethnics, and only weak evidence for technology mechanisms that focus on the impact of shared ethnicity on the productivity of teams.

does it generalize to first world?

Higher Intelligence Groups Have Higher Cooperation Rates in the Repeated Prisoner's Dilemma: https://ideas.repec.org/p/iza/izadps/dp8499.html
The initial cooperation rates are similar, it increases in the groups with higher intelligence to reach almost full cooperation, while declining in the groups with lower intelligence. The difference is produced by the cumulation of small but persistent differences in the response to past cooperation of the partner. In higher intelligence subjects, cooperation after the initial stages is immediate and becomes the default mode, defection instead requires more time. For lower intelligence groups this difference is absent. Cooperation of higher intelligence subjects is payoff sensitive, thus not automatic: in a treatment with lower continuation probability there is no difference between different intelligence groups

Why societies cooperate: https://voxeu.org/article/why-societies-cooperate
Three attributes are often suggested to generate cooperative behaviour – a good heart, good norms, and intelligence. This column reports the results of a laboratory experiment in which groups of players benefited from learning to cooperate. It finds overwhelming support for the idea that intelligence is the primary condition for a socially cohesive, cooperative society. Warm feelings towards others and good norms have only a small and transitory effect.

individual payoff, etc.:

Trust, Values and False Consensus: http://www.nber.org/papers/w18460
Trust beliefs are heterogeneous across individuals and, at the same time, persistent across generations. We investigate one mechanism yielding these dual patterns: false consensus. In the context of a trust game experiment, we show that individuals extrapolate from their own type when forming trust beliefs about the same pool of potential partners - i.e., more (less) trustworthy individuals form more optimistic (pessimistic) trust beliefs - and that this tendency continues to color trust beliefs after several rounds of game-play. Moreover, we show that one's own type/trustworthiness can be traced back to the values parents transmit to their children during their upbringing. In a second closely-related experiment, we show the economic impact of mis-calibrated trust beliefs stemming from false consensus. Miscalibrated beliefs lower participants' experimental trust game earnings by about 20 percent on average.

The Right Amount of Trust: http://www.nber.org/papers/w15344
We investigate the relationship between individual trust and individual economic performance. We find that individual income is hump-shaped in a measure of intensity of trust beliefs. Our interpretation is that highly trusting individuals tend to assume too much social risk and to be cheated more often, ultimately performing less well than those with a belief close to the mean trustworthiness of the population. On the other hand, individuals with overly pessimistic beliefs avoid being cheated, but give up profitable opportunities, therefore underperforming. The cost of either too much or too little trust is comparable to the income lost by forgoing college.

...

This framework allows us to show that income-maximizing trust typically exceeds the trust level of the average person as well as to estimate the distribution of income lost to trust mistakes. We find that although a majority of individuals has well calibrated beliefs, a non-trivial proportion of the population (10%) has trust beliefs sufficiently poorly calibrated to lower income by more than 13%.

Do Trust and … [more]
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august 2017 by nhaliday
Stages of Diversification
This paper studies the evolution of sectoral concentration in relation to the level of per capita income. We show that various measures of sectoral concentration follow a U-shaped pattern across a wide variety of data sources: countries first diversify, in the sense that economic activity is spread more equally across sectors, but there exists, relatively late in the development process, a point at which they start specializing again. We discuss this finding in light of existing theories of trade and growth, which generally predict a monotonic relationship between income and diversification. (JEL F43, F15, O40)

seems unhealthy to me (complacency)
pdf  study  economics  growth-econ  stylized-facts  correlation  curvature  wealth  wealth-of-nations  distribution  trade  heavy-industry  🎩  group-level  regional-scatter-plots  longitudinal  the-world-is-just-atoms  econ-metrics  econometrics  broad-econ  diversity  entropy-like  nonlinearity  convexity-curvature 
june 2017 by nhaliday
An Investigation of Genetic and Environmental Influences Across The Distribution of Self-Control (PDF Download Available)
Subsequent biometric quantile regression models revealed that genetic influences on self-control were maximized in the 50th and 60th percentiles and minimized in the tails of the distribution. Shared environmental influences were nonsignificant at all examined quantiles of self-control with only one exception.
study  psychology  cog-psych  self-control  discipline  variance-components  biodet  behavioral-gen  environmental-effects  curvature  correlation  null-result  convexity-curvature 
june 2017 by nhaliday
There Is No Such Thing as Decreasing Returns to Scale — Confessions of a Supply-Side Liberal
Besides pedagogical inertia—enforced to some extent by textbook publishers—I am not quite sure what motivates the devotion in so many economics curricula to U-shaped average cost curves. Let me make one guess: there is a desire to explain why firms are the size they are rather than larger or smaller. To my mind, such an explanation should proceed in one of three ways, appropriate to three different situations.
econotariat  economics  micro  plots  scale  marginal  industrial-org  business  econ-productivity  efficiency  cost-benefit  explanation  critique  clarity  intricacy  curvature  convexity-curvature  nonlinearity  input-output 
may 2017 by nhaliday
Estimating the number of unseen variants in the human genome
To find all common variants (frequency at least 1%) the number of individuals that need to be sequenced is small (∼350) and does not differ much among the different populations; our data show that, subject to sequence accuracy, the 1000 Genomes Project is likely to find most of these common variants and a high proportion of the rarer ones (frequency between 0.1 and 1%). The data reveal a rule of diminishing returns: a small number of individuals (∼150) is sufficient to identify 80% of variants with a frequency of at least 0.1%, while a much larger number (> 3,000 individuals) is necessary to find all of those variants.

A map of human genome variation from population-scale sequencing: http://www.internationalgenome.org/sites/1000genomes.org/files/docs/nature09534.pdf

Scientists using data from the 1000 Genomes Project, which sequenced one thousand individuals from 26 human populations, found that "a typical [individual] genome differs from the reference human genome at 4.1 million to 5.0 million sites … affecting 20 million bases of sequence."[11] Nearly all (>99.9%) of these sites are small differences, either single nucleotide polymorphisms or brief insertion-deletions in the genetic sequence, but structural variations account for a greater number of base-pairs than the SNPs and indels.[11]

Human genetic variation: https://en.wikipedia.org/wiki/Human_genetic_variation

Singleton Variants Dominate the Genetic Architecture of Human Gene Expression: https://www.biorxiv.org/content/early/2017/12/15/219238
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may 2017 by nhaliday
Concentration and Growth | Dietrich Vollrath
Ultimately, and this is my impression, not some kind of established fact, concentration likely lowers innovative activity. Put it this way, the null hypothesis should probably be that concentration lowers innovation. An individual industry needs to provide evidence they are on the “right side of the curve” in the first AAH figure to believe concentration would be good for productivity growth in the long run.
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may 2017 by nhaliday
Educational Romanticism & Economic Development | pseudoerasmus
https://twitter.com/GarettJones/status/852339296358940672
deleeted

https://twitter.com/GarettJones/status/943238170312929280
https://archive.is/p5hRA

Did Nations that Boosted Education Grow Faster?: http://econlog.econlib.org/archives/2012/10/did_nations_tha.html
On average, no relationship. The trendline points down slightly, but for the time being let's just call it a draw. It's a well-known fact that countries that started the 1960's with high education levels grew faster (example), but this graph is about something different. This graph shows that countries that increased their education levels did not grow faster.

Where has all the education gone?: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1016.2704&rep=rep1&type=pdf

https://twitter.com/GarettJones/status/948052794681966593
https://archive.is/kjxqp

https://twitter.com/GarettJones/status/950952412503822337
https://archive.is/3YPic

https://twitter.com/pseudoerasmus/status/862961420065001472
http://hanushek.stanford.edu/publications/schooling-educational-achievement-and-latin-american-growth-puzzle

The Case Against Education: What's Taking So Long, Bryan Caplan: http://econlog.econlib.org/archives/2015/03/the_case_agains_9.html

The World Might Be Better Off Without College for Everyone: https://www.theatlantic.com/magazine/archive/2018/01/whats-college-good-for/546590/
Students don't seem to be getting much out of higher education.
- Bryan Caplan

College: Capital or Signal?: http://www.economicmanblog.com/2017/02/25/college-capital-or-signal/
After his review of the literature, Caplan concludes that roughly 80% of the earnings effect from college comes from signalling, with only 20% the result of skill building. Put this together with his earlier observations about the private returns to college education, along with its exploding cost, and Caplan thinks that the social returns are negative. The policy implications of this will come as very bitter medicine for friends of Bernie Sanders.

Doubting the Null Hypothesis: http://www.arnoldkling.com/blog/doubting-the-null-hypothesis/

Is higher education/college in the US more about skill-building or about signaling?: https://www.quora.com/Is-higher-education-college-in-the-US-more-about-skill-building-or-about-signaling
ballpark: 50% signaling, 30% selection, 20% addition to human capital
more signaling in art history, more human capital in engineering, more selection in philosophy

Econ Duel! Is Education Signaling or Skill Building?: http://marginalrevolution.com/marginalrevolution/2016/03/econ-duel-is-education-signaling-or-skill-building.html
Marginal Revolution University has a brand new feature, Econ Duel! Our first Econ Duel features Tyler and me debating the question, Is education more about signaling or skill building?

Against Tulip Subsidies: https://slatestarcodex.com/2015/06/06/against-tulip-subsidies/

https://www.overcomingbias.com/2018/01/read-the-case-against-education.html

https://nintil.com/2018/02/05/notes-on-the-case-against-education/

https://www.nationalreview.com/magazine/2018-02-19-0000/bryan-caplan-case-against-education-review

https://spottedtoad.wordpress.com/2018/02/12/the-case-against-education/
Most American public school kids are low-income; about half are non-white; most are fairly low skilled academically. For most American kids, the majority of the waking hours they spend not engaged with electronic media are at school; the majority of their in-person relationships are at school; the most important relationships they have with an adult who is not their parent is with their teacher. For their parents, the most important in-person source of community is also their kids’ school. Young people need adult mirrors, models, mentors, and in an earlier era these might have been provided by extended families, but in our own era this all falls upon schools.

Caplan gestures towards work and earlier labor force participation as alternatives to school for many if not all kids. And I empathize: the years that I would point to as making me who I am were ones where I was working, not studying. But they were years spent working in schools, as a teacher or assistant. If schools did not exist, is there an alternative that we genuinely believe would arise to draw young people into the life of their community?

...

It is not an accident that the state that spends the least on education is Utah, where the LDS church can take up some of the slack for schools, while next door Wyoming spends almost the most of any state at $16,000 per student. Education is now the one surviving binding principle of the society as a whole, the one black box everyone will agree to, and so while you can press for less subsidization of education by government, and for privatization of costs, as Caplan does, there’s really nothing people can substitute for it. This is partially about signaling, sure, but it’s also because outside of schools and a few religious enclaves our society is but a darkling plain beset by winds.

This doesn’t mean that we should leave Caplan’s critique on the shelf. Much of education is focused on an insane, zero-sum race for finite rewards. Much of schooling does push kids, parents, schools, and school systems towards a solution ad absurdum, where anything less than 100 percent of kids headed to a doctorate and the big coding job in the sky is a sign of failure of everyone concerned.

But let’s approach this with an eye towards the limits of the possible and the reality of diminishing returns.

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/
https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/#comment-101293
The real reason the left would support Moander: the usual reason. because he’s an enemy.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/
I have a problem in thinking about education, since my preferences and personal educational experience are atypical, so I can’t just gut it out. On the other hand, knowing that puts me ahead of a lot of people that seem convinced that all real people, including all Arab cabdrivers, think and feel just as they do.

One important fact, relevant to this review. I don’t like Caplan. I think he doesn’t understand – can’t understand – human nature, and although that sometimes confers a different and interesting perspective, it’s not a royal road to truth. Nor would I want to share a foxhole with him: I don’t trust him. So if I say that I agree with some parts of this book, you should believe me.

...

Caplan doesn’t talk about possible ways of improving knowledge acquisition and retention. Maybe he thinks that’s impossible, and he may be right, at least within a conventional universe of possibilities. That’s a bit outside of his thesis, anyhow. Me it interests.

He dismisses objections from educational psychologists who claim that studying a subject improves you in subtle ways even after you forget all of it. I too find that hard to believe. On the other hand, it looks to me as if poorly-digested fragments of information picked up in college have some effect on public policy later in life: it is no coincidence that most prominent people in public life (at a given moment) share a lot of the same ideas. People are vaguely remembering the same crap from the same sources, or related sources. It’s correlated crap, which has a much stronger effect than random crap.

These widespread new ideas are usually wrong. They come from somewhere – in part, from higher education. Along this line, Caplan thinks that college has only a weak ideological effect on students. I don’t believe he is correct. In part, this is because most people use a shifting standard: what’s liberal or conservative gets redefined over time. At any given time a population is roughly half left and half right – but the content of those labels changes a lot. There’s a shift.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/#comment-101492
I put it this way, a while ago: “When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong.”
--
You just explained the Credo quia absurdum doctrine. I always wondered if it was nonsense. It is not.
--
Someone on twitter caught it first – got all the way to “sliding down the razor blade of life”. Which I explained is now called “transitioning”

What Catholics believe: https://theweek.com/articles/781925/what-catholics-believe
We believe all of these things, fantastical as they may sound, and we believe them for what we consider good reasons, well attested by history, consistent with the most exacting standards of logic. We will profess them in this place of wrath and tears until the extraordinary event referenced above, for which men and women have hoped and prayed for nearly 2,000 years, comes to pass.

https://westhunt.wordpress.com/2018/02/05/bright-college-days-part-ii/
According to Caplan, employers are looking for conformity, conscientiousness, and intelligence. They use completion of high school, or completion of college as a sign of conformity and conscientiousness. College certainly looks as if it’s mostly signaling, and it’s hugely expensive signaling, in terms of college costs and foregone earnings.

But inserting conformity into the merit function is tricky: things become important signals… because they’re important signals. Otherwise useful actions are contraindicated because they’re “not done”. For example, test scores convey useful information. They could help show that an applicant is smart even though he attended a mediocre school – the same role they play in college admissions. But employers seldom request test scores, and although applicants may provide them, few do. Caplan says ” The word on the street… [more]
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april 2017 by nhaliday
Fertility trends by social status
The study reveals that as fertility declines, there is a general shift from a positive to a negative or neutral status-fertility relation. Those with high income/wealth or high occupation/social class switch from having relatively many to fewer or the same number of children as others. Education, however, depresses fertility for as long as this relation is observed (from early in the 20th century).

- good survey with trends for different regions, including UK+North America
- Figure 4: quadratic for UK+NA, crossing zero around 1800 or so and quickly leveling off
http://imgur.com/a/xjwO1
- also Figure 5: fertility differential by total TFR (quadratic trend), so worst dysgenics in middle of demographic transition
- dataset: http://www.demographic-research.org/volumes/vol18/5/files/StatusFertilityDataset.xls

This article discusses how fertility relates to social status with the use of a new dataset, several times larger than the ones used so far. The status-fertility relation is investigated over several centuries, across world regions and by the type of status-measure. The study reveals that as fertility declines, there is a general shift from a positive to a negative or neutral status-fertility relation. Those with high income/wealth or high occupation/social class switch from having relatively many to fewer or the same number of children as others. Education, however, depresses fertility for as long as this relation is observed (from early in the 20th century).
pdf  study  demographics  sociology  fertility  correlation  dysgenics  britain  anglo  usa  history  early-modern  mostly-modern  trends  iq  education  status  compensation  money  class  gender  social-structure  🎩  🌞  world  demographic-transition  plots  science-anxiety  multi  pic  visualization  data  developing-world  deep-materialism  new-religion  stylized-facts  age-generation  s:*  nonlinearity  wealth  s-factor  chart  biophysical-econ  broad-econ  solid-study  rot  the-bones  meta-analysis  database  dataset  curvature  pre-ww2  modernity  time-series  convexity-curvature  hari-seldon 
march 2017 by nhaliday
Was the Wealth of Nations Determined in 1000 BC?
Our most interesting, strong, and robust results are for the association of 1500 AD technology with per capita income and technology adoption today. We also find robust and significant technological persistence from 1000 BC to 0 AD, and from 0 AD to 1500 AD.

migration-adjusted ancestry predicts current economic growth and technology adoption today

https://economix.blogs.nytimes.com/2010/08/02/was-todays-poverty-determined-in-1000-b-c/

Putterman-Weil:
Post-1500 Population Flows and the Long Run Determinants of Economic Growth and Inequality: http://www.nber.org/papers/w14448
Persistence of Fortune: Accounting for Population Movements, There Was No Post-Columbian Reversal: http://sci-hub.tw/10.1257/mac.6.3.1
Extended State History Index: https://sites.google.com/site/econolaols/extended-state-history-index
Description:
The data set extends and replaces previous versions of the State Antiquity Index (originally created by Bockstette, Chanda and Putterman, 2002). The updated data extends the previous Statehist data into the years before 1 CE, to the first states in Mesopotamia (in the fourth millennium BCE), along with filling in the years 1951 – 2000 CE that were left out of past versions of the Statehist data.
The construction of the index follows the principles developed by Bockstette et al (2002). First, the duration of state existence is established for each territory defined by modern-day country borders. Second, this duration is divided into 50-year periods. For each half-century from the first period (state emergence) onwards, the authors assign scores to reflect three dimensions of state presence, based on the following questions: 1) Is there a government above the tribal level? 2) Is this government foreign or locally based? 3) How much of the territory of the modern country was ruled by this government?

Creators: Oana Borcan, Ola Olsson & Louis Putterman

State History and Economic Development: Evidence from Six Millennia∗: https://drive.google.com/file/d/1cifUljlPpoURL7VPOQRGF5q9H6zgVFXe/view
The presence of a state is one of the most reliable historical predictors of social and economic development. In this article, we complete the coding of an extant indicator of state presence from 3500 BCE forward for almost all but the smallest countries of the world today. We outline a theoretical framework where accumulated state experience increases aggregate productivity in individual countries but where newer or relatively inexperienced states can reach a higher productivity maximum by learning from the experience of older states. The predicted pattern of comparative development is tested in an empirical analysis where we introduce our extended state history variable. Our key finding is that the current level of economic development across countries has a hump-shaped relationship with accumulated state history.

nonlinearity confirmed in this other paper:
State and Development: A Historical Study of Europe from 0 AD to 2000 AD: https://ideas.repec.org/p/hic/wpaper/219.html
After addressing conceptual and practical concerns on its construction, we present a measure of the mean duration of state rule that is aimed at resolving some of these issues. We then present our findings on the relationship between our measure and local development, drawing from observations in Europe spanning from 0 AD to 2000 AD. We find that during this period, the mean duration of state rule and the local income level have a nonlinear, inverse U-shaped relationship, controlling for a set of historical, geographic and socioeconomic factors. Regions that have historically experienced short or long duration of state rule on average lag behind in their local wealth today, while those that have experienced medium-duration state rule on average fare better.

Figure 1 shows all borders that existed during this period
Figure 4 shows quadratic fit

I wonder if U-shape is due to Ibn Kaldun-Turchin style effect on asabiya? They suggest sunk costs and ossified institutions.
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march 2017 by nhaliday
inequalities - Is the Jaccard distance a distance? - MathOverflow
Steinhaus Transform
the referenced survey: http://kenclarkson.org/nn_survey/p.pdf

It's known that this transformation produces a metric from a metric. Now if you take as the base metric D the symmetric difference between two sets, what you end up with is the Jaccard distance (which actually is known by many other names as well).
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february 2017 by nhaliday
Prékopa–Leindler inequality | Academically Interesting
Consider the following statements:
1. The shape with the largest volume enclosed by a given surface area is the n-dimensional sphere.
2. A marginal or sum of log-concave distributions is log-concave.
3. Any Lipschitz function of a standard n-dimensional Gaussian distribution concentrates around its mean.
What do these all have in common? Despite being fairly non-trivial and deep results, they all can be proved in less than half of a page using the Prékopa–Leindler inequality.

ie, Brunn-Minkowski
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february 2017 by nhaliday
The Brunn-Minkowski Inequality | The n-Category Café
For instance, this happens in the plane when A is a horizontal line segment and B is a vertical line segment. There’s obviously no hope of getting an equation for Vol(A+B) in terms of Vol(A) and Vol(B). But this example suggests that we might be able to get an inequality, stating that Vol(A+B) is at least as big as some function of Vol(A) and Vol(B).

The Brunn-Minkowski inequality does this, but it’s really about linearized volume, Vol^{1/n}, rather than volume itself. If length is measured in metres then so is Vol^{1/n}.

...

Nice post, Tom. To readers whose background isn’t in certain areas of geometry and analysis, it’s not obvious that the Brunn–Minkowski inequality is more than a curiosity, the proof of the isoperimetric inequality notwithstanding. So let me add that Brunn–Minkowski is an absolutely vital tool in many parts of geometry, analysis, and probability theory, with extremely diverse applications. Gardner’s survey is a great place to start, but by no means exhaustive.

I’ll also add a couple remarks about regularity issues. You point out that Brunn–Minkowski holds “in the vast generality of measurable sets”, but it may not be initially obvious that this needs to be interpreted as “when A, B, and A+B are all Lebesgue measurable”, since A+B need not be measurable when A and B are (although you can modify the definition of A+B to work for arbitrary measurable A and B; this is discussed by Gardner).
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february 2017 by nhaliday
mg.metric geometry - Pushing convex bodies together - MathOverflow
- volume of intersection of colliding, constant-velocity convex bodies is unimodal
- pf by Brunn-Minkowski inequality
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january 2017 by nhaliday
Ehrhart polynomial - Wikipedia
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane.
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january 2017 by nhaliday
Dvoretzky's theorem - Wikipedia
In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander Grothendieck. In essence, it says that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean. Equivalently, every high-dimensional bounded symmetric convex set has low-dimensional sections that are approximately ellipsoids.

http://mathoverflow.net/questions/143527/intuitive-explanation-of-dvoretzkys-theorem
http://mathoverflow.net/questions/46278/unexpected-applications-of-dvoretzkys-theorem
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january 2017 by nhaliday
Carathéodory's theorem (convex hull) - Wikipedia
- any convex combination in R^d can be pared down to at most d+1 points
- eg, in R^2 you can always fit a point in convex hull in a triangle
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january 2017 by nhaliday
(Gil Kalai) The weak epsilon-net problem | What's new
This is a problem in discrete and convex geometry. It seeks to quantify the intuitively obvious fact that large convex bodies are so “fat” that they cannot avoid “detection” by a small number of observation points.
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january 2017 by nhaliday
A Systematic Review of Personality Trait Change Through Intervention
gwern: https://plus.google.com/103530621949492999968/posts/6kFWRkUTXSV
Messy (noticeable levels of publication bias, high heterogeneity), but results look plausible: 8-week+ interventions can improve emotional stability and neuroticism, change Openness and Extraversion somewhat, but leave Conscientiousness largely unaffected.

hbd chick/murray: https://twitter.com/hbdchick/status/818138228553302017

- 8-week intervention -> d=.37 after (an average of) 24 weeks
- after 8 weeks, strong diminishing returns
- pretty much entirely self-report
- good page-length discussion of limitations at end
- there was actually a nonzero effect for conscientiousness (~.2). not sure it would remain w/o publication bias.
- what's the difference between Table 2 and 3? I guess RCT vs. something else? why highlight Table 2 in abstract then?
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january 2017 by nhaliday
Mental rotation and real-world wayfinding. - PubMed - NCBI
r ≈ .3

The results indicate that mental rotation skills are significantly correlated with wayfinding performance on an orienteering task. The findings also replicate sex differences in spatial ability as found in laboratory-scale studies. However, the findings complicate the discussion of mental rotation skills and sex because women often performed as well as men despite having lower mean test scores. This suggests that mental rotation ability may not be as necessary for some women's wayfinding as it is for men's navigation.

Sex Differences in Furniture Assembly Performance: An Experimental Study: http://onlinelibrary.wiley.com/doi/10.1002/acp.3182/abstract
fucking lol

Sex hormones predict the sensory strength and vividness of mental imagery: https://www.ncbi.nlm.nih.gov/pubmed/25703930
- not in the direction I would expect (women have more vivid mental imagery)
- visual working memory is different

Sex hormones and mental rotation: An intensive longitudinal investigation: http://www.sciencedirect.com.sci-hub.tw/science/article/pii/S0018506X12003066
For males and females, estradiol and testosterone were significantly linearly and quadratically related to interindividual variation in performance at the beginning of the study (progesterone was linearly related to performance for females). The association between testosterone and performance differed across sexes: for males, it had an inverse U-shape, for females it was U-shaped. Towards the end of the study, none of the hormones were significantly related to performance anymore. Thus, the relationship between hormones and mental rotation performance disappeared with repeated testing.

very confusing study. seems sketchy.

Is There a Relationship Between the Performance in a Chronometric Mental-Rotations Test and Salivary Testosterone and Estradiol Levels in Children Aged 9–14 Years?: http://sci-hub.tw/10.1002/dev.21333
Results showed a significant gender difference in reaction time and rotational speed in favor of boys, and a significant age, but no gender difference in testosterone and estradiol levels. We found no significant relationships between hormonal levels and any measure of mental-rotation performance.

Having a Male Co-Twin Masculinizes Mental Rotation Performance in Females: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4438761/
There were 351 females from same-sex pairs, 223 males from same-sex pairs, 120 females from opposite-sex pairs, and 110 males from opposite-sex pairs.

hmm:
Sex Differences in Mental Rotation Ability Are a Consequence of Procedure and Artificiality of Stimuli: https://link.springer.com/article/10.1007/s40806-017-0120-x
Our results suggest that the sex difference found on this test is not due to a male advantage in spatial ability, but is an artifact of the stimuli.
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december 2016 by nhaliday
Convex Optimization Applications
there was a problem in ACM113 related to this (the portfolio optimization SDP stuff)
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december 2016 by nhaliday
gt.geometric topology - Intuitive crutches for higher dimensional thinking - MathOverflow
Terry Tao:
I can't help you much with high-dimensional topology - it's not my field, and I've not picked up the various tricks topologists use to get a grip on the subject - but when dealing with the geometry of high-dimensional (or infinite-dimensional) vector spaces such as R^n, there are plenty of ways to conceptualise these spaces that do not require visualising more than three dimensions directly.

For instance, one can view a high-dimensional vector space as a state space for a system with many degrees of freedom. A megapixel image, for instance, is a point in a million-dimensional vector space; by varying the image, one can explore the space, and various subsets of this space correspond to various classes of images.

One can similarly interpret sound waves, a box of gases, an ecosystem, a voting population, a stream of digital data, trials of random variables, the results of a statistical survey, a probabilistic strategy in a two-player game, and many other concrete objects as states in a high-dimensional vector space, and various basic concepts such as convexity, distance, linearity, change of variables, orthogonality, or inner product can have very natural meanings in some of these models (though not in all).

It can take a bit of both theory and practice to merge one's intuition for these things with one's spatial intuition for vectors and vector spaces, but it can be done eventually (much as after one has enough exposure to measure theory, one can start merging one's intuition regarding cardinality, mass, length, volume, probability, cost, charge, and any number of other "real-life" measures).

For instance, the fact that most of the mass of a unit ball in high dimensions lurks near the boundary of the ball can be interpreted as a manifestation of the law of large numbers, using the interpretation of a high-dimensional vector space as the state space for a large number of trials of a random variable.

More generally, many facts about low-dimensional projections or slices of high-dimensional objects can be viewed from a probabilistic, statistical, or signal processing perspective.

Scott Aaronson:
Here are some of the crutches I've relied on. (Admittedly, my crutches are probably much more useful for theoretical computer science, combinatorics, and probability than they are for geometry, topology, or physics. On a related note, I personally have a much easier time thinking about R^n than about, say, R^4 or R^5!)

1. If you're trying to visualize some 4D phenomenon P, first think of a related 3D phenomenon P', and then imagine yourself as a 2D being who's trying to visualize P'. The advantage is that, unlike with the 4D vs. 3D case, you yourself can easily switch between the 3D and 2D perspectives, and can therefore get a sense of exactly what information is being lost when you drop a dimension. (You could call this the "Flatland trick," after the most famous literary work to rely on it.)
2. As someone else mentioned, discretize! Instead of thinking about R^n, think about the Boolean hypercube {0,1}^n, which is finite and usually easier to get intuition about. (When working on problems, I often find myself drawing {0,1}^4 on a sheet of paper by drawing two copies of {0,1}^3 and then connecting the corresponding vertices.)
3. Instead of thinking about a subset S⊆R^n, think about its characteristic function f:R^n→{0,1}. I don't know why that trivial perspective switch makes such a big difference, but it does ... maybe because it shifts your attention to the process of computing f, and makes you forget about the hopeless task of visualizing S!
4. One of the central facts about R^n is that, while it has "room" for only n orthogonal vectors, it has room for exp⁡(n) almost-orthogonal vectors. Internalize that one fact, and so many other properties of R^n (for example, that the n-sphere resembles a "ball with spikes sticking out," as someone mentioned before) will suddenly seem non-mysterious. In turn, one way to internalize the fact that R^n has so many almost-orthogonal vectors is to internalize Shannon's theorem that there exist good error-correcting codes.
5. To get a feel for some high-dimensional object, ask questions about the behavior of a process that takes place on that object. For example: if I drop a ball here, which local minimum will it settle into? How long does this random walk on {0,1}^n take to mix?

Gil Kalai:
This is a slightly different point, but Vitali Milman, who works in high-dimensional convexity, likes to draw high-dimensional convex bodies in a non-convex way. This is to convey the point that if you take the convex hull of a few points on the unit sphere of R^n, then for large n very little of the measure of the convex body is anywhere near the corners, so in a certain sense the body is a bit like a small sphere with long thin "spikes".
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december 2016 by nhaliday
real analysis - Proof of "every convex function is continuous" - Mathematics Stack Exchange
bound above by secant and below by tangent, so graph of function is constrained to a couple triangles w/ common vertex at (x, f(x))
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november 2016 by nhaliday
Decison Tree for Optimization Software
including convex programming

Mosek makes out pretty good but not pareto-optimal
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november 2016 by nhaliday
The Collapse of Complex Societies | Entitled to an Opinion
https://en.wikipedia.org/wiki/The_Ruin
The Ruin is an elegy in Old English, written by an unknown author probably in the 8th or 9th century, and published in the 10th century in the Exeter Book, a large collection of poems and riddles.[1] The poem evokes the former glory of a ruined city by juxtaposing the grand, lively past state with the decaying present.

https://coursewikis.fas.harvard.edu/aiu18/images/The_ruin.pdf

Splendid this rampart is, though fate destroyed it,
The city buildings fell apart, the works
Of giants crumble. Tumbled are the towers,
Ruined the roofs, and broken the barred gate,
Frost in the plaster, all the ceilings gape,
Tom and collapsed and eaten up by age.
And grit holds in its grip, the hard embrace
Of earth, the dead departed master-builders,
Until a hundred generations now
Of people have passed by. Often this wall
Stained red and grey with lichen has stood by
Surviving storms while kingdoms rose and fell.
And now the high curved wall itself has fallen.

...

The heart inspired, incited to swift action.
Resolute masons, skilled in rounded building
Wondrously linked the framework with iron bonds.
The public halls were bright, with lofty gables,
Bath-houses many; great the cheerful noise,
And many mead-halls filled with human pleasures.
Till mighty fate brought change upon it all.
Slaughter was widespread, pestilence was rife,
And death took all those valiant men away.
The martial halls became deserted places,
The city crumbled, its repairers fell,
Its armies to the earth. And so these halls
Are empty, and this red curved roof now sheds
Its tiles, decay has brought it to the ground,
Smashed it to piles of rubble, where long since
A host of heroes, glorious, gold-adorned,
Gleaming in splendour, proud and Hushed with wine,
Shone in their armour, gazed on gems and treasure,
On silver, riches, wealth and jewellery,
On this bright city with its wide domains.
Stone buildings stood, and the hot stream cast forth
Wide sprays of water, which a wall enclosed
ln its bright compass, where convenient
Stood hot baths ready for them at the centre.
Hot streams poured forth over the clear grey stone,
To the round pool and down into the baths.
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october 2016 by nhaliday
Democracy does not cause growth | Brookings Institution
64-page paper
Democracy & Growth: http://www.nber.org/papers/w4909
The favorable effects on growth include maintenance of the rule of law, free markets, small government consumption, and high human capital. Once these kinds of variables and the initial level of real per-capita GDP are held constant, the overall effect of democracy on growth is weakly negative. There is a suggestion of a nonlinear relationship in which democracy enhances growth at low levels of political freedom but depresses growth when a moderate level of freedom has already been attained.

The growth effect of democracy: Is it heterogenous and how can it be estimated∗: http://perseus.iies.su.se/~tpers/papers/cifar_paper_may16_07.pdf
In particular, we find an average negative effect on growth of leaving democracy on the order of −2 percentage points implying effects on income per capita as large as 45 percent over the 1960-2000 panel. Heterogenous characteristics of reforming and non-reforming countries appear to play an important role in driving these results.

Does democracy cause innovation? An empirical test of the popper hypothesis: http://www.sciencedirect.com.sci-hub.cc/science/article/pii/S0048733317300975
The results from the difference-in-differences method show that democracy itself has no direct positive effect on innovation measured with patent counts, patent citations and patent originality.

Benevolent Autocrats: https://williameasterly.files.wordpress.com/2011/09/benevolent-autocrats-easterly-draft.pdf
A large literature attributes this to the higher variance of growth rates under autocracy than under democracy. The literature offers alternative explanations for this stylized fact: (1) leaders don’t matter under democracy, but good and bad leaders under autocracy cause high and low growth, (2) leaders don’t matter under autocracy either, but good and bad autocratic systems cause greater extremes of high and low growth, or (3) democracy does better than autocracy at reducing variance from shocks from outside the political system. This paper details further the stylized facts to test these distinctions. Inconsistent with (1), the variance of growth within the terms of leaders swamps the variance across leaders, and more so under autocracy than under democracy. Country effects under autocracy are also overwhelmed by within-country variance, inconsistent with (2). Explanation (3) fits the stylized facts the best of the three alternatives.

Political Institutions, Size of Government and Redistribution: An empirical investigation: http://www.lse.ac.uk/internationalDevelopment/pdf/WP/WP89.pdf
Results show that the stronger democratic institutions are, the lower is government size and the higher the redistributional capacity of the state. Political competition exercises the strongest and most robust effect on the two variables.

https://twitter.com/GarettJones/status/899466295170801664
https://archive.is/sPFII
Fits the high-variance theory of autocracies:
More miracles, more disasters. And there's a lot of demand for miracles.

Measuring the ups and downs of governance: https://www.brookings.edu/blog/future-development/2017/09/22/measuring-the-ups-and-downs-of-governance/
Figure 2: Voice and Accountability and Government Effectiveness, 2016
https://twitter.com/whyvert/status/917444456386666497
https://archive.is/EBQlD
Georgia, Japan, Rwanda, and Serbia ↑ Gov Effectiveness; Indonesia, Tunisia, Liberia, Serbia, and Nigeria ↑ Voice and Accountability.

The logic of hereditary rule: theory and evidence: http://eprints.lse.ac.uk/69615/
Hereditary leadership has been an important feature of the political landscape throughout history. This paper argues that hereditary leadership is like a relational contract which improves policy incentives. We assemble a unique dataset on leaders between 1874 and 2004 in which we classify them as hereditary leaders based on their family history. The core empirical finding is that economic growth is higher in polities with hereditary leaders but only if executive constraints are weak. Moreover, this holds across of a range of specifications. The finding is also mirrored in policy outcomes which affect growth. In addition, we find that hereditary leadership is more likely to come to an end when the growth performance under the incumbent leader is poor.

I noted this when the paper was a working paper, but non-hereditary polities with strong contraints have higher growth rates.
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september 2016 by nhaliday
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