Pitfalls of rating systems

A few years ago, YouTube changed its rating mechanism from five-star rating to upvote–downvote system. And it makes sense after you look at the typical distribution of ratings:

Source

In most cases, users set either 1 or 5. That's not very informationally efficient, but it's the fact that users were reluctant to rate videos across the entire scale.

This J-shaped distribution creates problems because the mean here makes no sense. When a website reports an average rating of 3.0, it means one of two things. Either one person rated the video at 1 and another one at 5. Or both rated it at 3, which is almost never the case.

In an economy guided by ratings, the difference between these two interpretations is large and unpleasant. Since no one rates stuff around the mean, a decision based on this mean is uninformed. In the end, you watch something that you'd later rate at 1 or 5, not 3. It's like you'd ordered a steak and the waiter brought you sushi.

The worse thing about this risk is that it's implicit. Users look at ratings to reduce the risk of making a wrong choice, but instead they gamble between 1 and 5. Fortunately, the ratings aren't entirely random. They're conditioned on the stuff we observe, like gender, age, and interests. The means then may start working. Just check if those 1s and 5s were set by distinct demographic groups.

Of course, it's now about hundreds of 1s and 5s, because the degrees of freedom go down with each factor we get into the equation. How to get more ratings?

The solution is exactly what YouTube did: replace a five-star scale with a binary choice. Users don't like investing time in thinking about the proper rating, so thumbs up or down helps with decision fatigue.

More ratings allow computing the means for subgroups of users. These subratings become more relevant for those who search stuff by its rating. Though YouTube didn't make customized ratings yet, that's an option for many web services relying on user feedback.

While Uber and Fiverr can improve their rating systems by reducing it to binary choices, a scale is still a good choice for, say, IMDb. When you watch a movie for two hours, you try to rate it better than YouTube's typical three minutes. And then multiple peaks emerge for controversial movies:

You have the mean and median near to each other in a sort of Poisson distribution. The other two peaks are around radical 1 and 10. So, you need more than two grades on a scale.

Conventional hits have the YouTube pattern though:

Which again looks like the Poisson distribution with the disproportionate number of 1s.

In the end, a good rating system has to balance between the desirable number of votes and the size of the scale.

Answering questions already answered on Stack Exchange

In one of the previous posts, the relative distribution of upvotes on Stack Exchange showed that adding one more answer to a question isn't much demanded by readers because readers give at least half of upvotes to the first-placed answer alone:

(y-axis: the answer's mean fraction of upvotes in a question; x-axis is the position of the answer)

But the absolute number of upvotes tells why answers still appear:

(y-axis: mean of upvotes; other notation is the same)

Questions with few answers happen to be unpopular in general (that's why they have fewer answer in the first place). You can barely notice upvotes for questions with a single answer. But they grow as the graph says. The last frame describes the case of 16 answers, but it's better to be careful beyond that because the original sample has too few questions with many answers.

The bottom line is that answering a question with many answers may be more useful to users than answering questions with no answers at all. That's at least valid under the assumption of unconditional expectations. Controlling for time is the next most useful thing to do to understand how demand and supply operate in Q&A markets and what can be done to make them more efficient.

Athletes vs. data scientists

Competitions among athletes have quite a long history. Armchair sports don't. Chess, which comes to mind first, became an important sport, but only in the 20th century.

An even younger example is data-related competitions. Kaggle, CrowdANALYTIX, and HackerRank are major platforms in this case.

But do data scientists compete as furiously as athletes? Well, in some cases, yes. Here's one example:

(see appendix for how the datasets were constructed)

Merk and Census competitions have about the same number of participants and comparable rewards (but winners for the Census competition were restricted to US citizens only). It may seem surprising that their results look so different. I'll get back to this in the next post on data competitions.

Technically, all the competitions look alike. The lower bound is zero (minutes, seconds, errors), though only the baseline comparison makes sense. Over time, the baseline for sports declined:

(Winning time for 100m. Source.)

A two-second (-18%) improvement in 112 years.

Competitions in a single dataset look like this (more is better):

(Restricted sample taken from chmullig.com)

In general, the quality of predictions substantially increase over a few first weeks. Then marginal returns from efforts decrease. That's interesting because participants make hundreds of submissions to beat numbers three places beyond the decimal point. That's a lot of work for a normally modest monetary reward. And, well, the monetary reward makes no sense at all. A prize of $25–50K goes to winners who compete with 250 other teams. These are thousands of hours of data analysis, basically unpaid. This unpaid work doesn't sound attractive even to sponsors (hosts), which are very careful about paying for crowdsourcing. So, yes, it's a sport, not work.

Athletics has no overfitting, but that's an issue in data competitions. For example, comparison between public and private rankings for one of the competitions:

Username	Public rank	Private rank
Jared Huling	1	283
Yevgeniy	2	7
Attila Balogh	3	231
Abhishek	4	6
Issam Laradji	5	9
Ankush Shah	6	11
Grothendieck	7	50
Thakur Raj Anand	8	247
Manuel Días	9	316
Juventino	10	27

(Source)

The public rank is computed from predictions on the public dataset. The private rank is based on a different sample unavailable before the finals. The difference is largely attributed to overfitting noisy data (and submitting best-performing random results).

In data competitions, your training is not equal to your performance. That's valid for sports as well. Athletes break world records during training sessions and then finish far away from the top in real competitions.

This has a perfectly statistical explanation, apart from psychology. In official events, the sample is smaller. A single trial, mostly. Several trials are allowed only in non-simultaneous sports, like high jumps. The sample is many times larger during training. And you're more likely to find an extreme result in a larger sample.

Anyway, though these games look like fun and games, they're also simple models for understanding complex processes. Measuring performance has value for human lives. For instance, hiring in most firms is a single-trial interview. And HR folks use simple heuristic rules for candidate assessment. When candidates are nervous, they fail their trial.

Some firms, like major IT companies, do more interviews. Not because they want to help candidates, but because they have more stakeholders whose opinion matters. But this policy increases the number of trials, so these companies hire smarter.

We don't have many counterfactuals for HR failures, but we can see how inefficient single trials are compared to multiple trials in sports.

Appendix: The data for the first graph

This graph was constructed in the following way.

First, I took the data for major competitions:

• Athletics, 100m, men. 2012 Olympic Games in London. Link.
• Biathlon, 10km, men. 2014 Olympic Games in Sochi. Link.
• Private leaderboard. Census competition on Kaggle. Link.
• Private leaderboard. Merk competition on Kaggle. Link.

Naturally, ranking criteria are different. Minutes for biathlon, seconds for athletics, weighted mean absolute error for Census, and R^2 for Merk. All but Merk use descending ranking, when less is better. I converted metrics for Merk to descending ranking by taking ( 1 − R^2 ). That is, I ranked players in the Merk competition by the variance left unexplained by the models.

Then in each competition, I took the first place's result as 100% and converted other results as percentage of this result. After subtracting 100, I had the graph.

Stack Exchange and reward for being on the top

As mentioned in the previous posts, Stack Exchange has a very interpretable structure. It's a market in which demand for answering a question meets supply, and supply is paid with upvotes. Such a rude interpretation is necessary for learning how knowledge exchange works.

I once looked into a demand side of Stack Exchange, but now a few points on the supply side. In general, we are interested in efficient allocation of resources. Given the fact that sometimes one answer is enough (especially for software development questions), many answers may be a waste.

And that's the distribution of answers per question:

Well, it's a peak at 2 with a long tail. The details:

number of answers	Freq.	Percent	Cum.
1	2,123	18.35	18.35
2	2,601	22.48	40.83
3	2,138	18.48	59.3
4	1,458	12.6	71.9
5	967	8.36	80.26
6	674	5.82	86.09
7	461	3.98	90.07
8	325	2.81	92.88
9	190	1.64	94.52
10	135	1.17	95.69

About 80 percent of questions end with five answers or less.

The Reward for Being on the Top

But what's the reward for having your answer on the top of the others? These are the means of fractions of total upvotes by the position a given answer occupies:

It says that the answer on the top have an stable advantage over all answers to a given question. You can see that after the fifth answer, adding more answers does not decrease total upvotes given to the existing answers. And the first answer gets no less that half of all upvotes.

That's a huge bonus, since multiple other answers have to split the remaining half of upvotes. That may be discouraging for participants, as competition is high and the winner takes all.

Sample summary statistics

Variable	Obs	Mean	Std. Dev.	Min	Max
upvotes	45463	5.390141	24.11624	0	1553
downvotes	45463	0.1868992	0.9164532	0	82
net (up - down)	45463	5.203242	23.94713	-19	1552
position	45463	4.449794	6.709625	1	114
total_answers	45463	7.899589	10.94102	1	114
relative position	45463	0.6272573	0.2922457	0.0087719	1
total_uv_b~q	45463	67.75934	221.0013	0	2488
frac_uv	44188	0.2440255	0.3074606	0	1

NYT-speak continued

The New York Times' choice of words tells much about history and the media. As seen before, their Chronicle shows great snapshots of the newspaper's wording evolution.

Here, a few more cases.

Information sourcing

As Robert Fisk once noted, the media now rely more on what officials said, rather than sourcing news by themselves. That's a confirmation:

Money and knowledge in crises

Though in general money and knowledge move in the same directions, money moves in greater magnitudes. Also, notice that in the Great Depression, as well as in the Great Recession, the NYT mentioned money less frequently. And the opposite happened during stagflation in the 70s.

Inflation and unemployment

Mentions of unemployment and inflation went in different directions before the 70s: right until the economy happened to have both. But it was a short period and right now there're no mutual relations (at least, in wording).

In- and equality

Inequality never was an issue for the NYT. Even in the late 20s, when inequality was extremely high. So, it's a new topic. Meanwhile, previous mentions of equality are generally associated with civil rights movements, as in the 60s.

"Make war, not love"

At its peak, war themes took up to 30% of the newspaper materials. But local wars, like Iraq and Afghanistan, never draw so much attention.

Referring to minorities

A similar graph was in the previous post, but here changes in wording are clearer. Especially right after the Civil War, when politicians no longer needed support from the black population, and one hundred years later, when politicians and media had to update their vocabulary.

Sports becoming more popular

Top 1% on Stack Exchange, or inequality in Q&A markets

Yesterday's review of voting activity showed how Stack Exchange users evaluate each others' contributions. Contrary to some views, users don't go berserk despite anonymity and in general balance their judgment.

Upvotes are a currency in a moneyless economy, like one of Stack Exchange. It doesn't mean people do things for upvotes. In this survey, reciprocity comes first as motivation, while upvotes lag behind. But, like money, upvotes often measure one's contribution to the community. Though it's in unlimited supply, upvoting has its own costs (yes, costs of clicking on buttons), and can measure something. For instance, inequality.

Gini

Here's the distribution of upvotes that a particular user got over time:

The long tail is wagging behind, but the inequality is very high.

The Gini coefficient for Stack Exchange is 0.85 for upvotes. That's higher than in South Africa (0.63), which has the highest inequality among countries.

Top 1% and 0.1%

High inequality leads to the questions what does top 1% of users own. Well, they own 42.8% of all upvotes. Actually, it's just about the same percentage that the 1% of richest Americans now control in the national economy.

Top 0.1% users own 15.4% of all upvotes.

Also, Pareto's law nearly holds. Top 20% of users own 87.7% of upvotes.

How to get rich in this economy

In brief: by being rich. This is why:

(users with less than 10 votes in total are excluded as bypassers)

Until you earn about ten upvotes, the only thing that grows is your downvotes. That's a mentoring stage when novices are downvoted as someone who do not read rules. But after you accumulated this minimum, upvotes grow relatively to downvotes. And they grow rapidly.

This result is robust to including bypassers back in the sample (see how the line changes the slope at ln(downvotes) ≈ 2):

So, in general, you have more when you already have enough.

Data Appendix

Analysis is done with a 1% sample of users. Data is available at data.stackexchange.com, while replication files will soon be posted online.

Unrestricted evil

Online services before Facebook were mostly anonymous. At least, no one required real names and SMS confirmations. You sign up and write anything. I mean anything.

There were scary fairy tales about writing anything without putting your real name on it. Various regulations imposed on the Internet, especially in non-democracies, rely on these tales. But is the opposite—real names and full disclosure—really necessary for a good-standing community?

Let's check. The anonymous culture is still alive on some resources. Today is not about 4chan, but about Stack Exchange, a major Q&A website. Stack Exchange has an open data tool for querying data. The tool is quite useful for testing various hypotheses about human communities. It would be a service to humanity if other web services offered similar openness, but so far we have few.

Stack Exchange (SE) doesn't ask names and so on. Though real names are common and some employers ask candidates for links to their SE profiles, the service is basically anonymous. We expect dirty things to happen.

One dirty thing is excessive downvotes for questions and answers others post. Kind of vandalism. And here's the graph:

The graph shows net votes (upvotes - downvotes) for each user with 10+ upvotes or downvotes from a 1% sample (about 31K users). That small tick on the left is users who mostly downvote.

A slightly different perspective:

(The axes were log-linearized for easy reading.)

User behavior happens to be extremely balanced. Few users tend to upvote or downvote extremes. Most of them try to be honest.

So, showing your name is not necessary for good behavior. Online communities can manage themselves without references to the official world, regulations, and witch-hunting. It only matters what environment people want to be in, and then they'll be able to recreate it online.

Startups across countries

A few plots in addition to yesterday's post on startups.

Startups and economic development

Sources: CruchBase.com dataset and Penn World Table 7.0.

That's not a bad fit for relations between startups and GDP. The number of startups in the dataset seems to be a good indicator of entrepreneurial activity in general.

Startup nation

Here's an illustration for Dan Senor and Saul Singer's thesis about Startup Nation:

Israel has relatively more startups than the US. Tel Aviv and Silicon Valley drive the numbers for their countries, so it's not exactly a nation-wide phenomenon. You call the book Startup City, though the result is no less impressive.

Web data and language barriers

Like other sources based on voluntary reporting, CruchBase may have data biased on one or another way. For example, it may underrepresent countries, in which English is not a major language. And we expect a bias in favor of bigger firms. And here's the case:

China and Russia indeed either have bigger startups on average or just underreport to CrunchBase. The latter is the case because these are exactly two major countries that stand behind a language firewall. They have their own Facebooks, Twitters, and Amazons. So, we expect them to be less active on CruchBase. More so:

The surprising break after the 90th percentile separate countries into two groups. What are the groups? Look here:

(US and UK are excluded to make the graph readable. 100+ startup countries included.)

Group 1 are countries with < 0.02 startups per 1,000 inhabitants and Group 2 are the rest. And in result Group 2 contains countries with an explicitly high role of English language. So, the break indeed looks like a language thing.

Nevertheless, language per se is not a big factor in development, so it doesn't bias the data on GDP in a systematic way. (You can also control the very first plot for the percentage of English-speaking population.)

Investing and failures in startups

The efficient market hypothesis got a bad press after 2008. Not surprisingly. It's a half-truth. For instance, what Robert Shiller identified as genuine mispricing Robert Lucas called a minor deviation. Also, the hypothesis has many interpretations, and here's one of them.

(data link)

On the left we have the mean of money that startups received over their lifetime. On the right is a rude measure of risk: the ratio of acquisitions to closed companies in the respective market. So, enterprise software has three successful acquisitions per one failure. I dropped "operating" startups because it's difficult to interpret their success.

The graph is interesting because clean tech gets much funding but has one acquisition per two failures. Analytics gets small funds (not so sexiest as it was called?), but gives very stable outcomes. These two are exceptions because in general funding match the risk measure. And so in other markets: it's enough for one product (like housing) to have abnormal pricing for the entire market to be under risk.

That is an attempt to make complex things embarrassingly simple, of course. For example, some may insist that average funding is a measure of capital intensity, not of competition among investors. Or what we should honestly calculate returns, as was done here. But it all seems to be half-truths, including this piece. We have to keep watching.

The cost of being in the top, or when Zipf's law breaks

Many things in the world have a Zipfian distribution. Xavier Gabaix recently attempted to explain how this pattern may emerge for the case of cities. Lada Adamic covered how Zipf's law goes online. The literature is vast because any field has its own examples.

But Zipf's law is a market-type pattern: the outcome of many agents making decisions independently. When you have a planner, it may break.

Here's an example:

(Data comes from generous Wikipedians.)

Zipf's law implies that here you must see a nice linear relations along the ranks. Instead, you see three lines: top 3 (I), top 10 (II), and 30 songs (III). The slopes of the lines are different in an interesting way.

Line II and III have the same slope and discontinuity between 10 and 11. (Actually, the discontinuity is between 9 and 10, but the 10th song is Katy Perry's 2013 release, while songs around it are older. Kind of an outlier.)

This discontinuity is the bonus for being in Top 10. If any magazine or website mentions YouTube most viewed videos, it's usually something like top 3 or 10 or somethings like that. Other songs don't get much attention, even if they're equally good.

But there's another effect: the bonus for taking the first place. This is what Line I and Line II are about. Psy goes through the roof of Zipf's law just as Bieber did before him.

So, why it's about planning? Well, without the media, there would be no tops. And tops are coordinating devices that say what we should watch, listen, and do first of all.

That is planning.

Changes in NYT-speak

The New York Times released a tool for tracking words in the newspaper's historical issues. Google had done this for all books published after 1500, but NYT is a reputable source, and it's interesting to compare the results.

Civil Rights Movement in the 60s

The African-American minority remains discriminated and after the 1960, but the media changed their policies in telling stories about it:

Democracy on War

Mentions of "democracy" hike during international conflicts to mobilize the population:

Ideological enemies

You have an instant peak as the enemy appears, but gradually the topic comes out of fashion. Also, Communism lasted a little longer, though it's nothing compared to the mass media's reaction to 9/11. That's interesting because the Cuban Missile Crisis and other Cold War conflicts were far more dangerous than anything Bin Laden could do.

The Times started preferring different wording for Nazis before Hitler disclosed his plans in 1939:

National priorities

After being a marginal topic for almost a century, security took over 12.5% of the Times' publications (while security in fact increased over the same period). Values like freedom remained at stable 2.5% for over 150 years:

Definitions of economics

A list of various definitions given to economics by major authors in the field over the last two and a half centuries. I think it's missing the most recent popular definition, which circulates among economists, that economics is the study of incentives. Anyway, the official positions are the following ones:

• James Denham-Steuart, An Inquiry into the Principles of Political Oeconomy (1767): The great art therefore of political oeconomy is, first to adapt the different operations of it [the state] to the spirit, manners, habits and customs of the people; and afterwards to model these circumstances so, as to be able to introduce a set of new and more useful institutions.
• Adam Smith, The Wealth of Nations (1776): "A branch of the science of a statesman or legislator" with two objectives: providing the people with ‘plentiful revenue or subsistence’ and providing the state with enough revenue to provide public services.
• Jean-Baptiste Say, A treatise on political economy, or a simple account of the way in which wealth is formed, distributed and consumed (1803): A simple account of the way in which wealth is formed, distributed and consumed.
• John Stuart Mill, "On the Definition of Political Economy; and the Method of Investigation Proper to It" (1836): "The science which treats of the production and distribution of wealth, so far as they depend upon the laws of human nature" or "The science relating to the moral or psychological laws of the production and distribution of wealth"
• Thomas Carlyle, Latter Day Pamphlets (1850): Dismal science.
• Alfred Marshall, Principles of Economics (1890): Political Economy or Economics is a study of mankind in the ordinary business of life; it examines that part of individual and social action which is most closely connected with the attainment and with the use of the material requisites of wellbeing.
• Lionel Robbins, (1932): Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses.
• Jacob Viner (probably): Economics is what economists do.
• Paul Samuelson, Economics (1948): what, how and for whom to produce goods and services.
• Paul Samuelson, Economics (1967): Economics is the study of how men and society choose, with or without the use of money, to employ scarce productive resources, which could have alternative uses, to produce various commodities over time and distribute them for consumption, now and in the future, among various people and groups in society.
• Albert Rees, International Encyclopedia of the Social Sciences (1968): [Economics] is the social science that deals with the ways in which men and societies seek to satisfy their material needs and desires.
• Paul Samuelson, Economics (1970): Economics is the study of how men and society end up choosing, with or without the use of money, to employ scarce productive resources which could have alternative uses, to produce various commodities and distribute them for consumption, now or in the future, among various people and groups in society.
• N. Gregory Mankiw, Principles of Economics (2012): The study of how society manages its scarce resources.

Nontrivial Economics

In his biography Surely, You're Joking, Mr. Feynman, Richard Feynman recalled a story about mathematicians at Princeton challenging him with counterintuitive possibilities. One example they gave him was an orange:

It often went like this: They would explain to me, "You've got an orange, OK? Now you cut the orange into a finite number of pieces, put it back together, and it's as big as the sun. True or false?"

And that was true for the special orange that we can keep cutting indefinitely. A mathematical orange. After some time spent listening such examples, Feynman just responded to each such case with "It's trivial!"—parodying his interlocutors.

It happens in economics, too. Mathematician Stanislaw Ulam famously asked Paul Samuelson to name an economic idea that is true and nontrivial. Samuelson took a long pause and suggested Ricardian comparative advantage as an example: a country with absolute technical advantage in producing any goods still benefits from trading with less efficient nations. Like the US buying vegetables from Liberia, in which agriculture still contributes more than a half to the GDP.

The definition of "nontrivial" is itself a trivial question: you can define it as you like and get the desired property. But generally, "nontrivial" is something that goes against popular opinion. Mathematicians hold an advantage here because in math you define your own rules, and other people remain too far from this world to make educated guesses. Economists pursue a different task: finding nontrivial results in the everyday world. If the results don't go against popular opinion, then what's the point?

And these nontrivial results happen to be more numerous than Ricardo's logic exercise in the 19th century. Each field offers its own examples:

Growth theory. Geography is a long-standing favorite in explaining the income gap between countries. The impact of bad weather on work is so natural, and who needs more? Still, the geographical hypothesis is far more advanced than, say, the assertion that countries are poor because of natural intellectual limitations of their populations.

In contrast to both these stories, the institutional hypothesis suggests endogenous causes of growth. It warns against the China hysteria: the opinion that this model is viable for economically advanced societies, and we soon may see the demise of democracy. Third, it suggests that direct financial aid to developing countries not necessarily improves these countries' growth prospects.

Macroeconomics. Anything that we find out about relations between inflation and employment, or the absence of thereof, is non-trivial. What about the efficiency of fiscal policy in economic downturns? Important arguments here cannot be discovered with just common sense.

Labor economics. In the well-known 2000 study of New Jersey and Pennsylvania fast food restaurants, David Card and Alan Krueger discovered that the minimum wage increases employment. The result was so counterintuitive for economists themselves that David Card had to clarify their position to explain political attacks that followed.

The wage example shows that most interesting findings basically inform us about our gaps in understanding. We had a too-simple model of labor markets: here is one reason to look deeper. Unlike mathematics, economics has little a priori knowledge. Whether the first derivative of a labor demand function is greater or less than zero depends on our ability to discover this function's parameters. When we discover these parameters, they necessarily surprise us compared to our previous experience. Non-triviality in science is just new facts uncovering old mistakes.

Plough, Fertility, and Growth

Alberto Alesina et al. have a paper called "Fertility and the Plough," in which they show the connection between fertility and agriculture. Countries with plough agriculture tend to have lower fertility rates because the plough, authors suggest, requires physical strength:

We find a negative correlation between historic plough use and total fertility rates today across countries and among first- and second-generation immigrants in the US. We argue that the explanation for this result lies in the fact that children (like women) are less useful for plough agriculture. The plough requires strength and obviates the need for weeding, a task particularly suitable for women and children. Therefore, where plough agriculture was practiced, the cost of having children may have been lower (because women were more confined to the home), but the benefit of children was also lower (since they were less useful in agriculture). We also show that, consistent with this explanation, societies that historically used the plough were also more likely to have a preference for fewer children.

There's one more important channel the plough affects future economic decisions. Since the 1960s, Gary Becker do important theoretical work on family and education. One major point of his work is that parents invest their time in children, and the fewer children they have, the more investment each child gets. This investment is an investment in human capital, and human capital is a necessary condition for growth.

What does it have to do with the plough? Consider a few points about a plough economy:

1. The plough reduces economic incentives of having more children. That increases parent investment per child.
2. Since children are less useful in the major economic activity, they get better chances of doing other tasks, including learning.
3. Since women participate less in farming, they do more household work, which also has positive spillovers for children.

Of course, points (2) and (3) are rather weak: children and women did a lot of household work, which offset the impact of being relatively free from agriculture. This is an intertemporal tradeoff between early jobs and education. Even now developing countries underinvest in their youth's human capital because parents don't have resources to invest or prefer money coming from children now to the money that may come in the future.

Point (1) partly explains a well-known negative relations between fertility and GDP:

The plough acts like this: plough agriculture → incentive to have fewer children → lower fertility → higher investment per child → higher human capital → higher output per capita. Other channels include, for instance: more educated females → more job opportunities → fewer children → lower fertility. And lower fertility reinforces investments per child, so that the plough story continues from the middle to encourage more economic growth.

Transition to Market in China

In my previous post, I described the agency problem of the Soviet political elite reforming planned economies of the newly formed independent states. The following graph compared the post-1991 transitory period in Russia and a few Eastern European countries, former members of the Eastern Bloc:

The Russian privatization program kept public property away from producers. It redistributed ownership through vouchers, which were securities granting the right to privatized property. After they got these securities from the state, people sold them significantly lower their potential price. Vouchers happened to end in the hands of a few. Much of other public property had been privatized without any vouchers. For instance, through fraudulent shares-for-the-loan auctions organized by the Russian government in 1995.

Such was the essence of market reforms in Russia. Meanwhile, China had their own market reforms started one and a half decades earlier. And the Chinese elite did an interesting thing. No, the central government didn't act like a benevolent dictator who gives away his power by transferring property to producers. Instead, it allowed independent producers to appear by themselves. First in agriculture, then in industrial production.

The rationale behind liberalization of the economy was the following one. If the government cannot encourage politically stable growth rates, let the market support it, where possible. The government neither competed nor shared property with the private sector. The market delivered additional value, which would otherwise turn out to be a deadweight loss of a centrally planned economy.

The Party not only preserved all of its property, but also gained indirect control over the private sector, which had been intensively growing over the last three decades. Naturally, it emerged as much more powerful interest group than it was under a pure planned economy. And it did so without country's output falling to 1/2 of its pre-reform level.

That shows how various coalitions within elites lead to different policy decisions and economic outcomes. In a critical moment, the Soviet hierarchy was unable to make forward-looking decisions and balance the interest of intra-elite factions. In contrast, the Chinese counterparts came out of the similar situation as winners, through with a very powerful competitor growing next to them.