Gini Index in Hong Kong

As proof that inequality in Hong Kong has worsened, the Gini index is cited as evidence.  The Gini index is a statistical measure of income inequality.  The number ranges from 0.000 for perfect equality and 1.000 for perfect inequality.

The two Gini indices being cited for Hong Kong are 0.434 in 1996 (see UNDP) and 0.522 in 2003 (World Bank).  The fact that the Gini index went up is taken as proof that Hong Kong has become more unequal.

I am sure that there are technical discussions about the interpretation of Gini indices in Hong Kong.  Rather than spending time to find something satisfactory, I'll just write up my own counter-spin.  This is an informal discussion, and it should be easy to follow.


Before I proceed to talk about the Gini index, I should say something about statistics.  Everybody seems to like the title of the book Lies, Damned Lies and Statistics.  But let us agree that we are not talking about fabricated data here in the manner of agricultural production statistics during the Great Leap Forward in China (see previous post).  Let us say that the raw data, which come in the form of household income distributions, are not subject to sampling or measurement errors.

Let us say we have the annual household incomes for all 2 million households in Hong Kong.  You cannot show people a list of 2 million numbers.  So what are you going to present as a summary statistic?

The simplest statistic is the arithmetic mean.  You add up all the household incomes and you divide in by the number of households.  This is the mean household income.  Actually, most statisticians don't like using that number because it is not 'robust.'

The most popular illustration of non-robustness is this.  You walk into a pub and there are 100 people in there.  You ask each of them what his/her household income is, you add the numbers up and you divide it by 100.  You look at the calculator: it says 100 million dollars.  You are astonished.  You certainly don't have that much money.  Almost everyone else is astonished too.  And then people see that Bill Gates is in the room.  Ah, the presence of one person (Mr Gates) has destroyed the 'typicalilty' of the arithmetic mean!

Statisticians would have preferred to use a median instead.  You take down the household income of all 100 people in the pub, you rank those numbers from high to low.  You take the average of the 50-th and 51-st case and that is the median household income (50% are higher and 50% are lower).  Now all of a sudden, that number has come down to earth.  The presence of Mr. Gates has no impact.  In fact, even if Warren Buffet, Felix Rohatyn and Teresa Heinz Kerry are in the room, the median is the same.  It would have to bring 50 'fat cats' in that room to move the median, which is therefore said to be robust against outliers.

Neither the mean nor median are 'wrong' in any sense.  They are technical definitions.  They are what they are.  The mischief comes when people decide to report one as opposed to the other.  Once you understand the properties of these numbers, you can detect the bullshit.

For example, when someone says that the mean household income has gone up 10% during President George W. Bush's first term, your alarm system should go off immediately.  Why did they use a known non-robust statistic instead of the more traditional median?  You hit the databases at the Bureau of Labor Statistics, and then you will find the median household income has gone down from US$45,000 to US$43,000 during this period.  That big Bush tax cut has been very good for the 'fat cats,' but the middle-class has not done well.  But it is necessary to present a rosy number for the large number of middle-class voters.  Hence, the mean was reported instead of the median.  Spin, spin, spin.  This is how the lies come about.


The Gini index is another technical quantity that can be calculated from the distribution of household incomes.  It is a measure of income inequality.  Usually, it comes with the explanation that 0.000 means perfect equality and 1.000 means perfect inequality.

Now, the ordinary readers will form these quick impressions:

Accordingly, when the Gini index went from 0.434 to 1996 to 0.522 in 2003 of Hong Kong, things are heading for the worse.  That is the quick impression.

But do you really want perfect equality anyway, or even move towards it?  You probably have not thought about it, and I will show you what it looks like.

Perfect equality means everyone has the same household income.  An example of this occurred in Year Zero.  You don't remember that?  In 1975, the Khmer Rouge proclaimed the start of their new state as Year Zero, and packed everyone off to the countryside.  Nobody owned anything anymore, and everybody worked in the fields from dawn to night.  Nobody received any income.  That was perfect equality, and a couple of million people died during that process.  A similar experiment is the People's Commune in China, where everybody lived in the same big dormitory, ate the same food (one big pot of thin rice soup with a few floating vegetables), worked the same way for the same hours and get paid the same piddling amount (note: the story further down about Nanjie is about a modern-day commune).

Beyond the brutality of these two examples, these and other experiments also inform us that perfect equality has some bad unintended effects.  If people are guaranteed the same income regardless of work effort, they are no longer motivated to work hard.  Division of labor also leads to discontent, because why should you be the one to go into the coal mine while I watch movies and write reviews for the same pay?  If everyone has an 'iron rice bowl,' then why would anyone put out any hard effort?  You can only light a fire under people by punishing some people for being social parasites (by docking their pay or putting them in jail without pay) while rewarding other people for working harder beyond expectations.  In other words, you are heading down the path of inequality into an unequal individualistic capitalism out of necessity because your society will sink into oblivion otherwise.

So I suggest that an increasing (or decreasing) Gini index should not be automatically taken as bad (or good).  There is a host of other considerations, and I will discuss some of those in the following.


It is rare to look at only one Gini index for one country at one moment in time.  People are usually interested in comparisons.  The most typical comparison is for one country at two moments in time, as the case is here (namely, 0.434 in 1996 and 0.522 in 2003 in Hong Kong).

What do you have to be careful about?

In 1996, there were fewer than 6,000,000 persons in Hong Kong.  Today, the population is about 7,000,000.  So the comparison of 1996 vs. 2003 is confounded by the presence of 1,000,000 additional persons.  Some of them are no doubt newborn children, but the majority of them are immigrants, mostly from China.  

And what about those new Chinese immigrants?  We know that many of them come for family reunification.  Since they don't have the requisite job skills for high-end or middle-level jobs in the local economy, they tend to require public assistance or take low-paying jobs such as street-cleaning.  So it is no shock that the Gini index ought to go up.

It is not known is that how much of the Gini index increase is due to the influx of new immigrants or some other factors.  The Gini index can be reduced quickly by expelling those recent immigrants who are getting public assistance.  This kind of cleansing would be inhumane and unimaginable, of course.  Meanwhile, it is more politically convenient to talk about how the rich is stealing even more money than before (which may be true too but you need better proof than just the Gini index).  You can reduce the Gini index by taxing the rich severely and re-distributing the revenue among the poor.  But the rich are no longer motivated to work hard (or else they take up citizenship in tax havens; after all, even Hong Kong's flagship bank HSBC is registered in the Bahamas).

Addendum:  In 2006, the Quality Migrant Admission Scheme was introduced in Hong Kong.  QMAS admitted persons to residence in Hong Kong on the basis of education, age, working experience, language abilities, family background and achievements (such as Olympic medals, Nobel prizes, etc).  By 2008, about 500 such persons have been admitted.  This is clearly an elite group that fall into the top income bracket.


The other type of comparison is between countries.  The Gini index of 0.522 for Hong Kong is shocking because it is close to the third-world country of Mexico (at 0.531) and even much higher than China (at 0.403) (see World Bank).  It must have been the ultimate slap in the face for Hong Kong to be 'worse' than even China (which is renowned for inequality as shown in the NYT article China's Elite Learn to Flaunt It While the New Landless Weep, The Guardian article A tale of two countries and the China Daily article Wealth gap Threatens Development).

But the Gini index conceals certain aspects of the situation, and they are very relevant if you want to compare the human development situations among countries.

The first aspect deals with the poverty incidences.

Consider two countries:

The first one has a median household income of US$10,000 and a Gini index of 0.400.
The second one has a median household income of US$10,000 and a Gini index of 0.400.

They must be equally well off, right?  It all depends on the poverty incidence, and this is defined differently by country.  If the first country was like the United States of America, where poverty is defined as an annual household income of less than US$12,000 for a family of four (husband, wife and two children), the poverty incidence may be over 70%.  If the second country was like China, where poverty is defined as US$1,000 for a family of four (husband, wife and two children), the poverty incidence may be lower than 10%.  Thus, the second country is substantially better off than the first, even though they both have the same median household income as well as Gini index.

When compared to China or Mexico, Hong Kong would do much better in terms of poverty incidence.  The World Bank in fact reports zero poverty there.  In Hong Kong, there are no desperate struggles to stay alive by selling blood or working in the coal mines as in China, or the shocking sight of 5,000 people scrambling to pick garbage in the Mexico City dump.

The second aspect deals with the purchasing power parity.

Consider the same example of the two countries before.  We take the second country, and we halve the income of everybody.  Here are the new data (note: the Gini index is not affected by a scalar multiplication, just as it would not be affected if you change the currency from US dollars to Hong Kong dollars, RMB, or whatever):

The first one has a median household income of US$10,000 and a Gini index of 0.400.
The second one has a median household income of US$5,000 and a Gini index of 0.400.

The first country must be twice as well off as the second, right?  It all depends on what you can do with the money.  In purchasing power parity, you define a standard basket of goods and services and you determine its price in each country.  (Note: A quick-and-dirty method is to use of the price of a Big Mac hamburger)  In this case, you just may find that US$5,000 in the second country may buy much more than the US$10,000 in the first one (because of lower taxes, fuel costs, labor costs, transportation costs, etc).

So what is the situation really among China, Hong Kong and Mexico in 2003?  Here are the Gini index, GDP (per capita) and then a GDP adjusted for purchasing power parity.

  China Hong Kong Mexico
Gini index 0.403 0.522 0.531
GDP (per capita) US$845 US$24,010 US$5,817
GDP (Purchase Power Parity) US$4,995 US$28,027 US$9,135

I believe that what even the poorest people in Hong Kong can purchase in terms of goods and services are far above and ahead of the average person in China or Mexico.  Thus, the poor people in China and Mexico can be said to suffer from absolute poverty, whereas the people in Hong Kong suffer from relative poverty.  This would not be reflected in the Gini index alone.

There are other types of statistics used for income equality: entropy, Coulter coefficient, Hoover coefficient, the Schultz coefficient (or the Pietra ratio), Kullback-Leibler Redundancy, middle-quintile share, coefficient of variation, maximum equalization percentage (or the Robin Hood index), median/mean ratio, interquartile range, Studentized range, top quantile shares, bottom quantile shares, top/bottom quantile share ratios, etc.  Each taps into some aspects of income inequality while ignoring others.

There are still many other aspects of human development that ought to be considered.  For example, the United Nations Development Programme (UNDP) uses a Human Development Index that includes three components: a long and healthy life, knowledge and a decent standard of living (see link).  Healthcare and education are not covered by the Gini index.

So the question of inequality is not simple.  The statistics are just technical definitions that present certain aspects of a complex situation.  They are what they are and they do not lie.  The spin and counter-spin occur when people select some statistics over others.  The Gini indices are what they are, but the inferences that can be drawn are a lot trickier.  I am not convinced from the Gini index alone that rich businessmen are colluding with crooked government officials to steal the people's wealth, or that Hong Kong is falling behind China and Mexico in any real sense.  You can talk about income inequality, declining growth and all that, but it requires something more than citing a couple of Gini indices.

(Los Angeles Times via the Weekend Standard)  Mao's utopia made real.  By Ching-Ching Ni.  January 22, 2005.

The sky is still black when the village loudspeaker blazes the revolutionary song The East Is Red. A three-story-high statue of Chairman Mao Zedong looms over a Tiananmen-like square flanked by giant portraits of the socialist all-stars: Marx, Engels, Lenin and Stalin.

A new day has arrived in this commune on China's central plains where residents enjoy free food, housing, healthcare, schooling - even free weddings and funerals.

As the rest of China struggles with mounting social problems brought on by two decades of turbocharged economic reforms and vanishing social safety nets, the decidedly retro Nanjie seems to have found the good life. It is the best known of a handful of villages that have returned to the country's communist past.

Its definition of the good life doesn't include what village bylaws deem "excessive living.'' Fancy restaurants, karaoke bars, music clubs and mahjong are all forbidden. And though Nanjie is free of crime and unemployment, it is also free of all the trappings of personal freedom that are part of life for most Chinese citizens today. At work, villagers study Mao quotations and attend self-criticism sessions. To marry, they participate in a group wedding held once a year in front of a giant portrait of the Great Helmsman. Then the village buses them off to a honeymoon in Beijing - because that's where Mao lived, a villager explained.

At home they sit on identical village-issued, natural-wood-frame sofas, watch the same TV sets and tell the time on the same Mao clocks that are adorned with bright rays lighting up his face and the slogan "Chairman Mao is human, not God. But Chairman Mao's thoughts are greater than God.''

"The only thing I had to buy myself was the microwave and these plastic tulips,'' says 57-year-old villager Wang Fenghua. Although the teachings of Mao serve as the moral compass for the 3,100 people of Nanjie, the real secret to its collective well-being is, well, capitalist: Two dozen village enterprises manufacturing all sorts of things - noodles, beer, pharmaceuticals. One even promotes "red tourism.''

"The widening gap between the rich and the poor. Corruption. Crime. What is the root cause of all these social ills? Privatization. Our goal is to realize communism. But communism needs to make big money - only big money can make communism better.

"There is no contradiction in that,'' says Wang Hongbin, the 53-year-old village leader credited with lifting the village out of poverty by marrying communist ideals with capitalist mechanics.

It started about 20 years ago, shortly after Beijing began testing the waters of market reform by dismantling people's communes and giving individuals the incentive to create their own wealth.

The people of Nanjie also tried their hand at privatization, but they didn't like what they saw. In their view, the entrepreneurs who built factories exploited workers to line their own pockets and gave nothing back to the community.

That's when Wang decided to reverse course by persuading villagers to give their land back to the collective so they could run businesses together.

He led the village to take over the factories and re-collectivize the land. He sold the chickens at his egg farm and moved into the village flour mill to help direct operations.

Today, Nanjie is home to 26 enterprises and joint ventures and employs about 11,000 laborers, making it the wealthiest village in Henan province. But as its de facto chief executive officer, Wang is no millionaire. He makes US$30 (HK$234) a month, a sum he set for himself and the rest of the cadres in his small-town utopia. That's about what a poor Chinese farmer earns but only about a third of what an urbanite makes.

It's all part of his "fool's'' theory, written prominently in red ink on the walls behind the village square: "Only fools can save China.''

"China needs fools. The world needs fools,'' the down-to-earth Wang says. "What does it mean to be foolish? Self-sacrifice.''

But Wang is also realistic. Thirty dollars is not going to get him the kind of talent he needs to run his export-driven businesses in an increasingly competitive marketplace. That's why he didn't think twice about hiring an outside brewery executive with a PhD at an annual salary of US$60,000.

His adaptability is supported by another of his beloved slogans: Wai yuan nei fang, or "Circle on the outside, square on the inside.''

The circle refers to the flexibility of the market economy and the square is the dogma of communism. Their coexistence represents the "third way'' that allows Nanjie to hold on to Maoist nostalgia without rejecting the benefits of capitalism.

"I hate capitalism. But I have to face reality,'' Wang says. "Communism is our highest ideal. It will never go out of style.''

Style is another factor that sets Nanjie apart. A typical Chinese village consists of a cluster of weather-beaten stone houses or mud huts surrounded by open fields where each family tills a small plot. In that sense, Nanjie is not really a village at all. With its neat rows of factory buildings and low-rise apartment blocks, it looks like a modern industrial park, or at least a suburban factory town far from any farmland.

Only about 70 of its villagers still work in agriculture, and that's with tractors on a large collective farm, not water buffaloes on tiny individual plots.

The streets are broad, spotless and billboard-free, but they are eerily empty, giving Nanjie the feel of Pyongyang, the North Korean capital. No one can own a vehicle, so the only cars or motorbikes that pass through are from neighboring towns.

The few stores sell mainly Nanjie-made products, such as instant noodles, cookies, beer, wooden combs and, of course, rows and rows of Mao memorabilia.

For former peasants who earned next to nothing plowing the land, the village code of conduct that forbids keeping a messy house and speaking behind people's backs is a small price to pay for cradle-to-grave welfare.

"No one is happier than us,'' says Li Ruiyu, 57. "We get three pounds [1.5 kilograms] of meat a week, and it's more than I can eat. When we get sick, they pay our bills no matter how much. When we die, all the village leaders attend the funeral and pay for the cremation and a box. What else can I ask for?''

Although the Nanjie version of socialism has been copied by a handful of villages around the country, experts say it's hard to imagine the idea reproduced on a large scale.

"For China to go completely back to a collective economy, that's impossible,'' says Zhong Dajun, an independent analyst based in Beijing. "It doesn't mean it can't exist on a smaller scale. But their future depends on how well they manage the village enterprises and whether they can keep themselves from being contaminated by the outside world.''

There are already some signs of trouble. Factory earnings have been falling from their peak in 1997. Cash-flow problems have led to work stoppages at some factories. During a recent visit, two noodle facilities were idle.

But for many residents, the experiment cannot afford to fail.

Most have nothing in their bank accounts (the village discourages saving money) and everything to lose if the collective goes bankrupt. Last year, Nanjie turned to red tourism as a new cash crop. An estimated 400,000 people are said to visit each year for study tours, and the village has begun charging them.

Not all visitors are believers. Consider the look on the faces of a group of college students as their guide explains how her village succeeded in wiping out all private possessions.

A collective gasp fills the room.

"I wouldn't want to move here,'' one 19-year-old student says. "It's too far removed from reality.''

(Ming Pao) Income distribution and the Gini Index in Hong Kong (本港的收入分佈與堅尼系數).  By Kwok Kwok-chuen (郭國全).  February 12, 2007.

[in translation]

... The Gini index is a number based upon household income in order to summarize income distribution.  If all families receive the same income, the Gini index is 0; if one family receives all the income and no other family receives anything, the Gini index is 1.

The Gini index is simple and direct, but it can be easily misinterpreted.  A basic and frequent misinterpretation is that if all families receive the same income, then the distribution is fair.  Yet, families have different number of members, different number of workers, different age distributions, different levels of education and so on.  Therefore, equality of household income is a different kind of unfairness.

Hong Kong has been moving from the large families of the past to more smaller families now.  As family size continues to fall, there is a slowdown in household income growth.  There are now many more elderly families or single senior citizens, and therefore the number of low-income families is rising quickly.  Many elders live apart from their children.  They live off savings or are supported by their children and they receive social welfare subsidies.  Had these elders continued to live with their children, those kinds of families would not be considered to have low-income.

The Hong Kong economy has always been changing and creating values in the form of more high-paying job opportunities.  There are more professionals and managers with university education, and this has affected income distribution in several ways:

1. The income gap between high-paying and low-paying jobs has increased.

2. As the proportion of high-pay employees grows, the Gini index rises.

3. The income gap among high-pay employees is greater than that among low-pay employees.

4. The median income of low-pay employees will decrease after middle-age whereas the median income of high-pay employees will increase after middle-age.  Therefore, the ageing of the population causes the income gap to grow.

During an economic downturn, it is more common for low-pay employees to face unemployment, underemployment or wage reduction than for high-pay employees.  This caused the income distribution to become more spread out between 1998 and 2003.  The economy bounced back in 2003, which increased job opportunities for the grassroots and the situation for the low-pay workers has improved.

The government also provides services in education, healthcare, housing and welfare which has the effect of re-distributing income.  Income and property taxes also re-distributes income.  Most Hong Kong families, including "middle-class families," should have higher incomes with these items were factored in than without.

Some commentators compare Hong Kong's Gini index with foreign data.  Data from different places are based upon different definitions.  The Gini index reported for Hong Kong uses ordinary family income along with welfare payments, but it does not deduct any income tax.  By contrast, many other places uses income data after various kinds of taxes have been removed.  There are also some places which will include the impact of government redistribution  Therefore, it is easy to come to erroneous conclusions if the Gini index for Hong Kong is directly compared with foreign data.

In conclusion, the analysis of Gini index and household income distribution must consider other factors such as society, family structure, population ageing, economy and others before a reality-based conclusion can be made.  For example, if the number of low-income Hong Kong families is increasing.  If the main reason is that the number of elderly families is growing, then how shall their standard of living be improved?  Would you improve work wages?  Or would you improve retirement guarantees and other senior citizen benefits?

(Ming Pao; Business & Management professor Francis T. Lui, HKUST).  March 21, 2007.

When the Statistics Bureau released certain census data last year, Ming Pao claimed that Hong Kong is turning into an M-shaped society (i.e. increases in the percentage of rich and poor people with a diminishing middle class).  Here are the raw household income data:
Less than HK$10,000 per month: 23.9% in 1996; 27.9% in 2006
HK$10,000 to HK$29,999 per month: 51.3% in 1996; 45.2% in 2006
HK$30,000 or more: 24.9% in 1996; 26.9% in 2006.
This would seem to indicate that Hong Kong is an increasingly unequal society.  But what is economic equality?  One definition is "equality in outcomes", which means that everybody should make about the same amount of money no manner how hard/easy they worked.  The other definition is "equality in opportunities", which means that everybody should have the same opportunity to compete.
Before 1978 when the economic reforms began, China was basically following "equality in outcomes" with the consequence that "the national economy was near collapse" (that was the official government description).  Deng Xiaoping opened up the economy and since people have to be motivated to compete, Deng tossed out the old anti-capitalism ideas and proposed the shocking idea of "Let some people get wealthy first."  Today, China's per capita GDP is 8 times that in 1978!  Still, economic progress has developed unevenly,  For the past decade or so, income is rising 7-8% among urban dwellers and only 4-5% among rural dwellers.  Although the rural farmers have improved their lot compared to the pre-reform years, the rural-urban income gap is rising.  Thus, the Hu-Wen government has to propose the policy of building a "harmonious society."
Hong Kong has never gone through a socialist style "equality of outcomes."  Instead, "equality of opportunities" was always the mainstream thought.  So how has Hong Kong society changed in terms of its socio-economic structure?
The best way to measure income distribution is not through the Gini coefficient, nor to examine the income gap between the richest and poorest classes.  When income increases while distribution is unequal, the Gini coefficient may rise; but when distribution becomes more equal, the Gini coefficient may also rise.  Therefore, while the Gini coefficient is useful, it should not be misapplied.
As for the income gap between the richest and poorest classes, it is not meaningful.  One of the economic goals of the HK SAR government is to attract wealthy or productive professionals to emigrate to Hong Kong.  Their presence will certainly increase the income gap, but they are quite welcome because they will generate employment and income for the poorer people.
The better statistical measure would be the actual distribution of household income.  The census data cited by Ming Pao above are the raw unadjusted data.  There are three adjustments that are necessary in order to make the 1996 and 2006 data comparable to each other.
First, the number of persons per household had changed.  In 1996, there were 3.3 persons per household on the average.  In 2006, the number has gone down to 3.0.  As household size gets smaller (e.g. by families moving apart), household income goes down.
Second, the consumer prices fell by 4% from 1996 to 2006.
Third, since 2000, Hong Kong has a mandatory provident fund in which persons earning less than HK$20,000 will have an additional 5% of the monthly income deposited into a special retirement account.  The employee wages should include this consideration.
Therefore, if we have to make a comparison of 1996 and 2006 household income data, we must make the three adjustments above (which results in adjustments of 10%, 4% and 5% respectively for a total of 19%).  This means that a household earning HK$10,000 per month in 1996 is equivalent to a household making HK$8,100 per month in 2006; etc.  Here is the adjusted household income distribution:
Less than HK$10,000 per month: 23.9% in 1996; 21.6% in 2006
HK$10,000 to HK$29,999 per month: 51.3% in 1996; 42.8% in 2006
HK$30,000 or more: 24.9% in 1996; 35.6% in 2006. 
These data do not support the hypothesis of an M-shaped society in Hong Kong.
One additional point to note is that although the percentage of low-income household has decreased, the size of the change is small.  But the reason should be obvious.  Over these ten years, about 500,000 persons immigrated from mainland China to Hong Kong.  In 2001, the median household income for new migrant families was only HK$6,100, far less than the total median household income of HK$18,000.  When one group of low-income families moved into middle-class, another group of poorer migrant families arrives.  Thus, the percentage of low-income households cannot decrease significantly unless Hong Kong decides to use education and economic productivity as the basis for screening immigrants.