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"Reality is not a matter of opinion. Raw opinion is like math errors or typos - understandable human error, but uninformative. To err is human, to understand is hard work."
- Alan Reynolds, Income and Wealth
In a recent Citigroup report by Chua Hak Bin [1] who suggests that a dual track economy is emerging in Singapore. In that report, Chua and his colleagues made an argument using the Gini coefficient to justify that income inequality has risen as a result, which we quote:
Income inequality has risen as a result. The Gini coefficient - a measure of income inequality - has climbed steadily to 0.52 in 2005 from 0.49 in 2000. This largely reflects the divergent household income trends, where the higher income quartile group saw larger income gains relative to the lower quartile groups.
The Gini coefficient has become a discussion topic among bloggers and journalists on the issue of income inequality in Singapore [2]. The question is: just how conclusive is the Gini coefficient in providing the silver bullet to illustrate income inequality? To make life interesting, we demonstrate with a series of counter arguments that the known variations of the Gini coefficient based on income are not robust enough as economic measures of income inequality. Instead, we advance an argument (mainly attributed to Reynolds [3]) that consumption among the different income groups is more reliable as a measure for inequality. (Updated 29 Jan 2007)
The Gini Coefficient in a nutshell
A picture paints a thousand words and the best way to describe the Gini coefficient is to look at the graph above (extracted from Wikipedia). On the horizontal axis, you start with the lowest income (first 20%) all the way to the highest income (80-100%). On the vertical axis, you measure the cumulative share of the total income measured between zero to a hundred percent. Intuitively, if you believe that all income and wealth are distributed equally among everyone in society, the Lorenz curve is characterized as a diagonal 45 degree line on the graph. In reality, we know that income and wealth are never distributed equally in society, so the resultant picture will be a curve drawn below the straight line, shaped like a bow and string. Taking the ratio between the area bounded by the curve and the area bounded by the straight line, we obtained the Gini coefficient.
The easiest way to understand the Gini coefficient is the following. If the gap between the bow and the string is wider, it means that the Gini coefficient is large which translates to a greater degree of inequality as a result. The best way to calculate this ratio is to use the income distribution of the households (raw income before transfer and tax), which is adopted by the Census Bureau. In fact, online calculators are provided to convert such figures into a single Gini coefficient. The Census Bureau in the US will compute out 14 different variations of the Gini coefficients for comparison. However, the most common type used by analysts is based on the conventional measure of money income.
When Gini can be misleading
There are some situations which the Gini coefficient makes a poor metric to look at inequality. To simplify the discussion, I will discuss some possibilities how it can fail considerably and propose a solution based on qualitative economics in the next section.
Since the Gini coefficient is a mathematical construct, one should note with caution how the metric is computed out from the data. Alan Blinder [4] demonstrated a simple counter example that there exist cases where you can get two different Lorenz curves with different shapes, but they yield the same Gini coefficient. Imagine the following situation when you have 3.6% for the lowest quintile (the really poor) in the construction of curve A and 0.6% similarly for the same lowest quintile for curve B (see appendix 1). However, if you start tweaking the numbers in the other quintiles, you will end up with the same Gini coefficient.
It is known that the Gini index (even different variations of the metric constructed from income) is sensitive to the changes in the middle of the earnings distribution rather than the tails. Hence it is difficult for us to gauge from the Gini index, who is the real poor and who is the real rich. The mistake most people make is that once the Gini index demonstrates that there is inequality, their immediate inference is that the poor is getting poorer. From Blinder's example, you can already see that it may be the percentage of the real poor is decreasing, but the Gini coefficient is still advocating inequality. This is the kind of inference made by some politicians, journalists and activists in the application of the Gini index to make a non sequitur judgement for inequality and income. Seriously, even if the percentage of the really poor is decreased, the Gini index can still reflect a larger inequality gap.
So, if the metric is ambiguous in its interpretation from a mathematical viewpoint, the onus is on how the economic data is selected. Most of the time, these coefficients are computed in pre-transfer payments (for example, the progress package instituted by the Singapore government) and pre-tax (before your income tax sets in). It is known that the Gini index (without taking tax and transfer money payments) is increasing in the US. Once if the coefficient is adjusted for taxes and transfers, a different picture emerges. In fact, the household Gini coefficient was reduced to 0.4 in 2004 [5]. So, the two questions which eludes many readers (including myself) from Chua's analysis on the Citigroup report, "How is the Gini coefficient computed? Does it takes into account with the pre-transfer and pre-tax data?" In fact, the Gini coefficient was computed using the per capital household income from work by the Department of Statistics, Ministry of Trade and Industry [6] and the Citigroup report made their interpretation based on that report. Without further information, one can fathom a guess that they did not take taxation and transfer money payments into account.
Scheherazade's Gini: Income or Consumption?
Given the ambiguity of the Gini coefficent, we note that the trend towards rising inequality are dependent on several factors:
- How do we choose to measure real income and the period of time which that takes place?
- Are we using the mean or the median average for the income capita per household?
- Do we take into account of any major event that might create possible distortions to the computation, for example, if Singapore has gone through a major tax reform or recalibrate the way how they calculate their metrics?
The central thesis is that the Gini coefficient is measured primarily on income. However, it is just a snapshot and does not reflect anything about the standards of living in society. Before I go to my next point, consider the following situations:
- A poor homeless and jobless man in the UK is getting 200 pounds (=S$600) a day through begging and social net, but spends all his money on acquiring drugs. He gets his food and accommodation from the social workers and the church.
- A family with middle class income is splurging their money beyond their means on buying luxurious goods, for example, a sports car.
- A young urban professional earning about S$6-10K, paying his car and condominum.
- A Singaporean PhD student studying in the US with his spouse and kid and earning less than $1.5K a month
Some of these cases reflect what income cannot measure. Inherently the PhD student's earning capability changes when he graduates with his doctorate. The poor homeless man is not spending any money on food and accommodation, but on something else. You will realize that income is a static measure and may not adequately reflect reality. However, consumption on the other hand, provides a better measure on the inequality issue. By studying exactly how the poorest 10% of the population is spending their money, you know why and how they cannot cope. For example, in poor families, they tend to have more kids and education constitutes a major cost in their monthly budget. If 50% of the poor population in the UK is spending their money in buying drugs, the problem with the policy makers is not to pay them more via the social net, but to tackle the drug problem instead.
Living standards are better measured by consumption rather than by income. Consumption constitutes the quantity and quality of each household's food, clothing, housing, transportation and entertainment. In fact, one year's income is not definitive enough to describe anything about living standards. The real measure should comprise of both the past and future income. Think about the mortgages and loans, which allows consumption to happen from expected future income. Two more arguments actually justify this choice of construction:
- A household's income can appear to be lower if somebody in the family is experiencing transition periods, for example, a job loss or illness, and to be higher if someone in the family experience a windfall through 4D and Toto. The consumption averages out over the years by selling assets or borrowing in difficult times and saving in good times.
- The life-cycle pattern to income from work and savings is another indication why consumption is a better choice. Young people start out with wages and salaries far lesser than what they earned as they approach middle age. In Singapore, a lot of people have no time to accumulate significant savings and have to borrow against their future earnings to afford a house, a car or other expenditure. Once they hit middle age, they will have accumulated some assets, and reinforce their assets by making investments. Finally, when they retire, their savings are drawn upon to finance consumption. Hence, over the entire life cycle, consumption is averaged out.
By constructing a Gini coefficient based on consumer spending and income, you get a better reflection of how inequality in society looks (see the footnote in [7]).
How does that look in Singapore?
In Singapore, when someone claims that the income gap is widening, it does not really mean that there are more rich and more poor people. It can also mean that the middle class is being squeezed because their expenditure is growing while their income is stagnating. Using the Gini to infer such arguments can lead to wrong conclusions about what the actual picture is. Getting a hold on our spending habits will provide a clearer picture on how this inequality really looks.
Acknowledgments: The author thanks Huichieh & Speranza Nuova for helpful comments to this article. The author also thanks Andy Ho in providing the report [1].
References and Endnotes:
[1] Chua Hak Bin, Lim Jit Soon and Huang Yiping, "Singapore: A Dual Economy", Citigroup Report, 25 Jul 2006.
[2] Speranza Nuova, Inequality and Magic Gini (also published in Singapore Angle: Perspectives); Yaw Shin Leong, Of Wealth and Income Equality; Yawning Bread, Sir, may I have the can please?; Texo.sg, Flapping over Gini; Seksi Matashutyrmouf, GINI; Kway Teow Man, A Whole Load of Gibberish; Andy Ho, "Rich will get richer, as will the poor", The Straits Times, Sep 12, 2006.
[3] Alan Reynolds, Income and Wealth, Greenwood Guides to Business and Economics.
[4] Alan Blinder, Commentary, in Tax Matters and Inequality, page 40.
[5] US Census Bureau, "The effects of Government Taxes and Transfers on Poverty".
[6] Department of Statistics, Ministry of Trade and Industry, Republic of Singapore, General Household Survey 2005, Statistical Release 2: Transport, Overseas Travel, Households and Housing Characteristics, chapter 3: Household and Housing Characteristics.
[7] In Chapter 8 of [3], Reynolds wrote a review on Gini index constructed from US consumption data. It demonstrated that the inequality only happened between the period of 1981 and 1986, and appears to be a cyclical phenomenon. From 1986 to 2001, consumption inequality declined and wage inequality was unchanged.
Appendix 1: Comparison of Income Distributions Producing the Same Gini Index (Source: Alan Blinder in Reynolds "Income and Wealth").
| Income Share of | Distribution A | DIstribution B |
|---|---|---|
| Lowest Quintile | 3.6 | 0.6 |
| Second Quintile | 8.9 | 11.9 |
| Middle Quintile | 15.0 | 15.0 |
| Fourth Quintile | 23.2 | 26.2 |
| Top Quintile | 49.4 | 46.4 |
| Approximate Gini | 0.423 | 0.423 |
Comments (9)
Interesting.
It's still an important figure, give us a sense of magnitude. We just need to keep in mind not to over-infer from it.
Posted by yizheng | January 25, 2007 1:01 AM
If I understood it correctly, the Gini Co-efficient purports to measure income gap i.e. how much more the well-off are earning compared with those in the lower income quintiles. Most people assume the gap will alawys be huge anyway and this, per se, is not the cause of social discontent.
Again, if I understood it correctly, you propose that the focus should be more on consumption. But, as you noted, this measures the standard of living which a particular society offers its members in each quintile. Standard of living is a different thing from income gap. So, in gist, are you simply saying that it is less useful to centre discussion on the income gap and more useful to centre it around whether the standard of living of lower and middle income groups have gone down or stagnated ? you
Posted by Wong Hoong Hooi | January 26, 2007 1:49 PM
Hoong Hooi,
The answer to your question is that even if you want to use income as an input data to your Gini and make inference, you need to factor the tax and transfer money payments to get a better sense of the number. The US Census Bureau showed that if you do take that into account, the income gap does not actually increase, in fact, it decreases.
On the point on standard of living, what I am proposing is to look at the consumption distribution instead to compute the inequality index as a comparative measure. The number that I am interested is: how money does the household spend per month and what is the distribution of that spending look like? If you know that a household of lower income tend to have more kids and the majority of the costs in the kids education, you can formulate your policy in such a way that the children in this low income household can receive a proper education to move up their income level later.
Here is just a thought experiment: suppose if a significant proportion in the middle class are spending beyond their means like buying a car, does it mean that they are really "squeezed" by the economic downturn or their expectation on life has changed? In fact, if you read the papers recently, the COE numbers are going down because there is a lack of car buyers. Perhaps, the populace is beginning to adjust to the economic realities of having a car. Knowing how they consume provides a more dynamic measure to how the inequality between different economic stratas really look like, than just looking at their raw income distribution (which does not really say much).
Posted by Bernard Leong![[TypeKey Profile Page]](http://www.singaporeangle.com/nav-commenters.gif)
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January 26, 2007 2:20 PM
If the focus is purely on income inequality, then it's not going to say very much. In particular, it won't say very much about any economic inequality that would be of serious concern. Presumably when people worry about economic inequality, they are worried that there is a big chasm between the rich and the poor and all the problems--perhaps to do with social justice even--attendant upon that. But if this is the implied background, then income is only one aspect of the set of things the inequality of which is of concern. At one point in my life, my income was a lot lower than my Dad's; now, my income is a lot higher than his (he has retired)--but it would be hard to imagine how there would be anything to write home about here. A millionaire (or heiress, or retiree) who does not work and is living the fine life purely on inheritance, savings or dividends could well have technically less income than me, and it would be bizarre to focus on income inequality as what's unequal between us. If the GINI measures only income inequality, then sure, it does its job; but we don't have much warrant to infer economic inequality per se. Basing the measurements on consumption, however, at least proxies the outcomes of economic inequality more closely--presumably when we do worry about the disparity between the rich and the poor, the concern is that the latter does not have access to goods and services that the former enjoy.
Posted by Huichieh![[TypeKey Profile Page]](http://www.singaporeangle.com/nav-commenters.gif)
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January 26, 2007 2:28 PM
Hi, could some economist make sense of the latest GST comment from PMLee? Apparently we do not need the GST increase now, cos we still have money and economy is doing well, but we need it so that we can invest more in future? I thought it was to help the poor - but it is for further investment in future? I heard that chap was a Oxbridge Grad???
"Is it better to take your medicine sooner or stretch it out? Take medicine once or two times? I prefer to make my medicine early, why? This is something we need to do, once we have done it, we can move on; we have the resources to have the revenue from the GST that we use, for all the things we want, further investments, etc"
Thanks anybody.
Posted by tc | January 26, 2007 9:00 PM
The writer takes a wrong turn when saying this sentence "Instead, we advance an argument (mainly attributed to Reynolds [3]) that consumption among the different income groups is more reliable as a measure for income inequality." Strike off the word "income" from that sentence, and it may make some sense.
Measures based on consumption may arguably give a better sense of the inequality in living standards than measures based on income (though one may counter that asset accumulation from savings should be captured in a living standards measure).
But measuring income inequality has its own uses. Chua Hak Bin is trying to illustrate that the market (together with changes in CPF rates and limits) is rewarding people in increasingly unequal ways for their work efforts. For that purpose, a measure based on consumption is inferior to one based on income.
As for the deficiencies of the GINI itself, they are not anything to worry about, so long as people who are really interested can get to eyeball the associated Lorenz curves. GINI is a convenient summary measure. Quintiles state a little bit more and summarize less. Lorenz curves tell you everything.
Posted by Jason | January 27, 2007 3:55 PM
Jason,
Thanks for the note.
I have make the correction.
However, the question which I think that Hak Bin needs to answer is how he construct his arguments from the income distribution. Do note that the numbers and graphs are taken from the General Household Survey 2005, and the raw data is not present in the survey itself. Unless the income distribution presented by SingStat takes into account the changes you speak of, it is not possible to use those income distribution to infer anything.
I do agree with you on the point that Hak Bin's point can be due to the system rewarding people unequally. What will be an appropriate solution? Is it the workfare bonus that the government has been talking about?
Posted by Bernard Leong![[TypeKey Profile Page]](http://www.singaporeangle.com/nav-commenters.gif)
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January 29, 2007 12:05 PM
I don't remember writing about any changes :)
One thing that I should probably mention. Sometimes a measure is systematically biased in one direction. However, if the size of this bias doesn't shift around very much over a period of a few years, then a change in the size of this measure can still inform about the change in the underlying phenomenon. This is because the systematic error gets largely differenced away when you compare two years. This is why GDP is a flawed measure, but most people are quite comfortable with using changes in GDP to reflect how the economy is doing.
I think you can say that this works to some extent for GINI as well. Thus, I would not focus on the fact that GINI in 2005 was 0.52. Rather, I would look at GINI having increased from 0.49 to 0.52 in five years as indicating something serious is happening.
Anyway the General Household Survey's findings on income inequality are available online (just google). Chua Hak Bin merely copied the numbers to illustrate an increasing trend in inequality from the rewards of the marketplace. There are some quirks in the way the numbers are calculated (see below), but overall, I do not think the picture is all that different if you use other measures.
Some quirks:
* the incomes are that from work only i.e. excludes investment returns and capital gains.
* households are ranked (something that has to be done to construct the Lorenz curve) by per capita incomes from work. This implicitly weighs children and old folk equally. This also screws up the intention of using the numbers as a measure of what markets are rewarding (ok, ok labour force survey will be better for that issue :P )
* a different, also frequently used measure of inequality ( the ratio of top 20% to bottom 10% in income) is presented, and the trends are if anything scarier than the picture obtained from the GINI. In 2000, the top20/bottom10 ratio was 20 times. In 2005 it was 32 times.
Posted by Jason | January 29, 2007 9:18 PM
An interesting article by Brad Delong on inequality -> http://delong.typepad.com/sdj/2007/01/what_kinds_of_i.html
Posted by NoName | February 2, 2007 10:16 PM