A Statistical Thanksgiving: Global Income Distributions

In the United States, our Thanksgiving holiday is fast approaching. On this day, we give thanks for the good things in our lives.

For this post, I wanted to quantify how thankful we should be. Ideally, I’d quantify something truly meaningful, like happiness. Unfortunately, most countries are not like Bhutan, which measures the gross national happiness and incorporates it into their five-year development plans.

Instead, I’ll focus on something that is more concrete and regularly measured around the world—income. By examining income distributions, I’ll show that you have much to be thankful for, and so does most of the world!

Anatomy of the Income Distribution Graphs

To really understand incomes, we need to understand the distribution of incomes for whole populations. By assessing entire distributions, we can identify the most common incomes, probabilities for ranges of incomes, income inequality, and how all of these change over time and by location. Throughout this post, we’ll be using probability distributions and shading areas under the curve to find probabilities.

To graph these distributions, I’ll use probability distribution plots and parameter estimates calculated by Pinkovskiy and Sala-i-Martin (2009).*

This study found that the lognormal distribution best fits the income distributions. The lognormal distribution has two parameters, location and scale. Location describes how large incomes are and scale describes the spread of the values. Typically, both parameters get larger over time, which indicates both larger incomes and a larger spread between the rich and poor.

The distribution above shows the per capita income for the United States in 2006. Like all of the other income distributions you’ll see in this post, this one is right-skewed. Half the population falls within the shaded area between 0 and $28,788. This is typical of income distributions where the majority of values are jammed together on the left side and the distribution extends further to the right with a few people making very large amounts of money.

The x-axis is income “per capita” because it includes children and non-working adults, rather than just working adults. The intent is to show the amount of money that covers all individuals. For example, if a household of four has a total income of $80,000, each person in that house has a per capita income of $20,000.

Finally, all graphs display income in 2006 U.S. dollars, which allows you to compare across countries and time.

Why You Should Be Thankful!

Because you’re reading this blog, I can make some assumptions about you. You have electricity, and access to a computer and the Internet. Further, because you’re reading a statistical blog, I can assume that you have a higher level of learning. In fact, I can pretty much bet that both your income and wealth are higher than those of the majority of people on Earth, and probably very much higher than the global average!

Let’s take a look at a sample of income distributions from various countries to see how I reach this conclusion.

In the graph above, there is a cluster of developing countries on the left. Given that two of them are the rural populations of China and India, it’s easy to see how most people fall within this range. The United Kingdom and the United States have peaks that are shifted to the right and they stretch out much further to the right. In the middle is the Russian Federation, but it’s still well below the U.S. and UK.

China and the United States in 2006

Clearly, most people of the world fall far to the left on the income distribution. Let’s zoom in on two countries to show how the country you’re born in dramatically affects the probability of what your income will be.

I’ve shaded the curves for an income per capita that is less than $10,000. In China, this covers 98.3% of the population, and for the U.S. it covers 7.6%.

To create a global distribution, Pinkovskiy and Sala-i-Martin summed the income distribution curves for 119 countries using a population weighted method. They found that in 2006 the global mode for income was $3,300 and that over 50% of the world population had an income per capita of less than $5000.

Davies et al. (2008)* performed a similar analysis to look at the distribution of global wealth among adults in 2000. Wealth is net worth, or the value of all assets minus liabilities. In 2000, an adult needed wealth of just $2,138 U.S. dollars to be in the wealthiest half of the world, and needed $61,000 to be in the top 10%.

Being Thankful

If you’re like me, you might be surprised by the low values that are required to be in the top half, and higher, of the global distributions for income and wealth. Remember, these global distributions are right-skewed. Consequently, a high proportion of values are concentrated in the low end and the rest are spread out much further on the high end.

The last thing I want to do is to make this blog an exercise of patting ourselves on the back. Instead, I hope understanding the global distribution of wealth and income gives you a new perspective and reminds you of how much you have to be thankful for.

Let’s switch gears and use these distributions to assess global poverty and see how it has changed over the decades. How does the overall global welfare today compare to 1970? Do more people have their basic needs met? Is income inequality a big problem?

So instead of personal income levels, I’d like to assess something more meaningful: global well-being. How does the overall global welfare today compare to 1970? Do more people have their basic needs met?

To evaluate global well-being, I’ll assess how global poverty and income inequality have changed. There’s good news here!

Global Poverty Levels from 1970 to 2006

Depending on the organization and year, there are several official poverty lines for developing countries. I’ll use the $1 a day poverty line, which equates to US $312 in 2006 dollars. Using the other common poverty lines ($2, $3 a day, etc.) produces similar results.

Below are a couple of representative examples of developing countries to illustrate the global trend. The shaded region in the graphs show how the proportion of those living below the poverty line in Ecuador and rural China have dropped remarkably since 1970.

From 1970 to 2006, both Ecuador and China have reduced extreme poverty. Ecuador reduced it from 20.7% to 1.5%, while China saw reductions from 37.7% to 0.01%. These improvements are representative of overall world trends.

The same pattern applies to the United States. While it’s hard to match a single per capita income value to the different household sizes and incomes that the Census bureau uses to measure poverty, a per capita value of $5000 is close for most household sizes.

The graph shows that the percentage of those in the United States with a per capita income of less than $5000 has dropped from 5.7% to less than 1%.

To assess poverty changes on a global scale, Pinkovskiy and Sala-i-Martin combined 119 country distributions, and found:

Using the official $1/day line, we estimate that world poverty rates have fallen by 80% from 0.268 in 1970 to 0.054 in 2006. The corresponding total number of poor has fallen from 403 million in 1970 to 152 million in 2006. . . . We also find similar reductions in poverty if we use other poverty lines. . . We learn that not only are poverty rates falling, but that they are falling faster than population is rising.

Global Income Inequality from 1970 to 2006

While the poverty rates have dropped significantly over the past 30 years, income inequality within most countries has increased. I want to determine whether this negatively affects global well-being.

You can see the increasing inequality in the scale parameters that generally increase over time, which produces a wider spread in the graphs. There are more complex measures of inequality, such as the Gini coefficient, but I’ll illustrate the principle using the income ratio of the 90th and 10th percentile of earners in the United States.

The graph displays the per capita income values for the 10^th and 90^th percentiles in the United States. The ratio of the high to low incomes increases from 5.3 in 1970 to 6.6 in 2006. A similar pattern exists for most countries and indicates that income inequality is increasing within countries.

While increasing inequality may sound detrimental, keep in mind that it occurs during a time where both the proportion and absolute counts of people living in poverty are sharply declining. Also, counter-intuitively, while income inequality is increasing within most countries, it is actually decreasing globally.

Decreasing Global Income Inequality

The two graphs below use China and the United States as examples to show how this works. I picked these countries because they both have large economies and are representative of the global trend. Earlier, I compared these two countries to show how different they were in 2006. However, in 1970, they were far more different. Over the decades, China’s income distribution has gained ground.

These two graphs highlight the region where the two economies overlap in 2006. However, in 1970, there was almost no overlap. I shaded the range of $2500-$7500 for Chinese incomes in this overlap zone to illustrate the Chinese gains over time. In 1970, virtually no Chinese had per capita incomes in this range, while 53% were in this range in 2006. Also, note how the distribution for each country has a wider spread, which indicates that the within-country income inequality is increasing.

The global picture follows the same pattern: within-country inequality has increased but the between country inequality has decreased by an even greater amount. The net result is that global income inequality has decreased.

In short, income equality in 1970 was greater because more people were very poor. Inequality has increased since then because fewer people are living in severe poverty.

Perhaps the growing within-country inequality isn’t as bad as it first seems?

Pinkovskiy and Sala-i-Martin conclude, “We find that various measures of global inequality have declined substantially and measures of global welfare increased by somewhere between 128% and 145%.”

Progress but More Important Work Remains

All in all, I think this is great news and something we can all be thankful for! Poverty levels are sharply down and measures of global welfare are increasing. While income inequality is increasing, that simply reflects that fact that there are far fewer people living in poverty.

There is still a ways to go, because severe poverty has not been eliminated. In today’s world, severe poverty is generally found in Africa where the rates actually climbed much of the time and only recently began a slight decline. According to Pinkovskiy and Sala-i-Martin, “Welfare unambiguously deteriorated in 23 countries, totaling less than 5% of the world’s 2006 population.”

Looking beyond incomes, there are countries with human rights violations that are not reflected in these promising results. There’s also the issue of unequal rights and opportunities.

That said, these findings were a nice surprise to me because usually you only hear the bad news. The decrease in poverty is a longstanding trend that persists over decades, which is a great sign for the future!

Happy Thanksgiving!

References

Maxim Pinkovskiy, Xavier Sala-i-Martin, “Parametric Estimations of the World Distribution of Income“, NBER Working Paper No.15433, October 2009. I’d like to give Maxim Pinkovskiy a special thanks for sharing the parameter estimates with me as well as clarifying several points.

James B. Davies, Susanna Sandstrom, Anthony Shorrocks, Edward N. Wolff, “The World Distribution of Household Wealth“, United Nations University, Discussion Paper No. 2008/03.