Statistically, How Thankful Should We Be? Part 1

A look at global income distributions

Published: Tuesday, November 19, 2013 - 10:44

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 those data into its 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 must 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.

To graph these distributions, I’ll use Minitab’s 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.

The x-axis is income “per capita” because it includes children and nonworking 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 column, I can make some assumptions about you. You have electricity, and access to a computer and the Internet. Further, because you’re reading about statistics, 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 farther to the right. In the middle is the Russian Federation, but it’s still well below the United States and UK.

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 percent of the population, and for the United States, it covers 7.6 percent.

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 more than 50 percent of the world’s population had an income per capita of less than $5,000.

Davies et al. 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 percent.

Closing thoughts

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 farther on the high end.

The last thing I want to do is to make this 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.

In part two, I'll switch gears and use these distributions to assess global poverty and 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?

About The Author

Jim Frost

Jim Frost is a statistical technical communications specialist at Minitab Inc. He has a background in a wide variety of academic research and became known as the “data/stat guy” on research projects that ranged from osteoporosis prevention to quantitative studies of online user behavior. At Minitab, he is a technical writer who helps people use Minitab software to gain insights from their own data, whether they’re working in quality improvement, academic research, or another field entirely. He also writes in The Minitab Blog about various experiences and practical knowledge he’s learned along the way that may help others’ research endeavors.