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## Step Right Up and Pick a Country, Any Country

Let us examine how economic growth alters the way we observe and think about the “distribution” on income within a country. Below I present four examples and for each example I would like for you to think about which country you would “prefer.” What do I mean by prefer? You can think of it as which country you’d rather live in, or which country you think is somehow “better” according to a normative metric of your choosing.
Scenario #1
Two identical countries have the same initial income and distributions. In both country A and country B the poorest 40% of residents produce and earn 36.3% of income.
• Country A grows by 9%
• Country B grows by 18%
• Country A’s income distribution is more unequal – the poorest two-fifths now earn “only” 33.3% of the total income.
• Country B’s income distribution has also become more unequal – the poorest two-fifths earn 30.3% of the total income.

So, both economies grew

• Economy B grew faster
• Both became more unequal
• Economy B became more unequal

Which do you prefer?  The initial condition, Country A or Country B?

Scenario #2

Two identical countries each start with the  same workforce: in each country 10% work for \$2 a day (high wage) while 90% work for \$1 a day (low-wage)

• Country C sees its wage distribution change to 20% high earners and 80% low earners
• Country D sees its wage distribution change to 30% high earners and 70% low earners

So, in both countries larger shares of workers are in high paying jobs after the change. Which do you prefer?  The initial condition, Country C or Country D?

Scenario #3

Two identical countries each have the same amount of poverty. In each country the poorest 40% of residents earn \$40 per week.

• After a change, country E experiences no change for the poorest 40%, they still collectively earn \$40 per week.
• After a change, country F experiences no change for poorest 40%, they still collectively earn \$40 per week.

So, in both countries experience similar outcomes. Which do you prefer?  Initial condition, Country E or Country F? Does it make sense to even ask?

Scenario #4

In each country we know people’s current incomes and their former incomes. Comparing income shares before and after a change we learn that the poor lost share of average income in both countries and we also learn that the non-poor gained share of average income in both countries.

• Country G: the difference between average share gained by non-poor and average share lost by poor increased by 3.9%
• Country H: the difference between average share gained by non-poor and average share lost by poor increased by 4.7%

The poor lost income shares in both countries.  However, Country H had a more disparate mobility experience than Country G. Which do you prefer: the initial condition, Country G or Country H? Based on what you heard and given the AVAILABLE data I provided you with, can you tell me which condition you prefer in each of these cases?

The PUNCH LINE of course is that each of these examples came from the same underlying data.

• Country A, C, E, G are the same country (call it Wintercowistan)
• Country B, D, F, H are the same country (call it Bastiatistan)

I set it up so that each country has 10 residents. The initial income distribution in each looks like {1,1,1,1,1,1,1,1,1,2}. Suppose Wintercowistan pursues a particular strategy that delivers a new income distribution that results in the following pattern of wage earning:

• Wintercowistan:  {1,1,1,1,1,1,1,1,2,2}

Suppose also that Bastiatistan pursues a different growth strategy that produces the following pattern of wage earbnings:

• Bastiatistan changes to {1,1,1,1,1,1,1,2,2,2}

Let’s examine what happens to various measures in each of our two countries.

Growth in Income

• In Wintercowistan, income grows from \$11 to \$12.  So, income grows by \$1/\$11 or 9%
• In Bastiatistan, income grows from \$11 to \$13.  So, income grows by \$2/\$11 or 18%

Income Share of Poorest 40%

• In Wintercowistan, the poorest 40% initially earn \$4 of a total of \$11 (36.3%).  Later, these 40% earn \$4 of a total of \$12 (33.3%).
• In Bastiatistan, the poorest 40% initially earn \$4 of a total of \$11 (36.3%).  Later, these 40% earn \$4 of a total of \$13 (30.8%).

Percentages in Low and High Wage Jobs

• In Wintercowistan, initially 10% of workers are in a high wage job and 90% in low wage jobs.  Subsequently, 20% in a high wage jobs and 80% in low wage jobs.
• In Bastiatistan, initially 10% of workers are in a high wage job and 90% in low wage jobs.  Subsequently, 30% in a high wage jobs and 70% in low wage jobs.

Average Incomes of Poorest 40%

• In Wintercowistan, the poorest 40% earn \$1 per hour each for a standard 40 hour week.  Each worker earns \$40 per week, so average income is \$40.  They are in the same situation after reforms (at least in the short-run).
• In Bastiatistan, the poorest 40% earn \$1 per hour each for a standard 40 hour week.  Each worker earns \$40 per week, so average income is \$40.  Same they seem to be in the same situation after the  reforms.

Income Mobility Experiences of Poor and Non-Poor

Consider that \$2 in wages means that you are non-poor and that \$1in wages means that you are poor. Also assume that those who earned \$2 in the  initial state of the world keeps it after the reforms.

• In Wintercowistan, the income changes can be summarized as follows:
• 8 poor people do not have incomes change
• each initially earns \$1 of \$11 total (9.1%)
• after reform, each earns \$1 of \$12 total (8.3%)
• So, poor lost 0.8% of the overall share of income
• 1 poor person’s lot is improved
• she initially earns \$1 of \$11 total (9.1%)
• after reform, she earns \$2 of \$12 total (16.7%)
• So, this poor person, now non-poor increased her share of income by 7.6%
• 1 non-poor person’s lot remains the same
• she initially earns \$2 of \$11 total (18.2%)
• after reform, she earns \$2 of \$12 total (16.7%)
• So, this non-poor person lost 1.5% of the overall share of income
• The two final non-poor people average an increase of 3.1% (i.e. average 7.6% and -1.5%)
• The 8 poor people lost 0.8% of the share of income
• So, the average share increase for the non-poor was 3.1% and the average share decrease of the poor was 0.8%,  so the total change in the difference in the share of income held by the non-poor versus the poor is 3.9%
• In Bastiatistan, the income changes can be summarized as follows:
• 7 poor people do not have incomes change
• each initially earns \$1 of \$11 total (9.1%)
• after reform, each earns \$1 of \$13 total (7.7%)
• So, poor lost 1.4% of the overall share of income
• 2 poor persons lot’s are improved
• they initially earn \$1 of \$11 total (9.1%)
• after reform, each earns \$2 of \$13 total (15.4%)
• So, each poor person, now non-poor increased her share of income by 6.3%
• 1 non-poor person’s lot remains the same
• she initially earns \$2 of \$11 total (18.2%)
• after reform, she earns \$2 of \$13 total (15.4%)
• So, this non-poor person lost 2.8% of the overall share of income
• The three final non-poor people average an increase of 3.3% (i.e. average 6.3% for two people and -2.8% for one)
• The 7 poor people lost 1.4% of the share of income
• So, the average share increase for the non-poor was 3.3% and the average share decrease of the poor was 1.4%, so the total change in the difference in the share of income held by the non-poor versus the poor is 4.7%

I suspect that the different feelings you have about each of these countries depends on what you calculate for each country. Your opinions on development, economic growth and modern economic outcomes, and whether it is even occurring at all depends on this as well.  My sense is that half of my students would pick Country A over country B from scenario #1. When presented with scenario #2 virtually all of them select D. Imagine if instead of showing summary statistics I displayed the following full population of data of what is going on, economically, within each country as follows:

I now ask you one last time, which country do you prefer?

a)   {1,1,1,1,1,1,1,1,1,2}

b)  {1,1,1,1,1,1,1,1,2,2}

c)   {1,1,1,1,1,1,1,2,2,2}

Did your answer change based on how the data were processed? What does this tell you about how we present information on the distribution of income for an economy of 311 million people? Of course, income distributions do not change this cleanly, as some of the 2’s may become 1’s and sometimes new 3’s enter the distribution or sometimes new 0.5’s enter the distribution. But you ought to keep this exercise front and center to consider how such simple changes translate into changes in these measurable statistics.

### 3 Responses to “Step Right Up and Pick a Country, Any Country”

1. Rod says:

I’d rather live in a country with the fastest-growing economy, where opportunities for advancement abound, than in a slow-growing economy where my basic needs are underwritten by the government.

I’m now 66, and it’s hard for a person like me to get an entry-level job that would be a first step toward a new career. But my opportuniites are not limited by Walmart’s hiring policies: I can always go into business for myself and take advantage of a high-growth economy. Even if the economy stinks, maybe I can go into the currency business and sell gold and cigarettes to people who don’t want to hold Federal Reserve Notes for longer than a day or two. Maybe I can corner the wheelbarrow market!

2. Rod says:

I would argue that there are very few really poor people in the United States, and that many of the really rich people are self-made men or women, and that they’ve gotten rich through a combination of ambition, intelligence and hard work.

Many liberals/progressives (pick a term) I know think there is a “system” in this country that has to be overcome in order to deliver “social justice.” In the system, they say, an “old-boy” network of white men dominates society and ensures that generations and generations of a privileged class become financially successful, whereas those outside the system are perennially kept from getting ahead regardless of their ambition, intelligence and hard work. Thus a large part of one’s financial success is unearned and unjustly gained. Only government can right these wrongs through a combination of regulation and outright wealth redistribution.

You’ve noted in earlier posts that the percentage of workers earning the minimum wage is very small — three percent? ( I forget the figure, so I would probably flunk the pop quiz on this one) and not at all what most people would guess. My own experience as an employer is that I’ve always had to pay more than the minimum wage to attract and keep employees who will do a job right and not cost me more money than I am paying them. Indeed, most of my employees who were smart and hard-working enough to master the job they did for me eventually moved on to bigger and better jobs.

I joke now about selling everything I own now and converting it into Kruggerands, canned food, guns and fishing tackle, plenty of ammo and a sailboat. But then I wonder, after financial collapse and revolutionary disorder, where would I sail to to spend the rest of my life? The Cayman Islands? They have no armed forces of their own, so they’ll always exist as a country at the pleasure and consent of some nation that has an army and a navy.

3. […] This post is an outline of my lecture notes on the basics of measuring inequality. […]