# Median Household Income. The Truth. Nothing But the Truth. The Whole Truth. And the Statistics

There is a great vignette in the book Moneyball, illustrating the gulf between what actually happens on a baseball field and what the statistics reflect. Imagine the following situation…

Two outs. Runner on third. The pitcher throws his best pitch, fools the batter who hits a lazy fly ball towards right-center field. But the right fielder is a guy like Albert Belle — all bat, no range, no glove. The Belle-ish outfielder can’t get there and the lazy fly ball drops in for a clean single and the runner scores from third.

Now, what really happened? The pitcher succeeded. He made his pitch and got the lazy fly ball he wanted. The batter failed. His job was to hit the ball hard and he didn’t. He got fooled and hit what should have been an easy fly ball. The outfielder failed. His lack of range and bad jump on the ball caused the hit and is responsible for the run scored. The front office who decided that the bad defense was a good trade off for the big bat might be guilty too.

But what do the statistics record? The Batter gets rewarded with a hit, and with a run batted in. The Pitcher gets saddled with giving up a hit and an earned run. The front office and the outfielder get off scot-free.

This was brought to mind by James Pethokoukis’ recent post about Median Household Earnings. Does this statistic always prove illuminating? Does it give us clear picture of what is really happening? Or is there a bad outfielder getting off scot-free in there somewhere? Let’s do some thought experiments and see what can happen.

Lets begin by constructing a simple economy with five households. Here they are with their Household Earnings:

1. 100,000
2. 80,000
3. 60,000
4. 40,000
5. 20,000

Ok. Median Household Earning is \$60,000 and the gap between the top and bottom households is \$80,000. Remember, this is Household Earnings.

Let’s now suppose that two things change. A). Everybody gets a 10% raise. B). Household 3, a husband and wife each earning \$30,000, gets divorced. What does our income distribution look like now? Remember … from an earnings perspective, everybody is better off. They all got a 10% raise.

1. 110,000
2. 88,000
3. 44,000
4. 33,000
5. 33,000
6. 22,000

Old Household #3 is now two separate households — 4 and 5 — each earning 33,000. But even though everybody got a 10% raise, Median Household Income went down. Median Household Income has now plummeted to \$38,500! And the gap between the top and bottom households has grown to \$88,000. The statistics would have you believe that things are on an alarming downward trend.

Let’s go back to the start again and try something else. We started here…

1. 100,000
2. 80,000
3. 60,000
4. 40,000
5. 20,000

Now suppose that things change. But what happens is that times are hard, no one gets a raise. In fact, Household #5 — the recently graduated from college child of Household #4 gets their hours cut to part-time. They now only earn \$10,000. They can’t afford their apartment and move back with the parents. What does this new income distribution look like?

1. 100,000
2. 80,000
3. 60,000
4. 50,000

Ok. New Median Household Income has now grown to \$70,000 and the gap between the top and bottom households has shrunk to \$50,000. The statistics would have you believe things are going swimmingly!

Median Household Income statistics really have two distinct variables embedded in them — income and what we call a Household. Because we can’t tell what is going on with the Household composition, the statistic is kind of useless.

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1. Member

There was one year my household was in the top 5%. Why? Because I left one company and got a big payout (56 weeks’ pay), found another job almost immediately at a raise and got the equivalent of 120 week’s pay (at the old rate) got paid for two books (10 weeks’ pay) and my son (who was still living at home) graduated from college and got an engineering job that paid about 60% of my pay for 8 months. Which means my household – in one year – got about 290% more than we had the year before (or the next year). Especially since my son moved out at the start of the next year.

• #1
• September 13, 2018 at 1:26 pm
• 10 likes
2. Member

Well that’s the problem with math and statistics the devil is in the details.

• #2
• September 13, 2018 at 1:35 pm
• 4 likes
3. Contributor

Well that’s the problem with math and statistics the devil is in the details.

My father quotes his stats professor: “If you torture numbers enough, you can make them say anything. If you are really good, you won’t leave fingerprints.”

• #3
• September 13, 2018 at 1:45 pm
• 12 likes
4. Member

There was one year my household was in the top 5%. Why? Because I left one company and got a big payout (56 weeks’ pay), found another job almost immediately at a raise and got the equivalent of 120 week’s pay (at the old rate) got paid for two books (10 weeks’ pay) and my son (who was still living at home) graduated from college and got an engineering job that paid about 60% of my pay for 8 months. Which means my household – in one year – got about 290% more than we had the year before (or the next year). Especially since my son moved out at the start of the next year.

Sounds familiar. I was an independent consultant for most of the Obama administration (and before). The level of business I managed to generate typically lagged about 2-3 years behind the general economy. I did a lot of piece work over the years – 5 weeks on this project, a few weeks with nothing, 6 weeks with the next and so on. Along comes 2010. I not only landed a year long project (no dead spots between projects) but also had 2 sub-contracted consultants on the project that I was able to profit a small amount from.

So in 2010 I was officially an Obama Millionaire (gross exceeded \$250K). My wife who has been a homemaker/stay at home mom most of our marriage was working a part time position at the church we were attending so was bringing in some additional. We may not have hit the 290% but it was probably 125% higher than normal.

Starting in 2011 the Recession started catching up. That year household income was perhaps 15% higher than normal (but the tax bills from 2010 were also hitting, so it felt like a lot less). 2012 was maybe 80%. 2013 was about 75%, 2014 60%, and 2015 was a dismal 40% of what “normal” had been through 2009. Finally surrendered and went back to work for someone else first of 2016.

Mentioning all of this to point out additional issues with “Median Household Income”. On a year to year basis, my household alone was all over the map. If you measured once every 5 years you would have seen data points of approx \$300K in 2010 and \$50K in 2015. Definitely a worthless statistic in my eyes.

• #4
• September 13, 2018 at 1:56 pm
• 7 likes
5. Member

The “household income” issue is one of the challenges of public policy. Average (or median, I don’t remember which) has been declining for a while, which could contribute to a decline in median household income. But, since people sometimes combine into households in a self-directed method of improving living situations, we wouldn’t want to focus public policies onto individual incomes if that would involve creating policies that discourage people from rooming together for the purpose of improving their combined situation (two people can usually afford a two-bedroom apartment that is nicer than that one-bedroom apartment each of them could afford on his own).

• #5
• September 13, 2018 at 2:01 pm
• 6 likes
6. Member

Well that’s the problem with math and statistics the devil is in the details.

My father quotes his stats professor: “If you torture numbers enough, you can make them say anything. If you are really good, you won’t leave fingerprints.”

I’m stealing that!

• #6
• September 13, 2018 at 2:18 pm
• Like
7. Member

I have a simple rubric. If a statistic uses the word ‘household’ I stop paying attention.

• #7
• September 13, 2018 at 2:31 pm
• 5 likes
8. Member

When you look at statistics, the theory is that the anomalies even out over a sufficiently large population. That may be true for events like marriages and divorces. The problem with using median income is that there are events where the anomalies all tend to run in the same direction – such as high income workers retiring while new workers enter the workforce at the bottom level, or large numbers of low wage immigrants entering the labor pool and skewing the median downward. Every individual in the economy may be doing very well, but if you keep bringing in new workers at the bottom level the median will be stagnant or even decrease.

• #8
• September 13, 2018 at 4:30 pm
• 5 likes
9. Coolidge

Excellent post. Nice baseball analogy, and a simple example that dramatically shows the problems with the statistics.

The use of “household” isn’t entirely worthless though. In your second example, the couple that got divorced may individually been making 10% in income, but maintaining two households will cause their expenses to go way up from where they were before. So they really are worse off even though they’re making more money. The same is true in your third example. Even though the one household got a 50% pay cut, he also eliminated all his expenses for his own house. So the parents’ household, which he is now a part of, sees their income to expense ratio go up and financially as a household they’re better off. (There are some big non-economic costs though that no statistic about money will capture.)

• #9
• September 13, 2018 at 6:06 pm
• 1 like
10. Coolidge

Ekosj: Household composition, the statistic is kind of useless.

The original article acknowledged this limitation on household composition. If it didn’t I would have pointed it out. Variation in household composition does not make household statistics “useless”, it just means we need to understand the limitations. All of economics is multi-varaible statistics and those stats useful to the point they are useful.

• #10
• September 13, 2018 at 6:28 pm
• 1 like
11. Member

Ekosj: Household composition, the statistic is kind of useless.

The original article acknowledged this limitation on household composition. If it didn’t I would have pointed it out. Variation in household composition does not make household statistics “useless”, it just means we need to understand the limitations. All of economics is multi-varaible statistics and those stats useful to the point they are useful.

If you laid all of the economists in the world end to end, they’d never reach a conclusion.

– George Bernard Shaw

• #11
• September 13, 2018 at 6:58 pm
• 2 likes
12. Thatcher

I read somewhere that a good portion of the “decrease” in household incomes was due to a decrease in the size of households.

Another example: When my daughter was in High School, she made about \$4000 a year part time. The household income was \$104,000. Then she went to college and got a job paying about \$10,000 a year. The total income of the same group of people went up, but our average “household” income went from \$104,000 to \$55,000.

• #12
• September 14, 2018 at 1:39 am
• 2 likes
13. Member

Good examples. Thanks. The problem isn’t the statistics it’s the use of aggregates, averages, medians, they chop off and bury the important information. This is one of the reasons the government can’t manage an economy, regulate a sector and is almost always wrong. We can’t collect information on the economy without using averages and aggregates so the government is always acting blind, even were we not in a Hayekian world in which the important information can’t even exist.

• #13
• September 14, 2018 at 7:33 am
• 1 like
14. Member

Good work @ekosj. I had to chuckle with your second example. Obama and his crew must have used that one a lot. I am surprised the old saw has not yet been pulled. “Figures don’t lie, but liars can figure.”

• #14
• September 15, 2018 at 11:56 am
• 2 likes
15. Inactive

And of course, all your decent analysis gets blown to heck if someone like Bill Gates is included in the sample. Suddenly everyone in a community is a gazillion times better off, based on their yearly income averages.

• #15
• September 16, 2018 at 1:37 pm
• Like
16. Inactive

I read somewhere that a good portion of the “decrease” in household incomes was due to a decrease in the size of households.

Another example: When my daughter was in High School, she made about \$4000 a year part time. The household income was \$104,000. Then she went to college and got a job paying about \$10,000 a year. The total income of the same group of people went up, but our average “household” income went from \$104,000 to \$55,000.

Hmm your example must be the explanation for how it is that kids in their late teens feel they deserve so much… At the time my son was at such an age, I thought it was due to his not realizing the situation, but apparently they realize their \$55K worth down to the last dime.

• #16
• September 16, 2018 at 1:40 pm
• 1 like
17. Inactive

I read somewhere that a good portion of the “decrease” in household incomes was due to a decrease in the size of households.

Another example: When my daughter was in High School, she made about \$4000 a year part time. The household income was \$104,000. Then she went to college and got a job paying about \$10,000 a year. The total income of the same group of people went up, but our average “household” income went from \$104,000 to \$55,000.

Also there is simply no way for a government to figure out such things as perception of worth. When your daughter lived at home and made \$ 4K, she might have felt great about herself. And her parents thought it groovy too.

But if it had been a 40 year old ne’er do well brother living with you and they were making the same 4K a year, no one would feel that good about it. Yet for statistical analysis, it is the same.

• #17
• September 16, 2018 at 1:43 pm
• 1 like
18. Member

And of course, all your decent analysis gets blown to heck if someone like Bill Gates is included in the sample. Suddenly everyone in a community is a gazillion times better off, based on their yearly income averages.

Well, that wouldn’t affect the median, but medians have their own problems.

• #18
• September 16, 2018 at 2:05 pm
• 1 like