A simple way to raise the median wage

A number of people have been talking about the apparent contradiction in economic attitudes and economic facts. Many of these key on a particular figure, the (real) median wage, which is not increasing the way the some would like.

If we consider this the main measure of economic well-being, allow me to offer a modest proposal for bringing that figure up. Consider five workers earning the following:

Tom	$25K
Tanya	$50K
Dick	$75K
Jane	$100K
Harriet	$150K

A quick glance will show that their median wage is $75K. Let's imagine someone -- say, a Paul Krugman -- thinks this number should be higher. Easy. Fire Tom and Tanya.

Tom	$25K
Tanya	$50K
Dick	$75K
Jane	$100K
Harriet	$150K

The new median wage? $100K. That's 33% higher than it was before. Certainly, that's a good sign, and should be expected in a strong economy.

The question is, has anyone's economic well-being improved? Hmm.

OK, I must be doing something wrong. Let's start over. Tom and Tanya keep their jobs. Median wage back at $75K.

Tom	$25K
Tanya	$50K
Dick	$75K
Jane	$100K
Harriet	$150K

Now Harriet's business is doing really well. She needs some project managers. Starting wage: $50K. Wow! She needs three of them, right away.

Tom	$25K
Tanya	$50K
Sandy	$50K
Roger	$50K
Jim	$50K
Dick	$75K
Jane	$100K
Harriet	$150K

Sounds like Sandy, Roger and Jim's economic outlooks have improved considerably. That's $150K of new wealth every year that they keep working. Great for them and for the economy, no doubt.

But what's the new median wage? $50K. That's a drop of 33% from the median wage before these people got new jobs. Is it fair to conclude that things are getting worse?

------

Of course I am offering this as reductio ad absurdum. Economic well-being can improve for millions of people, generating billions in new wealth (and tax revenues), and yet the median wage may stagnate or even go down.

In fact, that sounds a lot like our current economy. The US has created over 5 million new jobs in the last five years.

If the median wage has been steady during all this job creation, we might assume these new jobs are very close to the median. Last I read, it's around $15.60/hour which equates to around $31K/year.

So, 5 million people's income has increased from $0 to somewhere around $31K in the last five years. That sounds like economic progress to me, to the tune of $150 billion in new wages per year. All with a stagnant median wage.

Comments

[Paul A'Barge]

I thought that the median wage was the one in the middle, unmoved by the distribution. In that case, even after adding 3 additional wage earners at $50K, would not the median wage still be the same, at $75K?

[Paul A'Barge]

http://en.wikipedia.org/wiki/Median

My bad, you're right.

Great didactic on statistics.

[Nancy]

The median is the midpoint (50th percentile) of the distribution, and if you change the distribution, the median changes. So the original example was correct.

The problem with this measure is that it is the median of *positive* wages. If zeros were included, the median would increase when more people got jobs.

[Martin L. Shoemaker]

Let's update your example one more time. Let's give Tom and Tanya raises:

Tom $74K
Tanya $74K
Dick $75K
Jane $100K
Harriet $150K

And yet, the median is stagnant.

Thanks! You opened my eyes. That median measure is pretty close to useless in the way it's cited.

[dorkafork]

I think your examples are seriously flawed. Tom and Tanya, for example, wouldn't necessarily just "disappear" if they got fired. Really it should look like:

Tom $0
Tanya $0
Dick $75K
Jane $100K
Harriet $150K

The median remains unchanged.

And if you're going to include Sandy, Roger, and Jim, then really you should do that from the start, right?

Sandy $0
Roger $0
Jim $0
Tom $25K
Tanya $50K
Dick $75K
Jane $100K
Harriet $150K

Median: $37.5K

Goes to:
Tom $25K
Sandy $50K
Roger $50K
Jim $50K
Tanya $50K
Dick $75K
Jane $100K
Harriet $150K

Median: $50K

Am I getting something wrong in the methodology used? When I follow the link to "Income data" in the census link to the P60-231 pdf, it says "Interviewers ask questions concerning labor
force participation about each member 15 years old
and over in sample households" out of the non-institutionalized population. Presumably that would include the unemployed. Or am I missing something?

[JorgXMcKie]

I'm reasonably sure they're not counting people with zero income or wage. If they did, we'd see greater changes in the Median income over time (especially during steep increases or decreases in employment numbers). That is not reflected in Bureau of Labor stats, anyway.

If the original report is not using $0 income as part of their data set, neither should other examinations.

Much of this confusion, by the way, seems to me to stem from a reluctance to change from methodologies developed in the 30s-50s when it was much harder to work with data.

Descriptives alone are a really, really crappy way to discuss policy.

[Matt S]

Thanks dorkafork. From the perspective of median wage statistics, those people would in fact disappear.

I confirmed this with Greg Mankiw a while back, and the idea to which you allude was the motivation of my post. The unemployed do not factor into wage statistics, which is why they are so often misleading.

[dorkafork]

Ah. That is very odd that they would do that.

[daniel]

All this academic analysis should be seasoned with a little reality:

Harriet owns the company. She fires Tom (who goes to work at Walmart)and hires Jose and Pepe, 2 illegal immigrants (who work off the books)to replace him. Good move, since now she gets more work output at less cost - and no benefits, either. Then she invests in a computer system that lets her expand her business without hiring new employees, and she can combine Tanya and Dick's jobs to boot!. She fires Dick who goes to work at Home Depot before joining the army and becoming an amputee in Iraq. Now Harriet pays $75k for one employee (Tanya) instead of $125 for two. Then, of course, she outsources Jane's job to India, and Jane goes back to school to study medical transcription. Finally, Harriet sponsors Vindi, an Indian system administrator on an H1B visa to maximize the productivity of the new computer system. Now the new distribution for Harriet's company looks like this:

Jose and Pepe: Don't count
Vindi: $30K
Tanya: $75K
Harriet: $350K

The increased productivity and sales combined with lower costs drives up the company's stock price, and Harriet back dates some options and nets $5 Million in capital gains. Then, after a series of bad decisions and worse luck, the company starts losing money and the board forces Harriet out. Oh, but she still gets the $10 Million severance package she negotiated when the stock was high.

[Tim]

Another good way to lower the median wage, would be to pass a lot of economy-stifling regulations in places with high costs of living, while not doing this in places with low costs of living.

So for example, if California were to do everything it could to stifle its economy, there would be little to no job growth in this expensive, high wage state.

While if Texas and other southern states chose to not stifle their economies, there would be robust job growth in these inexpensive, low wage states.

And this would result in a lower average national wage, as more and more jobs "migrated" to states with lower living costs, and therefore lower average wages.

[JorgXMcKie]

Sure, daniel, and we could tell that this is happening because the number of total jobs in the US would be decreasing. Obviously you have evidence of this from the Bureau of Labor stats, right? Oh, yeah, both the employer and the household counts of actual jobs has been increasing steadily for the past several years.

Oh, well, factual stuff has never been a Lefty strong point, has it? Or even a point at all in some cases.

And I still rue the day when all the buggy whip makers and blacksmiths were whipped from their labors and the US economy went into permanent depressioin.

Ooops. My bad again. That's more like what happens in 'planned' economies much more to daniel's probable liking, like Cuba, North Korea, and France. ;->=

[Vinnie]

Some factual stuff from BLS & Fed statistics:

The bottom 90% of wage-earners real wages have been decreasing since 2000.

For the bottom 60%, this has been the case since the 70s.

The % of GDP that goes to corporate profits (as opposed to incomes, tax receipts, etc.) was the highest its been since the stat has been measured. This record has been broken for the past 3 years straight.

Despite an unemployment rate of under 5%, the number of full-time workers not making enough money to be above the poverty line increased in 2005.

Daniel's vision still sound wrong, Jorg?

[mcdelta]

No offense, but the fact that you guys keep harping on just the 'median' makes me think that you guys are all idiots. I'm looking at the response, I'm guessing that either you guys have never taken a statistics class or are you familiar with data manipulation.

You cannot look at just one statistic and draw any reasonable conclusion. As the people above have shown, the meadian can easily be manipulated. For example, you can have 501 people who eaern $1,000,000 and 500 people who earn $1,000 a year and the median will show that the the average person earns $1,000,000/year.

You have to take into account many other statistics to truly understand any group of number. The mean of the group above is $500,999. Any large difference between the median and mean like this shows that the data is skewed.

Furthermore, the variance is over 249 billion and the standard deviation is almost 500,000 (for definitions of the SD and Variance, check wikipedia). This means that the data is extremely spread out from the mean, indicating that the mean is also not a good measure of the data and that many outliers exists.

Finally, you can also look at the mode, which is the most common variable to appear in the dataset. In this case, it would be $1,000,000.

You can also look at the top quartile and bottom quartile to see how the data compares (like the stats that show how much wealth the top 1% has). This will give you a better measure of where most people fit into the population.

In this example, the fact that there are such drastic differences between all of the statistical measure means that you cannot just look at one measurement and many other tests will be needed.

There are lies, damn lies, and statistics. Anyone relying on just median will infer data that is worse than a 'damn lie'.

[bridesmaiddresses]

Being a bridesmaid is an honor and a responsibility. Bridesmaids support the bride emotionally, help with wedding planning tasks of all sorts, and can bear a significant financial burden. While you want your maid of honor and bridesmaids to look beautiful at the wedding, you also want to keep their monetary obligation to a minimum.