Sunday, March 09, 2014

How do variations in cost of living and therefore real wages affect income inequality statistics?

Recently, I've been rooting in some rather deep wonkamole.  If you've been following this blog (don't know why unless you're an FBI agent tracking my deep Koch brothers connections) you know that I've been rather obsessed about the issue of income inequality, specifically why our friends that veer left get away with a rather cheap slur on our country, to wit:  that the United States is one of the most 'unequal' nations in the world and 'inequality' is increasing, therefore we need to do something, anything! no matter how counterproductive (minwage hikes) or not relevant to the issue at hand (earned income rate hikes).  Time is running out!

And if you've actually been reading it rather than simply placing your tablet computer over your face so you can sleep in peace, you'll know that it is my hypothesis that a lot of what passes for "Evil right wing business thievery and cruelty masterminded by those sick Koch bastards" is really simply 'diversity' in action.  The more differences people have in terms of race, religion, age, geography, weather, economy, country of origin, etc.  the more their economic outcomes are likely to differ.  In a previous post I presented some evidence that quite a bit of the variance (almost 40% to be specific) in levels of income inequality is explained by the level of racial diversity. No surprise there.

One of the areas where American 'diversity' wrongly exaggerates perceived inequality is in cost of living differences.  The United States is a massive continental scale empire. As such the economic conditions vary wildly from Albuquerque (balloons!) to Augusta (lobster!) to the other Augusta (one percenter golfers!).  And so does the cost of living.  Among metropolitan areas the cost of living index varies from a low of 80 in places like Harlingen, TX to 203 in Manhattan.  In other words, someone bringing down $203K in SoHo is living the functional equivalent of someone making $80K in the Rio Grande Valley or $90K in Austin (this index does not reflect differences in weirdness or tedium levels). This actually understates the cost of living differences in the country because there are tens of millions of Americans that live outside metro areas and their cost of living is often even lower.

So how should we account for these differences?  Is the $203K New Yorker an evil capitalist roader raping the humble $80K campesino drowsing in the town square under his sombrero?  Is Juan Valdez banned from moving to New York and exposing himself to nirvana's hellish cost of living or is Muffy Van Whitsonstonesum unable to grok the implications of Texas priced subdivisions?  Doubt it, even if it's Muffy Valdez and Juan Van Whitsonstonesum.  People live where they live based upon their opportunities and preferences.  And the $80K guy in Harlingen or $90K in Austin are as likely to be happy as Mr. Two-Oh-Three is. Perhaps happier given that the 'refugee' flow is from Manhattan to Texas.

So given that I'm already knee deep in the wonkamole why don't I just shut up, grab the data, and get the bleeding answer without involving all of you in the gory details?  I would but frankly it's too hard.  To do a cost of living adjusted Gini or top vs. bottom decile analysis right requires lots of data.  And probably some real skill in statistics and certainly a lot of time and patience none of which I have in excess supply at the moment. I mean I guess I could do it but I'm hoping someone in the economics business reads this and takes up my cudgel so to speak.

So in the meantime while I may not be willing to put the effort out to do the big "Oooh I'm an Econ Phd at Chicago look at me" analysis with all the bells and whistles I am willing to run a modest little simulation to see what impact cost of living and nominal wage differences could have on whether the Proggos denunciation of America's 'world record' inequality is justified or not.

A tale of two states
Running a simulation is how economists play pretend.  In this case I pretend there are two worlds with two different income and cost of living scenarios. In one scenario - let's call it Equityland, I pretend that there are ten citizens: five living in the Great State of Confusion and five in the Commonwealth of Despair.  Both Confusion and Despair have a cost of living index of 100 and nominal wages are the same.  When you plug their pretax and transfers incomes into the magic Gini machine you get the following:

Equityland
Lorenz Curve for a hypothetical two state world where both states have a cost of living index of 100. (The Lorenz curve is the blue line and Gini simply measures the variance between that curve and the straight diagonal line of perfectly equal incomes that you get in North Korea and Cuba - of course their food curves are so bent that they're almost broken).
Top decile income multiple of bottom decile:  13.33X
Gini: .424
OK, cool chart and no doubt you are impressed by my data entry skills but so what?  The so what occurs when we compare Equityland to the second scenario:  Plutocrat Planet.  In PP, there are once again two states:  One:  Cheapstate has a cost of living index of 100 and nominal wages to match, the other:  North Ripofistan has a cost of living index of 200 and the (nominally impressive) wages to match.  So here's how Plutocrat Planet scores:

Plutocrat Planet
Lorenz Curve for a hypothetical two state world, one with cost of living index 100 and one with cost of living index 200.  Real wages are identical.
Top decile multiple of bottom decile income:  26.67X
Gini:  .465

So the Lorenz curve is more 'bowed' in Plutocrat Planet because statistically the income values vary more than in Equityland.  So Plutocrat Planet sucks, right?  After all it has a Gini that's .041 higher which is a pretty big difference and the top to bottom decile income multiple doubles from 13.33 to 26.67.  It turns out that calling it Plutocrat Planet was right on.  No self respecting egalitarian would be caught dead in that rich man ghetto.  Scandinavians, hearing of the shameful lack of sameness there shake their heads and say something indecipherable but clearly disapproving in in their Nordic argle bargle.

Yet in real terms both scenarios have exactly the same level of real wages.  There is no real difference between Equityland and Plutocrat Planet.  The only differences are artifacts of our failure to recognize that cost of living differences can exacerbate perceived 'inequality' on a purely statistical basis.  And when you have lots of ideologues focused on the 'numbers' and running 'league tables' comparing a major league country like us to T Ball countries, it becomes a problem.

What does it all mean, Basil?
This is because the favorite pastime of the global 'fairness' Gestapo is to compare the United States of America, all 315 million of us smeared across 3.7 million square miles of land and at least seven time zones and spread from the Arctic circle to the Tropics to T-Ball countries like Denmark which has the population and land area of of Greater Atlanta without all the trees, hills or rednecks.  Or Sweden or Japan for that matter - most countries and all the more developed countries have substantially less cost of living diversity than the US which means - along with our other outlier attributes - that our level of 'inequality' looks worse it really is when (stupidly) compared to other countries.  So the first conclusion is:  Income inequality league table comparisons are stupid and are done primarily by people with axes to grind. They are misleading and so are the people who produce them.  So when someone says that the US has 'the worst' inequality you have my permission to hit them with a rolled up newspaper (don't use your tablet) until they recant or go back to Sweden.

But there's another way to examine the  impact of cost of living differences on inequality:   longitudinally which is boffin for look at something over time.  'Income inequality' has been 'rising' in America since about 1980.  Could some of that increase in inequality be due to diverging costs of living and nominal wages in different regions of the country?  Sadly, I was unable to find a long enough time series of costs of living by MSA - a set of statistics that our fearless Federales have been calculating for decades.  That is I couldn't find it without paying some rent seeking not for profit clown car of an institute who somehow have persuaded the Federales to privatize our data bought and paid for with my sodding taxes.  But the chaps at Case-Schiller who chronicle housing prices in major cities have been very helpful and open handed with their data.  So I plotted the housing price indices for five of the Case-Schiller 20 city index (that's the most you can do at one time, try it yourself here).  And given that housing is the largest part of family budgets and is the item that varies the most between different cities, it gives us quite a perspective on how the cost of living has changed in different major metros.

The first thing you notice is the 'great divergence' starting in about 2000 between the various metro areas:  DC, NYC and SFO have been on a rocket sled up and then down while Detroit has been depressed as expected.  The fastest growing of all these cities - Dallas has barely budged, either up or down.  Unsurprisingly, according to Demographia who chronicles these things: of these 5 cities the DFW Metro region is the only one that has a 'free market' supply of land for housing, the other cities having varying types of 'central planning' that in San Francisco, DC and NYC's case would rival a Breshnevite Gosplan for bloody minded pettifogging. But it helps explain why the cost of living varies so much in America and why we've seen inequality rising, at least since 2000.

But look closer and earlier.  The scale obscures it and the Case-Schiller data isn't available for all the cities but you can see the inflection points when housing prices started to surge in SFO, NYC and DC:  the 1980s.  I knew it was all Ronald Reagan's fault..  And remember that the biggest cities will have the biggest cost of living differential versus small towns and smaller MSAs.  So this is at least data driven anecdotal evidence that some of the 'deterioration' in income equality is a function of varying rates of housing inflation which results in higher nominal income places (NYC, DC, SFO are among the highest) to have much lower real wages.  It also explains why Dallas, Houston, Detroit and Austin are four of the ten highest income metro areas in the nation in real dollar terms.

So what do I believe I know now?

1. Cost of living variation has a significant measurable impact on 'inequality statistics' so beloved by class warriors the world over. Particularly in chock full of diversity America. 
2. The divergence in some large metro housing prices started in the 1980s and accelerated in 2000 or so when the already juiced market was given a double dose of speed, steroids and interest rate supplements.  Which means that some of our measured increase in inequality is spurious.  How much?  Don't know but it's real and it matters.  
3. It is bloody ironic that the oh so progressive chaps who are shrieking about 'inequality' run the real estate planning oops, I mean 'smart growth' rackets in the areas with explosive home price inflation which of course is the source of some of the spurious increases in inequality measures (not to mention lots of real hardship for the poor and working classes).  

Look, I am sure that income inequality has gone up over the past 35 years but it's not as bad as the left makes it out to be. Like with healthcare, global warming, and preschool or anything else progs want it is an overblown 'crisis' designed to stampede the electorate into allowing more manipulative state nonsense that makes prog lawyers so much money.  






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