The title overstates the case, but only a little.
The differences in the cost of living between metropolitan areas is driven mostly by differences in housing costs. And, the variability in housing costs between metropolitan areas has increased dramatically between 1980 and 2007.
The variability in wages between metropolitan areas has also increased dramatically between 1980 and 2007.
What has driven this change?
A new economics paper has a model that explains this quite well.
One key part of the model deals with how metropolitan areas with differing levels of land use regulation (measured with an index of actual land use regulation strength in each metropolitan area as of 2007). In places with little land use regulation, when new people move to an area, housing prices don't increase much. In places with strict land use regulation, when new people move to an area, housing prices increase a lot.
Another key part of the model is that the amount of land use regulation in an area is driven by (1) the relative proportion of voters who are renters v. home owners, and (2) the proportion of each group that are college educated (because college educated people are more effective at influencing politicians). Renters, on average, favor less land use regulation because that keeps rents lower and reduces the down payments they need to eventually buy a home. Home owners, on average, favor more land use regulation, because it increases the value of their investment in a home and the higher housing prices get, the more intense the desire for strict land use regulation is because home equity becomes a larger share of their wealth.
A third key part of the model is that high wage, high skill people are less discouraged from moving to a place by high housing costs than low wage, less skilled people.
A fourth key assumption of the model is that people are more productive and earn higher wages in cities with higher productivity and less productive and earn lower wages in cities with less productivity, even if they are not personally high skilled people.
Thus, less skilled people avoid more productive cities where they could earn more because the housing costs are too high, segregating whole cities into expensive to live places with lots of high wage earners and inexpensive to live places with lots of low wage earners whose wages are suppressed by leaving in these less productive places.
[T]he rise in regulation accounts for 23% of the increase in wage dispersion and 85% of the increase in house price dispersion across metro areas from 1980 to 2007. I find that if regulation had not increased, more workers would live in productive areas and output would be 2% higher. I also show that policy interventions that weaken incentives of local governments to restrict supply could reduce wage and house price dispersion, and boost productivity.
This happens, basically, because land use regulation decisions are made by local populations in their own self-interests without regard to the impact these decision have on people who might want to relocate there in the future, a classic case of an externality.
What are the policy responses the paper considers:
In the first, cities may choose their level of regulation up to an exogenous upper limit instituted and enforced by a central government. While this policy is not possible to implement due to legal constraints to federal involvement in local land use, it provides a ballpark estimate of what the central government could achieve with such a policy. In the second, the federal government introduces a tax that discourages regulation.
Basically, in the second option the tax increases taxes on owners of expensive homes and redistributes the funds to owners of less expensive homes.
Now, honestly, a 2% increase in GDP (actually 2.1%) over 27 years from a misallocation of labor isn't really all that impressive. The is a very lower order factor influencing GDP. As it is, mean hourly wages increased from $8.48 an hour in 1980 to $26.18 an hour in 2007. The study suggests that without increased land use regulation, hourly wages would have been $26.70 in 2007. Thus, instead of increasing by $17.70, they would have increased by $18.22 over that time period. Thus, a little more than 97% of wage growth is unrelated to land use regulation, and about 3% of wage growth might be lost due to land use regulation.
Inequality between geographic areas is powerfully driven by land use regulation, but this inequality has only a very modest impact on productivity and wages.
If either of the policies he considers were implemented, "output would be 1.5% higher, wage differences 5% smaller, and average house prices 25% lower."