The employees are the valuable assets that can claim higher wages because of the limited competition, but since the limited access is created by housing, the workers have to pass their wages on to their landlords. This is how high incomes and high rents remain sustainable.
But, different households have different demand elasticities for housing. Low income households spend more of their incomes on rent, and at the margin where the next family is forced to move out of the city, they are spending the maximum that they can possibly spend on housing. For those households, all of the economic rents they may be capturing are flowing through to their landlords.
But, as we move up the income distribution, households have more discretion about housing expenditures. So, for higher income households who live in a Closed Access city in order to tap the high incomes, they can choose to downsize their housing consumption, and by doing this they can retain some of the economic rents from limited access for themselves.
Now that I have data on total residential real estate values, by MSA, (Zillow rocks!) I can estimate mean home values by city. My hunch has been that housing expenditures would tend to skew negatively in the Closed Access cities.
Normally, most measures, like household income, skew positively because they grow on an exponential scale. In other words, there are a few households with very high incomes, but there are a lot of households with just under the median income, so a typical distribution has a hump that kind of leans to the left (lower values) with a long tail moving to the right (higher value). In this distribution, the mean value will be larger than the median value because those few very high incomes will raise the mean without changing the median.
Normally, we would expect housing to be less skewed than incomes, because households tend to spend more on housing as they earn higher incomes, but at less than a 1:1 ratio. My hunch was that in the Closed Access cities, housing expenditures would be less skewed than in other cities because high income households would prefer to downsize to capture the rents of their excessive wages.
For the peak boom year - 2005 - I divided total real estate value from Zillow for each MSA by the number of housing units (from the ACS - form B25024) to estimate the mean value of housing units in the MSA, and I compared that to the median home value as computed by Zillow. As with so many issues on this topic, my hunch proved to be understated. Not only are the Closed Access cities less skewed, but according to this estimate, they manage to be negatively skewed.
In 2005, of the 20 largest MSAs, there were 4 that had a significantly negatively skewed housing stock. Those are the 4 largest Closed Access cities.
The effects on economic stress are complicated here. In one way, national income inequality is overstated when we just compare incomes, because most of the high incomes are coming out of cities where most of the labor force appears to earn more than average, but really just spends it on rent. But, within those cities, income inequality is understated by incomes because as incomes rise the rent problem claims a lower proportion of income, and households use discretion to manage their expenses.
But, it would take a very detailed study to see the extent of any of these factors. It could be that even among quite high income workers, even after downsizing, they don't have enough market power to capture much of the excess income. Considering the rent problem appears to eat all the extra income of even the median households in the Closed Access cities, the lack of discretionary housing expenditures seems to rise quite a ways up the income distribution.
PS. Thinking about this more, I think the negative skew in housing consumption suggests that even at the top end of the income distribution, most rents are being funneled to landlords. I suspect that incomes are bid down to levels that are near to the after-cost equivalents in other cities. So high income households reduce their real housing expenditures but their incomes decline in some proportion with their lower costs.
This is why this topic is so difficult to tease out of the data. Average housing expenditures aren't that high in Closed access cities, by some measures I have seen, but this is because high income households in those cities have sharply reduced their real housing consumption. The interplay between real and nominal become complex.