Here is a scatterplot of annual Rent/Income and Income (normalized to US median). Up to 1995, we see the pattern that should be intuitive. Households with higher incomes tend to spend a lower portion of their incomes on housing. In 1986 and 1995, this pattern shows up in inter-city trends. Cities with higher incomes tended to spend less on housing. But, in the mid-1990s housing supply started to be the binding constraint for access to lucrative labor markets. So after 1995, we see this unusual new pattern where high rent becomes the entrance fee to a higher income.
Here is a scatterplot of Price/Income and Income. Here, we see that there was no relationship before the mid 1990s. Median home prices were generally a product of other factors and were unrelated to median incomes. After the mid 1990s, we see the same change in trend that we see with rents. In cities where the median household has a higher income, they pay a higher proportion of that income in order to buy a home. Note that if the housing market from 1995 to 2005 was characterized mainly by generous credit to low income households, we would have seen the opposite effect. But, this pattern suggests that home prices increased the most where marginal access to credit should have been less of a factor.
Here is a scatterplot of Price/Income and Rent/Income. Before the mid-1990s, there was a small relationship between these measures. In a pristine textbook world, we should expect the y-axis intercept of this relationship to be near zero. And, if rent is about 25% of incomes and Price is about 250%, we would expect the coefficient to be around 10. Factors like different property tax rates would cause the relationship to be weaker. And, if there was no supply constraint, we might expect rents to revert to the mean, which might also lower the coefficient.
After 1995, the coefficient of relative Price/Rent moves well above 10 and the relationship strengthens dramatically. In 1995, r-squared is .13. By 2015, it is .67! Rising prices in the housing boom and its aftermath are strongly associated with rising rents. This is because the supply constrained cities are associated with rent inflation and with expected future rent inflation. The imposition of local supply constraints means that rent expectations are no long mean reverting. Since the peak of the boom in 2005, constraints in mortgage lending have been an obstacle to new home building, holding prices down (because of the lack of access to capital) but pushing rents up (because of the lack of new supply). So, even while the regression line has moved down and to the right, the relationship between rents and prices has strengthened substantially.
We can see some unusual activity above the norm in 2005 among some cities that did not have unusually high rents or incomes, which points to some areas that saw temporary, and probably unsustainable, price movements at the end of the boom, but that was limited to a small number of smaller markets. The bulk of the country saw little deviation from the norm, and the largest cities have seen persistence in rent increases and a rebound in home prices in the decade since 2005, even in the absence of functional credit markets. We have a big supply problem which for a short period coincided with a small amount of unusual nominal price expansion.
Here is a comparison of Price/Incomes, by city, at each point in time (moving right to left), regressed against both Rent/Income and Relative Income. From 1995 to 2005, during the boom, median home prices in a city became much more correlated with rents, and even after accounting for this, also had a significant positive relationship with income. Even in 2005, even after accounting for what they were spending on rent, the median households in cities with lower incomes were paying significantly less for their homes than the median households in cities with higher incomes. To my eyes, this describes a supply constrained world, and it clearly does not describe a world where generous credit is pulling lower income households into overpriced houses.
Here is a paper (pdf) from Demers and Eisfeldt (HT: Commenter Wd at Arnold Kling's blog) about how total returns to rental home ownership tend to be relatively stable across cities. Where yields are lower, price appreciation has made up the difference. Using Zillow data, I also find that prices across cities have generally been justified by rent cash flows.
Here is a graph of real returns to the median home in each MSA, over time, based on median home prices and median rent in each MSA. For each MSA, I estimated future rents by assuming future rents would rise, in real terms, at the same rate they have risen since 1995. The bold black line is the US average, and the bold red line is the real return on 30 year inflation protected treasury bonds (TIPS). This is similar, but a somewhat more detailed approach, to previous measures I have used.
The first graph is for the largest 20 MSAs and the next graph is for the largest 151 MSAs for which Zillow has data. In both cases, we see fairly reasonable movements over time, with some unusual declines from 2004 to 2007 among a handful of cities. And, we see the divergence between housing returns and TIPS returns after 2007, with housing returns moving to the high end of the long term range and treasuries moving to very low levels.
Two points to keep in mind on these graphs:
1) I have applied a blanket expense ratio of 50% to gross rents. Cities with, say, higher property taxes would require higher gross returns, so that some cities might tend to run higher in this estimate of returns than others, though this shouldn't generally affect trends over time.
2) This is based on the median house over time. In cities with high levels of housing starts, new houses should tend to be more valuable than the existing median house, so my measure probably overstates returns over time, because rents on a particular house will grow at a slightly lower rate than the rent of the median home in the MSA. This effect will be larger in cities with more new housing, so while this probably causes the entire range of returns to be overstated, it also should cause the divergence during the boom to be lower, because cities where there was not as much of a price increase tended to have higher housing starts.