Hsieh, Moretti, Shiller, and the Rest: Part 3

Deflating real home price indexes with rents, locally

In Part 1 of this series, I argued that obstruction of urban housing, rather than an unusual development of urban productivity, has been the driving force behind rising home prices.

This has led to rising urban rents. Those high rents were limited mostly to a few of the most supply constrained cities before 2008, but a national rise in urban rents has followed 2008 as federal lending policies have lowered housing production everywhere.

There are surely reasons why moving to cities makes workers more productive, and that must be an important source of demand for living there. But, even without considering that issue, housing has been a drag to our economy because urban real estate has been claiming more of local incomes of long-time existing residents through rising rents.

In Part 2, I contrasted those points with the “housing bubble” concerns of economists like Robert Shiller. The Case-Shiller home price index has been an important citation in housing debates for the last 20 years. Shiller has written that high prices will induce new construction, so that one can assume that home prices and rents will converge with broader price trends over the long term. When he deflates the Case-Shiller index to estimate real housing prices over the long-term, he deflates it with aggregate prices (using the CPI). Over the past 50 years, however, rent inflation has outpaced aggregate inflation by 50% or more (give or take, depending on which indexes you reference).

Figure 1 here shows the difference between the Case-Shiller real home price index deflated with aggregate prices verses the index deflated with rents. About half the rise in real home prices is a product of rising rents.

Figure 1

Actually, I will argue below that rising rents can explain all of the increase in prices. I have done similar analysis with slightly different data and methods from time to time here at EHT. One of my Mercatus papers dives into the issue more thoroughly. The charts below are just one more way to feel the elephant.

First, let’s look at rent as a percentage of GDP (here using rental value of owner-occupied homes to compare to prices). In Figure 2, the red line is total owner-occupied rent as a percentage of GDP. The distance between the red and black lines is the portion of rent associated with excess rent inflation. That leaves the black line, which is the estimate of rent paid for shelter, without the excess inflation.

Figure 2

The idea here is that in a market open to new supply, home prices are tethered to the cost of construction. Rents are mostly for structures, which depreciate and need to be maintained. So, the gross rent yield must be high enough to provide a good return on capital after those costs. Conversely, the price/rent ratio on structures will tend to be lower to account for those costs.

But, inflated rents from obstructed supply are sort of free money. Depending on the jurisdiction, they might be associated with higher property taxes, but they aren’t associated with more maintenance costs. So, where rents are elevated by obstructed supply, the price/rent ratio on the inflated value will be higher.

Disaggregating rent, we can create a simple model of aggregate American owner-occupied real estate value. Here, I use 3 variables.

Value = B₁ + B_2*BR + B_3*ER + B₄*Dummy*CS + e

BR = base rent

ER = excess rent

CS = credit shock

The Dummy for the credit shock is 0.5 in 2008 and 1.0 after 2008.

You can think of the error term as the cyclical component.

Figure 3 compares the estimate of real estate value using just base rent, excess rent, and the credit shock.

Figure 3

Figure 4 shows the components of the real estate valuation estimate. Here, the base rent component includes both the constant and the coefficient on Base Rent (in other words, it is “B₁ + B_2*BR”). The cycle component is the residual from the equation.

Figure 4

This is a different methodology from the EHT monthly updates, but EHT subscribers will recognize this pattern. The credit shock has a coefficient that associates it with a decline in real estate values equal to about 25% of GDP. That’s in the same ballpark as the credit shock component in the Erdmann Housing Tracker that uses a different model with cross-sectional data.

The residuals fluctuate between +20% and -20% of GDP. This is the sort of cyclical deviation from flat trends in value that Shiller seems to be interested in, but since he ignores the secular rise in rents, he tends to misattribute high prices that are due to high rents. He attributes them to cyclical or irrational buyer behavior instead of to obstructed urban supply.

The Excess Rent component reflects the trends we see in the Supply Component of the Erdmann Housing Tracker. Though, again, this is a different methodology.

The coefficients are interesting. The coefficient on the Base Rent is 12.8. In other words, the average Price/Rent ratio on real estate that had no excess rental value would be about 12.8. The coefficient on Excess Rent is 36.1. In other words, the Price/Rent ratio on real estate whose value was almost entirely from excess rents due to something like an exclusive location would be about 36.1.

Those coefficients really are pretty good bookends on the cross-sectional extremes of price/rent ratios in American housing. (There are parts of some cities that have single-digit price/rent ratios, or at least there used to be. Low end price/rent ratios can get lower than that on older properties where a larger portion of rent goes to maintenance, renter risk, etc., or where value is reduced by negative amenities of the location, like crime.)

We could think about the inverse of those coefficients as yields. The yield on shelter (Base Rent) is about 8% (1/12.8). The yield on things like political location value (Excess Rent) is about 3% (1/36.1). These are real yields, before inflation.

Crop land in the US averages $5,460/acre. Rent averages $155/acre. That’s a Price/Rent ratio of 35.2. A yield of about 3%.

Price/rent ratios on housing should be mostly a function of the return on shelter - on improvements. Forty years ago they mostly were. Increasingly, it is a return on location - on unimproved land.

It isn’t really correct to say that prices have risen twice as much as rents. There are base rents and excess rents. Prices have risen roughly in proportion to each of those. Excess rents account for more of the total value of residential real estate than they used to, and they fetch a higher price multiple.

You can see the same pattern across cities. The cities that have the highest price/rent ratios are the cities that have the highest excess rents from supply obstructions.

The black line in Figure 5 is the black line from Figure 1 - the US Case-Shiller home price index, deflated with rents instead of with aggregate inflation.

In the left panel, the other lines are the Case-Shiller price index for 7 major cities, also deflated with national CPI rent. (I think these are the only cities with both CPI rent data and Case-Shiller data except for Detroit, but it was anomalous, so I have left it out of the charts.)

There has been a lot of variation between cities.

In the right panel, the other lines are the Case-Shiller price index for each city, deflated by each city’s individual CPI rent index.

Figure 5

Notice how the right panel is much more condensed than the left panel. The cities with especially high prices are the cities with especially high rents. Adjusting for local rents doesn’t eliminate all the price variation, but again, prices tend to rise more than rents. The excess rents lead to higher price multiples. The cities where prices are still high, even after adjusting proportionately for local rent inflation, are cities with high rents.

Using this data, these cross-sectional trends are a bit crude, yet I think the patterns are clear. This is just a confirmation of the pattern I find using other data. Using the same theory, but different data:

1. The Case-Shiller, Fed, and CPI data here, analyzing rent, rent inflation, and Case-Shiller home prices, both nationally and the averages of some cities.

2. The Erdmann Housing Tracker monthly data, analyzing income-sensitive price patterns within metropolitan areas which, like Shiller, ignores rents.

3. In my Mercatus papers, long-term rent, price, and income data from Zillow, both within and across cities.

And a few other stabs at the apple from time to time here at EHT. They all point to a housing market driven entirely by rents, which are driven by obstructed supply. For the most part, the cyclical fluctuations around that are fluctuations in how sensitive prices are to those rising rents.

Any way you cut it, prices are higher almost entirely because of the rents.

And, not to beat a dead horse, but the “irrational exuberance” thesis. The “Greater Fool” theory of home prices. The Case-Shiller real home price index that’s been causing nightmares for 20 years. It rejects by assumption the actual thing that is responsible for roughly 100% of it.

Shiller might say that this is what he would expect. When rents go up, it triggers froth in the marketplace that brings in too much new supply, pulling prices back down. He might say that irrational exuberance would be correlated with recent trends in rents. New buyers and builders benchmark to those rising rents and become overzealous. And, in fact, we would both agree that those high prices would be reversed with new supply. We’re both supply-siders. But the supply isn’t coming.

Both qualitatively and quantitatively, it is pretty amazing that his index is still, in the y-o-o-l 2024, assuming the supply has come, is coming, and will come.

Maybe he would say that he doesn’t assume that. Maybe he would argue today that housing isn’t in a bubble because there are supply constraints. It’s a bit of both. But, he is still deflating his index with broad prices instead of rents.

It is tempting to be conciliatory. Why can’t it be a little of both? There is irrational exuberance, herding, etc., and there are also cities with supply constraints which have increased prices permanently. But, even if that is the case, the cyclicality is generally in proportion to the permanent rise in rents and prices. The supposed cyclical over-reach happens the most where Shiller’s assumed supply has never come.

This is true before 2008, where the wide variation between cities was correlated with their rent inflation and their permanent supply constraints. And it’s true today, where there is much less variation between cities and price/rent ratios have broadly increased over time along with accumulating rent inflation (somewhat countered by lower price/rent ratios from inaccessible mortgage credit).