A basic rule of thumb in fixed income is that the value of a cash flow will shift in proportion to its time in the future. The present value of a cash flow one year from now will decline by 1% for each 1% rise in the one year discount rate. The present value of a cash flow 30 years from now will decline by about 30% for each 1% rise in the 30 year discount rate. For a bond, this sensitivity is called its "duration".

If we think of home ownership as a claim on all future rent value, then homes clearly have a very long duration - something similar to a 20 or 30 year bond. That means that, hypothetically, a 2% drop in real long term interest rates could justify something around a 50% increase in home prices.

It so happens that Price/Rent ratios did increase by about 60% from 1997 to 2005. So, it seemed possible to me that interest rates could explain that rise without requiring any influence from credit access, speculation, etc.

But, I was making a fundamental error, as I now know. There was no American housing market, per se. There were cities where Price/Rent ratios increased by maybe 20%. There were other cities where Price/Rent ratios more than doubled. That can't be explained by interest rates. And, in fact, I have come to the conclusion that local supply effects are a primary factor in rising home prices in the US and abroad.

It so happens that Edward L. Glaeser, Joshua D. Gottlieb, and Joseph Gyourko have estimated that home prices are not that sensitive to long term interest rates. They have a sensitivity of about 8% for each 1% change in long term interest rates. And, it so happens, if we apply that sensitivity to home prices among the major US metropolitan areas (MSAs), that sensitivity can justify home prices in cities where Price/Rent ratios only increased by about 20%.

In other words, with Glaeser, Gottlieb, and Gyourko's sensitivity, interest rates basically explain all of the changes in home prices from the 1990s to the peak of the boom in cities that didn't have supply constraints. That leaves most of the price increase in the Closed Access cities unexplained.

It also happens that there is a strong correlation between rent inflation and the unexplained rise in MSA home prices. In other words, where supply is limited, rents increase and are expected to continue to increase. Rents in cities like Dallas and Atlanta have risen at about the rate of general inflation, and home prices in those cities never depended on expectations of rising rents. On the other hand, excess rent inflation in the Closed Access cities has averaged about 2-3%, annually since the 1990s, and a basic cash flow valuation model for homes in those cities can justify their peak 2005 home prices with rent inflation somewhat lower than that for the next 20 years or so.

But, I still wonder if this sensitivity to interest rates is still a product of treating the national market as a single entity. I wonder if there may be a correlation between rent inflation and interest rates that is dependent on local supply constraints.

Here is a basic equation relating rent to the price of a home. (Rent here is after expenses and depreciation.)

This is just a specific version of a standard Gordon growth model. Cash flows are in the numerator and the discount rate is in the denominator. Here "C" is a multiple to reduce the sensitivity of home values to long term real interest rates. Using the estimate above, we might set this equal to the rate on a 30 year inflation protected treasury, with only a 40% sensitivity to changes in that rate.

Here's the tricky thing, though. In a city where supply can respond to price signals, we should see two mitigating forces. First, lower rates should increase the value of homes and this should induce more building. That new building - a rightward shift in supply - should reduce rents. In the equation above, "Growth rate" means the expected rate of future rent inflation, above general inflation. So, in a city with elastic supply, when the interest rate declines (lowering the value of the denominator), this should directly effect rent inflation. Rents should decline. And, since the growth rate is subtracted from the denominator, this should raise the value of the denominator.

In other words, in an open city, when homes have higher values because of declining interest rates, they should also have lower values because of decreasing rent expectations.

And, that would look a lot like a housing market where home prices were just less sensitive to interest rates. In fact, to the extent that this should happen pretty mechanically in an unencumbered market, I don't see how we would tell one from the other. Expected future rent would be an unmeasurable value. How could we determine this relationship quantitatively? I don't think we could very easily.

But, guess what happened in places like Dallas and Atlanta? When rates went down, housing starts went up, and rents went down. It's like Econ 101 in those cities.

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So, could it be the case that in Dallas and Atlanta, home values are as sensitive to long term real interest rates as we would expect a durable asset to be, but they are also sensitive to changing rent expectations that would naturally come along with those changing interest rates?

What if that is the case? Then, how would that change our model of home prices in the Closed Access cities? It is surprisingly indeterminate.

Let's rearrange the equation above so that we solve for the growth rate. In other words, given the rent and price in a given city, what rent inflation is required to justify prices in that city?

In the following scatterplots, I have plotted actual rent inflation from 1995 to 2005 for each city on the x-axis, and I have plotted the implied excess rent inflation from 2005 home prices on the y-axis. The first graph uses the low rate sensitivity (only 40% of the sensitivity of 30 year treasury bonds). The second graph uses a high rate sensitivity (the same sensitivity of 30 year treasury bonds, which is about 20 years, depending on rates).

These are all cities with both a Case-Shiller price index and a BLS rent measure. I would say that these two scatterplots could both be realistic.

In the first version of the model, future rent inflation expectations are less in every city than the trailing 10 year average rent inflation had been. So, there is nothing outrageous about the expected rent inflation implied by home prices in any city.

On the other hand, causation goes both ways. There had been a sharp housing correction in the early 1990s, and real interest rates were high throughout the 90s, with moderate housing starts. Rent inflation was high just about everywhere, and that shouldn't be expected to continue in a low rate environment.

In the second model, only the most expensive cities required any expectation of rent inflation. In this version of the model, low long term interest rates are responsible for most of the rise in home prices in just about every city. This also seems reasonable enough. Expected excess rent inflation in Atlanta and Dallas, with this version of the model, is between -1% and -1.8%. Well, during the boom, when rates were low and building was strong, excess rent inflation in those cities ranged from zero to -4%, as we saw above. And, at the national level, after a decade of persistent rent inflation, by 2005, rent inflation had finally declined down to about the general level of inflation.

If we had allowed housing starts to continue to be strong, we should have expected rent deflation.

So, is the sensitivity of home prices in the range of 8% for each 1% change in long term rates, or is it more like 20%? You tell me. I think it could be either. Either could be reasonable. I suspect it is somewhere in the middle, but I think the sensitivity might very well be closer to the high version here.

What I find interesting regarding the housing bubble thesis I have been building, in terms of the causes of the bubble, it doesn't matter what the sensitivity is. In either case, there is a strong relationship between rent inflation in a given city and home prices. Clearly, the difference between cities - and the difference between cities is the most important factor of the housing bubble - is largely about rent inflation. It is about supply.

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One reason I have slowly tended toward believing there is a higher rate sensitivity is the international data. Since 2007, the US market has been broken. Our supply problem is as bad as it has ever been, but we have sharply curtailed mortgage access, so we have created a regime shift in housing by creating a demand shock.

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When I look at Canadian data, housing starts and rent inflation in cities like Vancouver and Toronto don't seem as extreme as they are in the US Closed Access cities. There is some building - not nearly enough to meet demand, but some - and, at least as measured, rent inflation doesn't appear to be the reason for recent price appreciation.

Australia also appears to have boosted housing starts, but with little effect on prices.

This is what we would expect to see if interest rates were more important than expected rent inflation in explaining the high price levels.

Clearly, in the US, rent inflation has been correlated with price growth. But, could it be that those high prices don't depend so directly on rent expectations? Maybe, since homes are a low risk asset, and future rent expectations are an uncertain factor, homebuyers aren't willing to pay much of a premium for expected rent inflation. Maybe, in a Closed Access context, homes represent two sources of value - the low risk source of value (shelter and location) which calls for a low discount rate (a high price/rent ratio), and the high risk source of value (future rent expectations) which calls for a high discount rate, and thus doesn't really affect the price that much.

If that's the case, then once we get past a certain threshold, all Closed Access cities will sort of look the same. Once there are enough political limitations to housing growth that local housing starts just aren't that sensitive to shifting interest rates and rising prices, maybe it doesn't matter that much whether excess rent inflation might come in at 0%, 2% or 4%. Maybe it's enough to simply block the moderating influence of rising housing starts, so that declining interest rates don't trigger rent deflation. Then, that means that in all cities, home prices rise significantly when interest rates fall. And, then, there are cities where housing starts can rise, cyclically, pulling those prices back down. And, there are cities where housing starts can't rise, cyclically, so that the full effect of falling rates is felt.

FYI:

ReplyDeleteRents Have Increased Twice as Fast as Wages in New York City Since 2010

2017-08-16 07:00 ET - News Release

Median wages in NYC increased 1.8% annually since 2010, while rents rose at more than twice that rate over the same period, according to StreetEasy's annual rent affordability report

NEW YORK, Aug. 16, 2017 /PRNewswire/ --

Key facts:

Rent growth far outpaced incomes in New York City. City-wide asking rents increased by 33 percent from 2010 to 2017, or 3.9 percent annually, while median wages grew at less than half that pace: 13 percent since 2010, or 1.8 percent annually.

The lowest-priced rents increased the most. Homes with the lowest rents in NYC grew 4.9 percent annually, while the highest-price rentals grew just 3 percent per year.

The lowest earners faced the smallest wage growth. Wages for NYC workers in the bottom fifth of earners saw the smallest annual increases since 2010, while wages for top-earning professions grew the most.

Just to add to the confusion, Japan has mortgage rates like 1.25%. Very low.

ReplyDeleteNational house prices very steady since 2008, but condos an exception, and started rising in 2013.

Maybe if you drill down into numbers, you see luxury condos are being built…or condos in Tokyo mostly….

http://tochi.mlit.go.jp/english/secondpage/8628

Long term real interest rates should be the important rate here, and those should be fairly uniform across developed economies. Low rates in Japan are mostly due to lower inflation.

DeleteAnother thought:

ReplyDelete"for example, in Los Angeles County about 500,000 net new jobs have been created since 2010, but new housing production in the county is running around 20,000 units annually. "

from some recent pen-for-hire work of mine.

It is interesting. Comparing new jobs in a region to housing supply.

My guess is the Bay Area, Boston, NYC, have had solid job growth in last nine years, from the post-2008 nadir.