FRBSF Economic Letter
2004-27; October 1, 2004
House Prices and Fundamental Value
The performance of the residential
housing market over the last ten years has been remarkable. According
to the Office of Federal Housing Enterprise Oversight (OFHEO),
house prices have appreciated at an annual rate of 5.4% on average
(68.9% over the whole time period). Perhaps even more remarkable
is that the performance was strong even when economic activity
overall was weak. Average annual appreciation rates have been 7.4%
(26% in total) since the collapse of the Nasdaq in 2000 and 7.1%
(20% in total) since 2001:Q1, the beginning of the 2001 recession.
In contrast, since the start of the 2001 recession, the S&P
500 and Nasdaq have averaged negative annual returns of –2.43%
and –1.42% respectively.
These kinds of statistics have generated
an enormous amount of commentary along with suspicions of a house
price bubble. At first
glance, housing would appear to be just the type of market that
is susceptible to systematic mispricings. Most market participants
have little experience, making transactions only infrequently.
Asymmetric or incomplete information between buyers and sellers
about demand and prices is acute. Even with the advent of new technologies,
the matching of buyers with sellers remains cumbersome and slow.
And unlike other markets, there are no good ways to “short” the
housing market if prices get too high.
This Economic Letter describes
one of the measures commonly used to gauge the fundamental value
of housing—the price-rent
ratio. We describe the kinds of forces that cause the ratio to
move over time and document which forces appear to be most important.
We document the way that the housing market typically adjusts to
changes in economic fundamentals.
Fundamental value and the price-rent
ratio
The price of housing is determined by the forces of supply and
demand for the housing good. So, naturally, many economists try
to relate prices to variables that might shift supply and demand,
like interest rates and household income. Price dynamics are often
described in terms of the interactions between these variables
and the natural constraints on delivering new supply to the market
(see McCarthy and Peach 2004).
We borrow from the finance literature
to take a different approach. The finance paradigm holds that
an asset has a fundamental value
that equals the sum of its future payoffs, each discounted back
to the present by investors using rates that reflect their preferences.
For stocks, the payoffs requiring discounting are the expected
dividends. This approach can extend to housing by recognizing
that a house yields a dividend in the form of the roof over the
head
of the occupant. The fundamental value of a house is the present
value of the future housing service flows that it provides to
the marginal buyer. In a well-functioning market, the value of
the
housing service flow should be approximated by the rental value
of the house.
 A bubble occurs—in either the stock market or
the housing market—when the current price of an asset deviates
from its fundamental value. Right away we see that bubbles are
difficult
to detect because fundamental value is fundamentally unobservable.
No one knows for sure what future dividends are going to be, or
what discount rates investors will require on assets. Despite this
obstacle, analysts still find it helpful to construct measures
of fundamental value for comparison to actual valuations. One popular
measure is the price-dividend ratio, which corresponds to a price-rent
ratio for houses. The price-rent ratio for the U.S. housing market
is in Figure 1. The price series is the existing home sales price
index published by OFHEO; this index is a repeat sales index, meaning
that index changes are compiled from the price changes on individual
houses that turn over during the sample period. One of its drawbacks
is that it does not fully differentiate between pure house price
appreciation and price changes due to depreciation or home improvement.
The rent series is the owner’s equivalent rent index published
by the Bureau of Labor Statistics (BLS); this series is intended
to measure changes in the service flow value of owner-occupied
housing. The figure suggests that current prices are high relative
to rents. More precisely, house prices have been growing faster
than implied rental values for quite some time: currently, the
value of the U.S. price-rent ratio is 18% higher than its long-run
average.
It is tempting to identify a bubble as a large and long-lasting
deviation in the price-rent ratio from its average value, just
like the one that we see in Figure 1. But exactly how large and
how long-lasting a deviation must be to resemble a bubble is
far from obvious. There is no reason to believe that a price-dividend
ratio should be constant over time, even in the absence of bubbles;
in particular, Campbell and Shiller (1988) showed that the value
of the ratio today can increase only if there are expected future
increases in dividends, expected future decreases in returns,
or
both. This simple model of the price-dividend ratio is based
on a simple identity and the definition of a return as the sum
of
a dividend yield and a capital gain/loss.
To make the implications
of this simple model more concrete for our housing application,
imagine a real estate market near a
military base that has just been scheduled to close five years
from now.
The inevitable job loss associated with the closure is an adverse
shock to the demand for housing. This should cause a decrease
in the future value of the housing dividends on houses in the
area,
driving house prices down immediately. Current rental contracts,
however, should be relatively unaffected because the closure
is so far off in the future. Thus, the price-rent ratio should
decline.
Alternatively, suppose the government could credibly promise
to reduce taxes on real estate and keep them low forever. This
change
would probably lead to a higher demand for housing; at the
margin, households would have the incentive to shift savings from
financial
assets to housing. In addition, the elimination of uncertainty
about future tax rates would imply that houses are safer assets,
requiring lower future returns. In this case, the price-rent
ratio should increase.
What moves the price-rent ratio?
Given a notion of the sources of variability in the price-rent
ratio, it is natural to wonder which sources are most important.
Cochrane (1991) conducts this exercise for the case of stocks and
finds that most of the most variation comes from changes in returns.
We conduct Cochrane’s experiment for houses. To construct
the price-rent ratios we use OFHEO’s existing home sales
index and the owner’s equivalent rent index published by
the BLS. We use quarterly data, ranging from 1982:Q4 to 2003:Q1.
The constraint on the sample period is that the owner’s equivalent
rent series does not begin until 1982. We could extend the rental
series back further by using a pure rent series, but only at the
cost of severing the link between an owner-occupied price in the
numerator of our ratio and an approximation to an owner-occupied
service flow value in the denominator.
The basic insight of the
empirical research on price-dividend ratios is that movements in
the price-dividend ratio can be decomposed
into two parts: movements relative to future expected dividend
growth rates, and movements relative to future expected returns.
In theory, these future variables are unknown to the investors
when they set prices. In this application, we set the expected
future dividend growth rates and returns equal to the actual values
that occurred. Also in theory, we should assume all “future” dividend
growth rates and returns to mean those extended to infinity. Obviously,
this is not possible, so we study how the price-rent ratio moves
relative to the next 15 quarters of rental growth rates and returns.
(We experimented with other horizons, and found that the results
did not change much.) Note also that we are unable to incorporate
the current episode of price appreciation. We run out of observations
before we can say anything definitive about the recent house price
appreciation.
The main result from this decomposition is that the
behavior of the price-rent ratio for housing mirrors that of the
price-dividend
ratio for stocks. The majority of the movement of the price-rent
ratio comes from future returns, not rental growth rates. This
will not comfort everyone, as it implies that price-rent ratios
change because prices are expected to change in the future, and
seemingly out of proportion to changes in rental values. A more
comforting conclusion, however, is that, despite the well-known
frictions in real estate markets, the dynamics of a common valuation
measure are still similar to those observed in a near-frictionless
market like the stock market. It may appear that returns are quite
volatile relative to changes in rental values, but this is true
for stock prices as well and only serves to underscore our inability
to understand how expectations and required rates of return on
assets are formed.
Another result is that almost all of the movement
in the aggregate U.S. price-rent ratio was accounted for by two
factors—the
proxy for future growth in rents and the proxy for future returns.
Put another way, other factors, such as bubbles, do not appear
to be empirically important for explaining the behavior of the
aggregate price-rent ratio. At the same time, when applied to local
real estate markets, in many cases the movement in the price-rent
ratio predicted by the model is much greater than the actual movement;
specifically, the results indicate that something other than our
measures of future rent growth and returns explains price-rent
ratios. While we do not know what this “something other” is,
the more common overstatement of volatility is caused by a much
stronger comovement between the price-rent ratio and future returns
than the comovement between price-rent and future rent growth.
 The
excess of the price-rent ratio volatility (the difference between
the movement predicted by the model and the actual movement) can
be traced to the volatility of house prices in local markets. Most
recently, local housing markets that historically have had “excess” volatility
in future returns also exhibit high house prices compared to fundamentals.
This is shown in Figure 2, where the vertical axis measures the
excess volatility in percent terms; zero corresponds to the case
in which the model and our implementation explain the actual price-rent
ratio precisely. The horizontal axis measures the price-rent ratios
normalized to have the value of one in 1995:Q4.
The figure shows
that in some markets, such as Dallas and Chicago, the combination
of future growth in rents and future returns account
for most of the variation
in the price-rent ratio. Price-rent ratios in these markets appear to behave
as do those in the national market. Other markets, such as Boston, Los Angeles,
and San Francisco, have return streams that are much more variable than the
price-rent ratios they are supposed to be tied to. Perhaps not
coincidentally, these markets
are thought to be ones where the supply constraint on new construction is particularly
tight. Also, these are markets that now appear to be most highly valued.
Conclusions The price-rent ratio for the U.S. and many regional markets is
now much higher than its historical average value. We used a model
from the finance literature to describe how the price-rent ratio
can move over time. We found that most of the variance in the price-rent
ratio is due to changes in future returns and not to changes in
rents. This is relevant because it suggests the likely future path
of the ratio. If the ratio is to return to its average level, it
will probably do so through slower house price appreciation.
John
Krainer
Economist Chishen Wei
Research Associate
References
Campbell, J., and R. Shiller. 1988. “The
Dividend-Price Ratio and Expectations of Future Dividends and Discount
Factors.” Review of Financial Studies 1, pp. 195–227.
Cochrane,
J. 1991. “Explaining the Variance of Price-Dividend
Ratios.” Review of Financial Studies 5(2), pp. 243–280.
McCarthy, J., and R. Peach. 2004. “Are Home Prices the Next ‘Bubble’?” FRBNY
Economic Policy Review. http://www.newyorkfed.org/research/epr/forthcoming/mccarthy.pdf
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