This paper was presented at the conference "Policies to Promote Affordable Housing," cosponsored by the Federal Reserve Bank of New York and New York University's Furman Center for Real Estate and Urban Policy, February 7, 2002. It was part of Session 2: Affordable Housing and the Housing Market, and is a commentary on "The impact of building restrictions on housing affordability" by Edward L. Glaeser and Joseph Gyourko.Housing - Finance ; Housing - Prices ; Land use ; Construction industry ; Local government

Brendan O'Flaherty

English

Research Papers in Economics

FRBNY Economic Policy Review / June 2003 41
dward Glaeser and Joseph Gyourko present a good paper,
 but the paper is not what it claims to be, at least for lay 
readers who do not interpret words literally. For most people, 
“affordable housing” has something to do with housing for the 
poor. This conference, according to the program, aimed to 
“explore . . . strategies easing the housing problems of low- and 
moderate-income families.” This connection very likely takes 
liberties with the English language, but the connection has been 
made, and it makes good sense to respect it. 
Therefore, arguments for affordable housing policies ought 
to show either that poor people would be better off as they 
perceive it, or that the poor would be better off according to 
some metric not tied to desire/satisfaction. (Thus, housing 
policies for poor people are targeted not only at high supply 
prices or at poverty, but also at intrahousehold or inter-
household externalities—just as homeowner tax preferences 
are.) Although Glaeser and Gyourko acknowledge that such a 
link probably can be made—a contention that I think is 
plausible—they do not make it, and so they leave the paper 
incomplete as an affordable housing paper as the term is 
commonly (and probably mis-) understood.
The paper’s real interest lies in the finding that in some 
cities, land is very expensive—more expensive than people 
appear willing to pay for it. This finding makes Glaeser and 
Gyourko’s study important in that it is likely to spur a great 
deal of further research.
Basically, Glaeser and Gyourko fit an hedonic equation:
                                     , 
where S represents structure and L land. The authors find that 
, the known construction cost of structure in some 
metropolitan areas. They conclude that zoning is holding up 
the price of land, and provide evidence that zoning is more 
restrictive in areas where the difference is greatest. 
The step from   to “zoning is the problem” is a very big 
one. There is an instructive analogy in the study of household 
economics. Different methods (for example, replacement 
versus opportunity cost) produce radically different estimates 
of the hourly value of time devoted to household work. But that 
does not imply that a government policy, perverse or not, is 
causing the discrepancy. I think the consensus now is that the 
theories that imply no discrepancy are the ones that are wrong, 
even in the absence of government intervention. Similarly, we 
should look further at why the combination of Glaeser and 
Gyourko’s statistical methods and accepted urban economics 
theory fails to work before concluding that government 
policies are the only possible explanation. (The correlation—
absent regional dummies—between high estimated land prices 
and restrictive zoning, although suggestive, is certainly not 
definitive. Jewelry stores with more expensive wares spend 
more on security, but we do not think that the security 
expenditures are driving the value of the jewelry.)
P α S β L + =
α c >
α c >
Brendan O’Flaherty
The views expressed are those of the author and do not necessarily reflect the 
position of the Federal Reserve Bank of New York or the Federal Reserve 
System.
Commentary
Brendan O’Flaherty is an associate professor of economics 
at Columbia University.
E42 Commentary
Thus, we can look at two kinds of possible alternatives to the 
zoning conclusion—statistical and theoretical.
1. Statistical Alternatives
When examining this type of alternative, there might be 
omitted variable errors, collinearity problems, or measurement 
issues. To consider omitted variable errors, suppose that the 
true model is
                               ,
where b represents some other attribute, such as proximity to a 
train station or a school, or a scenic view. Neoclassical theory 
would lead us to think that the covariance between S and b 
would be positive and that the covariance between L and b 
would be negative. Both of these covariances imply that   
should be too big and that   should be too small. The Glaeser 
and Gyourko regressions have very poor measures of amenities 
and location.
In a note to their paper, Glaeser and Gyourko speculate that 
covariances might very well go in the opposite direction—that 
neoclassical urban theory might be wrong. This adds to the 
possibilities for new theories.
Collinearity problems could arise if land and structure, or 
aspects of structure, were correlated. This is not unlikely, since 
the aspects of structure that the authors measure include the 
presence of a garage and the number of rooms. I will give a not 
terribly implausible example below that shows how this 
collinearity can lead to serious underestimates of  .
Finally, the estimation procedure relies on construction 
costs and depreciation being the same in all metropolitan areas. 
There are several reasons why construction costs can differ, 
aside from differences in construction laws and regulations. 
Weather is one: colder climates entail more insulation, more 
solid windows and doors, and greater interest and scheduling 
costs due to winter delays. Notice that this supply 
interpretation works in the opposite direction from the 
demand-side January temperature used by Glaeser and 
Gyourko to measure amenities. Labor is another source of 
variation: because wages vary between metropolitan areas and 
wages are a substantial part of building costs, the cost of 
building identical structures will vary between metropolitan 
areas. Other inputs, such as electricity, also vary in price.
Depreciation is also likely to vary, because the rate at which 
houses depreciate depends on economic decisions about 
P α S β L γ b ++ =
α
β
β
maintenance, repair, and home improvement. Demand shocks 
that make housing in certain metropolitan areas more 
expensive may be correlated with greater home maintenance 
and home improvement expenditures. A thirty-five-year-old 
Cape Cod with 1,700 square feet in New York may, on average, 
be a very different house in ways unobservable to the 
econometrician in a similar house in Dallas.
2.T h e o r e t i c a l  A l t e r n a t i v e s
The basic premise of the Glaeser and Gyourko paper is that if 
you know the square footage of a lot, the price per square foot 
of land, and the construction costs of the structure, you know 
everything you need to find the price that would prevail in a 
market without zoning. This idea is probably wrong, although 
Glaeser and Gyourko are probably correct in interpreting this 
premise as an implication of standard urban economics. There 
are several reasons for this.
First, all relevant costs of a house are not incurred on the lot. 
The costs of roads, sewers, gas and electric, telephones, cable, 
and other infrastructure are quite hefty relative to the costs of a 
private structure—roads are going to account for at least 
20 percent of land in a new development, and the materials 
used in them are not cheap. In equilibrium, the (marginal) cost 
of new developments is going to be the replacement cost of 
existing houses, so the price of installed infrastructure is going 
to be part of the price of land—even without zoning. On the 
other side, some part of the capitalized value of property taxes 
is going to be subtracted from a house’s value. Infrastructure 
pricing practices, like taxes, may vary between metropolitan 
areas. Combined with the uncertainty about structure costs 
introduced by variations in construction costs and 
depreciation, these add up to a hefty uncertainty about the 
value of land.
Second, lumpiness and selection present problems. There 
are serious increasing returns to scale in housing, for example, 
from the 2/3 rule, the sharing of utility connections, and the 
sharing of furniture. The restriction to single-family detached 
houses further reduces the possibilities for using very small 
pieces of land. This means that small pieces of unused land are 
not going to be very valuable.
Consider a simple example. Suppose land is only one 
dimension, you are a profit-maximizing developer without any 
zoning constraints, and the marginal product of a plot of land 
of size x is x - x  2. Assume you are working with a plot of land of 
size z. If z = 3/4, or any multiple, you will build one house (or FRBNY Economic Policy Review / June 2003 43
the multiple), and the usual optimizing condition of marginal 
equals average will hold. But if z is not a multiple of 3/4, 
marginal will not equal average at the optimum. Let D(z) = 
average profit minus marginal profit, assuming optimal-sized 
lots. Then for z < 1, 
                              D(z) = z (2/3 z - 1/2),
which rises to 1/6 at z = 1. In general, D(z) goes up and down, 
crossing zero at 3/4 n for every n, and decreasing in amplitude 
as n increases. But for small n—the likely condition for small 
developers with physical constraints and existing buildings 
around them—marginal is likely to be very different from 
average. It could be bigger or it could be smaller. The hedonic 
equation measures at best the marginal value of land, while the 
construction-cost measures back out the average.
Third, land is not a quantity. I am not indifferent between 
my 5,000 contiguous rectangular square feet of New Jersey and 
720,000 randomly chosen square inches spread across the face 
of the earth.
One distinction that matters is frontage versus depth 
(assuming that plots are roughly rectangular, which is 
endogenous). Frontage is more costly to construct and is 
probably more valuable because it sets the minimum distance 
to neighbors. Depth is less valuable. Land area is the product of 
the two, and there is probably more variation in depth than in 
frontage. If that is the case, the hedonic is picking up the less 
valuable dimension.
To see how this can be compounded by collinearity, suppose 
a community has two kinds of houses—those with garages and 
those without. Houses with garages are on lots with greater 
frontage, otherwise all structures are identical. Frontage is 
much more valuable than depth. All houses of each type have 
the exact same frontage, but depth varies randomly. An 
hedonic regression with the presence of garages and the square 
footage of the lot would conclude that land was valueless, or 
close to it, no matter what it was really worth. The value of 
frontage would show up in the coefficient on garages.
Land also varies in topography and physical characteristics. 
Some land is just lousy to build on or live on (due, for instance, 
to the presence of rock outcroppings, steep slopes, or bad 
swamps). People who want land for less valuable purposes 
(privacy rather than construction) are likely to end up holding 
such land. Differences in lot size within a community therefore 
are also likely to reflect differences in bad rather than good 
land. This is similar to the frontage scenario.
Fourth, with two dimensions and physical obstacles, the 
optimal subdivision problem becomes very difficult. In 
operations-research terms, it is a suitcase problem. One 
interesting result of these difficult problems is that “greedy 
algorithms”—the sort of myopic hill-climbing you could 
expect from a bunch of independent developers—usually do 
not produce optimality. So it is not clear that in the absence of 
zoning, optimal subdivisions would occur. Without optimal 
subdivisions, there is no chance that marginal cost will equal 
average cost even with regard to a large problem.
Finally, even if neighborhoods were constructed originally 
with marginal cost equal to average cost of land on every lot, 
they would not stay that way for long. Unanticipated shocks 
would destroy this equality and change optimal density. Of all 
the ways to increase density in an existing neighborhood, 
increasing the number of single-family homes on existing 
single-family land is the most drastic and the most expensive. 
To make small changes, you have to move all of the existing 
houses. This is not easy: the arrangement of houses and lots in 
a neighborhood is not likely to change much unless everything 
is torn down. Thus, the equality of marginal and average cost of 
land upon which the Glaeser and Gyourko paper is based will 
not be observed very often in neighborhoods more than a few 
years old, even in the best of all possible cases.
3. Summary
Glaeser and Gyourko are probably correct in observing that 
excessive zoning in certain jurisdictions makes life worse for 
poor people who do not live there. In that regard, their paper 
did not dramatically change my view. The paper’s actual 
contribution is much more novel and much more funda-
mental: the authors have raised very deep questions about how 
urban economists think about land and land markets. It will 
probably be a long time before these questions are answered 
properly.
The views expressed are those of the author and do not necessarily reflect the position of the Federal Reserve Bank of New York 
or the Federal Reserve System. The Federal Reserve Bank of New York provides no warranty, express or implied, as to the 
accuracy, timeliness, completeness, merchantability, or fitness for any particular purpose of any information contained in 
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