The Plane of Living and the Pre-crisis Evolution of
Housing Values in the United States
John I. Carruthers ✩ The George Washington University, Sustainable Urban Planning Program;e-mail: jic@gwu.edu
Gordon F. Mulligan University of Arizona, School of Geography and Development; e-mail:mulligan@u.arizona.edu✩

Corresponding author

Submitted in final for to the Journal of Economic Geography, March 2001. This paper and related research have beenpresented at the 2008 meetings of the Regional Science Association International in São Paulo, Brazil; the 2009
meetings of the Southern Regional Science Association, in San Antonio, Texas; the 2009 meetings of the European
Regional Science Association, in Łódź, Poland; and (by press) the 2011 Global Conference on Economic Geography,
in Seoul, Korea. Special thanks to session participants, Alastair McFarlane, and to two anonymous referees for theirhelpful comments and suggestions.

Abstract This paper explores the relationship between quality-of-life differentials and housing
values in the run-up to the recent financial crisis in the United States. The analysis combinesolder spatial demographic methods (systematic mapping) with newer spatial econometricmethods (autoregressive modeling) to deliver a panoramic view of the contemporary plane ofliving and an evaluation of its influence on housing values through time and across space.
Housing values are inextricably bound to geography — both natural amenities and humanamenities matter, but in somewhat different ways. The influence of natural amenities is growing
more powerful, but human amenities offer important opportunities to address market conditions
because they can more readily be enhanced via public policy. Several general observations for
public policy follow from these findings. Keywords: amenities, quality-of-life, housing, spatial
econometric analysis; JEL Classification: C21, Q51, Q56, R21, R23“I wish I had been out in California, when the lights on all the Christmas trees went out…”— The Rolling Stones, Winter (1973)
1. Introduction
Over 70 years ago, Goodrich et al (1935) advanced the concept of the “plane of living” tocharacterize quality-of-life differentials across the United States. At the time, the nation was in1the grip of the Great Depression and policymakers had a pressing need to understand how the
distribution the population had evolved to that point — and, going forward, how to influence
migration flows in a way that enhanced economic opportunity and personal wellbeing (Goodrichet al 1936). The original plane of living map is reproduced in Figure 1, and it displays acomposite index of three variables that reflects, as a percentage of the national average: (i)household income; (ii) the proportion of homes having radios; and (iii) the proportion of homeshaving telephones.1 This map is one of the earliest examples of spatial demography — thedemographic analysis of spatial aggregates (Voss 2007) — and, also, of research that explicitly
connects place-to-place variation in quality-of-life to the greater economic landscape (Greenwood
and Hunt 2003).2 The work was exceptionally innovative for its time and it helped establish an
enduring framework wherein living conditions are viewed as fundamental to a wide array ofsocioeconomic processes and outcomes.
Today, the United States is enduring the fallout from another economic dislocation that is
widely considered to be the worst since that of the 1930s and, although the circumstances of thetwo eras are different, the plane of living is again central to understanding the nature of the crisis
and, perhaps, its legacy. In particular, the recession that (according to the National Bureau of
Economic Research3) commenced in December 2007 was brought on by the implosion of a
massive bubble4 in the housing market — a bubble that that extended nationwide but was
unevenly inflated (see also: Gyourko and Sinai 2003; Glaeser et al 2008; Glaeser and Gyourko
2008; Martin 2010) due, in large part, to geographic quality-of-life differentials. Housing is acomplex commodity and its consumption involves the concurrent consumption of any locationspecific amenities and disamenities associated with it. When viewed across the nation as a whole,factors that contribute to (take away from) quality-of-life, like mild (harsh) weather and quality(poor) public services, raise (lower) housing values because they increase (decrease) the level ofcompetition there is to occupy places that have (lack) them. In this way, households factor all
kinds of living conditions into their calculus when deciding where to live and at what cost,
meaning that the topography of housing values mirrors that of the plane of living. Although thisrelationship is widely known, its role in the run-up to the current crisis and its implications for
future outcomes are not.

1

The plane of living was also reproduced in Hoover’s classic (1948) text The Location of Economic Activity — which
is where the present authors first discovered it.
2Ravenstein (1885) is generally acknowledged to be the very first.
3
For information on NBER’s recession dating procedure, see: http://www.nber.org/cycles/recessions.html.
4
On December 15, 2008, the popular real estate website Zillow.com reported that, in that year alone, homes across theUnited States lost an estimated $2 trillion in value — an amount equal to about 20% of the nation’s GDP. See:
http://zillowblog.com/2-trillion-in-home-values-lost-in-08/2008/12/.

2

This paper addresses both dimensions of the question by examining the nation’scontemporary plane of living and using it to explore how housing values evolved to their precrisis levels through time and across space. There are three specific objectives: (i) to illustrate
how housing values vary from place-to-place and explain why quality-of-life differentials cause
them to vary so dramatically; (ii) to estimate a series of income capitalization models aimed atweighing the relative importance of the plane of living in the recent evolution of housing values;and (iii) to identify some forward-looking observations, with a particular eye toward thedissolution of the crisis. The analysis, which covers the entire continental United States, provides
a panoramic look at the housing value landscape in 1980, 1990, and 2000. Like Goodrich et al(1935, page 1), who observed that they “ought not try to say where people should move without
first learning where they have moved,” this work is concerned first-and-foremost withascertaining the temporal and spatial trajectories of housing values vis-à-vis household income,housing-related debt, and quality-of-life differentials, and then with suggesting ways ofinterpreting that information in a forward-looking way. Because “past is prologue” — andbecause housing values are inextricably, and increasingly, bound to the plane of living — theexperience of the last several decades holds valuable lessons for those yet to come.

2. Background Discussion
2.1 Regional Development and the Plane of Living
As early as the 1950s, Ullman (1954) — following an even earlier insight made by Hoover(1948) on the effects of both “physical” and “cultural” amenities — argued that “pleasant living
conditions” contribute to differential rates of regional development, and that these differentials
were likely to accelerate as the American population grew more footloose and wealthier. And,
indeed, they have: households are evermore free to choose where to live on the basis of both
economic opportunity and personal preference, and commonly exert their ability to do so (seeKahn 2006).5 Accordingly, migration research now recognizes that models specified without
measures of location-specific amenities suffer from omitted variable bias and, as a result, yield
perverse results (Graves 1980; Greenwood and Hunt 1989; Clark and Hunter 1992; Hunt 1993;
Mueser and Graves 1995; Clark et al 2003). Because of this changing balance between householdincome (opportunity) and quality-of-life (preference) there is every reason to expect that theresulting topography of housing values has shifted as well. Moreover, any nationwide recovery
5

See, for example, Withers and Clark (2006), Withers et al (2008) and Blackburn (2010) for analyses of how thesecomplex decisions impact the inner-workings of families.

3

from present circumstances in the housing market must ultimately confront the fact that different
geographic segments of the population face big differences in the relative costs and benefits ofhomeownership — explicitly spatial differences that cannot be explained by income alone(Perloff et al 1960) — so it is important to know more about how those differences came to be in
the first place.
The cross-national situation as it stood just prior to the 2007 collapse is illustrated inTable 1, which lists data for each of the 48 contiguous states plus Washington, DC in 1980 and
2005. In the earlier year, the median value (in 2010 dollars, rounded to the nearest $100) of owneroccupied housing units ranged from a high of $270,100, or 179.08% of the national median,which was then $150,800, in California to a low of $99,100, or 63.73% of the national median, in
Arkansas. In the later year, the median value of owner occupied housing units ranged from a highof $649,700, or 285.19% of the national median, which was then $227,800, in California to a lowof $112,500, or 49.37% of the national median, in Mississippi. Between the two years, housing
values grew the most, by $379,600, in California and at the fastest rate, by 215.82%, in
Massachusetts — meanwhile, values actually fell in three states, by $19,200, $9,000, and $8,000,
in North Dakota, Wyoming, and West Virginia, respectively, and they grew at the slowest rate, by
just 0.89%, in Louisiana. Clearly, these differences correspond to geographic patterns ofopportunity and, hence, household income, but they just as clearly reflect preferential responses
to quality-of-life differentials — namely, the plane of living.
Perhaps the best-known research on how households respond to the plane of living
originates from the hedonic price methodology formalized by Rosen (1974).6 Within this socalled “compensating differentials” framework, equilibrating processes — population,
employment, and wage growth (Carruthers and Mulligan 2008) — ensure that households are
indifferent among locations, a situation that implies that: the value of wages plus the value ofquality-of-life minus the cost of housing is more-or-less constant nationwide (see Glaeser 2007).
Rosen (1979) first used hedonic price analysis to estimate the value of quality-of-life differentials
by regressing wages (the transacted price of labor) on job and personal attributes, plus a set of
location-specific natural amenities. Roback (1982, 1988) then extended the approach to the
housing market by separating out the local real estate and labor markets, revealing that housing
values also capitalize quality-of-life differentials.7 In these studies, desirable (undesirable) living
6

See Bartik and Smith (1987), Gyourko et al (1999), and/or Mulligan et al (2004) for in-depth reviews and Freeman(2003) for an overview of research methodology.
7
Ideally, this kind of analysis is conducted with micro, or household-level, data, but that kind of data can be difficult, if
not impossible, to obtain for locations across the entire country — especially at multiple points in time. For this reason,
research of national scope commonly ends up using median housing value (and corresponding housing attribute) datareported by the Census Bureau (see, for example, Chay and Greenstone 2005; Welch et al 2007; Greenstone and4conditions negatively (positively) influence wages because, everything else being equal, people
living in attractive (unattractive) places demand less (more) pay for their work; conversely,
desirable (undesirable) living conditions positively (negatively) influence housing values because
people living in attractive (unattractive) places are willing to pay more (less) for their homes.8 In
terms of migration, the more appealing a place is, the greater the number of households thatdesire to live there — so there is increased competition in the both labor and housing markets,driving wages down and housing values up. (See DiPasquale and Wheaton 1998 for a “macro”
perspective on labor and housing markets).
These outcomes result from the fact that the contemporary regional development process
is driven by a combination of opportunity and preference: more-and-more, households nationwide
exhibit an attraction to places offering both jobs and quality-of-life — and, especially, a balance
between the two (Glaeser et al 2001; Glaeser and Shapiro 2003). The behavioral mechanisms
involved are well understood, but, less understood, are two broader, more systematic issues: (i)how the outcome plays out across the national migration system; and (ii) the relative importanceof the plane of living in the temporal and spatial evolution of housing values.
2.2. Stylized Facts
The continental United States is made up of 3,103 county equivalents, including all counties andindependent cities — of these: 1,082, containing about 83% of the population, belong tometropolitan areas; 687, containing about 10% of the population, belong to micropolitan areas;and 1,244, containing about 7% of the population, are not part of a core-based statistical area
(CBSA). To set the scene for the upcoming econometric analysis, the spatial distribution of the
population within individual counties is shown in Figure 2, a map of CBSA (blue and red) andnon-CBSA (white) counties with population-weighted center-points marking each county’s centerof gravity.9 These points were used to generate all remaining maps in this paper, via an inversedistance-weighting (IDW) procedure, the simplest method of interpolating a surface from point
data. Specifically, IDW estimates values between points i and j as a weighted average, where theGallagher 2008). The drawback of this approach lies in the risk of generating what is variously called “aggregationbias,” an “ecological fallacy,” or a “modifiable areal unit problem” (Wong 2009) — all of which are ways of describing
what happens when spatially aggregated data is used to draw conclusions about household-level behavior (Voss 2007).
That being noted, aggregated data do represent a viable alternative to micro data — just as long as care is taken when
making inferences from it.
8
Other important extensions of this approach include papers by Berger et al (1987), Hoehn et al (1987), and Blomquist
et al (1988), who developed quality-of-life rankings by simultaneously analyzing the effects of location-specificamenities both across and within metropolitan areas, and Gyourko and Tracy (1989, 1991) who demonstrated that local
fiscal conditions also account for interregional variation in wages and rents.
9
The population-weighted center-points were calculated in ArcGIS via the “mean center” (see, for example, Barber1988) tool using census tract level data from 1990.

5

weight given to each point is determined by a standard distance-decay function (Fotheringham etal 2000; Longley et al 2001):f (d ij ) =1/ d ij2 .

(1)

To generate the following maps, relevant data, all of which is available from the Census Bureau,
was attached (using ArcGIS) to the population weighted center points and the surfaces were!
interpolated from there: Figure 3 displays trend surfaces of population change across thecontinental United States for (3a) 1970 – 1980, (3b) 1980 – 1990, and (3c) 1990 – 2000; Figure 4
displays trend surfaces of median housing value (in 2010 dollars) in (4a) 1980, (4b) 1990, and(4c) 2000; Figure 5 displays trend surfaces of median household income (again in 2010 dollars)in (5a) 1979, (5b) 1989, and (5c) 1999; and Figure 6 displays trend surfaces of the medianmortgage payment — that is, the median monthly cost of owner occupied housing — as apercentage of median monthly household income in (6a) 1980, (6b) 1990, and (6c) 2000. The two
measures of income (annual income and the median mortgage payment as a percentage of themonthly income) are considered in order to evaluate, first, income itself and, second, income
relative to housing-related debt. Each group of maps shares a common scale, so the figures areinternally consistent — that is to say, (-a), (-b), and (-c) are directly comparable — and, for all,the darker the shading, the greater the value. Descriptive statistics and the specific source of theseand all other variables involved in this paper are listed in Table 2.
To begin, Figure 3 shows a systematic pattern of population deconcentration: from 1980
to 1990 to 2000, the maps reveal an intensifying pattern of spatial focusing (see Plane andMulligan 1997) in the nation’s migration system — a crystallization of growth and decline aroundwhat Frey (2002) has labeled the “Three Americas:” (i) the low-density, suburban “Sunbelt;” (ii)the high-density, urban “Melting-pot;” and (iii) the declining rural “Heartland.” Next, Figure 4
shows that, in 1980, housing values were relatively uniform beyond major metropolitan areas but,by 1990, they began to exhibit more polarization along the metropolitan ⇔ nonmetropolitan
continuum, a pattern that persisted in 2000, but with a key geographic twist — namely, thatvalues rose significantly nationwide.10 Across the United States, and, above all, in the rapid
growth areas visible in Figure 3, housing values had already reached unprecedented levels by
2000, the year the country had essentially locked in on a course toward the housing bubble and10

Although the median housing values reported by the Census Bureau are obviously not the same as sales prices —they are derived from homeowner-provided estimates — they have been found to be a remarkably good indicator of
actual market value (see Kiel and Zabel 1999).

6

subsequent financial collapse.11 Then, Figure 5 shows that, from 1979 to 1999, median householdincomes likewise hardened around major metropolitan areas but, at the same time, extended out
into formerly remote areas — recall that the interstate highways system was not completed until
the 1970s, and deregulation of the airline industry began lowering the cost of air travel in the
1980s12 — especially in the Atlantic Southeast and Rocky Mountain West. (Maps based on wages
would look rather different, but unearned components of income, including retiree pensions,dividend payments, and more, are integral to the matter at hand.) Finally, housing-related debt isshown in Figure 6, which reveals a nationwide climb over the course of the three decades: agreater proportion of monthly household income being channeled into mortgage payments,
especially in major metropolitan and/or rapid growth areas. As a set, these maps illustrate thegreat wealth and debt that was amassed in the housing market, plus the spatial deconcentration of
population, and, with it, household income, that has been realized in recent decades (Frey 1993,
2004; Fuguitt and Beale 1996). Together, they point to fundamental changes in the very nature of
housing consumption — structural changes directly attributable to the evolving importance of theplane of living.
As for the plane of living itself, both natural and human amenities matter so, to close out
this section, each is addressed in turn. About ten years ago, McGranahan (1999) constructed anatural amenities index covering all counties in the continental United States.13 The index isbased on six separate sub-indices: (i) January temperature; (ii) hours of sunshine in January; (iii)the January / July temperature gap; (iv) July humidity; (v) topographic variation; and (vi) relative
water area, including access to coasts. Values of the sub-indices were transformed into z-scoresand then aggregated (by adding them up) into a single composite index. As shown in Figure 7,
counties registering the highest (lowest) scores are located in the most (least) environmentally
appealing parts of the country — some specific counties are identified in the leftmost column ofTable 3, which lists the top and bottom 10 in their ordinal ranking. All of the top counties are
situated in the warm, sunny environs of coastal California, and all of the bottom counties are in
the cold-in-the-winter / hot-and-humid-in-the-summer environs of the flat, landlocked Great
Plains and Midwest. This index has been used in a wide variety of empirical research and is agood predictor of both migration and development, including land use change (see, for example,
Carruthers and Vias 2005).
11

Beginning in 2000, the conventional 30-year mortgage rate fell consistently through 2005, when it started slowly
rising again. See the Federal Reserve Bank of St. Louis’ FRED (Federal Reserve Economic Data) database:
http://research.stlouisfed.org/fred2/series/MORTG.
12
See various analyses from the Government Accountability Office: http://www.gao.gov/new.items/d06630.pdf.
13
The natural amenities scale and underlying data are available online from the USDA’s Economic Research Service,
here: http://www.ers.usda.gov/Data/NaturalAmenities/.

7

While the natural amenities index distinguishes areas of the country according to theirenvironmental appeal, a corresponding human amenities index is needed to identify thesocioeconomic dimensions of the plane of living. The index — which was constructed by theauthors for the purposes of this analysis — is composed of four sub-indices: (i) the percent of the
population 18 years and older having a college degree, from the Census; (ii) per capita local
government expenditure, from the Census of Governments; (iii) the per capita number ofentertainment establishments, from the Economic Census; and (iv) territorial density, or thecounty’s population divided by its land area, from the Census. The data from the Census
corresponds to decennial census years but, since the Census of Governments and the Economic
Census are conducted on off-census years, that data corresponds to 1977, 1987, and 1997. The
index itself was constructed in the same way as the natural amenities index: by calculating zscores for each of the sub-indices and adding them up. Figure 8 displays the resulting values in(8a) 1980, (8b) 1990, and (8c) 2000 and the remaining columns of Table 3 list the top and bottom
10 counties in their ordinal ranking for each year. As intended, the highest rated areas of thecountry are cosmopolitan places and resort destinations known for their abundant cultural,
recreational, and other human amenities and the lowest rated areas are more rural places that do
not have that same type of draw. Table 4, which contains a set of three correlation matrices (onefor each year) of the sub-indices making up the human amenity index, shows that they are
independent of one another. The index is, however, highly correlated — and, therefore, a stablemeasure — across years: the correspondence between 1980 and 1990 = 0.87; 1980 and 2000 =
0.83; and 1990 and 2000 = 0.87. The following paragraph briefly explains the rationale for eachof the four sub-indices; for further information on socioeconomic factors that enhance quality-oflife see in-depth reviews by Bartik and Smith (1987), Gyourko et al (1999), and/or Mulligan et al(2004).
First, analysts have long recognized the benefits of education, a measure of humancapital, for income (Glaeser and Maré, 2001) and human wellbeing more broadly (Putnam 2001).
These benefits are particularly great in major metropolitan areas, which are commonly sought outby, to name a few groups, Costa and Kahn’s (2000) college-educated “power couples” faced witha collocation problem, households and firms in Drennan’s (2002) “information economy,” andmembers of Florida’s (2002a, 2002b) “creative class.” Second, the benefits of local government
expenditure have important effects on housing values because of the kind of Tiebout (1956)
sorting it engenders (see Ladd 1998, Fischel 2001, and Oates 2002 for useful summaries). An
aggregate measure of public spending, total direct expenditure, is used because its value as acomposite amenity is what is of interest here — but Welch and Waldorf (2006) and Welch et al8(2007) explore how different kinds of spending influence both housing values and rents. Third,
entertainment establishments are a strong draw in both urban (Glaeser et al 2001) and rural(Deller et al 2001; McGranahan et al 2001) areas of the country. Certain households are
particularly drawn, for various reasons — see Black et al 2002 for a good example (gay couples)that readily generalizes to many other demographic and social groups — to areas abundant in
adult, as opposed to child, related entertainment amenities. Last, density is increasingly
recognized as a main factor influencing the comparative advantages of regions (Jacobs 1961;
Glaeser and Gottlieb 2006). For example, the “new economic geography” framework (Fujita et al
1999; Baldwin et al 2003; Brackman et al 2009) suggests that the kind of variety (above-andbeyond entertainment opportunities) found in dense urban agglomerations has advantages for
production and consumption alike.14 For present purposes, the idea is the same: counties that aredenser in population are more productive and provide their residents with a wider aray of highquality goods and services.
The trend surfaces shown in Figures 7 and 8 are analogues of the contemporary plane ofliving: they jointly depict the spatial distribution of quality-of-life differentials across the UnitedStates. Compared to Goodrich et al’s (1935, 1936) original conceptualization, reproduced in
Figure 1, today’s setting is more nuanced, particularly with its orientation toward naturalamenities, but it nonetheless bears a certain resemblance. The Northeast Corridor and the Pacific
Coast conurbations dominate the older and newer maps alike and, likewise, the Atlantic Southeast
and remote parts of the Southwest remain what Hoover (1948, page 204) called “problem areas”
even today. Then again, there are some big differences. Mainly, the great manufacturing regionsof the Midwest — now often pejoratively referred to as the “Rustbelt” — and select agriculturalareas as far west as the Great Plains stood out dramatically in the 1930s, but no more. Anotherlarge, more positive difference between the two eras is the wider Four Corners section of theSouthwest, which rated poorly in the 1930s, but now rates higher for its natural and humanamenities (see Mulligan and White 2002). Although the two indices are kept separate for the sakeof exposition and the analytics in the next section, the combination of them is what makes up theplane of living — it is the surface that modern American households negotiate as they decide
where to live, and at what cost.

14

Recent theoretical evidence suggests that natural amenities may also contribute in a similar way (Wang and Wu
2010)

9

3. Econometric Analysis
3.1 A Parallel Plane of Living
The point of departure for the econometric analysis is a simple income capitalization model of
housing values suggested by Tolley and Diamond (1982), Glaeser et al (2001), and Carruthersand Mulligan (2006):

mhv i* = "1 + " 2 # mhi i* + $ i .

(2)

In this equation, mhv i* is the natural log of median housing value in county i; mhi i* is the natural!log of median household income; "1 and " 2 are estimable parameters; and " i represents thestochastic error term. (Ideally, the analysis would use value per square foot of living space, along!
!
with — or perhaps instead of — median housing value, but no census variable exists that would!
!
!
facilitate this metric.) Note that, because the equation is in log-linear form, the parameter " 2 is anelasticity, meaning that it registers the percent change in median housing value induced by apercent change in the relevant explanatory variable — or, more specifically, the rate at which the!
household income capitalizes into housing value. Note, too, that, while many studies havefocused on estimating the income elasticity of demand for housing, a rule of thumb is that the“correct” income elasticity is somewhere around 1.0 (Muth 1969; Mills 1972; Mayo 1981).
Although the parameter on household income should not be confused with an actual, householdlevel income elasticity of demand because it is based on aggregated data — and, more to thepoint, equation (2) is not, in any way, a demand function — logically, it should still be in thevicinity of 1.0 if it representatively describes the cross-national relationship between householdincome and housing value.
An alternative, more exploratory way of examining how household income capitalizes
into housing values is to use the second measure of income identified in the backgrounddiscussion, the median mortgage payment as a percentage of the monthly income — a measurethat accounts for income relative to housing-related debt:

mhv i* = "1 + " 2 # mmpi* + $ i .

(3)

The notation is essentially the same as in equation (2), except that mmpi* is the natural log of the!monthly mortgage payment and; the " s replace the " s; and " i represents the error term. Unlike" 2 , it is not clear upfront what magnitude of value to expect out of " 2 , the parameter that!

!

measures the rate at which the mortgage payment as a percentage of monthly income capitalizes!
!
!
into housing value. While not as cut-and-dry as equation (2) this alternative specification is worth!
pursuing, if only for exploratory purposes, because it offers another type of insight into the10relationship between income and housing values — in particular, assuming that the size ofmortgage payments relative to income captures the degree of debt and equity associated withhomeownership, it gives some (admittedly exploratory) evidence related wealth.
Ordinary least squares (OLS) estimates of these two simple baseline models are listed,
respectively, in the left- and right-hand panels of Table 5.15 The fitted regression lines themselves,
along with their corresponding data points, are shown in Figure 9 and Figure 11, scatter plots ofthe two income variables (on the x-axis) versus housing value (on the y-axis) in (9a and 11a)
1980, (9b and 11b) 1990, and (9c and 11c) 2000. As expected, the income elasticities estimatedvia equation (2) fall around (though upward of) 1.0; the elasticities estimated via equation (3)start out negative 1980 and become increasingly large in 1990 and 2000. The table also showsthat median household income does a far better job of explaining housing value than the monthly
mortgage payment as a percentage of income: the adjusted R2s average ~0.58 for the former,
compared to just ~0.04 for the later.
A useful feature of these models — and, indeed, the whole point of estimating them inbivariate form the first place — is that their error terms represent amenity indices because they
expose the extent to which the income variables over- or under-predict housing value. In
particular, the error term (the observed value minus the predicted value in the scatter plots) is
positive (negative) when the model underestimates (overestimates) a county’s median housing
value, based on household income and mortgage payments. As explained in the backgrounddiscussion, the compensating differentials framework indicates that those living in attractive(unattractive) places pay more (less) for their homes as a result of competition in the real estatemarket. So, the extent to which housing is over (under) valued relative to the national baseline
may be interpreted as a measure of the premium (discount) that households pay for a given
county’s relative endowment of amenities — and, because of this, equations (2) and (3) can beused to construct analogues of the quality-of-life differentials mapped in Figures 6 and 7: aparallel plane of living.
To illustrate, trend surfaces of the residuals associated with the OLS regression lines
shown in the two sets of plots are mapped, again using IDW, in Figure 10 and Figure 12. Bothsets of maps square nicely with the maps of the natural and human amenity indices — and witheach other, though not perfectly: the correspondence between the two types of errors is 0.70 in
15

These and all subsequent models are estimated year-by-year because the parameters are expected to vary throughtime. In order to insure that the differences are statistically significant, Chow tests based on estimates of equations (2)and (3) were performed. In the Chow tests, the sum of squared residuals totaled across three years of estimation iscompared to the sum of squared residuals from a model containing all three years pooled together. The resulting Fstatistics for the income and mortgage payment models are 299.78 and 223.93, respectively – far greater than thecritical value of 2.71 needed to reject the null hypothesis that the parameters are the same across all three years.

111980; 0.46 in 1990; and 0.48 in 2000. Note how the trend surfaces shift through time. In Figure
10, the Pacific West and Rocky Mountain West stand out as having high amenity values (deeppurple) in all three panels, but, in the middle panel, the effect appears to settle somewhat —perhaps as a result of the brief reversal of migration trends that occurred in the 1980s (Frey 1993;
Fuguitt and Beal 1996) — before picking up again in the final panel.16 On the other side of thecountry, in the Northeast Corridor, the opposite happened: the amenity value, clearly visible in all
three panels, swells in the middle panel before returning to more-or-less previous levels in the
final panel. Meanwhile, the Great Plains and Midwest consistently register large disamenity
values (deep green) but, in central Texas, the effect dissipates in the middle panel before
returning again in the final panel. In the Atlantic Southeast, a region that experienced a great dealof growth between 1980 and 2000, the disamenity effect steadily declines (becoming moreyellow) over the three panels, producing corresponding amenity values that take shape year-byyear. Very similar patterns are visible in Figure 12, with one key exception: the Northeast
Corridor and major metropolitan centers of the Midwest and elsewhere consistently stand out (indeep red) as places where the housing-related debt as a percentage of monthly income debt
greatly underestimates median housing value.
The ten counties at the top and bottom ends of the two estimated amenity scales are listed
for each year in Table 6. The table shows some correspondence between the residuals fromequations (2) and (3) — but more between the top and bottom ends of the natural and humanamenity indices listed in Table 3. There are, however, two noteworthy differences, which help toillustrate just how well the estimated indices interface with the observed indices: (i) the top 10
counties include a blend of places along the Atlantic and Pacific seaboards rich in naturalamenities, human amenities, and/or both; and (ii) the bottom 10 counties are dominated byremote, declining, and/or impoverished places in the Great Plains and Southwest. Compared to
Figures 6 and 7, which illustrate the amenity-related quality-of-life differentials of the plane ofliving, Figures 10 and 12 represent its value-related differentials — that is, the former are
analogues of the amenities themselves and the latter are analogues of their economic value. The
two sets of maps are not so much alternative representations of the same thing as different,
parallel dimensions of the modern socioeconomic landscape. As such, the surfaces they display
are tightly interwoven: the amenity- and disamenity-related values shown in Figures 10 and 12
are direct outcomes of preferential actions taken by households in response to the quality-of-life
differentials pictured in Figures 6 and 7. Given this relationship, the logical next step is to connect
16

There is also evidence of households migrating out of California to comparatively less expensive locations
throughout the West (Henrie and Plane 2007) so an interesting issue for further research is the extent to which westernreal estate values and amenity consumption have been driven by a wealth effect from that state.

12the representations in a way that sheds light on how housing values evolved to their pre-crisis
levels, through time and across space.
3.1Economic Opportunity Versus Personal Preference
The relative importance of economic opportunity (income) versus personal preference (the planeof living) in the recent evolution of housing values is weighed by expanding equations (2) and (3)to include a spatially lagged dependent variable (Anselin 1988; Arbia 2006) that addresses spatial
autocorrelation in the median housing values of proximate counties, state-level fixed effects(Wooldridge 2000, 2002), a set of relevant explanatory variables — including the natural amenity
and human amenity indices:

mhv i* = " # Wij # mhv *j + $s + Xi* # % + &i .

(4)

Here, mhv i* again represents the natural log of median housing value in county i; Wij " mhv *j*!represents the endogenous spatial lag of the dependent variable; Xi represents a vector of

autoregressive! exogenous explanatory variables, all in natural log form; " represents a spatial!
parameter that registers how median housing value in county i is influenced by median housing!
value in proximate counties j; "s represents a vector of state fixed effects, including one for!
Washington, DC; " represents a vector of parameters on the exogenous explanatory variables;and "i represents the stochastic error term. By convention, Wij is used to denote a 3,103 × 3,103!
(n × n) row-standardized
spatial weights matrix that describes the connectivity of the dataset. The!

!

weights matrix was created using the population-weighted center of each county’s population —!
the points in Figure 2 — to identify neighbors. In the scheme, each county i is related to all
counties j having population centers located within 50 miles of its own population center or, inthe 65 cases where the distance to the nearest neighbor is greater than 50 miles, to a single
neighbor. Finally, the individual variables making up the vector Xi* are as follows: (i) either (inseparate estimations) median household income or the monthly mortgage payment as apercentage of monthly income; (ii) total population, a demand-side control; (iii) the median age!
of the population, another demand side control that addresses the tenure of homeowners; (iv) a
construction cost index, a supply side control measured the average wage in the constructionindustry divided by the average wage across all industries; (v) the natural and human amenity
indices, together representing the plane of living; and (vi) metropolitan and micropolitan area
indicator variables.
Before moving on, observe that equation (4) indicates that proximate housing values
influence one another — because, for example, nearby counties have common labor markets and,13

therefore, have real estate markets that are shaped by the same economic forces. In practice, theconnection means that median housing value in county i depends on median housing values incounties j and the other way around so the spatial lag, Wij " mhv *j , is endogenous to mhv i* and themodel cannot be properly estimated using OLS. A straightforward alternative is a spatial twostage least squares (S2SLS) strategy developed by Kelejian and Prucha (1998).17 In the first stage!
!
of the S2SLS algorithm, the spatially lagged dependent variable, Wij " mhv *j , is regressed on Xi
and Wij " Xi — the spatial lag of Xi — to produce predicted values. Then, in the second stage ofthe algorithm, the predicted values, say “ Wij " mhv *j -hat,”!are used in place of the actual! values in!

equation (4). This approach! yields efficient, unbiased parameter estimates, whether or not spatial
error dependence is also present (Das et al 2003). In order to carry the procedure out, the spatial!
variables, Wij " mhv *j and Wij " Xi , were calculated in GeoDa, a program for spatial computation(Anselin 2003; Anselin et al 2006), then imported into EViews, an econometrics program, withthe rest of the data, where the two-stage least squares (2SLS) regressions were run using panel!
!
settings to identify the states as cross-sections for fixed effects and as clusters for White-adjusted
standard errors.
Table 7 lists the S2SLS estimation results for equation (4), with the median housing value
version of the model shown in the left-hand panel and the monthly mortgage payment version of
the model shown in the right-hand panel. Nearly all of the parameters are statistically significant
with sensible signs and the adjusted R2 values indicate that each of the equations does a good jobof explaining variation in the dependent variable.18 The results are as follows. First, each of thespatial lags is positive and they generally show a steadily increasing level of connectivity amongproximate housing markets over the 30-year timeframe — that is, a substantive tightening of
spatial interdependence. Second, the parameters on median household income remain close to the
expected value of one, and grow closer to that value through time. The median mortgage payment
is not statistically significant in 1980, which is not surprising because that was an era of
exceptionally high interest rates — in the 1970s, the 30-year conventional mortgage rate began a
precipitous climb that peaked at 18.45% in October, 198219 — when many homeowners’
mortgage payments were skewed heavily toward interest rather than principle; the variable
becomes significant in 1990 and doubles in size between 1990 and 2000. Third, the parameters on
total population are positive, highly significant, and stable across the entire series of models.
17

See Anselin 2009 for a plainspoken overview of the procedure and its alternatives.
As a reminder: all parameters associated with continuous variables are elasticities, which are unit free metrics, sothey enable reasonably direct comparisons to be made among the different variables.
19
See: http://research.stlouisfed.org/fred2/series/MORTG?cid=114.
18

14

Fourth, the median age of the population is negative — signaling that tenure matters in the sensethat older households live in lower valued housing — and significant in all instances except one:the 2000 monthly mortgage payment model. Fifth, the construction cost index is positive andstatistically significant in both sets of models in 1980 and 1990, but not in 2000, perhaps due to anationwide retrenchment in, and evening out of, the cost of homebuilding due to gains in theefficiency of production.20 Sixth, the parameter on the natural amenity index is significant andpositive across all models, and, in the income models, it nearly doubles in size between 1980 and
1990. Seventh, the parameter on the human amenity index is also consistently significant andpositive, but it diminishes in size — probably due to an evening out of access to them throughtime. Last, the metropolitan and micropolitan area indicator variables register a fluctuating
influence both across years and between the two model specifications.
As a final step, in order to examine further spatial relationships in the model, theestimating equation is expanded again21 — this time, by adding spatial lags of the two amenity
indices into the mix:

mhv i* = " # Wij # mhv *j + $s + Xi* # % + Wij # Z i* # & + ' i .

(5)All notation is exactly the same as in equation (4) except for: the vector Z i* " Xi* — where Z i* is*!the natural amenity index and the human amenity index — so Wij " Z i represents the spatial lag ofand " i ,those two variables; " , a vector of parameters on the spatially!lagged amenity variables;!
the error term, in place of "i . This “spatial expansion” (Cassetti 1972) model is estimated the!
exact same!way as before except that, because it contains spatially lagged explanatory variables,!
second order spatial lags, or spatial lags of the spatial lags, are used as additional instrumental!
variables in the first stage of the S2SLS algorithm.22
Table 8 lists the estimation results, which remain much the same for most of the
explanatory variables, so the focus is on resulting differences. Across both panels of models,
adding the spatially lagged amenity variable reduces the parameters on the spatially lagged
dependent variables in 1980 and 1990 — but increases them slightly in 2000. In the first variantof the models, the parameter on the natural amenity index is reduced by the inclusion of its spatial
20
The coefficient of variation (mean / standard deviation) of the Census Bureau’s constant quality construction costindex across the Northeast, Midwest, South, and West regions fell from 0.19 in 1980 to 0.12 in 1990 to 0.11 in 2000.
See: http://www.census.gov/const/price_sold.pdf.
21
Adding independent variables to the models — especially in the form of spatial lags of extant independent variables— increases the possibility of their being hampered by multicollinearity. Multicollinearity arises when one or more of
the independent variables included are closely correlated and can result in inefficient estimates if the estimatedparameters have a large variance. In the present case, the large sample size helps minimize the issue — and what’s
really of interest is the extent to which the influence of the various amenities extends across geographic space while
controlling local conditions. See Wooldridge (2000) for a discussion of multicollinearity and its implcations.
22
Special thanks to Ingmar Prucha for his guidance on this.

15

lag, which carries a parameter that is larger or, in 2000, as large, as its non-lagged counterpart; inthe second variant of the models, adding the spatial lag of the natural amenity index has little
effect and, in fact, the spatial lag only comes in significant (and negative) in the 2000 model.
Meanwhile, the parameters on the human amenity index are unchanged by the inclusion of its
spatial lag, which exhibits a variable pattern of significance and influence, positive or negative,
across the series of models. In net, proximate human amenities don’t have much of an influenceon housing values. The finding is sensible given that, over time, human amenities have becomeless spatially concentrated and, therefore, less influential on nearby areas than they have been in
the past.
All together, the evidence reported in Tables 7 and 8 shows that the plane of living has
played a main role in the recent evolution of housing values — and that this role is not static: it
continues to evolve both through time and across geographic space. Setting aside the more
exploratory mortgage payment models, the relative importance of natural and human amenities isstraightforward to evaluate via the elasticities reported in the left-hand panel of Table 8.
Specifically, the elasticities are applied to percent changes associated with “transforming” acounty at the first quartile of the various amenity indices such that it was at the third quartile —that is, hypothetically, moving from the 25th percentile to the 75th. Such (cross-sectional) change
in terms of the natural amenity index and its spatial lag implies shifts of 29.31% and 22.18%;
such change in terms of the human amenity index and its spatial lag implies shifts of 60.10%,
56.26%, and 55.89% and 41.94%, 36.83%, and 37.69% in 1980, 1990, and 2000, respectively.
Applying the various elasticities to these numbers yields impacts of 3.37%, 6.11%, and 7.34%
and 4.34%, 5.20%, and 5.51% for the natural amenity index and its spatial lag, respectively,
across the three years; do the same for the human amenity index yields impacts of 8.81%, 8.47%,
and 5.90% and 4.35%, 0.00%, and –4.37%. These numbers are substantive enough to pay
attention to: they suggest that public policy aimed at enhancing the plane of living may alsobolster housing values and, in turn, household wealth.

4. Some Forward-looking Observations
Having explored the plane of living and evaluated its influence on housing values, the remainderof the discussion focuses on identifying some forward-looking observations in light of thefinancial crisis. To recap the main findings of the econometric analysis: (i) the quality-of-life
differentials of the plane of living are oriented around environmentally appealing, cosmopolitan
places; (ii) these amenity-related differentials give rise to corresponding value-related16

differentials that exhibit a parallel topography; (iii) over time, housing values have become
increasingly connected across space and have also come under greater influence of naturalamenities, but somewhat lesser influence of human amenities; and (iv) the influence of naturalamenities has an extensive reach that has grown more powerful with time, while just the opposite
appears to be the case for human amenities. As a whole, the evidence suggests that the plane ofliving played a big part in the ratcheting up of housing values evidenced in Figure 3 — aninterpretation consistent with other evidence that quality-of-life has increased substantially invalue over the past several decades (Costa and Kahn 2003; Kahn 2006). Several generalobservations follow from findings.
Foremost, an unhappy, and all-too-obvious, observation is that the implosion of the
housing bubble has left many Americans holding homes valued less than they paid for them —and owe on them.23 But, as the experience leading up to the crisis illustrates, a lot of these homes
are embedded in markets with abundant natural and human amenities and excellent intermediateto long-run prospects: California, to name just one state, is all-too-well acquainted boom and bustcycles, and has a demonstrated record of recovering from wild upheaval in its real estate markets.
That is, in net, places having an enduring appeal for their high quality-of-life may come out of theslowly-easing crisis comparatively well. On the other hand, places that do not have the same kindof prospects — whether because of dissipating labor markets, low natural and/or humanamenities, or, worse still, a combination of the two — are sliding down a steep and very slippery
slope. Indeed, the kind of place-based policy frameworks that some analysts (like Partridge andRickman 2006) have advocated as an approach to endemic poverty may eventually be needed toshore up housing markets with particularly grim outlooks. Power (1996) and Power and Barrett(2001) have suggested a plausible way forward for formerly resource-dependent areas of the
Rocky Mountain West — but the same kind of path is just not open to manufacturing-dependent
areas forsaken for their deteriorating economies and the character of their environments. As
unjust as it is, regions that fail to grow, along with those that remain stranded in perpetual
economic decline, may end up being permanent casualties of the financial crisis if, going forward,
great innovation and effort is not taken in the formation of place-based housing and development
policy.
23

A question that may gain increased traction in the wake of the crisis is: how have housing-related income tax benefits
contributed to the inflation of the housing bubble? And, by extension, to what extent have they subsidized theconsumption of amenities? Voith and Gyourko (2002) show that, with tax benefit capitalization, high-income
households consume greater quantities of land — and Gyourko and Saini (2003) find that the spatial distribution ofincome tax benefits for homeowners is highly skewed, with high-amenity states registering large positive net transfersand low-amenity states registering large negative net transfers. For these reasons (among others) Glaeser and Gyourko
recommend lowering the cap for the tax write off from $1 million to $300,000 — a move estimated to impact fewer
than one in 20 homeowners.

17Glaeser (2007) argues for people-based — as opposed to place-based — policies forcombating decline but, for its merits, the trouble with this perspective is that it literally assumes
geography away: for many reasons, geographic space is “sticky” meaning that households andfirms are not perfectly mobile and often cannot relocate very far, if at all. Consider, for instance,that people have entrenched family and social networks; aesthetic and psychological attachments
to place; different perspectives on, and practical alternatives in, the reach and scale of labormarkets; varying capacities, financial and otherwise, for relocation; and more. In short, ahousehold’s spatial behavior is influenced, in a very fundamental way, by its view of geography
itself (see Abler et al 1971). While some households may be ready, willing, and able to relocate
across the country, or even the world, for the sake of opportunity and/or preference, others findeven the idea of doing so an anathema. Indeed, if this were not the case, places, as the collectives
they are, would have no incentive to find ways of reinventing themselves — as Glaeser (2005)
documents that Boston has a several times over the course of its history. Moreover, households
that owe more on their mortgages than their homes are worth are generally unable to move at all(see, for example, Chan 2001 and Ferreira et al 2010) meaning that, for worse or for better, they
are quite literally stuck in place.
To that point, a general suggestion is that, to every extent possible, public policy should
focus on both preserving natural amenities and generating human amenities — and mostespecially human capital. Natural amenities were consistently observed to play a greater-andgreater role in the two sets of income capitalization models from 1980 – 2000 and, not only that,
their influence has appreciable (and growing) geographic reach: households pay a premium tolive in environmentally appealing places — and, also, to live near them. The continuing
importance of natural amenities to both migration and job growth attests to this (Clark et al 2003;
McGranahan 2008; Whisler et al 2008; McGranahan et al 2010). Although the influence ofhuman amenities has declined through the decades, they, unlike natural amenities, may readily begenerated by public policy. For example, Markusen (2004, 2006), McGranahan and Wojan(2006), Rupasingha et al (2006), Rupasingha and Goetz (2006), Wojan et al (2007), Florida et al
2008, and Florida and Mellander (2010) all illustrate various ways in which economic
development strategies designed around human capital and/or a “creative” mix contribute toincreased economic growth and stability. And, importantly, Storper and Scott (2009) and Scott(2009) argue that the role of footloose migration and, by extension, the natural amenities thathave historically driven it, may, in fact, be overrated and, therefore, prescribe greater investments
in human capital. At a time of widespread divestment among state governments in the system of
public higher education, the United States seems to be heading in the wrong direction — even if

18

that divestment has been forced, in part, by the financial crises and its impact on tax rolls. All of
this is to say that the present findings add more depth to the pool of evidence in favor of using
place-based policy frameworks to improve household economic security by enhancing the planeof living.

5. Summary and Conclusion
This paper began by setting out three specific objectives: (i) to illustrate how housing values varyfrom place-to-place and explain why quality-of-life differentials cause them to vary sodramatically; (ii) to estimate a series of income capitalization models aimed at weighing therelative importance of household income and mortgage debt versus the plane of living in the recent evolution of housing values; and (iii) to identify some forward-looking observations, witha particular eye toward the dissolution of the ongoing crisis. Having met those objectives, theclosing comments briefly refocus on the challenge the United States continues to face.
As noted at the onset, in 2008 alone, American homes lost an estimated $2 trillion invalue. Between October 2007 and October 2008, the year over which the crisis exploded, the 20
Case-Shiller24 housing price indices fell by a nationwide average of 16.41% — an aggregate
figure that, while bad, masks even worse region-specific news: greater than 30% single-year
declines in Phoenix, Las Vegas, and San Francisco; and greater than 20% single-year declines in
Miami, Los Angeles, San Diego, and Detroit. For most regions, the overall setback, while
nonetheless dramatic, is really a matter of a few years, with the price indices back at their ~2004– ~2005 levels. For others, however, the setback appears to be far more insurmountable, at leastin the foreseeable future: Cleveland, and Detroit, for example, experienced almost none of theboom between 2000 and 2007, and ended up back at more-or-less their 2002, and pre-2000 levels,
respectively, raising the specter of a “lost decade” in the appreciation of a main form of American
wealth. In Miami, San Diego, Phoenix, and other high natural amenity regions, it is reasonable toexpect that preference-driven migration will eventually drive housing values back up. Likewise,in Chicago, New York, the District of Columbia, and other high human amenity (not to mention
opportunity) regions, it is equally reasonable to expect that growth will eventually drive housing
values back up. But what about regions like Cleveland, Detroit, and many others that havesuffered from years of economic decline and even outright neglect? Although the human tragedyof the financial crisis extends nationwide, with a comprehensive recovery still only beginning toemerge, if at all, these parts of the country appear particularly vulnerable. They rest on the24

Available from Standard and Poor’s on line, here:
http://www2.standardandpoors.com/portal/site/sp/en/us/page.topic/indices_csmahp/0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0.html.

19

downside of the plane of living and will almost certainly present special challenges — even once
the long-gathering storm finally lets up.

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24

Table 1. Median Value of Owner–occupied Homes ($2010) by State in 1980 and 2005
1980
2005
Difference
Percent ofPercent ofMedian value US median Median value US median Value
Percent
US $150,824
100.00% $227,800
100.00% $76,976
51.04%
AL $108,120
71.69% $132,600
58.21% $24,480
22.64%
AZ $180,472
119.66% $252,144
110.69% $71,672
39.71%
AR $99,144
65.73% $118,864
52.18% $19,720
19.89%
CA $270,096
179.08% $649,672
285.19% $379,576
140.53%
CO $206,040
136.61% $303,688
133.31% $97,648
47.39%
CT $215,016
142.56% $369,240
162.09% $154,224
71.73%
DE $142,256
94.32% $277,168
121.67% $134,912
94.84%
DC $225,488
149.50% $522,784
229.49% $297,296
131.85%
FL $144,432
95.76% $257,720
113.13% $113,288
78.44%
GA $117,640
78.00% $200,600
88.06% $82,960
70.52%
ID $146,336
97.02% $183,464
80.54% $37,128
25.37%
IL $171,904
113.98% $250,104109.79% $78,200
45.49%
IN $118,592
78.63% $155,584
68.30% $36,992
31.19%
IA $129,472
85.84% $144,976
63.64% $15,504
11.97%
KS $120,496
79.89% $146,608
64.36% $26,112
21.67%
KY $109,072
72.32% $141,304
62.03% $32,232
29.55%
LA $137,088
90.89% $138,312
60.72% $1,224
0.89%
ME $120,904
80.16% $211,208
92.72% $90,304
74.69%
MD $188,768
125.16% $381,072
167.28% $192,304
101.87%
MA $154,632
102.52% $491,640
215.82% $337,008
217.94%
MI $124,440
82.51% $203,048
89.13% $78,608
63.17%
MN $173,128
114.79% $270,368
118.69% $97,240
56.17%
MS $100,096
66.37% $112,472
49.37% $12,376
12.36%
MO $117,096
77.64% $167,416
73.49% $50,320
42.97%
Source: United States Census Bureau.

1980
Percent ofMedian value US median
MT $147,968
98.11%
NE $121,176
80.34%
NV $220,728
146.35%
NH $153,136
101.53%
NJ $195,840
129.85%
NM $144,840
96.03%
NY $146,336
97.02%
NC $114,784
76.10%
ND $139,672
92.61%
OH $143,888
95.40%
OK $113,560
75.29%
OR $188,224
124.80%
PA $124,712
82.69%
RI $149,872
99.37%
SC $111,928
74.21%
SD $116,688
77.37%
TN $113,560
75.29%
TX $124,712
82.69%
UT $191,352
126.87%
VT $134,912
89.45%
VA $153,408
101.71%
WA $193,528
128.31%
WV $122,808
81.42%
WI $155,040
102.80%
WY $192,576
127.68%2005

Difference

Percent ofMedian value US median$178,976
78.57%$153,952
67.58%$385,424
169.19%$326,536
143.34%$454,104199.34%$170,680
74.93%$352,104154.57%$173,536
76.18%$120,496
52.90%$176,25677.37%$121,176
53.19%$273,632
120.12%$179,384
78.75%$382,568
167.94%$153,816
67.52%$138,312
60.72%$155,040
68.06%$144,160
63.28%$227,392
99.82%$235,824
103.52%$288,728
126.75%$309,672
135.94%$114,784
50.39%$207,536
91.10%$183,600
80.60%

Value
Percent$31,008
20.96%$32,77627.05%$164,696
74.61%$173,400 113.23%$258,264 131.88%$25,840
17.84%$205,768 140.61%$58,752
51.18%–$19,176 -13.73%$32,368
22.50%$7,616
6.71%$85,40845.38%$54,672
43.84%$232,696 155.26%$41,88837.42%$21,624
18.53%$41,480
36.53%$19,448
15.59%$36,040
18.83%$100,912
74.80%$135,320
88.21%$116,144
60.01%–$8,024-6.53%$52,496
33.86%–$8,976-4.66%

25

Table 2. Descriptive Statistics
1980
Min.

Med.
Max.
Mean
St. Dev.
SourceConstruction Cost Index
0.40
1.40
5.17
1.42
0.33
REIS
% College Degree
1.60
10.00
47.80
11.43
5.46
CBP
Entertainment Est. / Capita
0.00
0.01
0.14
0.01
0.01
Calculated
Human Amenity Index
1.48
5.68
40.51
6.00
2.52
CensusMedian Age of Population
19.20
30.70
57.10
31.05
3.91
CensusMedian Household Income
17,609.20
36,915.48
79,829.26
37,900.48
8,817.53
CensusMedian Housing Value
26,597.34
86,184.00
532,002.66
93,185.55
37,596.36
Census% Monthly Mortgage Payment
0.12
0.26
0.65
0.26
0.04
CensusPlane of Living — (2)
-1.47
-0.01
1.32
0.00
0.23
Estimated
Plane of Living — (3)
-1.21
-0.02
1.90
0.00
0.35
Estimated
Total Population
91.00
21,714.00
7,477,239.00
72,563.45
293,466.44
CensusTerritorial Density
0.15
36.18
24,094.72
174.54934.20CensusTotal Direct Spending / Capita
134.61
1,872.60
10,764.06
2,012.63
809.16
COG
1990
Min.
Med.
Max.
Mean
St. Dev.
SourceConstruction Cost Index
0.25
1.24
3.31
1.26
0.30
REIS
% College Degree
3.70
11.70
53.40
13.47
6.60
CBP
Entertainment Est. / Capita
0.00
0.01
0.20
0.01
0.01
Calculated
Human Amenity Index
0.88
5.61
40.30
6.00
2.51
CensusMedian Age of Population
20.00
34.30
55.40
34.41
3.64
CensusMedian Household Income
14,439.60
38,095.68
99,597.12
40,067.52
10,896.78
CensusMedian Housing Value
25,198.32
75,936.00
818,664.00
90,020.33
56,664.09
Census% Monthly Mortgage Payment
0.12
0.27
0.74
0.28
0.04
CensusPlane of Living — (2)-1.35-0.002
1.87
0.00
0.28
Estimated
Plane of Living — (3)
-1.31
-0.04
1.87
0.00
0.43
Estimated
Total Population
107.0022,242.00
8,863,164.00
79,614.74
328,980.12
CensusTerritorial Density
0.14
38.11
24,232.59
182.93931.38
CensusTotal Direct Spending / Capita
205.33
2,161.40
16,899.27
2,364.96
1,040.45
COG
2000
Min.
Med.
Max.
Mean
St. Dev.
SourceConstruction Cost Index
0.15
1.12
3.91
1.15
0.33
REIS
% College Degree
0.00
9.92
40.02
10.95
4.95
CBP
Entertainment Est. / Capita
0.00
0.02
0.31
0.02
0.01
Calculated
Human Amenity Index
0.48
5.66
41.21
6.00
2.54
CensusMedian Age of Population
20.60
37.40
54.30
37.38
3.99
CensusMedian Household Income
16,118.84
42,764.71
105,319.83
44,785.58
11,280.09
CensusMedian Housing Value
17,526.00
96,012.00
1,270,001.27
106,679.94
63,513.66
Census% Monthly Mortgage Payment
0.18
0.30
1.02
0.31
0.05
CensusPlane of Living — (2)
-1.76
0.003
2.13
0.00
0.28
Estimated
Plane of Living — (3)
-1.76
0.004
2.02
0.00
0.42
Estimated
Total Population
67.00
24,747.00
9,519,338.00
90,101.01
361,545.66
CensusTerritorial Density
0.16
41.48
24,366.01
192.71918.70CensusTotal Direct Spending / Capita
24.93
2,861.62
22,041.87
3,135.66
1,389.86
COG
Same Across All Years
Metro
0.00
0.00
1.00
0.35
0.48
Census
Micro
0.00
0.00
1.00
0.22
0.42
CensusNatural Amenity Index
3.60
9.86
21.17
10.05
2.29
ERS
Notes: all dollar values are in 2010 dollars; calculated means calculated by the authors; CBP is County Business Patterns;
Census is the decennial census; COG is the Census of Governments; ERS is the Economic Research Service report,
McGranahan (1999); estimated means estimated via equation (2) or equation (3); REIS is the Bureau of Economic
Analysis’ Regional Economic Information System.

26

Table 3. Natural Amenity Index and Human Amenity Index – Top 10 and Bottom 10 Counties
Top 10 Counties
Human Amenity Index
Natural Amenity Index
1980
1990
1. Ventura CountyCA
New York CityNY
New York City
2. Humboldt CountyCA
San Francisco CountyCA
San Francisco County
3. Santa Barbara County
CA
District of Columbia
DC
District of Columbia
4. Mendocino County
CA
Suffolk County
MA
Storey County
5. Del Norte County
CA
Philadelphia County
PA
Alpine County
6. San Francisco County
CA
Storey County
NV
Suffolk County
7. Los Angeles County
CA
Alexandria County
VA
Philadelphia County
8. San Diego County
CA
BaltimoreMD
Hudson County
9. Monterey County
CA
Hudson County
NJ
Hinsdale County
10. Orange County
CA
Menard County
TX
Alexandria County. Bottom 10 Counties.
Human Amenity Index. Natural Amenity Index
1980
1990
3094. Pennington County
MN
Carlisle County
KY
Lawrence County
3095. Grand Forks County
ND
Spencer County
KY
Taliaferro County
3096. Dodge County
MN
Morgan County
TN
Magoffin County
3097. Trail County
ND
Coosa County
AL
Livingston County
3098. Mower County
MN
Bollinger County
MO
Gallatin County
3099. Pembina County
ND
Edmonson County
KY
Van Buren County
3100. Norman County
MN
Bland County
VA
Jackson County
3101. Tipton County
IN
Jackson County
KY
Edmonson County
3102. Wilkin County
MN
Menifee County
KY
Menifee County
3103. Red Lake County
MN
Buffalo County
SD
Buffalo County

NY
CA
DC
NV
CA
MA
PA
NJ
CO
VA

2000
New York City
Gilpin County
San Francisco County
District of Columbia
Suffolk County
Arlington County
Hudson County
Philadelphia County
Alpine County
Kenedy County

NY
CO
CA
DC
MA
VA
NJ
PA
CA
TX

KY
GA
KY
KY
KY
TN
KY
KY
KY
SD

2000
Bledsoe County
Crawford County
Glascock County
Shannon County
Menifee County
Taliaferro County
Owsley County
Long County
Leslie County
Buffalo County

TN
GA
GA
SD
KY
GA
KY
GA
KY
SD

27

Table 4. Correlation Matrix of Sub-indices Making up the Human Amenity Index
1980% Population
Total DirectEntertainment
w/ College Degree
Spending Per Capita
Est. Per Capita% Population
1.00
w/ College Degree
Total Direct
0.28
1.00
Spending Per Capita
Entertainment
0.28
0.38
1.00
Est. Per Capita
Territorial
0.23
0.19
0.03
Density

Territorial
Density
1.00

1990% Population
w/ College Degree
Total Direct
Spending Per Capita
Entertainment
Est. Per Capita
Territorial
Density

1.00

-

-

-

0.24

1.00

-

-

0.33

0.40

1.00

-

0.29

0.13

0.05

1.00

1.00

-

-

-

0.25

1.00

-

-

0.42

0.36

1.00

-

0.25

0.15

0.06

1.00

2000
% Population
w/ College Degree
Total Direct
Spending Per Capita
Entertainment
Est. Per Capita
Territorial
Density28

Table 5. OLS Estimates of Baseline Income Capitalization Models
ln Median Household Income
ln Monthly Mortgage Payment
1980
1990
2000
1980
1990
2000
Est.
Est.
Est.
Est.
Est.
Est.
parametert-value parametert-value parametert-value parametert-value parametert-value parametert-valueConstant–0.8988 *** –4.21 –2.9199 n/s –10.56–3.5844 *** –14.66 11.1288 *** 146.01 12.2729 *** 142.93
12.4515 *** 139.67
ln Median Household Income
1.1674 *** 57.05
1.3455 *** 50.79
1.4100 *** 61.16
ln Mortgage Payment as % Monthly Income–0.1843 *** –3.34
0.7538 *** 12.04
0.8165 *** 11.35
n
3,103
3,103
3,103
3,103
3,103
3,103
Adjusted R2
0.57
0.60
0.58
0.01
0.06
0.07
Notes: all models were estimated using White-adjusted standard errors clustered by state; OLS is ordinary least squares; all hypothesis tests are two-tailed; ★★★ denotes significant
at p < 0.01; ★★ denotes significant at p < 0.05; n/s denotes not significant.

29

Table 6. Error Terms from Baseline Income Capitalization Models — Top and Bottom 10 Counties
Top 10 Counties
Median Household Income
Monthly Mortgage Payment
1980
1990
2000
1980
1990
1. Pitkin County
CO New York County
NY New York County
NY Pitkin County
CO Pitkin County
2. New York County
NY Pitkin County
CO Pitkin County
CO Marin County
CA Marin County
3. San Francisco County CA San Francisco County
CA Nantucket County
MA San Mateo County
CA San Mateo County
4. Mono County
CA San Luis Obispo County CA San Miguel County
CO Mono County
CA Santa Clara County
5. Marin County
CA Nantucket County
MA Taos County
NM New York County
NY Nantucket County
6. Santa Barbara County CA Santa Barbara County
CA San Juan County
WA Orange County
CA New York County
7. Inyo County
CA Santa Cruz County
CA Dukes County
MA Santa Clara County
CA Falls Church County
8. Lake County
CA San Mateo County
CA San Francisco County CA San Francisco County CA Westchester County
9. Santa Cruz County
CA Marin County
CA Santa Cruz County
CA Eagle County
CO San Francisco County
10. Alpine County
CA Los Angeles County
CA Williamsburg County VA Summit County
CO Fairfax County.
. Bottom 10 Counties. Median Household Income
Monthly Mortgage Payment. 1980
1990
2000
1980
1990
3094. Upton County
TX Harding County
NM Roberts County
TX La Salle County
TX Keweenaw County
3095. Slope County
ND Pawnee County
NE Boyd County
NE Ziebach County
SD Mellette County
3096. Kenedy County
TX Slope County
ND Miner County
SD Mora County
NM Aurora County
3097. Shannon County
SD Petroleum County
MT Steele County
ND Kiowa County
CO Shannon County
3098. McMullen County
TX Jewell County
KS Sanborn County
SD Harding County
NM Worth County
3099. Esmeralda County
NV Wheeler County
NE Kent County
TX Kenedy County
TX Todd County
3100. Harding County
NM Sanborn County
SD Jewell County
KS Blaine County
NE McPherson County
3101. Borden County
TX Borden County
TX Grant County
NE Todd County
SD McDowell County
3102. Kiowa County
CO King County
TX Loving County
TX Loving County
TX Loving County
3103. Loving County
TX Loving County
TX King County
TX Shannon County
SD Apache County

2000
CO Pitkin County
COCA Nantucket County MA
CA Marin CountyCA
CA New York County NY
MA Santa Clara County CA
NY San Mateo County CA
VA Los Alamos County NM
NY Santa Cruz County CA
CA Teton County
WY
VA Eagle County
CO

2000
MI Dickens County
SD Hall County
SD McPherson County
SD McDowell County
MO Blaine County
SD La Salle County
SD Zavala County
WV Shannon County
TX Loving County
AZ King County

TX
TX
SD
WV
NE
TX
TX
SD
TX
TX

30

Table 7. S2SLS Estimates of Amenity Models
ln Median Household Income
ln Monthly Mortgage Payment
1980
1990
2000
1980
1990
2000
Est.
Est.
Est.
Est.
Est.
tEst.
parameter t-value
parameter t-value parameter t-value parameter t-value
parameter
value parameter t-value
Constant
1.0778 ***3.16 –0.1699 n/s–0.54 –1.5059 ***–4.74 5.4759 ***15.43 4.4111 ***11.73 4.0053 *** 12.08
ln Spatial Lag
0.1349 ***6.07 0.2036 ***9.49 0.1738 ***6.94 0.4682 ***15.54 0.5419 ***18.51 0.5599 *** 20.33
ln Median Household Income
0.7466 ***26.74 0.8044 ***26.58 0.9664 ***25.78 ln Mortgage Payment as % Monthly
n/s
***
***
0.01770.56 0.0934
2.58 0.2772
6.48
Income
***
***
***
***
***
***
ln Population
0.04738.98 0.0509
9.33 0.0490
8.83 0.0633
12.19 0.0627
11.60 0.0568
9.10
ln Median Age of Population–0.0967 **–2.31 –0.2384 ***–5.19 –0.2331 ***–5.45 –0.2336 ***–5.58 –0.1870 ***–3.80 –0.0115 n/s–0.24
ln Construction Cost
0.0949 ***5.63 0.0662 ***4.56 –0.0112 n/s–1.07 0.0625 ***3.56 0.0821 ***4.92 –0.0051 n/s
–0.38
***
***
***
***
***
ln Natural Amenity Index
0.19948.22 0.3123
11.89 0.3669
12.95 0.1263
4.60 0.1611
5.17 0.1437 ***4.32
ln Human Amenity Index
0.1523 ***8.89 0.1511 ***7.97 0.0965 ***4.54 0.2232 ***11.37 0.2626 ***13.06 0.2482 *** 13.15
Metropolitan Area Indicator
0.0231 ***2.51 –0.0052 n/s–0.56 –0.0176 n/s–1.73 0.1120 ***12.19 0.1198 ***12.27 0.1345 *** 12.49
Micropolitan Area Indicator
0.0294 ***3.33 0.0100 n/s
1.19 0.0189 ***2.36 0.0743 ***7.71 0.0678 ***7.31 0.0807 ***
7.88
n
3,103
3,103
3,103
3,103
3,103
3,103
Adjusted R2
0.81
0.88
0.86
0.74
0.83
0.80
Notes: all state fixed effects have been suppressed in order to conserve space; all models were estimated using White-adjusted standard errors clustered by state; S2SLS is Kelejian
and Prucha’s (1998) spatial two-stage least squares estimator; all hypothesis tests are two-tailed; ★★★ denotes significant at p < 0.01; ★★ denotes significant at p < 0.05; n/s denotes
not significant.

31

Table 8. S2SLS Estimates of Spatial Expansion Amenity Models
ln Median Household Income
ln Monthly Mortgage Payment
1980
1990
2000
1980
1990
2000
Est.
Est.
Est.
Est.
Est.
Est.
parametert-value parametert-value parametert-value parametert-value parametert-value parametert-valueConstant
1.4399 *** 3.66
–0.2097 n/s –0.64–2.2376 *** –6.77
6.0035 *** 13.67
4.5674 *** 11.07
4.0818 *** 8.78
ln Spatial Lag
0.0560 ** 2.01
0.1622 *** 6.50
0.2007 *** 7.22
0.3998 *** 9.20
0.5233 *** 12.96
0.5628 *** 11.97
ln Median Household Income
0.7523 *** 26.50
0.8154 *** 26.52
1.0011 *** 27.29
ln Mortgage Payment as % Monthly Income
0.0319 n/s
0.99
0.1054 ***2.94
0.2890 *** 6.42
ln Population
0.0505 *** 9.17
0.0523 *** 9.36
0.0457 *** 8.03
0.0667 *** 12.05
0.0634 *** 11.11
0.0567 *** 8.63
**
***
***
***
***
ln Median Age of Population–0.0911–2.13–0.2376–5.13–0.2409–5.65 –0.2284–5.42 –0.1848–3.75–0.0095 n/s –0.21
ln Construction Cost
0.0958 *** 5.61
0.0668 *** 4.63
–0.0070 n/s –0.68
0.0603 *** 3.44
0.0831 ***4.98–0.0066 n/s –0.51
ln Natural Amenity Index
0.1148 *** 3.43
0.2086 *** 6.18
0.2503 *** 7.44
0.1388 *** 3.61
0.1871 ***4.55
0.2041 *** 4.79
***
***
***
n/s
n/s
ln Spatial Lag of Natural Amenity Index
0.19594.03
0.23464.87
0.24844.79 –0.0182–0.33 –0.0608–1.08–0.1381 ** –2.29
ln Human Amenity Index
0.1466 *** 8.42
0.1505 *** 7.85
0.1056 *** 4.85
0.2104 *** 10.74
0.2543 *** 12.60
0.2394 *** 12.79
***
n/s
***
***
n/s
ln Spatial Lag of Human Amenity Index
0.10363.17
0.04391.37–0.1160–3.66
0.14623.53
0.08511.83
0.0530 n/s 1.08
Metropolitan Area Indicator
0.0225 *** 2.38
–0.0063 n/s –0.65–0.0189 n/s –1.89
0.1096 *** 12.04
0.1167 *** 11.91
0.1312 *** 12.29
Micropolitan Area Indicator
0.0291 *** 3.25
0.0097 n/s
1.15
0.0186 *** 2.36
0.0731 *** 7.61
0.0673 ***7.27
0.0802 *** 7.79
n
3,103
3,103
3,103
3,103
3,103
3,103
Adjusted R2
0.80
0.87
0.86
0.74
0.83
0.80
Notes: all state fixed effects have been suppressed in order to conserve space; all models were estimated using White-adjusted standard errors clustered by state; S2SLS is Kelejian
and Prucha’s (1998) spatial two-stage least squares estimator; all hypothesis tests are two-tailed; *** denotes significant at p < 0.01; ** denotes significant at p < 0.05; n/s denotes not
significant.

32

Figure 1. The Plane of Living (Goodrich et al 1936)

Figure 2. The American Constellation of Population Centers and Core Based Statistical Areas (CBSAs)

33

(3a)

(4a)

(3b)

(4b)

(3c)

(4c)

Figure 3. Rate of Population Change in (3a) 1980, (3b)1990, and (3c) 2000

Figure 4. Median Housing Value ($ 2010) in (4a) 1980,(4b) 1990, and (4c) 2000

34

(5a)

(6a)

(5b)

(6b)

(5c)

(6c)

Figure 5. Median Household Income ($ 2010) in (5a)1980, (5b) 1990, and (5c) 2000

Figure 6. Mortgage Payment as a Percentage ofMonthly Income in (6a) 1980, (6b) 1990, and (6c) 2000

35

Figure 7. Value of Natural Amenity Index

(8a)

(8b)

(8c)
Figure 8. Value of Human Amenity Index in (8a) 1980,(8b) 1990, and (8c) 2000

36

13
ln Median Housing Value 1980
11
12
10
9.5

10

10.5
11
ln Median Household Income 1979

11.5

(10a)

10

ln Median Housing Value 1990
11
12
13

14

(9a)

9.5

10

10.5
11
ln Median Household Income 1989

11.5

(10b)

10

ln Median Housing Value 1900
11
12
13

14

(9b)

9.5

10

10.5
11
ln Median Household Income 1999

11.5

(9c)

(10c)

Figure 9. Natural Log of Median Household Income
Versus Natural Log of Median Housing Value in (9a)1980, (9b) 1990, and (9c) 2000

Figure 10. Plane of Living Estimated from MedianHousehold Income (10a) 1980, (10b) 1990, and (10c)
2000

37

13
ln Median Housing Value 1980
11
12
10

-2

-1.5
-1
ln Mortgage Payment – % Median Household Income 1979

-.5

(12a)

10

ln Median Housing Value 1990
11
12
13

14

(11a)

-2

-1.5
-1
-.5
ln Mortgage Payment – % Median Household Income 1989

0

(12b)

10

ln Median Housing Value 2000
11
12
13

14

(11b)

-2

-1.5
-1
-.5
ln Mortgage Payment – % Median Household Income 1999

0

(11c)

(12c)

Figure 11. Natural Log of Monthly Mortgage Payment
as a Percentage of Household Income Versus Natural
Log of Median Housing Value in (11a) 1980, (11b)1990, and (11c) 2000

Figure 12. Plane of Living Estimated from Monthly
Mortgage Payment (12a) 1980, (12b) 1990, and (12c)2000

38