American Economic Association
The Effect of Health Risk on Housing Values: Evidence from a Cancer Cluster
Author(s): Lucas W. Davis
Source: The American Economic Review, Vol. 94, No. 5 (Dec., 2004), pp. 1693-1704
Published by: American Economic Association
Stable URL: https://www.jstor.org/stable/3592841
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The Effect of Health Risk on Housing Values:
Evidence from a Cancer Cluster
By LUCAS W. DAVIS*
There is a substantial literature that examines
imply that houses in locations with high risks
trade-offs between money and health risks. This
must have lower prices than equivalent houses
in locations with low risks in order to attract
literature has shown that estimates of marginal
households to these locations. These equalizing
willingness-to-pay (MWTP) for changes in risk
can be inferred from a wide variety of market
differences may be recovered by estimating a
situations. Much of the work has focused on
hedonic price function (Sherwin Rosen, 1974).
mortality risks in the labor market (W. Kip The gradient of this function with respect to
Viscusi and Joseph E. Aldy, 2003), but substan- health risk is equal to household MWTP for an
tial work has also looked for compensating dif- incremental change in risk.
ferentials in the housing market. Significant In practice, hedonic price functions have
negative effects on housing values have been proven difficult to estimate because the amenity
found to be associated with hazardous waste
of interest is typically not distributed randomly
sites (Ted Gayer et al., 2000), water pollutionacross locations. For example, locations with
(Christopher G. Leggett and Nancy E. Bock- health risk due to air pollution tend also to be
stael, 2000), and air pollution (Kenneth Y. Chay urban, industrial areas with particular labor
market characteristics. When differences beand Michael Greenstone, 1998).
This literature has been primarily motivated tween locations are imperfectly measured and
by policy considerations. Policymakers have at covary with health risk and housing prices, it
their disposition many tools for reducing envi- becomes difficult to disentangle the price effects
ronmental health risks, including technology of health risks from the price effects of other
standards and incentive-based mechanisms, as locational amenities. The problem of omitted
well as water and air treatment facilities and
variables is compounded by an important sort-
hazardous waste remediation. The relative mer-
ing issue. Households move to locations enits of diverse risk-reducing policies must be dowed with amenities that match their
evaluated in terms of the value households put
on risk. The efficient level of public spending
preferences. When households near the amenity
of interest are not representative of the populafor risk-reduction is reached when the sum of
tion at large, it becomes difficult to interpret
households' MWTP is equal to marginal cost. observed price differentials.
Household MWTP for changes in environThis paper measures the effect of health risk
mental health risk is not directly observed in the on housing values by exploiting a natural exmarket. If the level of risk varies across locaperiment that mitigates both econometric probtions, however, and if households are mobile, lems. The analysis focuses on an isolated
then demand will be capitalized into property county in Nevada where residents have recently
values. Standard assumptions about preferences experienced a severe increase in pediatric leukemia. Housing prices are compared before and
after the increase with a nearby county acting a
* Department of Economics, University of Wisconsin,
1180 Observatory Dr., Madison, WI 53706 (e-mail:
ldavis@ssc.wisc.edu). This paper is part of my University
of Wisconsin Ph.D. dissertation. Comments from John Ken-
nan, Maurizio Mazzocco, James R. Walker, a co-editor, the
anonymous referees, and numerous seminar participants
substantially improved the paper. This research was made
possible through a National Institute for Child and Human
Development (NICHD) Training Grant (T32 HD07014) and
the Center for Demography and Ecology, which receives
core support from the NICHD (R24 HD 47873).
a control group. The variation in health risk
over time makes it possible to control for
unobserved differences across locations. In ad-
dition, because the leukemia cases were unanticipated there is no reason to expect sorting of
households according to preferences prior to the
increase. Finally, because many houses were
sold repeatedly during the sample period it is
possible to control for unobserved property-
1693
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1694
THE AMERICAN ECONOMIC REVIEW
DECEMBER 2004
specific heterogeneity. The results provide
for clustering
a
among the age 1-14 group using
robust estimate of the MWTP to avoid pediatric
a dataset that includes 40 percent of England
leukemia risk. Housing prices in the affected
and Wales during the period 1984-1993. The
term "cancer cluster" comes from the medical
county closely followed trends in housing
prices for the control county and the restliterature
of the and is used to describe a geographic
state of Nevada during the period leadingarea,
up to
time period, or group of people with a
the leukemia increase. Then, beginning
when
greater-than-expected
number of cancer cases.
The cause of leukemia is not known. Only
eight children were diagnosed in 2000, housing
prices in the affected county declined significhronic exposure to benzene, extraordinary
doses
of irradiation, and certain types of checantly. Least-squares estimates indicate
that
houses sold during the period of maximum
motherapy
risk
have been established as increasing
incidence of leukemia. Many environmental
sold for 15.6 percent less than equivalentthe
houses
not affected by the leukemia increase.factors
Fixedhave been studied for possible associaeffects estimates indicate a 14-percent differention with leukemia, including petrochemicals,
tial. The estimated MWTP to avoid pediatric
heavy metals, pesticides, volatile organic comleukemia risk is used to calculate the value of a
pounds, solvents, and consumer chemicals, but
statistical case of pediatric leukemia.
most researchers agree that definitive links with
these factors have not been established.
I. Profile of a Cancer Cluster
One of the reasons epidemiologists have a
difficult time identifying risk factors is that leu-
Prior to 1997, Churchill County, Nevada
kemia has a latency period. As a result, a child
(pop. 23,982) had no history of pediatric leukewho is exposed to an environmental hazard may
not become sick until many weeks, months, or
mia. Since 1997, 15 children have been diagnosed with acute lymphocytic leukemia and
even
a years later. This delay represents a potensixteenth with acute myelogenous leukemia.
A important feature of an economic analysis.
tially
joint investigation by the Nevada Health
DeDepending
on the latency period, current leukepartment and the U.S. Centers for Disease mia
Conincidence rates may or may not provide
trol has been unable to determine the cause of
information about current health risk. These dythe increase. No common characteristic has
namics should be incorporated as clinical evi-
been identified among the case families anddence
the increases our understanding of the
cases have not been linked to occupational latency
hazperiod.
ards, a certain neighborhood, or a particular
Initial publicity about the cluster may have
water source.
led local children to be more likely to be tested
Leukemia incidence of this magnitude
for far
leukemia. Due to the pathology of leukemia,
exceeds the population mean. The American
however, increased testing could not have afCancer Society estimates that 2,200 new fected
cases the pattern of diagnosis. According to
of leukemia were found in children in 2003. A
Martin D. Abeloff et al. (2000) the transition of
acute leukemia to its active state occurs sudlocation with the population of Churchill County
should expect to see one case of pediatric leukedenly and is accompanied by the abrupt appearmia every five years. Accordingly, little attention
ance of visible symptoms, so it is difficult for
was paid to Churchill County in 1997 or 1999
the disease to go undetected for an extended pewhen one and two cases were confirmed, but since
riod of time. Also, clinical tests cannot detect
eight cases were diagnosed in 2000 and an addileukemia before it is activated, so it is unlikely that
tional four cases in 2001 the story has consistently
increased frequency of testing by itself could have
meaningfully accelerated incidence rates.
made local and national news.
Rates of incidence of this magnitude are not Pediatric leukemia is typically treated with
without historical precedent. Similar clusters oftwo to three years of chemotherapy. A less
pediatric leukemia have occurred in Maryvale, common treatment for pediatric leukemia is
Arizona; Marion, Ohio; Toms River, New Jer- bone-marrow transplantation, which is a diffi-
sey; and Woburn, Massachusetts. There is cult treatment that involves a lengthy hospital
growing evidence in the medical literature thatstay. Both treatments cause severe side-effects
this clustering is widespread. E. Gilman et al. in the short term and long term. According to
(1999), for example, find significant evidence the American Cancer Society, five-year survival
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VOL. 94 NO. 5
DAVIS: THE EFFECT OF HEALTH RISK ON HOUSING VALUES
1695
are less clear. Diminishing marginal utilrates for acute lymphocytic leukemia andwork
acute
myelogenous leukemia are 85 percent and
45consumption implies that high-income
ity of
percent, respectively.
households will require a larger compensating
differential per unit risk. As a result, one exII. Location-Choice Model
pects to see high-income households moving
out of dangerous locations. This sorting makes
Households are assumed to have identical
it difficult to interpret observed price differenThe differential observed in the market
preferences and choose where to live among tials.
a
will underestimate the MWTP of high-income
set of locations indexed by i. In each location
households and overestimate the MWTP of
there are S states of the world indexed by s. The
low-income households. Other forms of houseprobability of realizing state s in location i during period t is denoted Tit. All locations are
hold heterogeneity cause similar sorting issues.
endowed with equally attractive amenities and In the next section, local health risk is estilabor employment opportunities but different
mated using local incidence rates. The stateprobabilities of realizing different states of the
dependent utility framework assumes that the
level of risk (7rit) is objectively known. Estiworld. Aggregate consumption of all non-housof health risk will take the place of rit by
ing goods is denoted cit and does not depend mates
on
the state of the world. Utility in period tappealing
is
to standard subjective probability theory. Francis J. Anscombe and Robert J. Auexpressed in expected utility form by appealing
mann (1963) showed that if preferences are
to the expected utility theorem for statestate uniform (>s = ?,> for any s and s') then
Consider the case where there are two states
preferences may be expressed in expected
of the world, "good" and "bad," which occur utility form treating expectations as if they
dependent preferences.
with probabilities 1 - r and ir, where uG and
uB are the utility functions associated with those
states and uG(c) _ uB(c) for all values of c.
Household utility in location i in period t may
be expressed in the following form:
were objectively known. The measurements of
health risk described in the next section are
arbitrary ways of specifying these subjective
probabilities.
III. Estimating Cancer Risk
U(7it, Cit) (1 - 7rit) G(Cit) + qitB(Cit).
Figure 1 shows four alternative measures of
pediatric leukemia risk for the period January
The price of housing must equalize utility in 1996 to September 2002 in Churchill County.
all inhabited locations. In particular, houses in The first measure is the cumulative number of
locations with high health risk must have lower leukemia cases. This measure is flat during the
prices than equivalent houses in locations with 1990s and then increases sharply in 2000 and
low risk in order to attract households to these
2001. The second measure is the cumulative
locations. This compensating-differentials argu- number of newspaper articles in the Proquest
ment has a straightforward empirical interpreta-
tion. Controlling for all other determinants of
house value, the difference in observed market
price between two locations with different locational health risks is the compensating differential for risk. Following Rosen (1974), a house
is described by a vector of its characteristics. In
a competitive market the price-characteristic locus is determined by the equilibrium interactions of buyers and sellers. The gradient of the
hedonic price function with respect to locational
health risk is equal to household MWTP for an
incremental change in risk.
newspaper database citing "leukemia" and
"Churchill County" or "Fallon" (the county
seat). This measure is flat until the middle of
2000 when the cluster began to receive media
attention. The third measure is a linear spline
that is zero through 1999, rises by 1/24 each
month during 2000 and 2001, and then takes the
value of one. This quasi-dummy variable captures the basic pattern of the other measures and
will be used for the main results.
The fourth measure of risk is generated using
a Bayesian learning process. Suppose that
households in location i draw health outcomes
When households are endowed with different
each period from a Bernoulli distribution with
levels of income, the implications of the frame- parameter Tri where, as above, ,ri is the annual
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1696
DECEMBER 2004
THE AMERICAN ECONOMIC REVIEW
Cumulative leukemia cases
Cumulative newspaper a
0
1cO
v-
r-
0
t
7-
0
t
0
T
0
t
1998 2000
1996
I
t
2002
996
Year
1998 2000
Year
2002
Bayesian risk estimat
Linear spline
0
0
r~ ..
80
0
I
9 t96
)96
I
I
I
i
I
I
1998 200 2002
r _, i ....
i
0
i
1
996
Year
I
i
2000 2002
1998
Year
FIGURE 1. INCIDENCE RATES INCREASE AFTER 1999:
ALTERNATIVE MEASUREMENTS OF PEDIATRIC LEUKEMIA RISK FOR CHURCHILL COUNTY, NEVADA
probability of realizing the unfavorable state.
the number of observed outcomes before 1997.
Households do not know rTi. By observing The more outcomes the household observes, the
draws from the distribution, however, they are lower the variance of the prior. For the standard
able to make inference. Their beliefs about this
prior, the mean is set equal to the average natrue level of risk are described by a secondtional incidence rate and the variance is con-
distribution. Morris H. DeGroot (1970) derives structed to reflect the cumulative population of
a closed-form solution for the updating mecha-Churchill County since 1970.
nism with a Beta distribution for beliefs. The
Two caveats are in order. First, all four meamean of the beliefs distribution represents the
sures of health risk ignore the possibility that
perceived level of annual pediatric leukemia
household risk perceptions may depend upon
leukemia rates in nearby locations. The next
To derive the Bayesian estimates of risk, a
section describes an adjacent county that will be
prior distribution is assumed for January 1,
used as a control group in the estimation. The
1997, and then updated daily using the diagnoNevada State Health Department reports that
sis pattern observed in Churchill County. A
residents of the control county have not expenatural candidate for the mean of the prior is the
rienced increased pediatric leukemia rates.
risk.
average national incidence rate for pediatric leukemia. It is important to consider, however, the
possibility that the baseline level of risk for
Churchill County could be different from that of
Their close proximity to the highly publicized
cases in Churchill County, however, may have
caused them to increase their own perceptions
of risk. If this is the case, the estimated differ-
the national mean. Because the county does not
have any superfund sites or a history of extensive mining or heavy industry, households may
ence in risk between the two counties will be
other locations. Because links between the en-
lieved to be linked to environmental factors.
have believed they faced lower risk than in
overstated. Second, several other forms of can-
cer, including adult leukemia, non-Hodgkin's
lymphoma, and brain cancer, are widely be-
vironment and leukemia are so poorly under-The Nevada State Health Registry has been
stood, however, it is difficult to know on what
analyzed and residents of Churchill County
have not exhibited increased rates of incidence
basis to compare locations. The choice of the
variance of the prior is equivalent to choosing
for these or any other form of cancer. Never-
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VOL. 94 NO. 5
DAVIS: THE EFFECT OF HEALTH RISK ON HOUSING VALUES
1697
theless, households in Churchill Countyproperty-level
may
sales records make it possible to
construct
these indices, using the same generalbelieve that whatever is responsible for the
increase of pediatric leukemia has put them
ized at
least squares first-differences methodology
increased risk for other health risks as well.
that
Ifthe OFHEO uses to construct the HPI for
this is the case, the estimated difference in
risk
the
state of Nevada. See William Stephens et al.
between the two counties will be understated.
(1995) for a detailed description of the HPI
IV. Housing Sales Records
methodology.
Figure 2 shows biannual house-price indices
for Churchill County, Lyon County, and the
The Churchill County assessor in Fallon, Nevada, and the Lyon County assessor in Yering-
state of Nevada. The indices reflect nominal
sales prices for single-family residences with
ton, Nevada, provided a record of all sales of the average value for the period 1990-1999
single-family residences between 1990 and normalized to 100 for each index. The dashed
2002.1 These offices maintain a record of all
private and commercial property sales within
lines indicate a ninety-fifth percentile confi-
dence interval around the index for Churchill
the boundaries of their respective counties.
County. Beginning in the first half of 2000 and
continuing until the end of the sample period,
the basis of median income and median house
the index for Churchill County is significantly
value. Lyon County lies immediately to the below the indices for Lyon County and Nevada.
west of Churchill County. Table 1 provides aHousing prices in Lyon County follow housing
comparison of the two counties prior to theprices in Nevada during the period of the cancer
increased leukemia incidence which includes
cluster. This lends support to the use of Lyon
housing, demographic, and labor-market charCounty as a control. Figure 3 shows the peracteristics. For Lyon County to be a valid concentage difference between the Churchill
trol group it must be unaffected by the cancer
County HPI and the Nevada HPI. During the
cluster. As mentioned in the previous section,1990s the Churchill County HPI fluctuates
around the Nevada HPI. Beginning in 2000 the
however, even though their leukemia rates have
not increased, residents of Lyon County mayindex for Churchill County diverges.
perceive higher leukemia risk because of their The basic contribution of this paper is to
connect the increase in leukemia incidence with
geographic proximity to the cases in Churchill
County. The leukemia cases may also havethe decrease in housing prices. The framework
described in the following section controls for
affected Lyon County indirectly by causing
unobserved time-invariant differences across
households to move from Churchill County to
locations and unobserved time effects. The
Lyon County. Either of these effects could bias
Lyon County was chosen to act as a control on
the estimated differential for risk.
analysis does not, however, rule out the possi-
bility that county characteristics other than
One way to assess the validity of Lyon
County as a control is to compare housingleukemia incidence may have changed simultaprices in Lyon County to housing prices in the
neously. In particular, a severe county-specific
downturn in the labor market could provide an
rest of Nevada. Property-level sales records are
not available for the entire state of Nevada.
alternate explanation for the observed decline in
housing prices. County-level employment data
However, the Office of Federal Housing Enterfrom the Bureau of Economic Analysis make it
prise Oversight (OFHEO) publishes the Conventional Mortgage Home Price Index (HPI)
possible to evaluate this possibility. During the
each quarter using mortgage transactions for1998-2001 period Churchill County employment levels decreased moderately in some secsingle-family houses. The HPI is not available
tors but total employment increased. The two
for Churchill County or Lyon County but the
hardest-hit sectors were agriculture, which went
from 6.3 percent to 5.6 percent of total employThree percent of sales were excluded from the analysis
ment, and government, which went from 23.8
due to missing values or miscoding: construction year miss-
percent to 22.4 percent. County-level unem-
ing (208); sales price missing (76); interior floor space
ployment data from the Bureau of Labor Statismissing (32); multiple parcel sales (26); duplicate records
tics reveal that from 1998 to 2002 annual
(12); and date of sale miscoded (1). The number of excluded
observations is shown in parentheses.
unemployment rates in Churchill County were
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1698
DECEMBER 2004
THE AMERICAN ECONOMIC REVIEW
TABLE 1-COMPARING THE TREATMENT AND CONTROL COUNTIES
Churchill
(n = 2495)
Housing characteristics:
Mean sales price
Mean lot size (acres)
Mean interior floor space (square feet)
Mean building age (years)
Mean class (range 1-5)
Demographic characteristics:
Population
Persons per square mile
Percentage under 18
Percentage over 65
Percentage white
Percentage high-school graduates
Percentage college graduates
Homeownership rate
Percentage multi-unit
Percentage below poverty
Median household income
$116,060
(52,791)
Lyon
(n = 3683)
$119,723
(55,060)
1.42
1.16
(3.97)
(6.21)
1493
1480
(461)
(438)
16.9
10.8
(20.8)
(15.6)
1.75
2.16
(.59)
(.76)
23,982
34,501
4.9
17.3
28.9
27.1
11.9
13.7
84.2
88.6
85.1
81.5
16.7
11.3
65.8
75.8
11.7
8.1
8.7
10.4
$40,808
$40,699
Labor market characteristics:
Percentage employed in services
Percentage employed in government
Percentage employed in trade
28.6
25.8
23.8
12.1
18.6
18.0
Percentage employed in F.I.R.E.*
8.6
7.2
Percentage
Percentage
Percentage
Percentage
Percentage
Percentage
6.3
8.2
5.8
9.6
5.6
14.1
2.2
3.3
employed in agriculture
employed in construction
employed in manufacturing
employed in utilities
employed in mining
of labor force unemployed
0.5
1.7
6.2
7.4
Notes: The housing characteristics are for single-family residences sold during the 1990-1998
period. Standard deviations are in parentheses. Sales prices have been deflated to reflect year
2000 prices using the Nevada Real Estate Price Index. Demographic characteristics are from
the 2000 Census. Percentage multi-unit refers to the percentage of housing units in multi-unit
structures. Median household income is for 1999. Employment statistics come from the
Bureau of Economic Analysis for 1998.
* F.I.R.E. includes finance, insurance, and real estate.
6.3 percent, 8.6 percent, 8.1 percent, 8.8 per-
cent, and 6.4 percent. It is difficult to make
PRICEjt, = lXjct + P2RISK,, + qCt + -jct.
definitive statements with the available data but
there appears to be little evidence to support the Here j indexes individual houses, c indexes
explanation that the decline in housing prices is county, and t indexes time. Observable housing
due to a labor market disturbance.
characteristics include lot size (acres), interior
floor space (square feet [100s]), building age
V. Estimation Strategy
(years), and overall condition (class), as well as
county, year, and month dummies. Class is a
Sales prices in logs are regressed on a vector discrete variable (1-5) assigned by the assessor
of housing characteristics, X, and the linear at the time of sale to reflect the overall condition
spline, RISK, or some alternative measurement of the property. The county dummy controls for
of local health risk:
county-specific fixed effects. The year dummies
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VOL. 94 NO. 5
DAVIS: THE EFFECT OF HEALTH RISK ON HOUSING VALUES
1699
0
ir
0-
0
0
0
-------
---------T-
I---I-----
--
-------------T-T--
-T----
-
-
--
---
1992 1994 1996 1998 2000 2002
Year
1990
-" Churchill County -- microdata
- Lyon County -- microdata
State of Nevada -- OFHEO
FIGURE 2. ASSESSING THE VALIDITY OF THE COUNTERFACTUAL:
HOUSE-PRICE INDICES FOR SINGLE-FAMILY RESIDENCES, 1990-2002
0
T"-
0
I
0
t
I
I
1990
I
1992
I
-t
1994
t
1996
Year
I
1998
Tt
2000
2002
FIGURE 3. FALL IN HOUSING PRICES AFTER 1999:
PERCENTAGE DIFFERENCE BETWEEN CHURCHILL COUNTY HPI AND NEVADA HPI
control for unobserved state-level trends and the
month dummies control for seasonal effects.
effect of a unit change in RISK on property
values.
The variance matrix is estimated taking into
The coefficient of interest, 32, is the percentage
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1700
THE AMERICAN ECONOMIC REVIEW
DECEMBER 2004
account that there are unobserved factors TABLE
rlct 2 DIFFERENCE-IN-DIFFERENCE ESTIMATOR: MEAN
LOG SALES PRICE BEFORE AND DURING LEUKEMIA INCREASE
that cause prices to vary from month to month
in each county. The correction procedure de1990-1999 2000-2002 Difference
scribed by Brent R. Moulton (1986) allows each
Churchill
County 11.587 11.550 -0.037
county-month group to have a different
and
(0.408) (0.407)
unrestricted covariance structure but assumes
n= 2800 n = 796
that errors are uncorrelated across groups. LeastLyon County 11.627 11.667 0.040
squares estimation is consistent if the explanatory
(0.403) (0.342)
n = 4323 n = 2285
variables are exogenous conditional on lct:
Relative difference -0.077
(0.019)
E{sjctlXjct, RISKt, 7c,t} = 0.
After including these covariates there remains
Sales prices throughout have been deflated
large unexplained variation in house prices beto reflect year 2000 prices using the Nevada
cause many of the characteristics that determine
HPI. Between the 1990-1999 period and the
the value of a house are unobserved. Much of
2000-2002 period the mean log sales price
the variation may be explained by unobservedof houses in Churchill County decreased by
factors that characterize particular properties0.037 while prices in Lyon County increased by
like geographical features, neighborhood char0.040. The period of increased perceived health
risk is associated with a difference-in-difference
acteristics, and design amenities. The specification with a property-specific fixed effect, a, of -0.077. The coefficient is significant at the
may be expressed as follows:
1-percent level. The difference-in-difference
methodology provides a baseline estimate of the
equalizing differential of interest but it does not
PRICEj,t = lXjt, + /2RISK,c + aj
control for changes in the composition of the
housing stock. On average the houses sold in
Churchill County between 2000 and 2002 had
considerably larger lots and more floor space
An appealing feature of the housing sales
than houses sold previously. The regression+ lct + Cjct'
records is that it is possible to link individualbased estimates take this compositional change
into account.
houses across years. By comparing the sales
price of these houses at different points in time Table 3 reports least-squares and fixedthe fixed-effects estimator controls for propertyeffects regression estimates for the linear spline.
specific heterogeneity and serves as an imporSpecification (1) includes the coefficients for lot
tant test of the robustness of the results. The
size, floor space, and building age. Coefficients
within transformation eliminates the property-for these characteristics are in the expected dispecific fixed effect, aj, along with all time-rection and comparable in magnitude to those
invariant regressors but does not eliminate thefound in Katherine A. Kiel and Katherine T.
county-month effect, ct. Thus the variance-McClain (1995) and Janet E. Kohlhase (1991).
covariance matrix for the fixed effects estimates
The coefficient for the linear spline indicates
will also be corrected for intragroup correlation.that houses sold during the period of maximum
Fixed effects estimation is consistent if the ex- risk in Churchill County sold for 12.3 percent
planatory variables are strictly exogenous con- less than equivalent houses not affected by the
cluster. In specification (2) the differential inditional on aj and rct:
creases to -15.6 percent after including county,
E{(jCtXjC,, RISK,, aj, T,,} = 0
V T.
class, time, and month dummies. The county
dummy controls for county-specific amenities
and indicates a time-invariant premium for
Churchill County. The fixed effects estimate
indicates a -14-percent differential. It would
Table 2 reports difference-in-difference appear
esti- that controlling for observable characmates of the equalizing differential for teristics
risk.
in the pooled cross-section captures
VI. Results
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VOL. 94 NO. 5
1701
DAVIS: THE EFFECT OF HEALTH RISK ON HOUSING VALUES
TABLE 3-THE EFFECT OF HEALTH RISK ON HOUSING VALUES
OLS
(1)
OLS
FE
(2)
Leukemia risk (linear spline) -0.123 -0.156 -0.140
(0.013) (0.017) (0.015)
Lot size (acres) 0.011 0.012
(0.002) (0.002)
Lot size squared -1.88E-05 -2.02E-05
(3.20E-06) (3.18E-06)
Floor space (square feet, 100s) 0.054 0.044
(0.001) (0.001)
Building age (years) -0.009 -0.006
(0.001) (0.001)
Building age squared 3.57E-05 1.20E-05
(8.61E-06) (8.42E-06)
Churchill County dummy 0.068
(0.009)
Class
dummies
no
yes
Year dummies no yes yes
Month dummies no yes yes
n
10204
R2
10204
0.60
0.63
4922
0.05
Notes:
The
sample
consists
counties.
The
dependent
va
rises
by
county
1/24
the
each
month
linear
heteroskedasticity
and
much
of
the
same
ity
controlled
for
For alternative measures of leukemia risk
the results are of similar magnitude to those
reported in Table 3. When the number of cu-
i
corr
prope
in
the
TABLE 4-COMPARING DIFFERENTIALS FOR
mulative leukemia cases is used as the measure-
ment of risk, the estimates indicate that the
period of maximum risk is associated with a
15.6-percent (OLS) and 14.1-percent (FE) de-
du
spline
DIFFERENT-SIZED HOMES
OLS
FE
Small homes -0.147 -0.159
2,000 square feet (.039) (.047)
n = 1230 n = 586
better with one regressor over the others. Table
4 reports equalizing differentials for risk for Notes: The OLS specification includes housin
small, medium, large, and very large houses.
tics, class dummies, time dummies, monthly
The coefficients are derived from eight separate a county dummy. The FE specification incl
regressions each including all of the observable monthly dummies. The mean 1990-1999 sal
Churchill County for the four groups are $84
characteristics described in Table 3. The ob-
$135,900, and $183,100, respectively. Stand
served differential is stable across segments corrected
of
for heteroskedasticity and correlated
county-month groups.
the housing market ranging from 14.1 percent to
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1702
THE AMERICAN ECONOMIC REVIEW
DECEMBER 2004
TABLE 5 LIFETIME ESTIMATES OF RISK AND THE STATISTICAL VALUE OF PEDIATRIC
LEUKEMIA
Low High
Standard Low Mean High Mean Variance Variance
Prior Prior Prior Prior Prior
Risk estimate 1997 2.59 1.29 5.18 2.59 2.59
(1.71) (1.21) (2.42) (1.25) (2.53)
Risk estimate 2002 14.5 13.6 16.4 9.82 22.6
(3.48) (3.37) (3.71) (2.23) (5.64)
VPL-least squares $5.55 $5.39 $5.88 $9.20 $3.28
(0.60) (0.58) (0.64) (0.99) (0.36)
VPL-fixed effects $5.00 $4.88 $5.26 $8.29 $2.97
(0.46) (0.44) (0.48) (0.75) (0.28)
Notes: The first two rows of the table report estimated life
10,000 individuals as of January 1, 1997, and January 1, 200
the beliefs distribution in parenthesis. The second two rows
case of pediatric leukemia (VPL) in millions of U.S. dollar
parenthesis. The VPL estimates are derived from ten separ
cation includes housing characteristics, class dummies, time
a county dummy. The FE specification includes time and mo
are corrected for heteroskedasticity and correlated errors wi
The price
a house should
the
16.5 percent (OLS) and from
12 of
percent
to capitalize
16.6
present discounted value of all future pediatric
percent (FE).
leukemia risk associated with living there. AcVII. Statistical Value of Pediatric Leukemia
cordingly, to calculate MWTP it is appropriate
to use a measure of lifetime risk. The Bayesian
estimates
are used to derive lifetime risk by
This section uses the Bayesian estimates
of
risk to estimate the MWTP for change inassuming
lifethat at every point in time the perceived
time pediatric leukemia risk. This tradeoff
is level of risk in all future years is equal to
used to calculate the value of a statistical case of
the perceived current level of risk. Households
pediatric leukemia (VPL). First articulated byare assumed to be infinitely lived and, following
Gary Fromm (1965) and later described by David M. Cutler and Elizabeth Richardson
Thomas C. Schelling (1968) and Richard H. (1997), future risk is discounted at 3 percen
Thaler and Rosen (1975), the statistical valueannually. For a 5-percent discount rate the VPL
(or "inferred value") of a health risk is the totalestimates are larger by a factor of 1.63.
amount of compensation a group would require Table 5 reports the estimates of lifetime risk
to face one expected unfavorable outcome from and the VPL. Using the standard prior, lifetime
within their group. The statistical value of apediatric leukemia risk increases from 2.59 to
health risk is derived by dividing MWTP by the14.5 per 10,000 individuals between January 1
risk increment.2
1997, and January 1, 2002. This corresponds t
a level of risk that rises from the national aver-
age to about six times the national average. To
2 Inferred values would appear to provide a common test the robustness of the results, lifetime pedi-
metric for comparing human health valuations across con- atric risk is constructed for four alternative pritexts. However, it is important not to overstate the general-ors: (i) mean equal to one half the national
ity of this transformation. Several models including Michael
Jones-Lee (1974) and Milton C. Weinstein et al. (1980)
average, (ii) mean equal to twice the national
predict that MWTP for a reduction in health risk is increas-average,
(iii) variance that reflects the cumula-
ing in the base level of risk. The gradient of the hedonictive county population since 1950, and (iv) variprice function gives the MWTP evaluated at one particularance that reflects the cumulative county
level of risk. It does not provide information about how
population since 1990. Depending on the choice
MWTP changes with the level of risk or about willingnessof
prior, the estimated change in perceived lifeto-pay for non-marginal changes. In practice this implies
that caution should be used in comparing estimates oftime
MWTP across contexts with different base levels of risk.
risk ranges from 7.23 to 20 per 10,000
individuals. The estimates of risk are particu-
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VOL. 94 NO. 5
DAVIS: THE EFFECT OF HEALTH RISK ON HOUSING VALUES
1703
larly sensitive to the choice of the variancelife
of of a child only if housing decisions were
the prior. The more outcomes the household
made on the expectation that pediatric leukemia
is terminal. More generally, value-of-cancer esobserves, the lower the variance of the prior,
and the smaller the effect individual leukemia
timates reflect MWTP to avoid mortality risks
and MWTP to avoid all other consequences of
cases have on perceptions of risk.
To generate the estimate of the VPL, this cancer. Both sources of valuation are important
measure of lifetime pediatric leukemia risk is for assessing the cost-effectiveness of environassigned to house sales by the date of sale and mental regulations. Analyses that consider
included in the price regression. The risk esti- only mortality risks will underestimate the
mates for the control county are set equal to thevalue of cancer risk reductions.
January 1, 1997, prior. The price regression
VIII. Concluding Remarks
indicates that for the standard prior household
MWTP is 1.22 (OLS) and 1.10 (FE) percent of
house-sales price per 1 in 10,000 change in
lifetime risk. The VPL estimates are calculated
In April of 2002, Senator Harry Reid (D-NV)
announced that he had succeeded in securing
by multiplying the MWTP estimates by mean nearly $28 million in federal funds for public
house price and dividing by the average number health projects in Churchill County. Together
of members per household in Churchill County with Senator Hillary Clinton (D-NY), he has
as reported in the 2000 Census (2.64). This
introduced the Health Tracking Act, which
second adjustment is necessary because the ob- would create a national network for tracking
served differential reflects household MWTP
chronic diseases with possible environmental
causes. The estimates from this project provide
whereas the risk estimates are calculated per
individual.
part of the information necessary to assess the
For the standard prior the least squares esti- cost-effectiveness of such programs. Much
mate indicates a VPL of $5.6 million. The fixed work remains to be done on the marginal cost
effects estimate indicates a VPL of $5 million. side of the equation. In particular, will this new
Point estimates for alternative priors range from spending allow epidemiologists to identify the
$3 million to $9.2 million. These estimates are source of the leukemia increase? What will have
comparable in size to previous estimates in the to be done to lower leukemia risk? How much
literature for the inferred value of cancer and
will it cost per leukemia case avoided? Together
mortality risk. In the study most similar to this
one, Gayer et al. (2000) derive value-of-cancer
estimates ranging from $4.3 million to $5 million from the effect of local superfund sites on
housing prices after the release of site risk assessments. This range is consistent with esti-
with the answers to these difficult questions, the
a broad range of contexts. See Viscusi and Aldy
(2003) for a recent survey. Estimates from mortality risks in the labor market typically range
from $4 million to $9 million. All estimates are
health. In 2002 the budget for the Environmental Protection Agency included $3.2 billion for
safe drinking water, $1.7 billion for waste man-
mates of the statistical value of life measured in
estimates from this project could be used to
evaluate programs like the Health Tracking Act
on the basis of efficiency. More generally, the
estimates from the paper provide a benchmark
for assessing the cost-effectiveness of a broad
range of public policies that affect human
agement, and $598 million for clean air. A
expressed in year 2000 prices.
primary motivation for this spending is to proThese estimates provide some of the first tect households from cancer-causing substances
and other environmental health risks. Reliable
market-based estimates of the value of health
for children. One of the reasons limited empir-estimates of household valuations of these risks
ical evidence is available is because wage-riskare imperative if programs are to be funded at
studies are impossible for individuals who are cost-effective levels.
not in the labor market. Considering the housing
market effects of environmental health risks that
predominantly affect particular age groups may
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Journal of Public Economics 96 (2012) 869–880
Contents lists available at SciVerse ScienceDirect
Journal of Public Economics
journal homepage: www.elsevier.com/locate/jpube
Valuing public goods using happiness data: The case of air quality☆
Arik Levinson
Georgetown University and NBER
a r t i c l e
i n f o
Article history:
Received 14 October 2011
Received in revised form 15 June 2012
Accepted 20 June 2012
Available online 30 June 2012
JEL classification:
Q51
Q53
H41
a b s t r a c t
This paper describes and implements a method for valuing a time-varying local public good: air quality. It
models survey respondents' self-reported happiness as a function of their demographic characteristics, incomes, and the air pollution and weather on the date and in the place they were surveyed. People with higher
incomes report higher levels of happiness, and people interviewed on days with worse local air pollution report lower levels of happiness. Combining these two concepts, I derive the average marginal rate of substitution between income and current air quality — a compensating differential for short-term changes in air
pollution.
© 2012 Elsevier B.V. All rights reserved.
Keywords:
Willingness to pay
Stated well-being
Pollution
Compensating differential
1. Introduction
Valuing local public amenities and other non-market goods is one of
the greatest challenges facing applied economics. Existing methods,
often applied to environmental quality, include travel-cost models,
hedonic regressions of property values, and contingent valuation
surveys in which people are asked directly their willingness to pay
for public goods. In this paper, I describe and test an alternative method
for estimating the economic benefit of a local public good. The fundamental idea is extraordinarily simple. I combine survey data with air
quality and weather information to model individuals' self-reported
levels of “happiness,” or “subjective well-being,” as a function of their
demographic characteristics, incomes, and the air quality and weather
at the date and place they were surveyed. I then use the estimated
function to calculate a marginal willingness to pay, or compensating
differential, for air pollution: the average marginal rate of substitution
between annual household income and current air quality that leaves
respondents equally happy.
This happiness-based methodology has a number of advantages
over existing tools for valuing environmental quality. The people
☆ This research is part of a project funded by the National Science Foundation grant
#0617839. I am grateful to Resources for the Future for its hospitality during part of the
time I worked on the paper, to Emma Nicholson and Jamie O'Brien for superb research
assistance, to Sarah Aldy for editorial support, to the research staff at the General Social
Survey for assisting me with matching confidential aspects of their data to geographic
information, and to John Helliwell, Chris Barrington-Leigh, Simon Luechinger, Erzo
Luttmer, Karl Scholz and Heinz Welsch for helpful suggestions.
E-mail address: AML6@georgetown.edu.
0047-2727/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
doi:10.1016/j.jpubeco.2012.06.007
most averse to air pollution choose to visit and live in clean locales;
as a result, travel-cost and many hedonic models may underestimate
the value of air quality. But because I include fixed effects and interactions by time and place, coefficients are identified from daily
fluctuations in pollution within a location and are not subject to
these sorting biases. Because I estimate marginal rates of substitution
between income and pollution directly, income effects do not
confound the approach, nor do large gaps between measures of
willingness to pay and willingness to accept. And because I do not rely
on asking people directly about environmental issues, the methodology
is not susceptible to the strategic biases and framing problems of the
contingent valuation approach.
Furthermore, although happiness studies have recently been used
to estimate tradeoffs made by public policies, including valuations of
public goods and bads, all of the previous work has relied on annual
average values across regions or countries. 1 If the public goods are
simultaneously determined by regional characteristics also associated
with happiness, studies using annual regional differences in public
goods will yield biased estimates of their value. Air quality, on the
other hand, varies daily within each location for reasons less likely
to be connected to any particular respondent's situation. The results
here are identified entirely from short-term changes in air quality at
1
Public policy issues studied have included price inflation (Di Tella et al., 2001),
state cigarette taxes (Gruber and Mullainathan, 2005), airport noise (van Praag and
Baarsma, 2005), inequality (Alesina et al., 2004), terrorism (Frey et al., 2009), and even
air pollution (Welsch, 2007; Di Tella and MacCulloch, 2008; Luechinger, 2009).
870
A. Levinson / Journal of Public Economics 96 (2012) 869–880
a given location, and consequently they mitigate concerns about
unobserved local characteristics correlated with both happiness and
air quality.
Because air quality is a public good that fluctuates day-to-day, the
results here will need to be interpreted somewhat differently from
typical valuations of public goods. If people become habituated to
levels of public goods, estimates based on daily fluctuations will
yield higher values than estimates based on longer-term levels,
because air quality presumably varies more quickly than people
become habituated. Any valuation derived from daily fluctuations
will omit the effect of habituation, but also will omit any long-term
effects of poor air quality because those will be absorbed by time
and place fixed effects. In the extreme case of perfect habituation,
there might well be significant differences in happiness in any one
place on days with low or high air quality, but no happiness differences across otherwise similar places with different average levels
of air quality. 2
Naturally, this approach also has disadvantages. It treats responses
to questions about happiness as a proxy for utility and then makes
interpersonal comparisons among respondents. It relies on a vague
question about how “things are these days.” It identifies the relevant
compensating differential based on trade-offs between fluctuations in
daily pollution and differences among respondents' annual incomes.
And it takes household income to be an exogenous determinant of
happiness, rather than potentially determined by happiness. The reason to pursue this line of research, therefore, is not that it is without
shortcomings. Instead, the attractive feature of this approach is that
its shortcomings differ so markedly from those of standard approaches
to valuing public goods, and thus it serves as a useful point of
comparison.
I present two main results. First, I show that happiness is related in
sensible ways to daily local air pollution. After accounting for
respondents' demographics, daily local weather conditions, as well as
temporal and geographic fixed effects and interactions, individuals
surveyed when the current local levels of airborne particulates are
higher report lower levels of happiness. This first step is a straightforward empirical exercise. It requires no strong assumptions except the
empirical specification, and I show that the results are robust to a variety
of those. I also show that reported happiness is not sensitive to local
levels of undetectable pollutants, such as carbon monoxide.
The second result uses the estimates from the first part to calculate marginal rates of substitution between pollution and income,
and then computes respondents' implicit willingness to pay for
improved air quality. This step does involve several strong assumptions, but I describe those in detail and argue they are no stronger
than the assumptions underlying travel cost, hedonic, or contingent
valuation estimates of willingness to pay for air quality. Moreover, because the assumptions I make differ entirely from the standard set, at a
minimum, the results serve as an alternative to the usual approaches.
The analysis here yields two important lessons. For the growing
literature on happiness and economics, the results provide yet another demonstration that subjective well-being varies in sensible ways
with respondents' observable circumstances. For environmentalists
and environmental economists, the results provide evidence that air
pollution, in addition to detrimentally affecting health and property,
has a direct negative effect on people's stated well-being, as well as
evidence that the monetary value of that effect may be quite large.
Using my preferred specification, I show that people appear willing to
sacrifice about $35 for an improvement of one standard deviation in
air quality for one day, a figure about twice as large as the highest
recent hedonic valuations of air quality (Bayer et al., 2009) or the U.S.
Environmental Protection Agency's (EPA) assessment of the economic
2
Habituation could also be relevant for hedonic estimates of compensating differentials. If owners of homes in polluted regions become habituated, those houses may
have smaller measured compensating differentials.
benefits of the 1970 and 1977 Clean Air Act Amendments (EPA, 1999,
2011).
2. Happiness in economics
Happiness, as defined by respondents' answers to simple survey
questions, has received a recent surge of serious attention from
economists. Much of the academic and popular happiness literature addresses the decades-old findings of Easterlin (1974): stated happiness
does not increase with income across countries or within a country
over time, but it does increase with income across individuals within
a country at any given point in time. Some recent work challenges
this Easterlin Paradox, showing that happiness increases with GDP per
capita across countries in expected ways (Stevenson and Wolfers,
2008; Deaton, 2008; Helliwell et al., 2010). But in other recent work
the paradox remains, and stated happiness appears unchanged over
time even as per capita incomes have increased (Oswald, 1997;
Layard, 2006). If true, the paradox has two obvious interpretations.
One is that people become habituated to their situations and change
their reference level of well-being.3 Another is that happiness depends
on relative income — the richest man in a poor town may be happier
than the poorest man in a rich town, even if the rich man is poorer in
absolute terms. 4
Under either interpretation, the Easterlin Paradox has implications
for using happiness to measure willingness to pay for public goods. If
happiness does not increase with income across regions or over time,
it may also be invariant to the level of any particular public good, for
similar reasons. For income, happiness does increase relative to other
people in the same locale at the same time. The analog for pollution is
that happiness may increase with air quality relative to the current
regional norm, but not relative to other regions or within regions
over long periods of time. That is why a key feature of this analysis
identifies the relationship between happiness and the place-specific,
date-specific air quality, at the place and date where the happiness
question was asked. I compare stated happiness by statistically similar respondents, at the same locale, during the same season of the
same year, who just happen to have been surveyed on days when
the air quality differed.
While much of the economics literature on happiness focuses on
deep questions about the rationality of economic actors, interpersonal
comparisons of ordinal utility functions, and links between economics
and psychology, economists are also attempting practical, policyrelevant applications. Recent work uses happiness surveys to evaluate
people's willingness to trade unemployment for inflation and argue
that central bankers place too much emphasis on combating inflation
(Di Tella et al., 2001), examine the welfare consequences of German
reunification on different groups (Frijters et al., 2004), assess the degree to which state cigarette taxes make smokers better off by helping
them quit (Gruber and Mullainathan, 2005), and estimate the degree
to which the marginal utility of consumption increases or decreases
when people become ill (Finkelstein et al., 2009). Happiness measures
have also been used to try to place a monetary value on airport noise
(van Praag and Baarsma, 2005), flood disasters (Luechinger and
Raschky, 2009), terrorism (Frey et al., 2009), and weather and
climate (Rehdanz and Maddison, 2005; Barrington-Leigh, 2008).5 All
3
Kahneman (2000) writes about individuals having a base level of stated well-being,
which major life events such as divorce or injury perturb at most for a few years. Others,
such as Oswald and Powdthavee (2008), show incomplete recovery of happiness after
such events. Graham (2009) provides evidence that people become habituated to crime,
corruption, democracy, and health.
4
See Luttmer (2005). Also, recent work suggests this relative interpretation may be
optimal from an evolutionary standpoint (Rayo and Becker, 2007).
5
These applications raise concerns among critics. Smith (2008) writes, “[T]he [happiness economics] train is precipitously close to leaving the station and heading for use
in full-scale policy evaluation.”
A. Levinson / Journal of Public Economics 96 (2012) 869–880
use annual average measures of the public good (or bad), raising the
possibility that endogeneity or omitted variables bias their answers.
Several papers close in spirit to this one use happiness measures
to value air quality. Welsch (2002, 2006, 2007) estimates values of
willingness to pay for air quality using various cross-sections and
panels of country-level data. The 2006 paper, for example, estimates
that the reductions in nitrogen dioxide and lead pollution in Europe
from 1990 to 1997 were worth $1200 per capita and $2200 per capita,
respectively, in 2008 dollars. Di Tella and MacCulloch (2008) regress
happiness on income and the national, annual, per capita emissions
of sulfur dioxide (SO2), and show that an increase of one standard
deviation in SO2 correlates with a decline in happiness equivalent to
a 17% reduction in income. As first uses of happiness data to estimate
willingness to pay for air quality, these works break new ground.
However they also share a drawback common to this literature:
they use average annual national measures of air quality. Aggregating
environmental quality across entire countries masks much of its
heterogeneity. The standard deviation of particulate air pollution in
the U.S. is twice as large if we look at daily observations within states
instead of averages across states or years.
One recent paper (Luechinger, 2009) avoids the problems associated with inter-country comparisons of happiness by looking across
regions within Germany, using annual mean concentrations of SO2
at 533 monitoring stations over a 19-year period. To control for
sorting by individuals into different locales within Germany, he
cleverly instruments for air quality using respondents' locations upwind
and downwind of large power plants that installed SO2 emissions control
equipment. Luechinger finds a marginal willingness to pay of $232 for a
one microgram per cubic meter (μg/m3) reduction in SO2, while average
SO2 concentrations fell by 38 μg/m3 over the time period.6
Two final issues complicate most prior attempts to value air quality
using happiness data. First, work based on cross-country pollution
differences must compare survey questions asked in diverse languages
and cultures, where notions of happiness may differ. Second, air pollution and weather are correlated. Studies of happiness and weather
omit pollution (Rehdanz and Maddison, 2005; Barrington-Leigh,
2008), while studies of happiness and pollution omit weather
(Welsch, 2007; Luechinger, 2009; Di Tella and MacCulloch, 2008). To
date, none have included both, a potentially important source of
omitted variable bias.
This paper addresses these problems. It focuses entirely on the
United States, so fewer language and cultural differences complicate
the responses to questions about happiness. It controls for the current
local temperature and precipitation, both of which are correlated
with both happiness and pollution. Instead of aggregate national or
yearly measures of pollution, it uses the environmental quality at
the time and in the location where the happiness survey question
was asked. Fixed effects and interactions by time and place mean
that the measured effect of pollution on happiness will be relative
to similar respondents who were interviewed in the same place
during the same month, but happen to have been interviewed on a
day when the air quality differed.
3. Data and methodology
For happiness measures, I rely on the General Social Survey (GSS),
which the National Opinion Research Center conducts annually. 7
Several thousand U.S. respondents are interviewed in person each
year, usually in March. The key GSS question asks, “Taken all together,
how would you say things are these days? Would you say that you are
6
$232 is €183 in 2002, converted to 2008 dollars using the average 2002 exchange
rate and the CPI-U-RS.
7
See www.norc.org/GSS+Website/.
871
very happy, pretty happy, or not too happy?” This question forms the
basis for the dependent variable. In addition to asking about happiness,
the GSS contains the usual demographic information, including age,
household income, race, education, sex, and marital status.
Some may be concerned about measurement error in the income
variable, either because the GSS income variable is categorical,
because self-reported income has errors, or because happiness is really
a function of consumption which is in turn only approximated by income. The GSS includes numerous categories each year (21 in 1993),
mitigating the first concern somewhat, and I use the GSS reported
real income (Ligon, 1989) which converts the categories into real
values by taking the midpoints of the ranges and adjusting for inflation
and top coding. I also attempt to control for attenuation bias in general
by instrumenting for income using average incomes by respondents'
and spouses' industries and occupations.
Importantly for this purpose, the GSS contains the date each
respondent was questioned. I have obtained from the GSS staff the
confidential codes identifying the county or city in which each respondent was surveyed. Knowing the date and place allows me to match
the GSS to the particular air quality on the day and in the place
where the survey was administered.
For pollution information, I turn to the EPA's Air Quality System
(AQS). The AQS contains the raw hourly and daily data from
thousands of ambient air quality monitors throughout the United
States. The data include the latitude and longitude of each monitor,
the types of pollutants monitored, and the hourly observations. 8 For
current local weather conditions, I use data from the National Climate
Data Center, which reports daily temperature and rainfall at each of
the thousands of weather monitoring stations throughout the United
States.
To merge the survey data with the weather and air quality data, I
take the population-weighted centroid of each GSS respondent's
county and draw an imaginary 25-mile circle around it. I then take a
weighted average of all the air quality and weather monitors within
the circle, where the weights are equal to the inverse of the square
root of their distance to the population-weighted centroids. 9 The
number of monitor station readings used in the spatial interpolation
ranges from 1 to 22, with a mean of 3.9 and a standard deviation of
3.3. Currie and Neidell (2005) confirm the accuracy of a similar
weighted-distance measure by predicting pollution levels at the
location of actual monitors using readings from nearby monitors.
Moreover, they note the measurement error introduced by the
procedure will only tend to bias the pollution effect towards zero.
The air quality monitors contain data on ambient concentrations
of criteria air pollutants, but not all data are available in all places or
during all time periods. Carbon monoxide (CO), for example, does
have consistently measured data in many locations going back to
the early 1970s. However, CO is odorless and invisible at the current
ambient concentrations in these pollution data, and I would not
expect it to affect happiness responses in the survey data. Airborne
particulates, on the other hand, cause physical discomfort, especially
particles smaller than 10 μm (PM10). In addition, small particles
form visible haze that reduces visibility and may affect people
aesthetically. Chay and Greenstone (2003) and Chay et al. (2003)
show that particulates have adverse effects on adult and infant mortality, and Neidell and Zivin (2009) show that people avoid outdoor
8
Recent years are available on the AQS Web site, earlier years by special request to
the EPA. More information about the AQS can be found at www.epa.gov/ttn/airs/
airsaqs.
9
Other weights, such as a simple average of all the monitors in a county, yield similar
results. The GSS has surveyed about 275 areas, and the names given to these areas do
not typically correspond to U.S. Census or U.S. Postal Service names. The GSS geographic
codes sometimes correspond to individual cities, sometimes to counties, and occasionally
to multi-county areas. (This last group is dropped). I first translated the GSS place names
to Census county codes by hand, then assigned each county its population centroid, and
merged those with the data from the weather and pollution stations within 25 miles.
872
A. Levinson / Journal of Public Economics 96 (2012) 869–880
activities when local newspapers report poor air quality. The AQS
contains PM10 readings beginning in the mid-1980s, so I begin this
analysis in 1984.
For particulates, monitoring stations only record ambient concentrations every six days. As a result, many of the happiness survey
questions were asked on days when no nearby air quality monitors
recorded data. Moreover, in any given location, different days may
be recorded by different sets of nearby monitoring stations. To
smooth out this variation and use as many of the happiness survey
responses as possible, I interpolate linearly between six-day observations for each monitoring station. In the robustness checks below, I
also report results for the subset of observations with uninterpolated
values.
The GSS has 19,491 observations between 1984 and 1996, of
which 10,193 have identifiable counties and could be matched to
PM10 readings from the AQS. Of these, 994 are missing household incomes, another 606 could not be matched to local weather, 2498 are
missing self-reported health status, which I worry may be correlated
with pollution, income, and happiness, and another 26 are missing
one of the other household demographics. The resulting dataset has
6035 complete observations.
3.1. Methodology
I estimate versions of the following function:
0
H ijt ¼ αP jt þ γlnY i þ X ijt β þ δj þ ηt þ δj yeart þ ijt ;
ð1Þ
where Hijt is the stated happiness of respondent i in location j at date
t. The variable Pjt is the air pollution at location j at date t. The log of
income (lnYi) conveniently captures the declining marginal effect of
income on happiness, consistent with typical papers estimating happiness functions, and it translates directly into an increasing marginal
willingness to pay for air quality. 10 Below I show that the estimated
trade-offs between pollution and income are unchanged if I substitute
the log of pollution, the level of income, or ordered probit versions of
those; or estimate a binomial probability that Hijt > H* for an arbitrary
H*. This robustness to empirical specification is especially important
given the limited reporting categories for the happiness variable in
the GSS. The vector Xijt contains a set of other demographic and
local characteristics, δj is a location-specific fixed effect, ηt is a
month and year fixed effect, and δj × yeart captures location-specific
trends.
Once estimated, I can totally differentiate the function, set dH = 0,
and solve for the average marginal rate of substitution between pollution and income, ∂Y/∂P:
∂Y
∂P
dH≡0
¼ −Y
^
α
;
^
γ
ð2Þ
the amount of annual income necessary to compensate for a one-unit
increase in air pollution on the survey date. 11 To avoid the cumbersome phrase “average marginal rate of substitution,” henceforth I
will use the term “willingness to pay” (WTP), fully recognizing that
Eq. (2) represents no one person's stated willingness. Rather, it
10
If happiness successfully proxies for utility, we would expect diminishing marginal
happiness/utility. Happiness as reported to the GSS, in three discrete categories, may
not follow the same distribution. In what follows I show that the estimates are robust
to a variety of functional form assumptions for Eq. (1).
11
Naturally, alternative formulations of (1) lead to different expressions for willingness to pay in (2). For example, using the level of income instead of its log means that,
^ =γ^ .
conveniently, ∂Y/∂P is simply the ratio of the coefficients on pollution and income, α
represents an estimate of the trade-offs between income and air quality that will leave people, on average, equally happy.
3.2. Some theoretical and practical concerns
Using Eq. (2) to measure marginal rates of substitution places
some strong assumptions on the underlying utility functions. We
typically assume individuals make choices as though they are
maximizing some unobserved utility function, observe market prices
and the choices people make, and infer from those prices and choices
properties of their utility functions, such as risk aversion, impatience,
and altruism. The fundamental challenge facing economists valuing
public goods is that we do not observe market prices or choices.
Public goods such as air quality have no markets, and individuals cannot “choose” their own level of public goods directly, except by voting
or relocating. So instead, this analysis proposes turning the typical
economics around. We will observe utility, or a proxy for utility, and
infer what choices people would be willing to make and what prices
would therefore be optimal.
The first problem with this approach is that “happiness” as
recorded by questions on surveys is not utility. Kahneman (2000)
addresses this, distinguishing between “decision utility,” which is
economists' notion of the individual welfare function that drives
economic choices, and “experience utility,” something closer to stated
happiness, experienced moment to moment. We do not observe
either type of utility directly. Perhaps the easiest way to think about
this methodology is that it uses respondents' stated happiness as a
proxy for their utility, or as an observable manifestation of latent
utility. As long as respondents with higher latent utility are more
likely to say they are happier, this approach is consistent with a
wide variety of discrete choice models in economics.
A second potential concern with the proposed approach is that the
GSS happiness question is unclear about what length of time it covers,
asking only how happy people are “these days.” Ideally the GSS would
have asked people two happiness questions: one about their overall
life satisfaction and one about their happiness at the moment the
question is asked. If “these days” refers to several months or years,
the happiness response should not be influenced by temporary
changes, such as the current daily level of air pollution relative to a regional seasonal norm. Psychologists and economists have found,
however, that responses to life satisfaction questions differ based on
short-term situations. Schwarz and Strack (1991) describe how
people interviewed after making a photocopy were significantly
more satisfied with their lives if they found a dime on top of the
copy machine. Clark and Georgellis (2004) test whether reported
“job satisfaction” proxies for “experience utility.” They find that
both current and lagged values of reported job satisfaction predict
the likelihood British laborers will quit, suggesting that reported
satisfaction has a current component. In other words, if people who
are asked about their overall satisfaction with life in general respond
in a way that is sensitive to current conditions, it may not matter that
the GSS question has a vague time horizon.
On a related note, Loewenstein et al. (2003) develop a behavioral
theory of “projection bias” wherein people misestimate their future
preferences based on current circumstances — buying too much
food at the grocery store if they shop while hungry. And Conlin et
al. (2007) provide empirical support for projection bias, showing
that people are more likely to return cold-weather gear purchased
from catalogs if they made those purchase orders on colder days —
overestimating their future demand for parkas based on current temperatures. Projection bias could conceivably distort hedonic estimates
of WTP if people bid too much for houses on unpolluted or sunny
days. One appeal of valuing air quality using happiness responses to
daily pollution changes is that the valuations do not rely on people
assessing their future preferences based on current circumstances,
as they might when deciding where to live. Instead I measure WTP
A. Levinson / Journal of Public Economics 96 (2012) 869–880
873
Table 1
Happiness, pollution, and income: linear regressions and particulates (PM10).
Means
Coefficients
Pollution and income only
PM10 daily (μg/m3) [α]
log(income) [γ]
Average PM10 by county and year
Age (÷10)
Age (÷10) squared
Female
Married
Kids
Employed
Unemployed
College graduate
Health fair or worse
Health poor
Rain (indicator)
Rain (0.01 inches)
Temperature mean (10 ° F)
Temperature squared
Temp. diff. (daily max–min)
Constant
Year, month, county f.e.'s, county-trends
Day-of-week and holiday fixed effects
R2
No. of obs. = 6035
Years: 1984–1996, skipping 1992, 1995
WTP to pay for a 1 μg/m3 reduction for one year
WTP to pay for a one std. dev. reduction for one day
Add average pollution
Add time and county f.e.'s
Baseline specification
(1)
(2)
(3)
(4)
(5)
30.4 (14.4)
3.75 (0.97)
−0.00143* (0.00061)
0.133* (0.012)
−0.00169* (0.00062)
0.133* (0.012)
0.00183 (0.00121)
−0.00122† (0.00064)
0.135* (0.008)
−0.00136* (0.00065)
0.065* (0.010)
1.72* (0.04)
No
No
0.044
1.67* (0.05)
No
No
0.044
−3.02 (7.21)
Yes
No
0.054
−0.112* (0.030)
0.014* (0.003)
0.042* (0.016)
0.251* (0.018)
−0.111* (0.020)
−0.031 (0.020)
−0.190* (0.054)
0.036† (0.019)
−0.250* (0.022)
−0.203* (0.042)
−0.0035 (0.0190)
0.0002 (0.0004)
0.064* (0.029)
−0.0063† (0.0034)
0.0092 (0.0127)
–
Yes
Yes
0.129
$459* (188)
$18
$541* (194)
$21
$386† (205)
$15
$891* (446)
$35
4.4 (1.7)
22.0(16.4)
0.56
0.51
0.70
0.66
0.023
0.24
0.20
0.044
0.45
9.48 (24.23)
4.37 (1.42)
21.1 (12.4)
2.01 (0.78)
* Statistically significant at 5%. † Statistically significant at 10%. Std. deviations in column (1). Standard errors in columns (2)–(5) adjusted for clustering by county. Standard errors of
WTP use the delta method. The dependent variable “happiness” has mean 2.17, std. dev. 0.63. Income is measured in thousands of dollars per year and has been converted to 2008
dollars using the CPI-U.
using current tradeoffs based on current circumstances, an approach
closer in spirit to experience utility than decision utility.
A third likely objection to this approach is that economists normally assume utility is ordinal rather than cardinal, and that interpersonal comparisons based on stated happiness are impossible. If an
unpolluted day moves person #1 from “not happy” to “very happy,”
and person #2 from “not happy” to “pretty happy,” that does not
mean that person #1 gets more utility from clean air than person #2,
or that person #1 would be willing to pay more for clean air. Put differently, we could alter some people's happiness functions by a positive
monotonic transformation while leaving others' unchanged, and it
would yield the same rank ordering of outcomes for each individual.
It would not, however, yield the same estimates of Eq. (1).
Economists studying happiness have responded in several ways.
Some, like Ng (1997), have argued that ordinal utility is an overly
restrictive assumption, and that ample evidence shows people's utilities are interpersonally comparable and cardinal. Others have implicitly
assumed that happiness is ordinal but interpersonally comparable. If
the latent utility of person #1 is higher than that of person #2, then
the stated happiness of person #1 will also be higher. This allows
researchers to estimate an ordered discrete choice model such as an
ordered logit or probit. Alesina et al. (2004), Blanchflower and Oswald
(2004), and Finkelstein et al. (2009) follow this empirical approach.
Most researchers who have applied both approaches have found little
difference between the results of a linear regression and an ordered
logit or probit (Ferrer-i-Carbonell and Frijters, 2004).12 Since I am not
interested in the marginal utility of income or air quality separately,
but only the ratio of the two as in Eq. (2), my analysis is less sensitive
to these issues. I show below that the estimates of Eqs. (1) and (2) are
robust to a variety of empirical specifications.
Finally, economists should be concerned that income may be measured with error or endogenous with respect to happiness. While
more income may make people happier, inherently happier people
may earn higher incomes. Very few papers address this. Luttmer
(2005) instruments for household income using interactions between
the respondents' and spouses' industry, occupation, and location.
Powdthavee (2009) uses time series data on the number of household members working. 13 Both find that the income coefficient in IV
specifications is larger than in OLS specifications — three times larger
in Luttmer's case. This suggests that Eq. (2) will overstate the marginal WTP for air quality. Although industry wage differentials have been
used as instruments for income in many contexts outside of this
happiness literature, Pischke and Schwandt (2012) cast considerable
doubt on their exogeneity with respect to other individual characteristics correlated with income, undermining their validity as instruments.
For the sake of discussion, I report results from one specification where
I instrument for income using a version of Luttmer's occupation and
industry-based prediction of income, yielding somewhat smaller estimates of WTP.
In the end, my focus is on obtaining convincing evidence for the effect of pollution on happiness, based on local daily variation, and then
using that cautiously to infer a marginal WTP. All I can do is
remain cognizant of these strong assumptions, remind readers that
standard approaches to valuing environmental quality — travel costs,
hedonics, contingent valuation — have their own sets of strong assumptions, and demonstrate that the results obtained from this
12
One key advantage of the regression approach over the ordered probit is that the
former can easily include fixed effects, so any individual or region-specific norms for
happiness can be differenced out.
13
Gardner and Oswald (2007) circumvent the endogeneity by examining the mental
wellbeing of lottery winners.
874
A. Levinson / Journal of Public Economics 96 (2012) 869–880
approach yield plausible valuations that are robust to different samples
of the data and different empirical specifications.
4. Results
Table 1 begins by estimating versions of Eq. (1). The first column
contains the means and standard deviations of the right-hand-side
variables. Column 2 estimates Eq. (1) but excludes every right-hand
side variable except income and daily local pollution, measured
using particulates (PM10). Happiness decreases with pollution on
the day of the interview and increases with annual household
income. The coefficients suggest that a 10 μg/m 3 increase in local
daily particulates is associated with a decrease in happiness of
0.014, on a three-point scale. The log income coefficient suggests
that a 10% increase in annual income is associated with an increase
of happiness of 0.013. Since happiness may be regarded as only
ordinal (or a proxy for utility which is ordinal), I do not want to overemphasize the absolute magnitudes. More important is the ratio of
the two coefficients, or the trade-off between pollution and income
that leaves people at the same level of happiness.
To place a dollar value on air pollution, we need to calculate
^ and 42.5 for the
^ , 0.133 for γ,
Eq. (2). Plugging in − 0.0014 for α
mean income (in $1000 s), the WTP is ∂Y/∂P = $459, as reported at
the bottom of Table 1. A 1 μg/m 3 increase in PM10, on the day of
the interview, reduces an average person's stated happiness by an
amount equal to a $459 decline in annual income. What does this
mean? This $459 figure represents an estimate of the amount of
annual income that increases happiness (at the mean log income in
the sample) by the same amount as a 1 μg/m 3 reduction in PM10
pollution, but the PM10 coefficient is identified from daily fluctuations
in air quality. If we divide the $459 by 365 days, we get an estimate of
$1.26 per day. To put this into context, note that the standard deviation
of PM10 is 14.4 μg/m3. Our estimate, then, corresponds to a WTP of $18
(14.4 × $1.26) for a one-standard-deviation improvement in air quality,
for one day.14 Or, a one-standard-deviation decline in air quality makes
people feel worse off by an amount equivalent to a decline in annual
income resulting in having $18 less to spend per day.
Column (3) of Table 1 adds to the regression the average particulate
count for each respondent's location for the month in which the survey
was taken.15 The income coefficient remains unchanged, the daily
pollution coefficient increases in absolute value to −0.0017, and the
monthly pollution level is insignificant and even wrong-signed. The
implied WTP for a one-standard-deviation daily change would be $21
rather than $18. One interpretation is that the local monthly values
are merely imprecise measures of the daily values, which is what people really care about. Another is that people become habituated to their
environments and respond only to daily departures from the local
norm.16
Column (4) of Table 1 drops the average local pollution levels, and
adds instead year, month, and county fixed effects, and countyspecific trends. Now the daily PM10 measure is identified from the
difference between air quality on the day of the survey and the local,
seasonal, trend-adjusted average air quality. None of the year or
month fixed-effect coefficients, and only three of the county
and year× county coefficients, are statistically significant. The daily
14
This standard deviation of 14.4 μg/m3 represents variation both across and within
year-month-county “cells.” The average standard deviation within cells is 5.7 μg/m3.
The sample includes an average of 774 observations per year, 2298 per month, and
142 per county. The average year-month-county cell has 11 observations, ranging from
1 to 59.
15
The correlation between daily and monthly pollution levels is 0.74.
16
The standard errors on the monthly values are large, meaning we cannot differentiate between these two interpretations. Monthly fixed effects, added next, also account for seasonal effects. If people are happier in spring and particulates are lower
in the spring, that would bias the results absent monthly fixed effects.
pollution coefficient decreases slightly, and is only marginally statistically significant, suggesting a WTP of $15 rather than $18. In sum, controlling for local conditions, either with a measure of local monthly air
pollution or with a set of fixed effects including location-specific trends,
does not change the basic findings. Local pollution on a given day appears to diminish the probability that people report high levels of
happiness.
Finally, column (5) adds a battery of demographic and local covariates. Happiness decreases and then increases with age, falling to a
minimum at about age 40. Women and people who are married, not
unemployed, and healthy are happier. All these results conform
with standard findings in this literature. If anything, adding the
demographic variables halves the coefficient on income, thereby
doubling the estimate of WTP to $35 for a one-standard-deviation
change in PM10. This raises the possibility that other unobserved
respondent characteristics may also be correlated with both income
^ and thereand happiness, biasing the estimated income coefficient γ
fore the calculation of WTP. On the other hand, including weather,
day-of-week, and respondents' characteristics has no effect on the
^ supporting the claim that the
estimated pollution coefficient, α,
coefficient on local daily pollution does not suffer from omitted variable
bias.
One particular demographic characteristic stands out: health. GSS
respondents are asked whether their “own health, in general, is excellent, good, fair, or poor.” The answers are highly correlated with income. Respondents in poor health in the sample report average
annual family income of $28,000; those in excellent health report
$74,000. Health also correlates with reported happiness. Respondents
in poor health report average happiness of 1.7 on the three-point
scale; those in excellent health report 2.4. So health is clearly related
to happiness. If health and air pollution are also correlated then
omitting health could impart a potentially severe omitted variable
bias. Health and air pollution could interact in a number of ways.
Air pollution could cause declines in self-reported general health
status, either on a daily basis or over the long term, or air pollution
could have different effects on happiness for healthy and unhealthy
people. In Tables 3 and 5 below I explore both of these possibilities.
In the meantime, column (5) of Table 1 shows that health is an
important determinant of happiness, and that including it in the estimation of Eq. (1) does not change the effect of daily local air pollution
on happiness for the average respondent, although it does affect the
WTP estimate through the coefficient on income.
The weather variables are included because pollution levels are
positively correlated with temperatures and negatively correlated
with rainfall, and because happiness has been shown to be affected
by weather. Happiness rises with temperature at low temperatures,
falls with temperature at high temperatures, and rises in the
difference between the daily maximum and minimum, which proxies
for clear skies and low humidity. The two temperature coefficients in
column (5) imply that a 10° rise in temperature from 30 to 40 °F
makes people happier by an amount equivalent to having an extra
$36 per day, while a rise from 80 to 90 makes people less happy by
$55. The rainfall coefficients are highly correlated with the other
variables, and not statistically significant, but the point estimate
implies that a rainy day makes people worse off by $6 per day. More
importantly, the additional demographic and location characteristics
do not change the basic result that happiness increases with income
and decreases with local daily pollution.
After including multiple fixed effects and interactions, standard
household demographics, and five measures of the current local
weather, the pollution coefficient remains approximately the same
magnitude. The remaining pollution variation in column (5) could
result from wind direction, local or upwind construction, traffic, fuel
changes at factories or utilities, road paving, or other unmeasured
activities. I cannot rule out that some of those might be correlated
with both happiness and pollution levels, imparting an omitted
A. Levinson / Journal of Public Economics 96 (2012) 869–880
875
Table 2
Happiness, pollution, and income: alternative functional forms and PM10.
PM10 daily (μg/m3) [α]
Income [γ]
Other covariates and fixed effects as in column (5) of Table 1
R2
No. obs.
Years: 1984–1996, skipping 1992, 1995
WTP to pay for a 1 μg/m3 reduction [−α/γ]
WTP to pay for a one std. dev. reduction for one day
⁎
PM10 without interpolation
Linear in income
ln(income) ln(PM10)
Ordered probit: ln(income)
(1)
(2)
(3)
(4)
−0.0017⁎ (0.0008)
0.082⁎ (0.015)
Yes
0.154
2567
−0.0014⁎ (0.0006)
0.0013⁎ (0.0002)
Yes
0.130
6035
−0.044⁎ (0.021)
0.065⁎ (0.010)
Yes
0.129
6035
−0.0027⁎ (0.0013)
0.130⁎ (0.020)
Yes
$838† (443)
$42
$1075⁎ (516)
$42
$947⁎ (483)
$37
$890⁎ (442)
$35
6035
See the footnotes to Table 1.
variable bias to the models in Table 1. All I can do is include as many
local covariates as possible, and point out that their inclusion does
not dramatically change the pollution coefficient from the bare-bones
specification in column (2).
Table 2 presents a sample of some alternative specifications. First,
the results so far use air quality measures that interpolate between
readings that occur every six days. As an alternative, I tried using
only the 40% of cases where uninterpolated daily readings were
available for a nearby station. Those results are summarized in
column (1) of Table 2. The effects of pollution and income on happiness
are both slightly larger than in the basic specification shown in column
(5) of Table 1, leading on balance to a nearly identical estimate of WTP
for a 1 μg/m3 reduction in PM10 ($838). Because the variance across the
uninterpolated values is higher than for the interpolated values
(18.2 μg/m 3 rather than 14.4 μg/m 3), the WTP for a one-day change of
one standard deviation is slightly higher at $42. Column (2) uses the
level of income rather than its log. Nothing changes except the formula
for calculating WTP (see footnote 11). Column (3) uses both the log of
income and the log of PM10, again with no meaningful change in the
calculated WTP. Column (4) estimates Eq. (1) as an ordered probit.17
Respondents' stated happiness varies systematically with their incomes
and the local daily air quality in ways that are robust to a variety of
empirical specifications.
Table 3 addresses some deeper issues with the approach. Column
(1) includes a control variable for the PM10 count the previous day, to
account for the possibility that the effects of pollution on happiness
may be cumulative. Here I limit the sample to the 25% of cases
where uninterpolated readings were available two days in a row.
The coefficient on yesterday's pollution is positive and insignificant,
but its inclusion increases the negative effect of the current day's air
pollution on happiness, resulting in a larger measured WTP. However,
given the high degree of correlation between the two air quality measures, the point estimate of WTP over the two-day period is about the
same as for the basic specification in Table 1. 18
Columns (2) and (3) of Table 3 address the concerns about the measure of respondents' incomes: that it is measured with error, serves as
an approximation for consumption, or is endogenous. First, the GSS
asks respondents to place their household incomes into categories
representing income ranges, rather than asking them to report their
actual incomes. It then takes the midpoint of each range and adjusts
for inflation and top coding to report intertemporally consistent
income values (Ligon, 1989). Although the survey has more than 20
income categories each year, the procedure raises the possibility of
measurement error and attenuation bias, which would reduce the income coefficient and inflate the calculated WTP. A second, deeper
17
Estimates of Eq. (1) as linear probabilities and probits that H > 1 or H > 2 yield the
similar results.
18
For the 1588 observations in column (1) of Table 3, the standard deviation of PM10
is 18.5.
issue involves the endogeneity of income. Happiness and household incomes are correlated, but we do not know if that is because income
causes happiness, or because happy people earn higher incomes.
The solution to these problems — attenuation bias from mismeasurement and endogeneity of incomes — is to find an instrument
for household income, something that is correlated with income but
with no independent effect on happiness. Powdthavee (2009) uses
panel data to instrument for household incomes using changes over
time in the number of household members working. His approach approximately doubles the coefficient on household income. Luttmer
(2005) instruments for household incomes using the respondents'
and spouses' industry, occupation, and location. Respondents who
work in occupations and industries with high wages, or whose
spouses do so, are likely to have higher household incomes and are
therefore more likely to report higher levels of happiness. Using this
instrument, Luttmer finds the coefficient on income is three times
as large as when he uses household income directly, which suggests
I should divide the estimated WTP of $35 per day by three.
To address both the possible mismeasurement and endogeneity of
respondents' incomes, I estimate a version of Luttmer's (2005) instrumental variables approach. While Pischke and Schwandt (2012) raise
concerns about using industry wage differentials as instruments for
income, the approach seems worth replicating here, if nothing else
as a comparison with other recent papers that have done so. First, I
use the Consumer Population Survey (CPS) to calculate the average
annual earnings by year, state, industry, and occupation. I then
match each GSS respondent and spouse to the relevant CPS earnings.
Finally, I use the respondents' and spouses' matched CPS earnings as
instruments for the GSS reported household income. The underlying
assumption is that industry and occupation do not predict happiness
independently of the average incomes earned in those occupations,
and that innately happier people are not disproportionately represented in higher-paying industries or occupations.
Column (2) of Table 3 reports the first-stage regression of log real
household income from the GSS on the other right-hand side
variables plus the log average wage for the respondents' and spouses'
year, state, industry and occupation. The sample size shrinks due to
the number of GSS respondents with missing or mismatched industry
or occupation codes. The regression fit is good, and the excluded
instruments are jointly and individually statistically significant.
Column (3) reports the second stage. The instrumented income coefficient (0.126) is twice as large as in the baseline specification in column
(5) of Table 1, consistent with Luttmer (2005) and Powdthavee (2009),
resulting in a smaller WTP for air quality. The doubling of the income
coefficient would cut the point estimate of WTP in half except for the
fact that the coefficient on daily pollution is also a bit larger in this
smaller sample. As a result, the estimate of WTP falls to $29 per day.
Column (4) runs the baseline specification without instrumenting for
income, but using this smaller sample. A slightly smaller income coefficient and larger pollution coefficient lead to a larger WTP estimate
of $76 per day.
876
A. Levinson / Journal of Public Economics 96 (2012) 869–880
Table 3
Alternative approaches.
Instrument for income using average income by
state, occupation and industry
PM10 daily (μg/m3) [α]
PM10 previous day
log(income) [γ]
log(CPS real income by year, state,
occupation, industry)
log(CPS real income for spouse's
occupation, industry)
Other covariates and fixed effects
as in column (5) of Table 1.
R2
No. of obs.
Years: 1984–1996, skipping
1992, 1995
F(2,2441) test excluded insts.
Sargan overid test p-value
WTP to pay for a 1 μg/m3 reduction
WTP to pay for a one std.
dev. reduction for one day
Lagged
environment
First stage: dependent Second stage: dependent Baseline specification Health as
Main specification
variable = log(income) variable=happiness
with smaller sample dependent variable without health
(1)
(2)
−0.0018† (0.0011) −0.0014 (0.0013)
0.0009 (0.0011)
0.071⁎ (0.019)
0.301⁎ (0.028)
(3)
(4)
(5)
(6)
−0.0021⁎ (0.0010)
−0.0022⁎ (0.0011)
−0.0005 (0.0008)
−0.0014⁎ (0.0007)
0.126† (0.072)
0.050⁎ (0.016)
0.153⁎ (0.013)
0.090⁎ (0.010)
0.020† (0.012)
Yes
Yes
Yes
Yes
Yes
Yes
0.146
1588
0.43
2599
0.152
2599
0.120
2599
0.164
6035
0.096
6035
0.43
$728 (566)
$29
$1922† (1126)
$76
59.0
$1057 (697)
$54
$679⁎ (322)
$27
⁎
See the footnotes to Table 1. Column (1) includes only observations where pollution was monitored in a county on successive days. Column (1) also includes lagged temperature and rainfall. In column (5), health is coded from 1 (“poor...
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