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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 Accessed: 05-11-2018 21:57 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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- This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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- This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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 REFERENCES be one approach for refining age-based mea- sures of the value of health. The VPL estimates Abeloff, Martin D.; Armitage, James 0.; Lichter, may be interpreted as the statistical value of the Allen S. and Niederhuber, John E. 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Review of Thaler, Richard H. and Rosen, Sherwin. "The Economics and Statistics, 2000, 82(3), pp. Value of Saving a Life: Evidence from the 439-51. Labor Market," in N. Terleckyj, ed., HouseGilman, E.; McNally, R. and Cartwright, hold R. production and consumption. Cam"Space-Time Clustering of Acute Lymphobridge: National Bureau of Economic blastic Leukaemia in Parts of the U.K. Research, 1975. (1984-1993)." European Journal of Cancer, U.S. Environmental Protection Agency. "Budget 1999, 35(1), pp. 91-96. in Brief," http://www.epa.gov/ocfo/budget/ Jones-Lee, Michael. "The Value of Changes in budget.htm., 2003. the Probability of Death or Injury." Journal Viscusi, W. Kip and Aldy, Joseph E. "The Value of a Statistical Life: A Critical Review of of Political Economy, 1974, 82(4), pp. 83549. Market Estimates throughout the World." Keil, Katherine A. and McClain, Katherine T. 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This content downloaded from 149.125.250.159 on Mon, 05 Nov 2018 21:57:04 UTC All use subject to https://about.jstor.org/terms 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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Running head: REFEREE REPORT

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REFEREE REPORT

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Article one: Valuing public goods using happiness data: The case of air quality
Motivation
The motivation comes mainly from the way the paper is arranged. It is separated into
different sections that flow well and enable the readers to understand the flow of the idea of the
author. Another motivation is found on the fact that the quality of air was used to determine
happiness from different people who come from different economic status. Another motivation
was the theoretical vs. practical concerns from the study.
Research questions


What is the likelihood that happiness questions can be used to value public goods?



How often do people value public goods such as air?



What increases the level of happiness?



Does the quality of air affect the level of happiness?
Background and Literature
Implementation of the methods for valuing of public goods is essential as this helps in
determining the happiness of different people. Different factors are used such as demographic
characteristics and incomes are used to determine the level of happiness. There was a higher
level of happiness for individuals who have high incomes compared to those with low-income
levels. The concept of income was essential in deriving the marginal rate for the substitution
between the quality of air and income (Levinson, 2012). Other studies had been condu...


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Really helped me to better understand my coursework. Super recommended.

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