Measuring the General Equilibrium Benefits of Air Quality Regulation in Small Urban Areas

Household and Housing Characteristics

The housing transactions data were obtained from two sources. Housing characteristics were obtained from the Clark County Assessor’s office. The data provide transaction records for residential properties located in Clark County. Each record includes the property’s physical address, history of transactions, transaction sale price, and property characteristics. We matched the housing characteristics with information on mortgage amount and lender obtained from Realquest (www.realquest.com). The housing transactions dataset consists of residential properties sold in the Las Vegas metropolitan area from January 2006 through December 2006. The Las Vegas metropolitan area is a 600 square mile basin that encompasses the incorporated cities of Las Vegas, North Las Vegas, Henderson, and Boulder City. The housing transaction dataset contains 31,815 single and multifamily owner-occupied residences. Each record includes the property location coordinates, the transaction sale price, and a detailed set of structural characteristics of the home. The house unit sale price is converted to a monthly rental price as follows:

[1]

where T_h represents the length of the mortgage in months, i represents the annual interest rate on the mortgage, and τ represents the property tax rate. For each house, we obtained the mortgage term, interest rate, and property tax payment in 2006 from the Realquest database.

Housing transactions provide a more precise location for each house and a more comprehensive set of housing characteristics than the housing records available from U.S. Census long form. However, these data do not provide information on the households occupying the houses. As a result, they do not allow one to estimate richer preference specifications, such as those used by Tra (2010), where preferences for location amenities vary across household characteristics. To address this issue, we supplemented the housing transaction data with household characteristics available in the HMDA database. These data provide income and race information of the home purchaser. The HMDA was enacted by Congress in 1975 and requires lending institutions to report information on their loan applicants.³ The HMDA database provides information on the loan applicant (including race and household income), the loan amount, the lender’s name, and the census tract in which the property is located. The purpose of the database is to determine whether lending institutions are serving the housing demands of their localities, to assist policymakers in allocating public investments, as well as to identify discriminatory lending patterns. Not all lending institutions are required to report their loan data by HMDA. The 2006 HMDA reporting criteria applied to federally insured or regulated lending institutions (banks, credit unions, or savings associations) with assets of more than $35 million, who had a home or branch office in a metropolitan statistical area.

From the 2006 HMDA database we obtained records from all conventional loan applications approved for the home purchase of an owner-occupied dwelling in Clark County, Nevada. Following Bayer, Ferreira, and McMillan (2007), we then constructed an identifier for each record, which consists of the lender’s unique record number, the loan amount, and the census tract. HMDA records with a unique identifier were then merged with the housing transaction records. From this process we recovered 12,990 housingunit and household records with nonmissing income or race information. Table 2 compares the characteristics of the final housing sample with the original housing transaction dataset. The final housing sample appears to be very representative of the original housing transaction dataset. The mean and median values are virtually the same for sale price, total bedrooms, total bathrooms, lot size, and building size. The median housing-unit age is higher in the final housing sample (6 years) compared to the original housing transaction data (2 years), although the average age is closer across the two samples when one accounts for the standard deviation.

Ozone Air Pollution Data

The purpose of this study is to evaluate the benefits of ozone air pollution regulation. Ozone air pollution in the Las Vegas Valley is captured via a network of monitors located throughout the area. This pollutant has been shown to have a significant impact on housing prices in Los Angeles (Sieg et al. 2004; Tra 2010). Ozone pollution in 2006 was measured as the highest daily maximum of 8-hour average concentrations at each monitor. Maximum values are used because most of the research in epidemiology and toxicology suggests that the most damage from air pollutants arises from acute episodes of concentrations (Banzhaf 2005). The Clark County air quality monitoring system comprises a total of 16 monitors (Figure 1).⁴ Hence, we rely on interpolation methods to obtain the air pollution measures to each house. We do this by assigning to each house the pollution measure from the closest monitor. Similar interpolation techniques have been used in the literature (see Sieg et al. 2004; Neill, Hassenzahl, and Assane 2007). In previous runs we investigated a distance-weighted interpolation approach, where we assigned to each house the distance-weighted average of the ozone reading from the two closest monitors. The two approaches yielded similar results.

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Figure 1

Clark County Air Pollution Monitors and 2006 Zip Code Boundaries

Neighborhood Quality Data

While it has been shown that ozone air pollution affects housing choices and prices, a number of other neighborhood quality variables are also likely to influence sorting. These include environmental variables such as traffic, noise pollution, and fine dust, as well as neighborhood economic and demographic characteristics. More importantly, such variables may be partly correlated with ozone pollution, so that their omission can potentially bias the estimated preference parameters for air quality. The empirical estimation uses several neighborhood variables as a proxy for neighborhood quality. Neighborhood economic activity is captured by the zip code employment density in 2006, the total zip code business establishments in 2006, the 2004-2006 zip code employment growth, and the 2004-2006 zip code business establishments’ growth. These variables also control for traffic, noise, and fine dust, which are highly correlated with business activity. We also control for neighborhood demographic characteristics using the proportion of minorities in the 2000 Census tract, the median income in the Census tract, the zip code population density in 2006, the zip code housing density in 2006, the 2004-2006 zip code population growth, and the 2004-2006 zip code housing growth.

In addition to neighborhood quality, the presence of parks or green spaces may mitigate the negative effects of ozone pollution on house prices. Omission of these characteristics may also potentially bias the preference estimates for air quality. We use two variables to characterize neighborhood open space. The distance from each house to the nearest park is used as a proxy for the access to open space. We also use the interaction of the distance to the closest park with the park’s total acreage as a proxy for the amount of open space available at each house.

Assumptions of the Sorting Framework

The residential sorting framework makes several implicit assumptions that should be discussed. First, we assume that an individual would have the same income if he or she chooses a different neighborhood location in the Las Vegas metropolitan area. This is not a strong assumption in a small urban area, like Las Vegas, where commuting times are generally not an issue. Hence, an individual would not like likely change jobs when moving to a new neighborhood.⁵

The second implicit assumption of the sorting model is that the housing price, ph, of a residential location h in 2006 is set to the observed transaction price at location h in 2006 and is exogenous to the household. This essentially says that the housing market is in equilibrium in 2006, so that an individual choosing a residential location h does not affect the price ph. This assumption is essential to applying the residential sorting equilibrium framework. As statedby Bayer, Keohane, and Timmins (2009), this assumption represents a cost to this framework. The benefit is that it allows one to estimate rich preference patterns that can provide detailed insight on the heterogeneity of preferences for amenities, as well as capture nonmarginal changes in amenities, either of which cannot be captured in the reduced-form framework of the hedonic model.⁶ We should note that our estimation addresses the potential endogeneity of the housing price that would arise if this assumption fails to hold. This is discussed in the estimation issues below. We should also note that the housing price assumption is relaxed in the computation of general equilibrium welfare measures, as housing prices are solved endogenously via simulation.

The equilibrium framework also makes the implicit assumption that the supply of each housing type h is fixed, that is, perfectly inelastic. However, it is quite possible, intheory, that both the price and the quantity of housing will adjust as a result of an amenity change, and that the price response will be bigger (and the quantity adjustment smaller) in areas that have less undeveloped land (Hilber and Mayer 2009). The implication is that the estimate of the MWTP for air quality may be inaccurate given that capitalization will vary across neighborhoods. Following Hilber and Mayer (2009), in the empirical estimation below, we use the zip code housing density as a proxy for the neighborhood’s residential land supply elasticity.

The capitalization of amenities in the presence of supply side adjustments is an important theoretical problem with potential ramifications for empirical work. Brasington (2002) develops a theoretical model that shows that there should be a stronger rate of capitalization toward the interior of an urban area, where the housing supply is relatively inelastic, and a weaker capitalization of amenities toward the edge of a city, where more land is available and the housing supply tends to be very elastic. However, the empirical analysis by Brasington (2002) does not fully confirm the hypothesis of his theoretical model. A recent empirical study by Stadelmann and Billon (2012) analyzes this problem in greater detail and shows that it may not be that relevant empirically.

Characterizing Housing Types

We use the sample of 12,990 housing units in our merged dataset to characterize the housing product space in the Las Vegas metropolitan area in 2006. Following the approach of Bayer, Ferreira, and McMillan (2007) and Takeuchi, Cropper, and Bento (2008), we assume that each of the 12,990 housing units chosen by the households in our sample represents a housing type and that there are many houses of the same type in the Las Vegas market. This seems to be a reasonable assumption, as it was shown (see Section II) that the sample was very representative of the housing transactions in the Las Vegas area in 2006.

An alternative to characterizing the housing product space is to use discrete housing types. This is the approach used by Tra (2010) and Klaiber and Phaneuf (2010). While using housing types rather than housing units to characterize residential locations significantly reduces the number of alternatives in the housing market, Tra (2007) has shown that alternative characterization of the product space using a smaller versus a larger number of housing types yields very similar parameter estimates.

Determining the Choice Set of Households

The household’s relevant choice set or feasible set of alternatives is an essential component of the estimation. A sampling approach is also used to construct the choice set. Potentially, one could set the household’s choice set as the 12,990 housing types in the sample. However, this would render the estimation computationally intractable. The reason is that the computational burden of the estimation grows linearly with the size of the household’s choice set (Ben-Akiva and Lerman 1985). An alternative is to construct the choice set by sampling a few alternatives from the full set of available alternatives. In particular, the household’s choice set includes (1) the household’s chosen residential location and (2) a random sample of 100 residential locations from the remaining nonchosen alternatives. McFadden (1978) has shown that such a scheme will yield consistent parameter estimates for the multinomial logit model.

Estimation of the Household Preference Parameters

The parameters (α, β₁, β₂) of the household indirect utility are estimated from a multinomial logit model. The mechanics of the estimation require rewriting the indirect utility in [2] as

[3a]

[3b]

where δ_h is a location-specific constant that represents households’ common valuation of the residential attributes. This valuation is shared by households regardless of their characteristics. The estimation follows a two-stage approach. In the first stage, we the estimate (J - 1) location-specific constants⁷ (δh) and the parameters (α, β₁) characterizing the household-specific tastes, via maximization of the log-likelihood:

[4]

where I_ih is a dummy that equals 1 whenever household i chooses location h in the data, and C_i represents the choice set of household i. P_ih represents the multinomial logit probability that household i chooses housing product h, and is given by

[5]

In practice, the maximization of the log-likelihood in [4] with respect to the 12,990 location-specific constants and household-specific parameters (α, β₁) is computationally demanding.⁸ A contraction mapping proposed by Berry, Levinsohn, and Pakes (1995) allows one to circumvent this computational burden by solving for the alternative-specific constants separately using the first-order conditions of the log-likelihood function. The second-stage estimates the vector of mean taste parameters (β₂) in a least-squares regression using the estimated vector of alternative constants as the dependent variable:

[6]

The underlying assumption of the second-stage regression is that the housing and neighborhood attributes in x_h are uncorrelated with the unobserved attributes of the residential location. The consistency and asymptotic normality of the first and second-stage estimations are established in the technical appendix provided by Bayer, Ferreira, and McMillan (2007).

As we mentioned previously, a potential bias may arise, in the second-stage regression, when unobservable neighborhood disamenities are correlated with neighborhood air pollution. For instance, local economic activity is likely to be correlated with neighborhood air quality and housing prices (Bayer, Keohane, and Timmins 2009). As a result, the ozone pollution variable may be endogenous. Chay and Greenstone (2005) and Bayer, Keohane, and Timmins (2009) developed instrumental variable approaches based on national countylevel data. However, these methods are not applicable in a local setting. In this study we address this issue by including several neighborhood variables in an attempt to capture various types of neighborhood disamenities. These neighborhood variables are described in Section II.

Some horizontal sorting models (see Bayer, Ferreira, and McMillan 2007; Klaiber and Phaneuf 2010) have used an instrumental variable approach to deal with the potential endogeneity problem that arises when the housing price enters the second stage. This endogeneity is caused by the fact that housing prices could be correlated with unobserved characteristics of residential locations. This is not the case in our specification, as housing prices enter the first-stage estimation only via the nonlinear term log(Income - Rental price). The presence of residential location fixed effects in the first-stage estimation will eliminate the potential bias that would arise from the correlation between housing prices and unobserved characteristics of residential locations.⁹ Hence, our identification of the income effect relies on the log functional form assumption. This approach was also used by Takeuchi, Cropper, and Bento (2008) and Tra (2010). A similar strategy was used by Bayer, Keohane, and Timmins (2009). Alternative functional form assumptions (such as square root) are investigated as a robustness check.

Finally, some authors have found that controlling for employment locations substantially improves the fit of the residential sorting models to the data (see Bayer, McMillan, and Rueben 2004; Takeuchi, Cropper, and Bento 2010). However, the extent to which inclusion of the household employment location alters the estimated preference parameters is not clear. Tra (2007) estimates a residential sorting model of the Los Angeles area and finds that controlling for the household’s employment zone has little effect on the key preference parameters of the sorting model. While controlling for employment location may matter in large urban areas such as Los Angeles, this is less likely to be the case in metropolitan areas with small geographic boundaries, such as the Las Vegas area, were commuting distances are generally short and congestion during peak hours is not a major issue.

Sorting Model Estimates

Table 3 summarizes the results of the estimation. Additional robustness checks are shown in the Appendix (Table A2). Panel A of Table 3 shows the first-stage estimates of the household-specific taste parameters. We find that households with higher income levels have a higher valuation for air quality and school quality. This is in accordance with the hypothesis that air quality and school quality are normal goods. This result falls in line with empirical results presented by Tra (2010) and Finney, Goetzke, and Yoon (2011) and is consistent with the location theory of urban land use (Alonso 1964). Panel B shows the second-stage common taste parameters. The second-stage taste parameters generally have the expected signs. On average, households are found to prefer more bedrooms, a pool, a larger lot, more bathrooms, a fireplace, better school quality, and better air quality.

Using the indirect utility in [2], the mean MWTP for a change in air quality (Δq) is given by¹⁰

[7]

The results in Table 3 suggest that the estimated MWTP for air quality is robust with respect to the inclusion of neighborhood amenities and disamenities. The mean MWTP is $98/year, compared to $101/year when controlling for neighborhood sociodemographics, neighborhood economic activity, and neighborhood parks. While empirical studies using national data (see Chay and Greenstone 2005; and Bayer, Keohane, and Timmins 2009) find that controlling for the endogeneity of air quality leads to larger estimates of the MWTP for air quality, our result may be an indication that the endogeneity of air pollution is not a serious issue in a small urban setting.

The estimated MWTP of $101 for ozone pollution falls somewhat in the in middle of the wide range of estimates in the existing hedonic literature on air quality. Estimates of the MWTP for air quality range from $18 to $280, in 2006 dollars, in the hedonic literature (Sieg et al. 2004). The MWTP estimates in this study are also comparable to recent estimates of the MWTP for ozone air pollution. Using a hedonic approach, Banzhaf (2005) finds a MWTP for a 1% change in ozone-free days ranging from $49 to $140/year when inflated to 2006 dollars. Applying a residential sorting model to the same data as Banzhaf’s (2005), Sieg et al. (2004) find a MWTP of $94 for a 1% change in ozone concentrations in the Los Angeles area. Tra (2010) also uses a residential sorting model and finds a MWTP range of $52 to $77/year, in 2006 dollars, for a 1% reduction in ozone concentration in the Los Angeles area.

Welfare Computation

We use the horizontal sorting model estimated in Section III to evaluate the benefits of ozone regulation, mandated by the 1990 Clean Air Act Amendments, to Las Vegas area households. For the purpose of evaluating the benefits of the changes in air quality across the Los Angeles area two welfare measures are of interest. The first measure asks what households are willing to pay for the change in air quality at their residence, holding housing prices and all other attributes fixed. We will refer to this welfare measure as the partial equilibrium WTP measure (WTP^pe). For a policy regime that leads to ozone air pollution reductions from to , WTP^pe is implicitly defined by

[8]

The superscript zero indicates the 1990 market conditions, and the superscript one indicates the market conditions after the air quality changes. The partial equilibrium WTP measure does not, however, provide a complete picture of the welfare impact of the changes in air quality across the Los Angeles area. Bartik (1988) shows that WTP^pe provides a lower bound to the full, that is, general equilibrium, welfare impact of the air quality changes. The general equilibrium welfare measure incorporates induced changes in housing prices that would result from the nonmarginal improvement in air quality across the Las Vegas area. These induced housing price changes are obtained by simulation using the procedure described by Tra (2010). This essentially entails simulating the counterfactual equilibrium that would have emerged in 2006 if the ozone level at each location had been capped at the national daily standard, while all other housing attributes and household characteristics remained at their 2006 levels. The general equilibrium welfare measure (WTP^ge) is implicitly defined as

[9]

The household’s residential location choice j in the ex post equilibrium differs from the location h in the benchmark equilibrium, implying that the household might change its residential location choice as a result of the change in air quality.

The computation of the welfare effects holds the housing supply fixed. The implication of this assumption is that the computed WTP measures would reflect the short-run benefits of the policy change (Takeuchi, Cropper, and Bento 2008). The assumption of fixed housing supply may be too strong if the housing supply is very elastic and new houses are built in areas with lower air pollution. This would imply that the elasticity of the housing supply with respect to air quality is very high. While we do not have empirical estimates of the elasticity of the housing supply with respect to air quality, we checked for the empirical correlation between ozone air pollution and the 2004-2006 zip code housing growth in the Las Vegas valley. The correlation coefficient is 0.04, which suggests that the elasticity of the housing supply with respect to air quality is likely to be very low in the study area.

Welfare Results

Table 4 presents the mean partial equilibrium and general equilibrium benefits of meeting the 2008 8-hour daily ozone standard of 0.075 ppm. The average daily maximum 8-hour ozone level in the Las Vegas valley during 2006 was 0.083 ppm. Columns (VI) through (IX) show the general equilibrium impacts of the air quality improvements. We find that meeting the 2008 air quality standard was worth on average $1,644 per year for each household. The partial equilibrium welfare measures are shown in Columns (III) through (V). These welfare measures capture the direct welfare impact of the air quality change on households, while ignoring the fact that the underlying sorting equilibrium may change. Allowing households to relocate after the air quality changes leads to higher welfare gains, on average. This is consistent with the theoretical result of Bartik (1988) and the empirical findings of Sieg et al. (2004) and Tra (2010). However, the partial equilibrium welfare effects do not differ substantially from the general equilibrium WTP measures. This is unlike Tra (2010) who finds that the mean general equilibrium WTP is almost 20% higher than the partial equilibrium mean WTP. This divergence of findings may be explained by the small housing price changes in this study (see Column VI), which suggests that the air quality improvements do not cause many households to change their location choices.

In addition to presenting the mean welfare benefits of air quality for households across Las Vegas, Table 4 provides additional information with respect to the distribution of welfare estimates. Columns (VIII) and (IX) show the general equilibrium WTP for the top and bottom quartiles of the household income distribution. For the lowest quartile (bottom 25%), we hnd a mean general equilibrium WTP of $360, which compares with a mean general equilibrium WTP of $4,656 for the highest quartile (top 25%) of the income distribution.

The Last two rows of Table 4 show the benefits of cleanup across the least-polluted neighborhoods and the neighborhoods with the most ozone pollution. These two rows show that the mean WTP in the cleanest neighborhoods (bottom 10% in ozone levels) is substantially higher than the mean WTP in the neighborhoods with the worst air quality. This finding is consistent with that of Tra (2010) and is partly due to two factors. First, households in the cleaner neighborhoods have on average higher income and as a result place a higher value on air quality improvements. The second factor contributing to the higher benefits in the cleanest areas is that these areas experience a decrease in housing prices in the household sorting that follows after the air quality improvements, whereas the most polluted areas experience an increase in housing prices after sorting (see Column VI).

The Last two rows of Table 4 also suggest that there is substantial heterogeneity across income groups with respect to the way that the benefits air quality regulation vary across the neighborhoods. Indeed, while low-income households in cleanest and most polluted areas experience similar benefits (Columns IV and VIII), we find that benefits of the regulation are almost twice as much for rich households in the cleanest neighborhoods as compared to rich households in the most polluted neighborhoods (Columns V and IX). This could be due to the fact that rich households have a better ability to relocate, while poor households may be Iess mobile as their housing choices may be limited. This finding differsfrom that of Tra (2010) who finds little variation in benefits across neighborhood ozone levels for both poor and rich households. This divergence in findings is likely due to the relatively coarse spatial characterization of neighborhoods studied by Tra (2010), where housing locations are defined by the Census PUMA.

Table 5 reports the benefits of meeting the 2008 daily national ozone standards across the incorporated cities of the Las Vegas metropolitan area. We find substantial variation in benefits across the cities. The mean general equilibrium WTP in the city of Las Vegas, the largest incorporated area, is $1,656. In contrast, in the city of North Las Vegas, the incorporated area with the lowest average income and the highest average ozone pollution, the mean general equilibrium WTP is $1,020. The largest mean general equilibrium WTP is found in Henderson, the city with the highest average income in the valley.

The benefits of air quality regulation in this study can be compared with the results of Tra (2010), Sieg et al. (2004), and Smith et al. (2004), who estimated general equilibrium benefits of ozone reductions in the Los Angeles area, a large urban area known for serious ozone problems. For the ozone reductions that took place between 1990 and 1995, Tra (2010) identifies annual benefits for the Los Angeles area of about $1,156 per household, in 2006 dollars, and compares his result with empirical evidence reported by Sieg et al. (2004) for a mean benefit of $1,850 per household, in 2006 dollars. While recognizing that the welfare measures are based on different reductions in ozone pollution, our annual general equilibrium WTP for meeting the 2008 daily ozone standard of $1,644 per household in the Las Vegas area appear to be fairly similar. In addition, we find that the wide variation in air quality benefits, across income and locations, which is observed in the Los Angeles area by Tra (2010) and Sieg et al. (2004), also emerges in a relatively small urban setting like the Las Vegas Valley. The welfare estimates for meeting the 2008 ozone standards also compare with those of Smith et al. (2004) who report a range of $50 to $3,700 across different school districts in the Los Angeles area, in 2006 dollars. This analysis provides new evidence on the benefits of air quality regulation for small urban jurisdictions like the Las Vegas Valley. We show that even in these relatively small urban areas, households value air quality regulation and that these values vary substantially by location and household income.